provides separate limits on $\mu_{\mathrm{ZH}}$ and $\mu_{\mathrm{WH}}$, and
Appendix G.1 shows the expected uncertainties for the inclusive and
production-mode specific signal strengths reported in Figure 12.

Table 7: Expected and observed significances of the VBF, $VH$ and top quark associated production mode signal strengths. Measurement | Expected $Z_{0}$ | Observed $Z_{0}$
---|---|---
$\mu_{\mathrm{VBF}}$ | $2.6\leavevmode\nobreak\ \sigma$ | $4.9\leavevmode\nobreak\ \sigma$
$\mu_{\mathrm{VH}}$ | $1.4\leavevmode\nobreak\ \sigma$ | $0.8\leavevmode\nobreak\ \sigma$
$\mu_{\mathrm{top}}$ | $1.8\leavevmode\nobreak\ \sigma$ | $1.0\leavevmode\nobreak\ \sigma$
Table 8: Observed and expected upper limits at 95% CL on the signal strengths $\mu_{\mathrm{VH}}$ and $\mu_{\mathrm{top}}$. The median expected limits are given for either the case when the true value of the signal strength under study is the SM value ($\mu_{i}=1$) or zero. The $\pm 1\leavevmode\nobreak\ \sigma$ and $\pm 2\leavevmode\nobreak\ \sigma$ intervals for the expected upper limit in the case $\mu_{i}=0$ are also reported.  Measurement | Observed | Expected Limit | Expected Limit | $+2\sigma$ | $+1\sigma$ | $-1\sigma$ | $-2\sigma$
---|---|---|---|---|---|---|---
|  | ($\mu_{i}=1$) | ($\mu_{i}=0$) |  |  |  |
$\mu_{\mathrm{VH}}$ | 2.3 | 2.5 | 1.5 | 3.1 | 2.2 | 1.1 | 0.8
$\mu_{\mathrm{top}}$ | 1.7 | 2.3 | 1.2 | 2.6 | 1.8 | 0.9 | 0.6
Figure 13:  Summary of asymptotic limits for the signal strengths of the
associated production processes ($VH$ and top).

#####  8.2.3 Production-mode cross sections

The production-mode cross sections for $m_{H}=125.09\pm 0.24$ GeV in a region
with Higgs-boson rapidity $|y_{H}|<2.5$, multiplied by the branching ratio of
the Higgs boson decay to diphotons, are evaluated in the following way. The
fitted value of $\sigma_{\mathrm{top}}$ corresponds to the sum of $t\bar{t}H$,
$tHq$, and $tHW$ production-mode cross sections under the assumption that
their relative ratios are as predicted by the SM. The $VH$ production-mode
cross section value is fitted under the assumption that the ratio of the $WH$
and $ZH$ production mode cross sections is as predicted by the SM and includes
both production from quark and gluon initial states. Such results are obtained
through signal+background fits to the diphoton invariant mass distribution in
each category by expressing, in the likelihood, the signal yield
$N_{\mathrm{sig,}m}^{i}$ in each category $i$ for a particular production mode
$m$ as $N_{\mathrm{sig,}m}=\int
L\,\mathrm{d}t\times\sigma_{m}^{\mathrm{SM}}\times
B^{\mathrm{SM}}(H\to\gamma\gamma)\times\epsilon_{m}^{i}$ using the same
notation as in Section 8.2.2.

The production-mode cross sections are summarized in Figure 14 and Table 9.

Table 9:  Best-fit values and uncertainties of the production-mode cross sections times branching ratio. The SM predictions [7] with their uncertainties are shown for each production process. Uncertainties smaller than 0.05 are displayed as 0.0.  Process | Result | Uncertainty [fb] | SM prediction
---|---|---|---
($|y_{H}|<2.5$) | [fb] | Total |  | Stat. | Exp. | Theo. |  | [fb]
ggH | 82 | ${}^{+19}_{-18}$ | $\Big{(}$ | $\pm 16$ | ${}^{+7}_{-6}$ | ${}^{+5}_{-4}$ | $\Big{)}$ | ${102}^{+5}_{-7}$
VBF | 16 | ${}^{+5}_{-4}$ | $\Big{(}$ | $\pm 4$ | $\pm 2$ | ${}^{+3}_{-2}$ | $\Big{)}$ | $8.0\pm 0.2$
$VH$ | 3 | $\pm 4$ | $\Big{(}$ | ${}^{+4}_{-3}$ | $\pm 1$ | ${}^{+1}_{-0}$ | $\Big{)}$ | $4.5\pm 0.2$
Top | 0.7 | ${}^{+0.9}_{-0.7}$ | $\Big{(}$ | ${}^{+0.8}_{-0.7}$ | ${}^{+0.2}_{-0.1}$ | ${}^{+0.2}_{-0.0}$ | $\Big{)}$ | $1.3\pm 0.1$
Figure 14: Summary plot of the measured production-mode cross sections times
the Higgs to diphoton branching ratio. For illustration purposes the central
values have been divided by their SM expectations but no additional theory
uncertainties have been added to the uncertainty of the ratio. The
uncertainties in the predicted SM cross sections are shown in gray bands in
the plot. The fitted value of $\sigma_{\mathrm{top}}$ corresponds to the sum
of $t\bar{t}H$, $tHq$, and $tHW$ production-mode cross sections under the
assumption that their relative ratios are as predicted by the SM. The $VH$
production mode cross-section values are determined under the assumption that
the ratio of the $WH$ and $ZH$ production-mode cross sections is as predicted
by the SM and includes production from both the quark and gluon initial
states. The $b\bar{b}H$ contributions are merged with ggH.

The 68% and 95% CL two-dimensional contours of $\sigma_{\mathrm{ggH}}\times
B(H\to\gamma\gamma)$ and $\sigma_{\mathrm{VBF}}\times B(H\to\gamma\gamma)$ are
shown in Figure 15, profiling $\sigma_{\mathrm{VH}}\times B(H\to\gamma\gamma)$
and $\sigma_{\mathrm{top}}\times B(H\to\gamma\gamma)$ in the fits. The SM
expectation of $\sigma_{\mathrm{ggH}}\times B(H\to\gamma\gamma)$ vs
$\sigma_{\mathrm{VBF}}\times B(H\to\gamma\gamma)$ is within the 95% CL contour
of this measurement.

Figure 15: Likelihood contours in the $(\sigma_{\mathrm{ggH}}\times
B(H\to\gamma\gamma),\sigma_{\mathrm{VBF}}\times B(H\to\gamma\gamma))$ plane,
compared to the Standard Model prediction (red cross) for a Higgs boson mass
$m_{H}=125.09\text{Ge\kern-1.00006ptV}$.

To remove the impact of possible deviations in the $H\to\gamma\gamma$
branching ratio, ratios of the production-mode cross sections to the ggH cross
section are also extracted. Such ratios, normalized for convenience of
presentation to the central values of their SM predictions, are666The quoted
theory uncertainty only accounts for the uncertainty in the acceptance. The
production cross-section uncertainties are not included in the uncertainty
budget. Uncertainties smaller than 0.05 are displayed as 0.0.

$\displaystyle\frac{\sigma_{\mathrm{VBF}}/\sigma_{\mathrm{ggH}}}{(\sigma_{\mathrm{VBF}}/\sigma_{\mathrm{ggH}})^{\mathrm{SM}}}$
$\displaystyle=2.5\ ^{+1.3}_{-0.9}=2.5\ ^{+1.1}_{-0.8}\,\mathrm{(stat.)}\
^{+0.5}_{-0.3}\,\mathrm{(exp.)}\ ^{+0.5}_{-0.3}\,\mathrm{(theo.)}$
$\displaystyle\frac{\sigma_{\mathrm{VH}}/\sigma_{\mathrm{ggH}}}{(\sigma_{\mathrm{VH}}/\sigma_{\mathrm{ggH}})^{\mathrm{SM}}}$
$\displaystyle=0.9\ ^{+1.3}_{-1.0}=0.9\ ^{+1.2}_{-0.9}\,\mathrm{(stat.)}\
^{+0.3}_{-0.3}\,\mathrm{(exp.)}\ ^{+0.2}_{-0.1}\,\mathrm{(theo.)}$
$\displaystyle\frac{\sigma_{\mathrm{top}}/\sigma_{\mathrm{ggH}}}{(\sigma_{\mathrm{top}}/\sigma_{\mathrm{ggH}})^{\mathrm{SM}}}$
$\displaystyle=0.7\ ^{+0.8}_{-0.7}=0.7\ ^{+0.8}_{-0.7}\,\mathrm{(stat.)}\
^{+0.2}_{-0.1}\,\mathrm{(exp.)}\ ^{+0.2}_{-0.0}\,\mathrm{(theo.)}$

The ratios are also given in Table 10, along with their statistical,
experimental and theoretical uncertainties without the normalization to the
central values of the SM predictions. Both the measurements of the ggH and VBF
production modes and the evaluations of the $VH$ and top production modes
agree within $1$–$2\leavevmode\nobreak\ \sigma$ with the SM expectations.
Appendix G.2 provides the expected uncertainties for the production mode cross
sections.

Table 10:  Ratios of the production-mode cross sections with respect to the ggH cross section and uncertainties are shown. The SM predictions [7] with their uncertainties are shown for each production process.  Process | Result | Uncertainty | SM prediction
---|---|---|---
($|y_{H}|<2.5$) |  | Total |  | Stat. | Exp. | Theo. |  |
$\sigma_{\mathrm{VBF}}/\sigma_{\mathrm{ggH}}$ | 0.20 | ${}^{+0.10}_{-0.07}$ | $\Big{(}$ | ${}^{+0.09}_{-0.06}$ | ${}^{+0.04}_{-0.02}$ | ${}^{+0.04}_{-0.02}$ | $\Big{)}$ | ${0.078}^{+0.005}_{-0.006}$
$\sigma_{\mathrm{VH}}/\sigma_{\mathrm{ggH}}$ | 0.04 | ${}^{+0.06}_{-0.05}$ | $\Big{(}$ | ${}^{+0.06}_{-0.04}$ | ${}^{+0.01}_{-0.01}$ | ${}^{+0.01}_{-0.01}$ | $\Big{)}$ | ${0.045}^{+0.004}_{-0.005}$
$\sigma_{\mathrm{top}}/\sigma_{\mathrm{ggH}}$ | 0.009 | ${}^{+0.010}_{-0.009}$ | $\Big{(}$ | ${}^{+0.010}_{-0.009}$ | ${}^{+0.002}_{-0.001}$ | ${}^{+0.002}_{-0.001}$ | $\Big{)}$ | ${0.012}^{+0.001}_{-0.002}$

#####  8.2.4 Simplified template cross sections

As the current data are not yet sensitive to all of the 31 regions with
$|y_{H}|<\nobreak 2.5$ (assuming SM acceptance) of the “stage-1” scheme of the
simplified template cross-section framework, simplified template cross
sections are reported for 10 phase space regions obtained from merging the
initial 31 as described in Section 1.2 and Table LABEL:tab:STXS. To retain
sensitivity to BSM Higgs boson production, the $p_{\text{T}}^{H}>\nobreak
200\,\text{Ge\kern-1.00006ptV}$ gluon–gluon fusion and
$p_{\text{T}}^{j}>\nobreak 200\,\text{Ge\kern-1.00006ptV}$ VBF regions are not
merged with other regions. This scheme has been chosen to reduce strong anti-
correlations between the measured cross sections and to keep measurements near
or below 100% total uncertainty. In the likelihood, the signal yield
$N_{\mathrm{sig}}^{i}$ in each category $i$ is the sum over the yields
$N_{\mathrm{sig},r}^{i}$ expected from each of the 9 regions $r$ of phase
space, where $N_{\mathrm{sig},r}^{i}=\int
L\,\mathrm{d}t\times\sigma_{r}^{\mathrm{SM}}\times
B^{\mathrm{SM}}(H\to\gamma\gamma)\times\epsilon_{r}^{i}$ and the additional
region corresponds to the difference of the cross sections for the
$p_{\text{T}}^{H}>\nobreak 200\,\text{Ge\kern-1.00006ptV}$ gluon–gluon fusion
and $p_{\text{T}}^{j}>\nobreak 200\,\text{Ge\kern-1.00006ptV}$ VBF regions.
The observed cross sections are reported in Table 11. These measurements have
been defined to minimize theoretical uncertainties and are strongly dominated
by experimental uncertainty, hence only the total systematic uncertainty is
reported.

Table 11:  Best-fit values and uncertainties of the simplified template cross sections times branching ratio. The SM predictions [7] are shown for each region.  Measurement region | Result | Uncertainty | SM prediction
---|---|---|---
($|y_{H}|<2.5$) | Total |  | Stat. | Syst. |  |
$\text{ggH},\mathrm{0\leavevmode\nobreak\ jet}$ | 37 | ${}^{+16}_{-15}$ | $\Big{(}$ | $\pm 14$ | ${}^{+6}_{-5}$ | $\Big{)}$ | fb | $63\pm 5$ | fb
$\text{ggH},\mathrm{1\leavevmode\nobreak\ jet},p_{\text{T}}^{H}<60$ GeV | 13 | ${}^{+13}_{-12}$ | $\Big{(}$ | $\pm 12$ | ${}^{+5}_{-4}$ | $\Big{)}$ | fb | $15\pm 2$ | fb
$\text{ggH},\mathrm{1\leavevmode\nobreak\ jet},60\leq p_{\text{T}}^{H}<120$ GeV | 5 | $\pm 6$ | $\Big{(}$ | $\pm 6$ | ${}^{+2}_{-1}$ | $\Big{)}$ | fb | $10\pm 2$ | fb
$\text{ggH},\mathrm{1\leavevmode\nobreak\ jet},120\leq p_{\text{T}}^{H}<200$ GeV | 2.8 | ${}^{+1.7}_{-1.6}$ | $\Big{(}$ | ${}^{+1.6}_{-1.5}$ | ${}^{+0.7}_{-0.5}$ | $\Big{)}$ | fb | $1.7\pm 0.3$ | fb
$\text{ggH},\geq 2\leavevmode\nobreak\ \mathrm{jet}$ | 20 | ${}^{+9}_{-8}$ | $\Big{(}$ | $\pm 8$ | ${}^{+4}_{-3}$ | $\Big{)}$ | fb | $11\pm 2$ | fb
$qq\rightarrow Hqq,p_{\text{T}}^{j}<200$ GeV | 15 | ${}^{+6}_{-5}$ | $\Big{(}$ | $\pm 5$ | ${}^{+3}_{-2}$ | $\Big{)}$ | fb | $10\pm 0.5$ | fb
$\text{ggH}+qq\rightarrow Hqq,\mathrm{BSM-like}$ | 2.0 | $\pm 1.4$ | $\Big{(}$ | $\pm 1.3$ | $\pm 0.6$ | $\Big{)}$ | fb | $1.8\pm 0.4$ | fb
VH, leptonic | 0.7 | ${}^{+1.4}_{-1.3}$ | $\Big{(}$ | ${}^{+1.4}_{-1.2}$ | ${}^{+0.4}_{-0.3}$ | $\Big{)}$ | fb | $1.4\pm 0.1$ | fb
Top | 0.7 | ${}^{+0.8}_{-0.7}$ | $\Big{(}$ | ${}^{+0.8}_{-0.7}$ | ${}^{+0.2}_{-0.1}$ | $\Big{)}$ | fb | $1.3\pm 0.1$ | fb

The evaluated cross sections including their correlations are summarized in
Figures 16 and 17. The expected Standard Model correlations can be found in
Appendix H. All observed cross sections are in agreement with the Standard
Model values. The Standard Model prediction is determined using the generators
in Section 4 and the theory uncertainties due to missing higher-order
corrections and due to the chosen PDF set are constructed as described in
Section 7.3. The largest deviation ($1.7\leavevmode\nobreak\ \sigma$) from the
SM prediction is found in the $\text{ggH},\mathrm{0\leavevmode\nobreak\ jet}$
bin. The difference of the cross sections for the $p_{\text{T}}^{H}>\nobreak
200\,\text{Ge\kern-1.00006ptV}$ ggH and $p_{\text{T}}^{j}>\nobreak
200\,\text{Ge\kern-1.00006ptV}$ VBF regions is found to be $4.8^{+2.9}_{-2.7}$
fb.

Figure 16: Summary plot of the measured simplified template cross sections
times the Higgs to diphoton branching ratio. For illustration purposes the
central values have been divided by their SM expectations but no additional
theory uncertainties have been included in the uncertainty of the ratio due to
this. The uncertainties in the predicted SM cross sections are shown in gray
in the plot. The definition of the measured regions can be found in Table
LABEL:tab:STXS. The fitted value of $\sigma(\mathrm{top})$ corresponds to the
sum of $t\bar{t}H$and $tH$ production-mode cross sections under the assumption
that their relative ratios are as predicted by the SM. The
$\sigma(\mathrm{VH,leptonic})$ cross-section values are determined under the
assumption that the ratio of the $WH$ and $ZH$ production mode cross sections
is as predicted by the SM and includes production from both the quark and
gluon initial states. The $b\bar{b}H$ contributions are merged with ggH.
Figure 17: Observed correlations between the measured simplified template
cross sections, including both the statistical and systematic uncertainties.
The color indicates the size of the correlation.

Limits at 95% CL on the $\text{ggH}+qq\to Hqq$ BSM-like
($p_{\textrm{T}}^{j}>200\,\text{Ge\kern-1.00006ptV}$) bin are set, profiling
all other parameters, as shown in Table 12. Appendix G.3 provides the expected
uncertainties for all quoted simplified template cross sections.

In Appendix B additional measurements are reported for a “minimally merged”
set of 15 cross sections of kinematic regions defined by the requirement that
the fits to expected event yields be stable even in the presence of large
uncertainties or correlations.

Table 12: Observed and expected upper limits at 95% CL on the simplified template cross section times the Higgs to diphoton branching ratio in the BSM sensitive phase space with $p_{\textrm{T}}^{j}>200\,\text{Ge\kern-1.00006ptV}$. The median expected limits are given for either the case when the true value of the cross section under study is SM-like ($\sigma=\sigma_{\mathrm{S}M}$) or zero. The $\pm 1\leavevmode\nobreak\ \sigma$ and $\pm 2\leavevmode\nobreak\ \sigma$ intervals for the expected upper limit ($\sigma=0\,\,\text{fb}$) are also reported.  Measurement | Observed | Expected Limit | Expected Limit | $+2\sigma$ | $+1\sigma$ | $-1\sigma$ | $-2\sigma$
---|---|---|---|---|---|---|---
|  | ($\sigma=\sigma_{\mathrm{S}M}$) | ($\sigma=0\,\,\text{fb}$) |  |  |  |
$ggH+qq\to Hqq$, | 4.4 fb | 4.3 fb | 2.7 fb | 5.3 fb | 3.8 fb | 2.0 fb | 1.5 fb
$\mathrm{BSM-like}$ |  |  |  |  |  |  |

#####  8.2.5 Coupling-strength fits

Following the tree-level-motivated framework and benchmark models recommended
in Ref. [17], measurements of Higgs boson coupling-strength modifiers
$\kappa_{j}$ are implemented. In the narrow width approximation for the Higgs
boson, the cross section $\sigma(i\rightarrow H\rightarrow\gamma\gamma)$ can
be parameterized as

$\sigma(i\rightarrow
H\rightarrow\gamma\gamma)=\frac{\sigma_{i}(\vec{\kappa})\,\Gamma^{\gamma\gamma}(\vec{\kappa})}{\Gamma_{H}},$

where $\Gamma_{H}$ is the total width of the Higgs boson and
$\Gamma^{\gamma\gamma}$ is the partial decay width to two photons. A set of
coupling-strength modifiers, $\vec{\kappa}$, is introduced to parameterize
possible deviations from the SM predictions of the Higgs boson coupling to SM
bosons and fermions. For a given production process or decay mode $j$, a
coupling-strength modifier $\kappa_{j}$ is defined such that:

$\kappa_{j}^{2}=\sigma_{j}/\sigma_{j,\mathrm{SM}}\ \,\,\mathrm{or}\
\,\,\kappa_{\gamma}^{2}=\Gamma^{\gamma\gamma}/\Gamma^{\gamma\gamma}_{\mathrm{SM}},$

where all $\kappa_{j}$ values equal unity in the SM. Here, by construction,
the SM cross sections and branching ratio include the best available higher-
order QCD and EW corrections. This higher-order accuracy is not necessarily
preserved for $\kappa_{j}$ values different from unity, but the dominant
higher-order QCD corrections factorize to a large extent from any rescaling of
the coupling strengths and are therefore assumed to remain valid over the
entire range of $\kappa_{j}$ values considered.

Individual coupling-strength modifiers corresponding to tree-level Higgs boson
couplings to different particles are introduced as well as two effective
coupling-strength modifiers, $\kappa_{g}$ and $\kappa_{\gamma}$, which
describe the loop processes for ggH production and $H\to\gamma\gamma$ decay.
This is possible because BSM particles that might be present in these loops
are not expected to appreciably change the kinematics of the corresponding
process. The $gg\to H$ and $H\to\gamma\gamma$ loop processes can thus be
studied through these effective coupling-strength modifiers, providing
sensitivity to potential BSM particles in the loops. In contrast, the $gg\to
ZH$ process, which occurs at LO through box and triangular loop diagrams, is
always taken into account by resolving the loop in terms of the corresponding
coupling-strength modifiers ($\kappa_{Z}$ and $\kappa_{t}$). No decays to
particles other than those predicted in the SM are assumed to take place.
These considerations and the limited sensitivity of the data available in this
analysis lead to introducing two distinct models.

In the first model, the two parameters $\kappa_{g}$ and $\kappa_{\gamma}$
introduced above are tested assuming that all other couplings are as in the
SM. The 68% and 95% CL two-dimensional contours of both effective couplings
are shown in Figure 18(a) and the best fit values and uncertainties are
$\kappa_{g}=0.76^{+0.17}_{-0.14}$ and $\kappa_{\gamma}=1.16^{+0.14}_{-0.14}$.

In a second model, universal coupling-strength modifiers, $\kappa_{F}$ (for
all fermions) and $\kappa_{V}$ (for all bosons), are defined that resolve the
$gg\to H$ and $H\to\gamma\gamma$ loops:

$\begin{split}\kappa_{F}&=\kappa_{t}=\kappa_{b}=\kappa_{\tau}=\kappa_{\mu}\,,\\\
\kappa_{V}&=\kappa_{W}=\kappa_{Z}\,.\end{split}$

The 68% and 95% CL two-dimensional contours of both parameters are shown in
Figure 18(b) and the best fit values and uncertainties are
$\kappa_{F}=0.64^{+0.18}_{-0.14}$ and $\kappa_{V}=0.92^{+0.08}_{-0.07}$. Due
to the very limited sensitivity to $\kappa_{b},\kappa_{\tau}$ and
$\kappa_{\mu}$, the shown CLs would not change if these coupling-strength
modifiers would be fixed to the SM expectation.

The SM prediction is found within the 68% CL contour for the first model and
within the 95% CL contour for the second model.

((a))

((b))

Figure 18:  Likelihood contours in (a) the $(\kappa_{g},\kappa_{\gamma})$
plane, and (b) the $(\kappa_{V},\kappa_{F})$ plane, compared to the Standard
Model prediction (red star) for a Higgs boson mass
$m_{H}=125.09\,\text{Ge\kern-1.00006ptV}$. In (a), all coupling-strength
modifiers other than $\kappa_{g}$ and $\kappa_{\gamma}$ are fixed to their SM
value. In (b), the $gg\to H$ and $H\to\gamma\gamma$ loops are resolved in
terms of two universal coupling-strength modifiers $\kappa_{F}$ and
$\kappa_{V}$, under the assumption that $\kappa_{V}=\kappa_{W}=\kappa_{Z}$ and
$\kappa_{F}=\kappa_{t}=\kappa_{b}=\kappa_{\tau}=\kappa_{\mu}$.

Finally, a set of three ratios is constructed to probe the loop vertices
($\kappa_{g}$, $\kappa_{\gamma}$), total width ($\kappa_{H}$), and the vector
and top couplings ($\kappa_{t}$ and $\kappa_{V}$ respectively):
$\kappa_{g\gamma}=\kappa_{g}\kappa_{\gamma}/\kappa_{H}$,
$\lambda_{Vg}=\kappa_{V}/\kappa_{g}$, and
$\lambda_{tg}=\kappa_{t}/\kappa_{g}$. The parameter $\lambda_{tg}$ is allowed
to be negative to exploit the sensitivity to the relative sign from the $tH$
and $gg\to ZH$ processes. The expected and observed sensitivities to the
relative sign are illustrated in Figure 19. The bottom quark Yukawa coupling
strength is kept fixed to the top quark Yukawa coupling strength
($\lambda_{bg}=\lambda_{tg}$); this contribution is irrelevant to the
$\lambda_{tg}$ measurement as there is no sensitivity to $b\bar{b}H$ in the
analysis. All other parameters are assumed to be positive without losing
generality. The inclusion of $\kappa_{H}$ in the parameterization allows for
non-SM decays of the Higgs boson, but this parameter is not determined
directly. The best fit values of these coupling ratios are summarized in Table
13.

Table 13: Best-fit values and uncertainties of $\kappa_{g\gamma}$, $\lambda_{Vg}$, and $\lambda_{tg}$.  Parameter | Result | Uncertainty
---|---|---
Total |  | Stat. | Exp. | Theo. |
$\kappa_{g\gamma}$ | 0.90 | $\pm 0.10$ | $\Big{(}$ | $\pm 0.09$ | $\pm 0.04$ | ${}^{+0.04}_{-0.03}$ | $\Big{)}$
$\lambda_{Vg}$ | 1.41 | ${}^{+0.31}_{-0.26}$ | $\Big{(}$ | ${}^{+0.28}_{-0.23}$ | ${}^{+0.10}_{-0.07}$ | ${}^{+0.04}_{-0.03}$ | $\Big{)}$
$\lambda_{tg}$ | 0.8 | ${}^{+0.4}_{-0.6}$ | $\Big{(}$ | ${}^{+0.4}_{-0.6}$ | $\pm 0.1$ | ${}^{+0.1}_{-0.0}$ | $\Big{)}$
Figure 19: The profile of negative log-likelihood $\Lambda$ of the observed
and expected coupling-strength modifier ratio
$\lambda_{tg}=\kappa_{t}/\kappa_{g}$. The parameters $\kappa_{g\gamma}$ and
$\lambda_{Vg}$ are also profiled within the fit. The intersections of the
solid and dashed curves with the horizontal dashed line at $\Lambda=1$ and
$\Lambda=4$ indicate the 1 and 2 $\sigma$ confidence intervals of the observed
and expected results, respectively.

###  9 Measurement of fiducial integrated and differential cross sections

The measurement of fiducial integrated and differential cross sections
provides an alternative way to study the properties of the Higgs boson and to
search for physics beyond the Standard Model. The fiducial volumes are defined
to closely mimic the detector-level photon and object selections described in
Section 5. This reduces the model-dependence of the quoted cross sections in
contrast to the per production mode simplified template cross-section
measurements of Section 8.2.4. The cross sections are determined by correcting
measured signal yields for experimental inefficiencies and resolution effects,
and by taking into account the integrated luminosity of the data. Rather than
separating individual production modes, fiducial regions are defined such that
they are enriched with a given production mode: Fiducial cross sections are
measured in a variety of phase space regions, sensitive to for instance
gluon–gluon fusion Higgs boson production, vector-boson fusion production, but
also to production of the Higgs boson in association with charged leptons, top
quarks and neutrinos. Differential and double-differential cross sections are
reported for variables related to the diphoton kinematics and the jet activity
produced in the Higgs boson events. The observed signal yields are corrected
for detector effects resulting in cross sections measured at the particle
level. The full statistical and systematic correlations between measured
distributions are determined and are available in HepData along with the
central values of the measured fiducial and differential cross sections to
allow future comparisons and interpretations.

####  9.1 Particle-level fiducial definition of the Higgs boson diphoton cross
sections

The fiducial volume at particle level is defined using particles with a mean
lifetime $c\tau>10$ mm. Only photons and leptons which do not originate from
the decay of hadrons are considered.777Leptons originating from the decay of
$\tau$ leptons are only considered if the $\tau$ lepton itself did not
originate from the decay of hadrons. The two highest-$p_{\mathrm{T}}$ photons
with $|\eta|<2.37$ – excluding $1.37<|\eta|<1.52$ – are selected as the
diphoton system. The leading (subleading) photon is required to satisfy
$p_{\mathrm{T}}/m_{\gamma\gamma}>0.35\ (0.25)$, where
$m_{\gamma\gamma}=m_{H}=125.09\,\text{Ge\kern-1.00006ptV}$. Furthermore, for
each photon the scalar $p_{\mathrm{T}}$-sum of charged particles with
$p_{\mathrm{T}}>1$ GeV within a cone of $\Delta R=0.2$ around the photon is
required to be less than 5% of the photon $p_{\mathrm{T}}$. The lepton four-
momentum is defined as the combination of an electron (or muon) and all nearby
photons within $\Delta R<0.1$ that do not originate from the decay of a
hadron. Muons are required to have $p_{\mathrm{T}}>15$ GeV and $|\eta|<2.7$.
Electrons are required to have $p_{\mathrm{T}}>15$ GeV and $|\eta|<2.47$,
excluding the region $1.37<|\eta|<1.52$, and are rejected if the distance
$\Delta R$ to a photon with $p_{\mathrm{T}}>$ 15 GeV is less than 0.4. Jets
are reconstructed from all particles, excluding muons and neutrinos, using the
anti-$k_{t}$ algorithm with a radius parameter of 0.4. Unless stated
otherwise, jets are required to have $p_{\mathrm{T}}>30$ GeV, $|y|<4.4$ and to
be well separated from photons with $p_{\mathrm{T}}>$ 15 GeV ($\Delta R>0.4$)
and electrons ($\Delta R>0.2$). The acceptance for the VBF-enhanced fiducial
region (introduced in Section 9.2) is increased by loosening the
$p_{\text{T}}$ cut to 25 GeV. Jets are considered to originate from a
$b$-hadron if there is a $b$-hadron with $p_{\mathrm{T}}>5$ GeV within a cone
of size $\Delta R=0.4$ around the jet.

The missing transverse momentum is defined as the vector sum of neutrino
transverse momenta, for neutrinos that do not originate from the decay of a
hadron. The particle-level fiducial definition is summarized in Table 14.

Table 14: Summary of the particle-level definitions of the five fiducial integrated regions described in the text. The photon isolation $p_{\text{T}}^{\text{iso,0.2}}$ is defined analogously to the reconstructed-level track isolation as the transverse momentum of the system of charged particles within $\Delta R<0.2$ of the photon.  Objects | Definition
---|---
Photons |  $|\eta|<1.37$ or $1.52<|\eta|<2.37$, $p_{\text{T}}^{\text{iso,0.2}}/p_{\text{T}}^{\gamma}<0.05$
Jets | anti-$k_{t}$, $R=0.4$, $p_{\mathrm{T}}>30$ GeV, $|y|<4.4$
Leptons, $\ell$ |  $e$ or $\mu$, $p_{\mathrm{T}}>15$ GeV, $|\eta|<2.47$ for $e$ (excluding $1.37<|\eta|<1.52$) and $|\eta|<2.7$ for $\mu$
Fiducial region | Definition
Diphoton fiducial |  $N_{\gamma}\geq 2$, $p_{\mathrm{T}}^{\gamma_{1}}>0.35\,m_{\gamma\gamma}=43.8$ GeV, $p_{\mathrm{T}}^{\gamma_{2}}>0.25\,m_{\gamma\gamma}=31.3$ GeV
VBF-enhanced | Diphoton fiducial, $N_{j}\geq 2$ with $p_{\mathrm{T}}^{\mathrm{jet}}>25$ GeV,
|  $m_{jj}>400$ GeV, $|\Delta{y_{jj}|}>2.8$,
$|\Delta\phi_{\gamma\gamma,jj}|>2.6$
$N_{\mathrm{l}epton}\geq 1$ | Diphoton fiducial, $N_{\ell}\geq 1$
High $E_{\text{T}}^{\text{miss}}$ | Diphoton fiducial, $E_{\text{T}}^{\text{miss}}>80$ GeV, $p_{{\mathrm{T}}}^{\gamma\gamma}>80$ GeV
$t\bar{t}H$-enhanced | Diphoton fiducial, $\left(N_{j}\geq 4,\,N_{b\text{-jets}}\geq 1\right)$ or $\left(N_{j}\geq 3,\,N_{b\text{-jets}}\geq 1,N_{\ell}\geq 1\right)$

####  9.2 Fiducial integrated and differential cross sections

The cross section ($\sigma_{i}$) in a fiducial integrated region, and the
differential cross section (${\mathrm{d}}\sigma_{i}/{\mathrm{d}}x$) in a bin
of variable $x$, are given by

$\sigma_{i}=\frac{N_{i}^{\mathrm{sig}}}{c_{i}\int
L\,\mathrm{d}t}\quad\quad\quad\text{and}\quad\quad\quad\frac{\mathrm{d}\sigma_{i}}{\mathrm{d}x}=\frac{N_{i}^{\mathrm{sig}}}{c_{i}\,\Delta
x_{i}\int L\,\mathrm{d}t},$

where $N_{i}^{\mathrm{sig}}$ is the number of signal events as introduced in
Section 6.3, $\int L\,\mathrm{d}t$ is the integrated luminosity of the data
set, $c_{i}$ is a correction factor that accounts for detector inefficiency
and resolution, and $\Delta x_{i}$ is the bin width. The correction factors
are determined using the simulated samples discussed in Section 4. This bin-
by-bin method showed similar performance to that of the non-regularized
inversion of the full migration matrix and of regularized methods [112, 113,
114] within the current statistical accuracy and systematic uncertainties.

The correction factor is $0.75\pm 0.03$ in the diphoton fiducial region,
defined to unfold all signal events to the fiducial definition of Section 9.1,
which is dominated by the photon identification and isolation efficiency. The
correction factor also accounts for migrations caused by detector energy
resolution and migration in and out of the fiducial phase space due to
detector effects. In addition, the correction factor removes a small fraction
(0.5% for the diphoton fiducial region) of reconstructed $H\to ff\gamma$
Dalitz decays.888Here $f$ denotes any fermion but the top quark.

The correction factor is different in fiducial regions defined by associated
jet activity, for example, taking values of $0.66$ and $0.87$ for the
$t\bar{t}H$ and VBF fiducial regions defined in the next section,
respectively. For the diphoton fiducial region the uncertainty in the
correction factor is dominated by the theoretical modeling uncertainty. For
the $t\bar{t}H$ and VBF fiducial regions the uncertainties in the correction
factors are dominated by uncertainties associated with the knowledge of the
jet energy scale and energy resolution, as well as the theoretical modeling. A
more complete breakdown is given in Section 9.5.6 and Table 16.

The measured differential cross sections in different observables are
partially statistically correlated, since they correspond to the same data set
in a given fiducial region. These correlations are obtained using a random
sampling with replacement method on the detector-level data, often referred to
as ’bootstrapping’ [115]. Bootstrapped event samples are constructed from the
data by assigning each event a weight pulled from a Poisson distribution with
unit mean. All measured differential distributions are then reconstructed
using the weighted events, and the signal yields in each bin of a differential
distribution are determined using an unbinned maximum-likelihood fit of the
diphoton invariant mass spectrum. The procedure is repeated with statistically
independent weights and the correlation between two bins of different
distributions is determined from the obtained cross sections. Figure 20 shows
as an illustration the determined correlations between
$p_{{\mathrm{T}}}^{\gamma\gamma}$, $N_{\mathrm{j}ets}$, $m_{jj}$,
$|\Delta\phi_{jj}|$, and $p_{\mathrm{T}}^{j_{1}}$: the lowest
$p_{{\mathrm{T}}}^{\gamma\gamma}$ bin, reconstructing events with a Higgs
boson $p_{\mathrm{T}}$ between 0 and 20 GeV, is highly correlated with the
zero-jet bin. The lowest $p_{\mathrm{T}}^{j_{1}}$ bin, reconstructing events
with a jet $p_{\mathrm{T}}$ between 30 and 55 GeV, is strongly correlated with
the one-jet bin. And the lowest $m_{jj}$ bin, reconstructing events with at
least two jets and a dijet mass between 0 and 170 GeV, is strongly correlated
with the two jet bin. The systematic correlations are obtained by fully
correlating identical error sources described in Section 7 across bins and
observables to construct the corresponding systematic covariance matrix.
Knowledge of these correlations allows to simultaneously analyze all fiducial
regions, differential and double differential cross sections. This is
illustrated later in Section 9.5.8 with a simultaneous fit of the shown five
variables of Figure 20 to set limits on new physics contributions.

Figure 20:  The observed statistical correlations between
$p_{{\mathrm{T}}}^{\gamma\gamma}$, $N_{\mathrm{j}ets}$, $m_{jj}$,
$|\Delta\phi_{jj}|$, and $p_{\mathrm{T}}^{j_{1}}$ are shown. These
correlations were determined from an ensemble of 100,000 bootstrapped data
sets which are each reanalyzed using an unbinned maximum-likelihood fit of the
diphoton invariant mass spectrum to extract the correlations.

####  9.3 Measurements of cross sections of fiducial integrated regions

Cross sections in five fiducial integrated regions are measured that target
either specific Higgs boson production mechanisms or are sensitive to the
presence of physics beyond the Standard Model. The selection criteria defining
these regions are summarized in Table 14 and a description of each region
follows:

  1. 1.

Diphoton fiducial: This region unfolds all signal events after the selection
presented in Section 5.

  2. 2.

VBF-enhanced: This region retains all events with at least two jets and with
an invariant dijet mass $m_{jj}$ of at least 400 GeV, a large rapidity
separation $\left|\Delta y_{jj}\right|>2.8$, and an azimuthal difference
between the Higgs boson and the dijet pair of
$|\Delta\phi_{\gamma\gamma,jj}|>2.6$. All variables are computed using the two
highest-$p_{\mathrm{T}}$ jets in the event with
$p_{\mathrm{T}}>25\,\text{Ge\kern-1.00006ptV}$ with matching detector-level
cuts.

  3. 3.

$N_{\mathrm{l}epton}\geq 1$: This region retains events that contain at least
one electron or one muon with $p_{\mathrm{T}}>15$ GeV. For electrons the
pseudo-rapidity needs to satisfy $\left|\eta\right|<2.47$ (excluding
$1.37<|\eta|<1.52$) and for muons $\left|\eta\right|<2.7$ is required. Such
events are enriched in Higgs bosons produced in association with a vector
boson.

  4. 4.

High $E_{\mathrm{T}}^{\mathrm{m}iss}$: This region retains events with missing
transverse momentum $E_{\mathrm{T}}^{\mathrm{m}iss}>80$ GeV and
$p_{{\mathrm{T}}}^{\gamma\gamma}>80$ GeV is defined to study $VH$ production
and possible contributions of Higgs boson production with dark matter
particles. The simultaneous requirement that the Higgs boson system balances
the missing transverse momentum reduces the fraction of selected events at
detector level without particle-level $E_{\mathrm{T}}^{\mathrm{m}iss}>80$ GeV.

  5. 5.

$t\bar{t}H$-enhanced: This region retains events with either at least one
lepton and three jets or no leptons and four jets to study Higgs boson
production in association with top quarks. In addition, one of the jets needs
to be identified as originating from a bottom quark.

The expected composition of Higgs boson events in the Standard Model after
reconstruction and at particle level is summarized in Figure 21. At particle
level the VBF-enhanced fiducial region contains about 65% VBF and 32% ggH
events. The particle-level $N_{\mathrm{l}epton}\geq 1$ region is dominated by
$WH$ (47%), $t\bar{t}H$ (37%) and $ZH$ (13%) production. The particle-level
high $E_{\mathrm{T}}^{\mathrm{m}iss}$ region is populated by about equal
amounts of $WH$, $ZH$, and $t\bar{t}H$ (32%, 30%, and 35%). Finally, the
particle-level $t\bar{t}H$-enhanced region contains about 80% $t\bar{t}H$
events.

The fitted invariant mass spectra for all regions are shown in Figures 22 and
23. The results of signal-plus-background fits to these spectra is shown,
displaying both the total sum and the background-only component as well as the
residuals between the data and the background. In the diphoton fiducial
region, the Higgs boson signal is clearly visible on the falling non-resonant
background. In total, $1491\pm 248\,\text{(stat.)}\pm 64\,\text{(syst.)}$
Higgs boson signal events are extracted. Clear evidence for Higgs boson
production is observed in the VBF-enhanced region with $117\pm
26\,\text{(stat.)}\pm 4\,\text{(syst.)}$ signal events, corresponding to an
observed significance of 4.2 standard deviations.

The remaining three regions all show positive signal yields with large,
predominantly statistical, uncertainties: $14\pm 11$, $19\pm 11$, $6\pm 15$
for the $N_{\mathrm{l}epton}\geq 1$, high $E_{\mathrm{T}}^{\mathrm{m}iss}$,
and $t\bar{t}H$-enhanced fiducial regions, respectively, and the error
corresponds to the sum of the statistical and systematic uncertainties.

((a))  ((b))

Figure 21: The expected composition of Higgs boson events in each fiducial
region (a) after the reconstruction and (b) at particle-level. Details about
the reconstruction can be found in Section 5 and the definition of the
particle-level fiducial volume is given in Section 9.1.  Figure 22:  Diphoton
invariant mass $m_{\gamma\gamma}$ spectrum observed in the 2015 and 2016 data
at $\sqrt{s}=$ 13 TeV for events in the diphoton fiducial region. The solid
red curve shows the fitted signal-plus-background model when the Higgs boson
mass is constrained to be $125.09\pm 0.24$ GeV. The background component of
the fit is shown with the dotted blue curve. The signal component of the fit
is shown with the solid black curve. The bottom plot shows the residuals
between the data and the background component of the fitted model.

((a)) VBF-enhanced

((b)) $N_{\mathrm{l}epton}\geq 1$

((c)) High $E_{\mathrm{T}}^{\mathrm{m}iss}$

((d)) $t\bar{t}H$-enhanced

Figure 23:  Diphoton invariant mass $m_{\gamma\gamma}$ spectra observed in the
2015 and 2016 data at $\sqrt{s}=$ 13 TeV for events in the (a) VBF-enhanced,
(b) $N_{\mathrm{l}epton}\geq 1$, (c) high $E_{\mathrm{T}}^{\mathrm{m}iss}$,
and (d) $t\bar{t}H$-enhanced fiducial regions. The solid red curve shows the
fitted signal-plus-background model when the Higgs boson mass is constrained
to be $125.09\pm 0.24$ GeV. The background component of the fit is shown with
the dotted blue curve. The signal component of the fit is shown with the solid
black curve. The bottom plot shows the residuals between the data and the
background component of the fitted model.

The cross section for $pp\to H\to\gamma\gamma$ measured in the diphoton
fiducial region is

$\displaystyle\sigma_{\mathrm{f}id}=55\pm 9\,\text{(stat.)}\pm
4\,\text{(exp.)}\pm 0.1\,\text{(theo.)}\,\text{fb}\,,$

which is to be compared with the Standard Model prediction of $64\pm
2\,\text{fb}$. The gluon–gluon fusion contribution to the Standard Model
prediction and its uncertainty are taken to be the N3LO QCD and NLO EW
prediction of Refs. [31, 32, 33, 34, 24, 7] corrected for the
$H\to\gamma\gamma$ branching ratio and the fiducial acceptance. The fiducial
acceptance is defined using the Powheg NNLOPS prediction for gluon–gluon
fusion [23]. The contributions to the Standard Model prediction from the VBF,
$VH$, $b\bar{b}H$ and $t\bar{t}H$ production mechanisms are determined using
the particle-level predictions normalized with theoretical calculations as
discussed in Section 4, and are collectively referred to as $XH$. The measured
cross section is compatible with the Standard Model prediction and the
observed ggH coupling strength measured in Section 8, as the diphoton fiducial
region is dominated by gluon–gluon fusion production.

The cross section of the VBF-enhanced region is measured to be

$\displaystyle\sigma_{\mathrm{V}BF-enhanced}=3.7\pm 0.8\,({\mathrm{s}tat.})\pm
0.5\,({\mathrm{e}xp.})\pm 0.2\,\text{(theo.)}\,\text{fb}\,,$

which is to be compared with the Standard Model prediction of $2.3\pm
0.1\,\text{fb}$. The gluon–gluon fusion part of the SM prediction is
constructed from the Powheg NNLOPS prediction for gluon–gluon fusion
normalized with the N3LO in QCD and NLO EW prediction of Refs. [31, 32, 33,
34, 24, 7]. This prediction is labeled as “default MC” in the following and
includes all theory uncertainties related to gluon–gluon fusion as discussed
in Section 7.3.

For the $N_{\mathrm{l}epton}\geq 1$, high $E_{\mathrm{T}}^{\mathrm{m}iss}$,
and $t\bar{t}H$-enhanced fiducial regions, limits on the cross sections are
reported at the 95% CL.999The quoted CL values were obtained using the
unfolded cross sections and their corresponding uncertainties assuming
Gaussian errors.

Figure 24 and Table 15 summarize measured cross sections of the fiducial
regions and limits, and compare both to the Standard Model expectations,
constructed as outlined above. The Powheg NNLOPS prediction, without any
additional corrections, is also shown. The uncertainty band is estimated using
a set of scale variations and includes PDF uncertainties from eigenvector
variations. The Standard Model predictions of all fiducial regions are in
agreement with the corresponding measured cross sections.

Figure 24: The measured cross sections or cross-section upper limits of the diphoton, VBF-enhanced, $N_{\mathrm{l}epton}\geq 1$, high $E_{\mathrm{T}}^{\mathrm{m}iss}$, and $t\bar{t}H$-enhanced fiducial regions are shown. The intervals on the vertical axis each represent one of these fiducial regions. The data are shown as filled (black) circles. The error bar on each measured cross section represents the total uncertainty in the measurement, with the systematic uncertainty shown as a dark gray rectangle. Each cross section limit is shown at the 95% confidence level. The measured cross sections are compared to a range of predictions and a detailed description of each prediction can be found in the text. All comparisons include the SM predictions arising from VBF, $VH$, $t\bar{t}H$, and $b\bar{b}H$, which are collectively labeled as $XH$.  Table 15:  The measured cross sections in the diphoton, VBF-enhanced, $N_{\mathrm{l}epton}\geq 1$, high $E_{\mathrm{T}}^{\mathrm{m}iss}$, and $t\bar{t}H$-enhanced fiducial regions. The gluon–gluon fusion contribution to the Standard Model prediction of the diphoton fiducial region is taken to be the N3LO prediction of Refs. [31, 32, 33, 34, 24, 7] corrected for the $H\to\gamma\gamma$ branching ratio and the fiducial acceptance. The gluon–gluon fusion contribution to the Standard Model for all the other regions is taken from the Powheg NNLOPS prediction normalized with the N3LO prediction and includes all theory uncertainties related to gluon–gluon fusion as discussed in Section 7.3. The contributions to the Standard Model prediction from VBF, $VH$ $t\bar{t}H$ and $b\bar{b}H$ production mechanisms are determined using the particle-level predictions described in Section 4 normalized with theoretical calculations.  Fiducial region | Measured cross section | SM prediction
---|---|---
Diphoton fiducial | $55\pm 9\,\text{(stat.)}\pm 4\,\text{(exp.)}\pm 0.1\,\text{(theo.)}\,\text{fb}$ | $64\pm 2\,\text{fb}$ | [N3LO + $XH$]
VBF-enhanced | $3.7\pm 0.8\,({\mathrm{s}tat.})\pm 0.5\,({\mathrm{e}xp.})\pm 0.2\,\text{(theo.)}\,\text{fb}$ | $2.3\pm 0.1\,\text{fb}$ | [default MC + $XH$]
$N_{\mathrm{l}epton}\geq 1$ |  $\leq$ 1.39 fb 95% CL |  $0.57\pm 0.03$ fb | [default MC + $XH$]
High $E_{\mathrm{T}}^{\mathrm{m}iss}$ |  $\leq$ 1.00 fb 95% CL |  $0.30\pm 0.02$ fb | [default MC + $XH$]
$t\bar{t}H$-enhanced |  $\leq$ 1.27 fb 95% CL |  $0.55\pm 0.06$ fb | [default MC + $XH$]

####  9.4 Measurements of cross sections of inclusive and exclusive jet
multiplicities

The production of Higgs bosons in association with jets is sensitive to the
theoretical modeling in QCD and to the contribution of different Higgs boson
production mechanisms. In the SM, events with zero or one jet are dominated by
gluon–gluon fusion production. In events with two jets the contributions from
VBF and $VH$ production modes become more important. Higgs boson production in
association with top quarks ($t\bar{t}H$) can be probed in events with the
highest jet multiplicities. In BSM scenarios, the jet multiplicity
distribution is sensitive to new heavy particles coupling to the Higgs boson
and vector bosons. For the measurements presented here, jet multiplicity bins
with zero, one, two, and at least three jets with $p_{\mathrm{T}}$ larger than
30 GeV and absolute rapidity $\left|y\right|<4.4$ are defined. In addition,
jet multiplicity bins with a $p_{\mathrm{T}}$ larger than 50 GeV are defined
for zero, one, or at least two jets. The measured cross sections are compared
to a range of predictions of gluon–gluon fusion production:

  * •

The parton-level N3LO QCD and NLO EW prediction of Refs. [31, 32, 33, 34, 24,
7]. This prediction is shown for the inclusive zero-jet cross section.

  * •

The parton-level JVE$+$N3LO prediction of Ref. [116], which includes NNLL
resummation in QCD of the $p_{\mathrm{T}}$ of the leading jet which is matched
to the N3LO total cross section. This prediction is shown for the inclusive
one-jet cross section.

  * •

The parton-level STWZ-BLPTW predictions of Refs. [99, 101], which include
NNLL′+NNLO resummation for the $p_{\mathrm{T}}$ of the leading jet in QCD,
combined with a NLL′+NLO resummation in QCD for the subleading jet.101010The
prime indicates that the leading contributions from N3LL (resp. NNLL) are
included along with the full NNLL (resp. NLL) corrections. The numerical
predictions for $\sqrt{s}=13\,\text{Te\kern-1.00006ptV}$ are taken from Ref.
[7]. This prediction is shown for the inclusive zero-, one- and two-jet cross
sections as well as for the exclusive zero- and one-jet cross sections.

  * •

The parton-level NNLOJET prediction of Refs. [117, 118] is a fixed-order NNLO
prediction in QCD for inclusive $H+$one-jet production. This prediction is
shown for the inclusive one-, two-jet, and three-jet cross sections as well as
for the exclusive one- and two-jet cross sections.

  * •

The parton-level GoSam prediction of Refs. [119, 120], which provides the
fixed-order loop contributions accurate at NLO in QCD in the inclusive $H$ \+
zero-jet, $H$ \+ one-jet, $H$ \+ two-jet, and $H$ \+ three-jet regions. The
real-emission contributions at fixed order in QCD are provided by Sherpa [64].
This prediction is shown for the inclusive one-, two-jet, and three-jet cross
sections as well as for the exclusive one- and two-jet cross sections.

  * •

The default MC prediction (Powheg NNLOPS normalized with the N3LO in QCD and
NLO EW cross section) introduced in Section 9.3. This prediction is shown for
all measured inclusive and exclusive jet cross sections.

  * •

The Powheg NNLOPS prediction which is already described in Section 4. This
prediction is shown for all measured inclusive and exclusive jet cross
sections.

  * •

The Sherpa (Meps@Nlo) prediction of Refs. [64, 121, 122, 123, 124, 125, 126,
127, 120, 65, 128, 129] is accurate to NLO in QCD in the inclusive $H$ \+
zero-jet, $H$ \+ one-jet, $H$ \+ two-jet, and $H$ \+ three-jet regions and
includes top-quark mass effects. The one-loop corrections are incorporated
from GoSam [119, 120] and the different jet multiplicity regions are merged
using the Meps@Nlo multijet merging technique. This prediction is shown for
all measured inclusive and exclusive jet cross sections.

  * •

The MG5_aMC@NLO prediction of Refs. [46, 105], which includes up to two jets
at NLO accuracy using the FxFx merging scheme [106]. The central merging scale
is taken to be 30 GeV. The generated events are passed to Pythia8 [29] to
provide parton showering and hadronization to create the full final state
(without underlying event). This prediction is shown for all measured
inclusive and exclusive jet cross sections.

All predictions but NNLOJET and Sherpa (Meps@Nlo) use the NNLO PDF set
following the PDF4LHC15 recommendations. The NNLOJET prediction uses the CT14
NNLO PDF set [130] and Sherpa (Meps@Nlo) uses the NNPDF3.0PDF set [47]. GoSam,
Sherpa (Meps@Nlo), and NNLOJET apply the kinematic selection on the final-
state photons. For all other predictions, the fiducial acceptance is
determined using Powheg NNLOPS. The cross sections of all parton-level
predictions are multiplied with isolation correction factors to account for
the efficiency of the fiducial photon isolation criterion. The additional
uncertainties in the isolation correction are determined by studying multiple
event generators and/or event generator tunes, and are included in the
uncertainty bands of the parton-level predictions. No correction factors nor
additional uncertainties to account for the impact of hadronization and the
underlying event activity are applied, so the theory uncertainties in the
parton-level predictions may be incomplete, but example values for such
corrections and their uncertainties can be found in Table 24 in Appendix D.
All other acceptance and correction factors along with their associated
uncertainties can also be found in Appendix D.

No $K$-factors are applied to the predictions and the contributions from $XH$
are also included in the comparison using the corresponding generators and
cross sections described in Section 4.

Figure 25(a) shows exclusive and inclusive zero-, one- and two-jet cross
sections and the inclusive three-jet cross section for jets defined with
$p_{\mathrm{T}}>30\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$. Figure
25(b) shows the exclusive zero- and one- and the inclusive two-jet cross
section with $p_{\mathrm{T}}>50\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}$. The measured cross sections are in agreement with
the Standard Model predictions, although there is a 1.5 $\sigma$ deficit in
the $N_{\mathrm{j}ets}$= 0 cross section for jets defined with
$p_{\mathrm{T}}>30\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$. As shown in
Figure 20, there is a sizeable positive correlation between zero-jet and
low-$p_{{\mathrm{T}}}^{\gamma\gamma}$ events, and a similar deficit is
observed there (cf. Section 9.5.1).

((a))

((b))

Figure 25:  Cross sections for $pp\to H\to\gamma\gamma$ as a function of
inclusive and exclusive jet multiplicities for jets with (a)
$p_{\mathrm{T}}>30\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$ and (b)
$p_{\text{T}}>50\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$. The data are
shown as filled (black) circles. The vertical error bar on each data point
represents the total uncertainty in the measured cross section and the shaded
(gray) band is the systematic component. The measured differential cross
sections are compared to a range of predictions and details can be found in
the text. The width of the bands of each prediction reflects the total
theoretical uncertainty. The small contribution from VBF, $VH$, $t\bar{t}H$,
and $b\bar{b}H$ is also shown as a (green) histogram and denoted by $XH$.

####  9.5 Measurements of differential and double-differential cross sections

Eleven fiducial differential cross sections are measured that characterize the
Higgs boson production kinematics, the kinematics of jets produced in
association with the Higgs boson, the spin and CP quantum numbers of the Higgs
boson and variables sensitive to the VBF production mechanism. In addition,
two double-differential cross sections are reported. The measurement of seven
additional variables can be found in Appendix C.

#####  9.5.1 Measurements of cross sections probing the Higgs boson production
kinematics

Measuring the transverse momentum of the diphoton system,
$p_{{\mathrm{T}}}^{\gamma\gamma}$ , probes the perturbative QCD modeling of
the ggH production mechanism which is mildly sensitive to the bottom- and
charm-quark Yukawa couplings [12]. The distribution at high transverse
momentum is sensitive to new heavy particles coupling to the Higgs boson and
to the top-quark Yukawa coupling. The rapidity distribution of the diphoton
system, $|y_{\gamma\gamma}|$, is also sensitive to the modeling of the ggH
production mechanism. The differential cross sections for $pp\to
H\to\gamma\gamma$ as a function of $p_{{\mathrm{T}}}^{\gamma\gamma}$ and
$|y_{\gamma\gamma}|$ are shown in Figure 26. The chosen bin widths are a
compromise between retaining a sufficiently significant signal and providing
spectra with good granularity. Each bin is chosen such that it retains an
expected significance of at least two standard deviations, estimated using the
Powheg NNLOPS and additional predictions described in Section 4 as well as
using a fit to $m_{\gamma\gamma}$ sidebands. The measurements are compared to
several predictions of gluon–gluon fusion:

  * •

The default MC prediction (Powheg NNLOPS normalized with the N3LO in QCD and
NLO EW cross section) introduced in Section 9.3.

  * •

Hres [131, 132], which provides predictions at NNLO with $p_{\mathrm{T}}^{H}$
resummation at NNLL and differentially in
$p_{{\mathrm{T}}}^{\gamma\gamma}$Ḟinite top-, bottom-, and charm-quark masses
are included at NLO accuracy. The renormalization and factorization scales are
chosen to be $\frac{1}{2}\sqrt{m_{H}^{2}+(p_{\mathrm{T}}^{H})^{2}}$, and the
two resummation scales are chosen to be $m_{H}/2$ and $2m_{b}$.

  * •

RadISH+NNLOjet [133], which provides predictions using a $p_{\mathrm{T}}^{H}$
resummation to NNLL and matching to the one-jet NNLO differential spectrum
from NNLOJET [117, 118]. The shown $p_{{\mathrm{T}}}^{\gamma\gamma}$
RadISH+NNLOjet prediction does include corrections from the finite top and
bottom quark masses.

  * •

SCETlib+MCFM8 which provides predictions at NNLO+NNLL′φ accuracy derived by
applying a resummation of the virtual corrections to the gluon form factor
[134, 135] and differentially in $|y_{\gamma\gamma}|$ and
$|\cos\theta^{*}|$.111111The subscript $\varphi$ refers to the fact that the
applied resummation is to the gluon form factor. The underlying NNLO
predictions are obtained using MCFM8 with zero-jettiness subtractions [136,
137].

No additional $K$-factors are applied to the predictions, which all use the
NNLO PDF set following the PDF4LHC15 recommendations, and the fiducial
acceptance for RadISH+NNLOjet is determined using Powheg NNLOPS. The
SCETlib+MCFM8 and Hres predictions include the kinematic acceptance and are
corrected and apply correction factors accounting for the photon isolation
efficiency as described in Section 9.4. As also mentioned in Section 9.4, no
correction factors to account for the impact of hadronization and the
underlying-event activity are used. The SM prediction shows a slight excess at
low transverse momentum and low rapidity, and shows a slight deficit at large
transverse momentum. The slightly harder Higgs boson transverse momentum shown
in Figure 26 is consistent with the ATLAS Run 1 measurements in both the
$H\to\gamma\gamma$ and $H\to ZZ^{*}\to 4\ell$ decay channels [9, 138] and the
measured zero-jet cross section. The Standard Model prediction is in agreement
with the measured distributions.

((a))  ((b))

Figure 26:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $p_{{\mathrm{T}}}^{\gamma\gamma}$ and (b) $|y_{\gamma\gamma}|$
are shown and compared to the SM expectations.

#####  9.5.2 Measurements of cross sections probing the jet kinematics

The transverse momentum and absolute rapidity of the leading jet,
$p_{\mathrm{T}}^{j_{1}}$and $|y_{j_{1}}|$, as well as the transverse momentum
and absolute rapidity of the subleading jet, $p_{\mathrm{T}}^{j_{2}}$ and
$|y_{j_{2}}|$, are sensitive to the theoretical modeling and to the relative
contributions of the different Higgs boson production mechanisms. The
transverse momentum distribution of the leading jet probes the emission of
energetic quarks and gluons. In events with two jets, the contributions of VBF
and $VH$ productions become more important. The differential cross sections
for $pp\to H\to\gamma\gamma$ as a function of $p_{\mathrm{T}}^{j_{1}}$,
$|y_{j_{1}}|$, $p_{\mathrm{T}}^{j_{2}}$, and $|y_{j_{2}}|$ are shown in Figure
27. The chosen bin widths are a compromise between keeping migrations between
bins small whilst retaining enough statistical power to measure the
differential spectra. The measured $p_{\mathrm{T}}^{j_{1}}$ spectrum shown in
Figure 27(a) is compared to the default MC prediction as introduced in the
previous section as well as to the NNLOJET and SCETlib(STWZ) [135, 99]
predictions. Both the NNLOJET and SCETlib predictions are corrected using
isolation correction factors to account for the impact of the isolation
efficiency. In addition, the NNLOJET prediction is corrected for the kinematic
acceptance and the uncertainties in these corrections is included in the
uncertainty bands of both NNLOJET and SCETlib. The first bin of the leading
jet $p_{\mathrm{T}}$ spectrum represents zero-jet events that do not contain
any jet with $p_{\mathrm{T}}$> 30 GeV. The predicted $p_{\mathrm{T}}$
distributions slightly exceed the measured distribution at low transverse
momentum and all show a slight deficit at large transverse momentum. Both are
compatible with the observed slightly harder Higgs boson transverse momentum
distribution. The measured $|y_{j_{1}}|$ distribution shown in Figure 27(b) is
compared to the default MC and the NNLOJET predictions: Both show a slight
excess at low rapidity. In Figure 27(c) the measured subleading jet
$p_{\mathrm{T}}$ distribution is shown. The first bin of
$p_{\mathrm{T}}^{j_{2}}$ represents one-jet events that do not contain two or
more jets with $p_{\mathrm{T}}$> 30 GeV. The measured distribution is compared
to the default MC, Sherpa (Meps@Nlo), and GoSam predictions, as introduced in
Section 9.4. Finally, in Figure 27(d) the subleading jet rapidity
distribution, $|y_{j_{2}}|$, is shown and compared to the expectation from the
default MC, Sherpa (Meps@Nlo), and GoSam predictions. The SM predictions are
in agreement with the measured distributions and no significant deviations are
seen.

((a))  ((b))

((c))  ((d))

Figure 27:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $p_{\mathrm{T}}^{j_{1}}$, (b) $|y_{j_{1}}|$, (c)
$p_{\mathrm{T}}^{j_{2}}$, and (d) $|y_{j_{2}}|$ are shown and compared to the
SM expectations. The data and theoretical predictions are presented in the
same way as in Figure 26. In addition, the NNLOJET and SCETlib(STWZ)
predictions, the NNLOJET prediction, and the Sherpa (Meps@Nlo) and GoSam
predictions, described in the text, are displayed in (a), (b) and (c+d),
respectively.

#####  9.5.3 Measurements of cross sections probing spin and CP

The absolute value of the cosine of the angle between the beam axis and the
photons in the Collins–Soper frame [11] of the Higgs boson,
$|\cos\theta^{*}|$, can be used to study the spin of the Higgs boson. The
azimuthal angle between the two leading jets, $\Delta\phi_{jj}$,121212 To
preserve the sign information, the azimuthal angles of the jets are ordered
according to the jet with the highest rapidity. This definition of
$\Delta\phi_{jj}$ is invariant under a redefinition of the ordering by
choosing the opposite beam axis, as explained in Ref. [139]. in events
containing two or more jets is sensitive to the charge conjugation and parity
properties of the Higgs boson interactions with gluons and weak bosons in the
gluon–gluon fusion and the VBF production channels, respectively [140, 139,
141, 142].

The differential cross sections for $pp\to H\to\gamma\gamma$ as a function of
$|\cos\theta^{*}|$ and $\Delta\phi_{jj}$ are shown in Figure 28. For a scalar
particle $|\cos\theta^{*}|$, shows a strong drop around 0.6 due to the
fiducial requirement on the photon system, whereas for a spin-2 particle, an
enhancement would be present in precisely this region. The charge conjugation
and parity properties of the Higgs boson are encoded in the azimuthal angle
between the jets: For example, in gluon–gluon fusion, its distribution for a
CP-even coupling has a dip at $\pm\frac{\pi}{2}$ and present peaks at 0 and
$\pm\pi$, whereas for a purely CP-odd coupling it would present as peaks at
$\pm\frac{\pi}{2}$ and dips at 0 and $\pm\pi$. For VBF the SM prediction for
$\Delta\phi_{jj}$ is approximately constant with a slight rise towards
$\Delta\phi_{jj}$$=\pm\pi$. Any additional anomalous CP-even or CP-odd
contribution to the interaction between the Higgs boson and weak bosons would
manifest itself as an additional oscillatory component, and any interference
between the SM and anomalous couplings can produce distributions peaked at
either $\Delta\phi_{jj}$$=0$ or $\Delta\phi_{jj}$$=\pm\pi$ [139, 141, 142].
The shape of the distribution is therefore sensitive to the relative
contribution of gluon–gluon fusion and vector-boson fusion, as well as to the
tensor structure of the interactions between the Higgs boson and gluons or
weak bosons. This is exploited in Section 9.5.8 to set limits on new physics
contributions. To quantify the structure of the azimuthal angle between the
two jets, a ratio is defined as

$\displaystyle
A_{|\Delta\phi_{jj}|}=\frac{\sigma(|\Delta\phi_{jj}|<\frac{\pi}{3})-\sigma(\frac{\pi}{3}<|\Delta\phi_{jj}|<\frac{2\pi}{3})+\sigma(|\Delta\phi_{jj}|>\frac{2\pi}{3})}{\sigma(|\Delta\phi_{jj}|<\frac{\pi}{3})+\sigma(\frac{\pi}{3}<|\Delta\phi_{jj}|<\frac{2\pi}{3})+\sigma(|\Delta\phi_{jj}|>\frac{2\pi}{3})}\,,$

which is motivated by a similar ratio presented in Ref. [141]. The measured
ratio in data as determined by measuring $|\Delta\phi_{jj}|$ in three bins is

$\displaystyle
A_{|\Delta\phi_{jj}|}^{\mathrm{m}eas}=0.45^{+0.18}_{-0.24}\,{\mathrm{(}stat.)}\,{}^{+0.10}_{-0.11}\,{\mathrm{(}syst.)}\,.$

This value can be compared to the SM prediction from the default MC
simulation. The predicted value is
$A_{|\Delta\phi_{jj}|}^{\mathrm{S}M}=0.44\pm 0.01$, consistent with the
measured ratio.

((a))  ((b))

Figure 28:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $|\cos\theta^{*}|$ and (b) $\Delta\phi_{jj}$ are shown and
compared to the SM expectations. The data and theoretical predictions are
presented in the same way as in Figure 26. In addition, the SCETlib+MCFM8
prediction and the Sherpa (Meps@Nlo) and GoSam predictions, described in the
text, are displayed in (a) and (b), respectively.

In summary, the measured $|\cos\theta^{*}|$ and $\Delta\phi_{jj}$
distributions are consistent with Standard Model predictions for a CP-even
scalar particle.

#####  9.5.4 Cross sections probing the VBF production mode

The distribution of the dijet rapidity separation, $|\Delta{y_{jj}|}$, the
azimuthal angle between the dijet and diphoton systems,
$|\Delta\phi_{\gamma\gamma,jj}|$, and the invariant mass of the leading and
subleading jets, $m_{jj}$ for events with two or more jets are sensitive to
the differences between the gluon–gluon fusion and VBF production mechanisms.
In vector-boson fusion, the $t$-channel exchange of a $W/Z$ boson typically
results in two moderate-$p_{\mathrm{T}}$ jets that are well separated in
rapidity. Furthermore, quark/gluon radiation in the rapidity interval between
the two jets is suppressed in the VBF process when compared to the gluon–gluon
fusion process, because there is no color flow between the two jets. The
$|\Delta\phi_{\gamma\gamma,jj}|$ distribution for VBF production is therefore
expected to be steeper and more peaked towards
$|\Delta\phi_{\gamma\gamma,jj}|=\pi$ than for gluon–gluon fusion.

The differential cross sections for $pp\to H\to\gamma\gamma$ as a function of
$|\Delta{y_{jj}|}$, $|\Delta\phi_{\gamma\gamma,jj}|$, and $m_{jj}$ are shown
for events with at least two jets with $p_{\mathrm{T}}$ > 30 GeV in Figure 29.
These variables are used to discriminate between gluon–gluon fusion and the
VBF production of the Higgs boson and enter the multivariate classifier
introduced in Section 8.1.4 that defines the categories used for the
simplified template cross-section and coupling measurements. The measured
distributions are in agreement to the default MC, Sherpa (Meps@Nlo), and the
GoSam predictions. The accuracy of the fixed-order parton-level prediction
from GoSam breaks down in the lowest bin of
$\pi-|\Delta\phi_{\gamma\gamma,jj}|$ and the measured cross section moderately
exceeds the SM predictions at high $m_{jj}$ values.

((a))  ((b))

((c))

Figure 29:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $|\Delta{y_{jj}|}$, (b) $\pi-$
$|\Delta\phi_{\gamma\gamma,jj}|$, and (c) $m_{jj}$ are shown and compared to
the SM expectations. The data and theoretical predictions are presented in the
same way as in Figure 26. In addition, the Sherpa (Meps@Nlo) and GoSam
predictions are shown for all three cross sections.

#####  9.5.5 Double-differential cross sections

The double-differential cross section for $pp\to H\to\gamma\gamma$ as a
function of $p_{{\mathrm{T}}}^{\gamma\gamma}$ and $N_{\mathrm{j}ets}$, for
jets with $p_{\mathrm{T}}>30$ GeV, and $p_{{\mathrm{T}}}^{\gamma\gamma}$ and
$|\cos\theta^{*}|$ are shown in Figure 30. These cross sections are sensitive
to the modeling of the Higgs boson kinematic, its production mechanisms, and
its spin-CP properties. Both double-differential cross sections are in
agreement with the Standard Model expectation.

((a))  ((b))

Figure 30:  The double-differential cross section for $pp\to H\to\gamma\gamma$
as a function of (a) $p_{{\mathrm{T}}}^{\gamma\gamma}$ and
$N_{\mathrm{j}ets}$, for jets with $p_{\mathrm{T}}>30\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}$, and (b) $p_{{\mathrm{T}}}^{\gamma\gamma}$ and
$|\cos\theta^{*}|$ separating the two regions of $|\cos\theta^{*}|<0.5$ and
$|\cos\theta^{*}|>0.5$ from each other. The data and theoretical predictions
are presented in the same way as in Figure 26.

#####  9.5.6 Impact of systematic uncertainties on results

A summary of the uncertainties in the measured cross sections of the fiducial
regions are shown in Table 16. As an example concerning the differential
measurements, a breakdown of the systematic uncertainties in the differential
cross sections as a function of $p_{{\mathrm{T}}}^{\gamma\gamma}$ and
$N_{\mathrm{j}ets}$ is shown in Figure 31. The measurements are dominated by
the statistical uncertainties. For the systematic uncertainties, the
uncertainty in the fitted signal yield, due to the background modeling and the
photon energy resolution, is typically more important than the uncertainty in
the correction factor due to the theoretical modeling. The jet energy scale
and resolution uncertainties become increasingly important for high-jet
multiplicities and in the $t\bar{t}H$\- and VBF-enhanced phase space.

((a))  ((b))  ((c))  ((d))

Figure 31:  The relative size of systematic uncertainties associated with the signal extraction, the correction factors (experimental and theoretical modeling) and the luminosity on the differential cross sections are shown as a function of (a) $p_{\mathrm{T}t}^{\gamma\gamma}$ and (b) $N_{\mathrm{j}ets}$. The statistical uncertainty associated with the signal extraction is also shown as a gray band. For completeness, the relevant components of the uncertainties in the correction factors are shown as a function of (c) $p_{\mathrm{T}t}^{\gamma\gamma}$ and (d) $N_{\mathrm{j}ets}$. Table 16: The expected uncertainties, expressed in percent, in the cross sections measured in the diphoton fiducial, VBF-enhanced, $N_{\mathrm{l}epton}\geq 1$, $t\bar{t}H$-enhanced, and high $E_{\mathrm{T}}^{\mathrm{m}iss}$ regions. The fit systematic uncertainty includes the effect of the photon energy scale and resolution, and the impact of the background modeling on the signal yield. The theoretical modeling uncertainty is defined as the envelope of the signal composition, the modeling of Higgs boson transverse momentum and rapidity distribution, and the uncertainty of parton shower and the underlying event (labeled as “UE/PS”) as described in Section 7.4.  Source | Uncertainty in fiducial cross section
---|---
| Diphoton | VBF-enhanced | $N_{\mathrm{l}epton}\geq 1$ |  $t\bar{t}H$-enhanced | High $E_{\mathrm{T}}^{\mathrm{m}iss}$
Fit (stat.) | 17% | 22% | 72% | 176% | 53%
Fit (syst.) | 6% | 9% | 27% | 138% | 13%
Photon energy scale & resolution | 4.3% | 3.5% | 3.1% | 10% | 4.1%
Background modeling | 4.2% | 7.8% | 26.7% | 138% | 12.2%
Photon efficiency | 1.8% | 1.8% | 1.8% | 1.8% | 1.9%
Jet energy scale/resolution | - | 8.9% | - | 4.5% | 6.9%
$b$-jet flavor tagging | - | - | - | 3% | -
Lepton selection | - | - | 0.7% | 0.2% | -
Pileup | 1.1% | 2.9% | 1.3% | 2.5% | 2.5%
Theoretical modeling | 0.1% | 4.5% | 4.0% | 8.1% | 31%
Signal composition | 0.1% | 4.5% | 3.1% | 8.1% | 25%
Higgs boson $p_{\mathrm{T}}^{H}$ & $|y_{H}|$ | 0.1% | 0.9% | 0.2% | 0.7% | 0.1%
UE/PS | - | 0.3% | 0.7% | 1.1% | 31%
Luminosity | 3.2% | 3.2% | 3.2% | 3.2% | 3.2%
Total | 18% | 26% | 77% | 224% | 63%

#####  9.5.7 Compatibility of measured distributions with the Standard Model

Table 17: Probabilities from a $\chi^{2}$ test for the comparison between data and the default SM prediction. Distribution | Default MC Prediction
---|---
$p_{{\mathrm{T}}}^{\gamma\gamma}$ | 51%
$|y_{\gamma\gamma}|$ | 57%
$p_{\mathrm{T}}^{j_{1}}$ | 32%
$|y_{j_{1}}|$ | 66%
$p_{\mathrm{T}}^{j_{2}}$ | 61%
$|y_{j_{2}}|$ | 56%
$|\cos\theta^{*}|$ | 47%
$\Delta\phi_{jj}$ | 64%
$|\Delta{y_{jj}|}$ | 53%
$|\Delta\phi_{\gamma\gamma,jj}|$ | 43%
$m_{jj}$ | 54%
$N_{\mathrm{j}ets}$($p_{\mathrm{T}}>30$ GeV) | 56%
$N_{\mathrm{j}ets}$($p_{\mathrm{T}}>50$ GeV) | 19%

The compatibility between the measured distributions and the Standard Model is
tested by comparing the first and second moments of the measured
distributions. Figure 32 shows the first and second moments (mean and RMS) of
the distributions and compares them to the moments of the default MC
prediction, as calculated from the measured and predicted cross-section bins.
The theory uncertainties are constructed as outlined in Section 7.3. The
measured Higgs boson transverse momentum has somewhat higher first and second
moments than the Standard Model prediction, which is consistent with the
previous observations [9, 138]. The leading-jet $p_{\mathrm{T}}$ spectrum
shows the same feature. In addition a $\chi^{2}$ test is carried out for all
distributions reported in Section 9: The resulting $p$-values are reported in
Table 17, which confirms that within the current uncertainties the data are in
agreement with the SM predictions.

((a))  ((b))

Figure 32:  (a) The ratio of the first moment (mean) of each differential
distribution predicted by the Standard Model to that observed in the data. The
SM moment is calculated by using the default MC distributions for gluon–gluon
fusion and the other production mechanisms. (b) The ratio of the second moment
(RMS) of each differential distribution predicted by the Standard Model to
that observed in the data. The intervals on the vertical axes each represent
one of the differential distributions. The band for the theoretical prediction
represents the corresponding uncertainty in that prediction (see text for
details). The error bar on the data represents the total uncertainty in the
measurement, with the gray band representing only the systematic uncertainty.

#####  9.5.8 Search for anomalous Higgs-boson interactions using an effective
field theory approach

The strength and tensor structure of the Higgs-boson interactions can be
investigated using an effective field theory approach, which introduces
additional CP-even and CP-odd interactions that change the event rates and the
kinematic properties of the Higgs boson and associated jet spectra from those
in the Standard Model. The parameters of the effective field theory are probed
using a fit to five of the most relevant differential cross sections. The
effective Lagrangian of Ref. [143] is used which adds dimension-six operators
of the Strongly Interacting Light Higgs formulation [13] to the Standard Model
interactions. The $H\to\gamma\gamma$ differential cross sections are mainly
sensitive to the operators that affect the Higgs boson interactions with gauge
bosons and the relevant terms in the Lagrangian can be specified by

$\displaystyle{\cal L}_{\mathrm{e}ff}=$ $\displaystyle\bar{c}_{g}{\cal
O}_{g}+\bar{c}_{HW}{\cal O}_{HW}+\bar{c}_{HB}{\cal O}_{HB}$
$\displaystyle\quad+\,\,\tilde{c}_{g}\tilde{\cal
O}_{g}+\tilde{c}_{HW}\tilde{\cal O}_{HW}+\tilde{c}_{HB}\tilde{\cal O}_{HB},$

where $\bar{c}_{i}$ and $\tilde{c}_{i}$ are dimensionless Wilson coefficients
specifying the strength of the new CP-even and CP-odd interactions,
respectively, and the dimension-six operators ${\cal O}_{i}$ and $\tilde{{\cal
O}_{i}}$ are those described in Refs. [143, 144]. In the SM, all of the Wilson
coefficients are equal to zero. The ${\cal O}_{g}$ and $\tilde{\cal O}_{g}$
operators introduce new interactions between the Higgs boson and two gluons
and can be probed through the gluon–gluon fusion Higgs production mechanism.
The ${\cal O}_{HW}$ and $\tilde{\cal O}_{HW}$ operators introduce new $HWW$,
$HZZ$ and $HZ\gamma$ interactions. The $HZZ$ and $HZ\gamma$ interactions are
also impacted by ${\cal O}_{HB}$ and $\tilde{\cal O}_{HB}$. The ${\cal
O}_{HW}$, $\tilde{\cal O}_{HW}$, ${\cal O}_{HB}$ and $\tilde{\cal O}_{HB}$
operators can be probed through vector-boson fusion and associated production.
Other operators in the full effective Lagrangian of Ref. [143] can also modify
Higgs-boson interactions but are not considered here due to the lack of
sensitivity of the $H\to\gamma\gamma$ decay channel. Combinations of some of
the CP-even operators have been constrained using global fits to experimental
data from LEP and the LHC [143, 145, 146].

The effective Lagrangian has been implemented in FeynRules [144].131313The
implementation in Ref. [144] involves a redefinition of the gauge boson
propagators that results in unphysical amplitudes unless certain physical
constants are also redefined. The original implementation did not include the
redefinition of these physical constants. However, the impact of redefining
the physical constants is found to be negligible on the predicted cross
sections across the range of Wilson coefficients studied. The relative change
in the predicted Higgs boson cross sections as functions of the different
Wilson coefficients is also found to agree with that predicted by the Higgs
characterization framework [147], with less than 2% variation across the
parameter ranges studied. Parton-level event samples are produced for specific
values of Wilson coefficients by interfacing the universal file output from
FeynRules to the MG5_aMC@NLOevent generator [46]. Higgs bosons are produced
via gluon–gluon fusion with up to two additional partons in the final state
using leading-order matrix elements.

The generated events are passed to Pythia8 [29] to provide parton showering,
hadronization and underlying event and the zero-, one- and two-parton events
are merged using the MLM matching scheme [148] to create the full final state.
Event samples containing a Higgs boson produced either in association with a
vector boson or via vector-boson fusion are produced using leading-order
matrix elements and passed through the Pythia8 generator. For each production
mode, the Higgs boson mass is set to 125 GeV and events are generated using
the NNPDF2.3LO PDF set [47] and the A14 parameter set [48]. All other Higgs
boson production modes are assumed to occur as predicted by the SM.

Event samples are produced for different values of a given Wilson coefficient.
The particle-level differential cross sections are produced using Rivet [149].
The Professor method [150] is used to interpolate between these samples, for
each bin of each distribution, to provide a parameterization of the effective
Lagrangian prediction. The parameterization function is determined using 11
samples when studying a single Wilson coefficient, whereas 25 samples are used
when studying two Wilson coefficients simultaneously. As the Wilson
coefficients enter the effective Lagrangian in a linear fashion, second-order
polynomials are used to predict the cross sections in each bin. The method was
validated by comparing the differential cross sections obtained with the
parameterization function to the predictions obtained with dedicated event
samples generated at the specific point in parameter space.

The model implemented in FeynRules fixes the Higgs boson width to be that of
the SM, $\Gamma_{H}=4.07$ MeV [17]. The cross sections are scaled by
$\Gamma_{H}/(\Gamma_{H}+\Delta\Gamma)$, where $\Delta\Gamma$ is the change in
partial widths due to a specific choice of Wilson coefficient. The change in
partial widths is determined for each Higgs coupling using the partial-width
calculator in MG5_aMC@NLOand normalized to reproduce the SM prediction from
Hdecay [18].

The leading-order predictions obtained from MG5_aMC@NLOare reweighted to
account for higher-order QCD and electroweak corrections to the SM process,
assuming that these corrections factorize from the new physics effects. The
differential cross section as a function of variable $X$ for a specific choice
of Wilson coefficient, $c_{i}$, is given by

$\frac{{\mathrm{d}}\sigma}{{\mathrm{d}}X}=\sum_{j}\left(\frac{{\mathrm{d}}\sigma_{j}}{{\mathrm{d}}X}\right)^{\mathrm{r}ef}\cdot\left(\frac{{\mathrm{d}}\sigma_{j}}{{\mathrm{d}}X}\right)_{c_{i}}^{\mathrm{M}G5}/\left(\frac{{\mathrm{d}}\sigma_{j}}{{\mathrm{d}}X}\right)_{c_{i}=0}^{\mathrm{M}G5},$

where the summation $j$ is over the different Higgs boson production
mechanisms, ‘MG5’ labels the interpolated MG5_aMC@NLOprediction and ‘ref’
labels a reference sample for SM Higgs boson production. For the reference
sample the default MC simulation is used.

The measured differential cross sections of $p_{{\mathrm{T}}}^{\gamma\gamma}$,
$N_{\mathrm{j}ets}$, $m_{jj}$, $|\Delta\phi_{jj}|$, and
$p_{\mathrm{T}}^{j_{1}}$ are compared in Figure 33(a) to the SM hypothesis and
to two non-SM hypotheses, specified by $\bar{c}_{g}=2\times 10^{-4}$ and
$\bar{c}_{HW}=0.05$, respectively. The new CP-odd gluon–gluon fusion operator
results in a large increase in rate and the additional CP-even $WH$ operator
leads to a larger number of Higgs boson with sizeable $p_{\text{T}}$ and an
increased number of zero-jet events.

((a))

((b))

Figure 33:  (a) The measured differential cross sections as a function of
$p_{{\mathrm{T}}}^{\gamma\gamma}$, $N_{\mathrm{j}ets}$, $m_{jj}$,
$|\Delta\phi_{jj}|$, and $p_{\mathrm{T}}^{j_{1}}$ are compared to the SM
hypothesis and two non-SM hypotheses with $\bar{c}_{g}=1\times 10^{-4}$ and
$\bar{c}_{HW}=0.05$, respectively. (b) Ratios of differential cross sections,
as predicted for specific choices of Wilson coefficient, to the differential
cross sections predicted by the SM: the impact of non-zero $\bar{c}_{g}$ and
$\tilde{c}_{g}$ is shown relative to the SM ggH prediction, while the impact
of non-zero $\bar{c}_{HW}$ and $\tilde{c}_{HW}$ is shown relative to the SM
VBF+$VH$ prediction.

The ratios of the expected differential cross sections to the SM predictions
for some representative values of the Wilson coefficients are shown in Figure
33(b). The impact of the $\bar{c}_{g}$ and $\tilde{c}_{g}$ coefficients are
presented for the gluon–gluon fusion production: it displays a large change in
the overall cross-section normalization. The $\tilde{c}_{g}$ coefficient also
changes the shape of the $\Delta\phi_{jj}$ distribution, which is expected
from consideration of the tensor structure of CP-even and CP-odd interactions
[139, 141]. In contrast, the impact of the $\bar{c}_{HW}$ and $\tilde{c}_{HW}$
coefficients are presented specifically for the VBF$+$VH production channel:
one expects large shape changes in all of the studied distributions and the
$\Delta\phi_{jj}$ distribution is known to discriminate between CP-even and
CP-odd interactions in the VBFproduction channel [140].

Limits on Wilson coefficients are set by constructing a likelihood function

$\displaystyle\mathcal{L}=\frac{1}{\sqrt{\left(2\pi\right)^{k}|C|}}\exp\left(-\frac{1}{2}\left(\vec{\sigma}_{\mathrm{d}ata}-\vec{\sigma}_{\mathrm{p}red}\right)^{T}C^{-1}\left(\vec{\sigma}_{\mathrm{d}ata}-\vec{\sigma}_{\mathrm{p}red}\right)\right)\,,$

where $\vec{\sigma}_{\mathrm{d}ata}$ and $\vec{\sigma}_{\mathrm{p}red}$ are
$k$-dimensional vectors from the measured and predicted differential cross
sections of the five analyzed observables,
$C=C_{\mathrm{s}tat}+C_{\mathrm{s}yst}+C_{\mathrm{t}heo}$ is the $k\times k$
total covariance matrix defined by the sum of the statistical, systematic and
theoretical covariances, and $|C|$ denotes its determinant. The theory
covariance is constructed as outlined in Section 7.3 and includes no
additional uncertainty to account for the factorization assumption in Eq.
9.5.8. Based on this likelihood, one can construct a $\chi^{2}$ test to test
the compatibility of the five distributions with the SM and a probability of
93% is found. In what follows, the likelihood function is numerically
maximized to determine $\mathcal{L}_{\mathrm{m}ax}$ and confidence limits for
one or several Wilson coefficients are determined via

$\displaystyle
1-\text{CL}=\int_{-2\ln\mathcal{L}(c_{i})+2\ln\mathcal{L}_{\mathrm{m}ax}}^{\infty}\,\text{d}x\,f(x)\,,$

with $\mathcal{L}(c_{i})$ denoting the likelihood value evaluated for a given
Wilson coefficient value $c_{i}$, and $f(x)$ denoting the distribution of the
test statistic. The coverage of the confidence limit is determined using
ensembles of pseudo-experiments. Form factors are sometimes used to regularize
the change of the cross section above a momentum scale
$\Lambda_{\mathrm{F}F}$. This was investigated by reweighting the VBF$+$VH
samples using form-factor predictions from VBFNLO [151]. The impact on the
$\bar{c}_{HW}$ and $\tilde{c}_{HW}$ limits is negligible for
$\Lambda_{\mathrm{F}F}>$1 TeV.

In Table 18, the observed and expected 95% CL limits for four Wilson
coefficient fits are given. The limit for $\bar{c}_{g}$ is derived by fixing
all other Wilson coefficients to zero. This additional interaction can
interfere with the corresponding SM interaction and destructive interference
causes the gluon–gluon fusion production-mode cross section to be zero at
$\bar{c}_{g}\sim-2.2\times 10^{-4}$. The $\tilde{c}_{g}$ coefficient is also
derived after setting all Wilson coefficients to zero. Due to the CP conjugate
structure of the interaction, no interference with the SM process is possible.
The 95% CL limit for $\bar{c}_{HW}$ is obtained after setting
$\bar{c}_{HB}=\bar{c}_{HW}$ to ensure that the partial width for $H\to
Z\,\gamma$ is unchanged from the SM prediction (Values of
$\left|\bar{c}_{HW}-\bar{c}_{HB}\right|>0.03$ lead to a very large decay rate
for the $H\to Z\gamma$ process that is contradicted by the experimental
constraints reported by ATLAS [152, 153]) and setting all other Wilson
coefficients to zero. Finally, the 95% CL limit for $\tilde{c}_{HW}$ is given
after setting $\tilde{c}_{HB}=\tilde{c}_{HW}$ to ensure a SM decay rate for
$H\to Z\,\gamma$ and all other Wilson coefficients to zero. The observed
limits are improved by about a factor of two compared to the Run 1 analysis of
Ref. [14].

Figure 34 shows the 68% and 95% confidence regions obtained from scanning
$\bar{c}_{HW}$ and $\tilde{c}_{HW}$ simultaneously, with the other two Wilson
coefficients set to $\bar{c}_{HB}=\bar{c}_{HW}$ and
$\tilde{c}_{HB}=\tilde{c}_{HW}$. All other Wilson coefficients are fixed at
zero. The $\bar{c}_{HW}$ and $\tilde{c}_{HW}$ Wilson coefficients produce
large shape changes in all distributions, as shown in Figure 33, and the
obtained limits are strongest when fitting all five distributions
simultaneously. The shape of the observed 68% confidence regions thus results
from both shape and yield differences between data and expectations: the
operators proportional to $\bar{c}_{HW}$ can destructively interfere with the
SM contributions, a negative value of $\bar{c}_{HW}$ reduces the overall
predicted cross section in the zero-jet and the lowest $m_{jj}$ bins, where
deficits are observed in the data. The operators proportional to
$\tilde{c}_{HW}$ can only increase the cross section from its SM value and can
increase the predicted cross sections in the higher jet bins and the tails of
the distributions (cf. Figure 33). If only shape information is used to
constrain the Wilson coefficients, the reported limits on $\bar{c}_{HW}$ and
$\tilde{c}_{HW}$ weaken by about 20% and 50%, respectively. As also shown in
Figure 34, these results display significant improvements on similar limits
obtained from the Run-1 analysis [14]. All reported results assume that QCD
effects and new physics effects factorise. This assumption cannot be avoided
with the current state-of-the-art implementation of the effective Lagrangian
of Ref. [143]. The full statistical and systematic correlations between
measured distributions and all measured fiducial and differential cross
sections are available in HepData to allow future interpretations with better
models.

Table 18:  Observed allowed ranges at 95% CL for the $\bar{c}_{g}$ and $\bar{c}_{HW}$ Wilson coefficients and the CP-conjugate coefficients. Limits on $\bar{c}_{g}$ and $\tilde{c}_{g}$ are each derived with all other Wilson coefficients set to zero. Limits on $\bar{c}_{HW}$ and $\tilde{c}_{HW}$ are derived with $\bar{c}_{HB}=\bar{c}_{HW}$ and $\tilde{c}_{HB}=\tilde{c}_{HW}$, respectively.  Coefficient | Observed 95% CL limit | Expected 95% CL limit
---|---|---
$\bar{c}_{g}$ |  $[-0.8,0.1]\times 10^{-4}$ $\cup$ $[-4.6,-3.8]\times 10^{-4}$ |  $[-0.4,0.5]\times 10^{-4}$ $\cup$ $[-4.9,-4.1]\times 10^{-4}$
$\tilde{c}_{g}$ | $[-1.0,0.9]\times 10^{-4}$ | $[-1.4,1.3]\times 10^{-4}$
$\bar{c}_{HW}$ | $[-5.7,5.1]\times 10^{-2}$ | $[-5.0,5.0]\times 10^{-2}$
$\tilde{c}_{HW}$ | $[-0.16,0.16]$ | $[-0.14,0.14]$
Figure 34:  The observed 68% (dark) and 95% (light) confidence level regions
from the simultaneous fit to the $\bar{c}_{HW}$ and $\tilde{c}_{HW}$ Wilson
coefficients. The values of $\bar{c}_{HB}$ and $\tilde{c}_{HB}$ are set to be
equal to $\bar{c}_{HW}$ and $\tilde{c}_{HW}$, respectively, and all other
Wilson coefficients are set to zero, except for $\bar{c}_{HB}$ and
$\tilde{c}_{HB}$ which are set to be equal to $\bar{c}_{HW}$ and
$\tilde{c}_{HW}$, respectively. The SM expectation at $(0,0)$ is also shown,
together with the Run-1 confidence regions reported in Ref. [14].

###  10 Summary and conclusions

Measurements of Higgs boson cross sections in the Higgs boson to diphoton
decay channel are performed using $pp$ collision data recorded by the ATLAS
experiment at the LHC. The data were taken at a center-of-mass energy of
$\sqrt{s}=13\,\text{Te\kern-1.00006ptV}$ and correspond to an integrated
luminosity of $36.1$ fb-1. All measurements assume a Higgs boson mass of
$125.09\pm 0.24$ GeV. The measured signal strength relative to the Standard
Model expectation is found to be:

$\displaystyle\mu$ $\displaystyle=0.99\ ^{+0.15}_{-0.14}\ .$

Signal strengths of the main production modes are measured separately via
event reconstruction categories that are designed to be sensitive to the
specific production modes. They are found to be:

$\displaystyle\mu_{\mathrm{ggH}}=0.81\
^{+0.19}_{-0.18}\,,\quad\mu_{\mathrm{VBF}}=2.0\
^{+0.6}_{-0.5}\,,\quad\mu_{\mathrm{VH}}=0.7\
^{+0.9}_{-0.8}\,,\quad\mathrm{and}\quad\mu_{\mathrm{top}}=0.5\
^{+0.6}_{-0.6}\,.$

The total uncertainties of both the global and the production mode signal
strengths is dominated by their respective statistical uncertainties. The
global signal strength measurement improves on the precision of the previous
ATLAS measurement in the diphoton channel by a factor of two [154]. The ggH
(VBF) signal strength is measured to be $1\leavevmode\nobreak\ \sigma$ below
($2\leavevmode\nobreak\ \sigma$ above) the Standard Model expectation. The
precision of the coupling-strength measurements involving top quarks improves
by about a factor of three compared to the previous ATLAS measurement in the
diphoton channel [154]. These improvements result from a combination of the
larger Higgs boson sample collected at $\sqrt{s}=13$ TeV, from the use of
multivariate techniques to target the VBF, $VH$, and top-quark associated
production modes more efficiently, from the improved precision of the ggH
Standard Model theory predictions, and from a significant reduction of some of
the experimental uncertainties such as the photon energy resolution.
Production mode cross-section measurements for a Higgs boson of rapidity
$|y_{H}|<2.5$ for gluon–gluon fusion, vector-boson fusion, and Higgs boson
production in association with vector bosons or a top quark pair are reported:

$\displaystyle\sigma_{\mathrm{ggH}}=82{}^{+19}_{-18}\,\mathrm{fb}\,,\quad\sigma_{\mathrm{VBF}}=16{}^{+5}_{-4}\,\mathrm{fb}\,,\quad\sigma_{\mathrm{VH}}=3\small\pm
4\,\mathrm{fb}\,,\quad\mathrm{and}\quad\sigma_{\mathrm{top}}=0.7{}^{+0.9}_{-0.7}\,\mathrm{fb}\,.$

These values can be compared to the Standard Model expectations of

$\displaystyle\sigma_{\mathrm{ggH}}^{\mathrm{SM}}={102}^{+5}_{-7}\,\mathrm{fb}\,,\quad\sigma_{\mathrm{VBF}}^{\mathrm{SM}}=8\pm
0.2\,\mathrm{fb}\,,\quad\sigma_{\mathrm{VH}}^{\mathrm{SM}}=5\pm
0.2\,\mathrm{fb}\,,\quad\sigma_{\mathrm{top}}^{\mathrm{SM}}=1.3\pm
0.1\,\mathrm{fb}\,,\quad$

and show a similar level of agreement as that obtained with the coupling-
strength measurements.

Nine measurements of so-called simplified template cross sections, designed to
measure the different Higgs boson production processes in specific regions of
phase space, are reported:

$\displaystyle\sigma(\mathrm{ggH},\mathrm{0\leavevmode\nobreak\ jet})$
$\displaystyle=37{}^{+16}_{-15}\,\mathrm{fb}\,,$
$\displaystyle\sigma(\mathrm{ggH},\mathrm{1\leavevmode\nobreak\
jet},p_{\text{T}}^{H}<60\ \text{Ge\kern-1.00006ptV})$
$\displaystyle=13{}^{+13}_{-12}\,\mathrm{fb}\,,$
$\displaystyle\sigma(\mathrm{ggH},\mathrm{1\leavevmode\nobreak\ jet},60\leq
p_{\text{T}}^{H}<120\ \text{Ge\kern-1.00006ptV})$ $\displaystyle=5\small\pm
6\,\mathrm{fb}\,,$
$\displaystyle\sigma(\mathrm{ggH},\mathrm{1\leavevmode\nobreak\ jet},120\leq
p_{\text{T}}^{H}<200\ \text{Ge\kern-1.00006ptV})$
$\displaystyle=2.8{}^{+1.7}_{-1.6}\,\mathrm{fb}\,,$
$\displaystyle\sigma(\mathrm{ggH},\geq 2\leavevmode\nobreak\ \mathrm{jet})$
$\displaystyle=20{}^{+9}_{-8}\,\mathrm{fb}\,,$
$\displaystyle\sigma(qq\rightarrow
Hqq,p_{\text{T}}^{j}<200\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV})$
$\displaystyle=15{}^{+6}_{-5}\,\mathrm{fb}\,,$
$\displaystyle\sigma(ggH+qq\rightarrow Hqq,\mathrm{BSM-like})$
$\displaystyle=2.0\small\pm 1.4\,\mathrm{fb}\,,$
$\displaystyle\sigma(\mathrm{VH},\mathrm{leptonic})$
$\displaystyle=0.7{}^{+1.4}_{-1.3}\,\mathrm{fb}\,,$
$\displaystyle\sigma(\mathrm{top})$
$\displaystyle=0.7{}^{+0.8}_{-0.7}\,\mathrm{fb}\,.$

All reported results show agreement with the Standard Model expectation.

Higgs boson coupling-strength modifiers are reported and two models are
investigated: the first one reports results on effective coupling-strength
modifiers for Higgs boson production in gluon–gluon fusion and decay,
$\kappa_{g}$ and $\kappa_{\gamma}$, respectively. They are found to be:

$\displaystyle\kappa_{g}=0.76^{+0.17}_{-0.14}\,,\quad\mathrm{and}\quad\kappa_{\gamma}=1.16^{+0.14}_{-0.14}\,.$

The second model resolves the Higgs boson production and decay loops in terms
of the more fundamental fermionic and vector boson couplings under the
assumption of universal coupling-strength modifiers for all fermions and
vector bosons, namely $\kappa_{V}$ and $\kappa_{F}$, respectively. They are
found to be:

$\displaystyle\kappa_{V}=0.92^{+0.08}_{-0.07}\,,\quad\mathrm{and}\quad\kappa_{F}=0.64^{+0.18}_{-0.14}\,.$

Fiducial cross-section measurements are reported for a Higgs boson decaying
into two isolated photons with transverse momentum greater than 35% and 25% of
the diphoton invariant mass (corresponding to a photon $p_{T}$ of $43.8$ GeV
and $31.3$ GeV), and with $|\eta|<2.37$, excluding the region of
$1.37<|\eta|<1.52$. The total fiducial cross section is measured to be

$\displaystyle\sigma_{\mathrm{f}id}=55\pm 9\,\text{(stat.)}\pm
4\,\text{(exp.)}\pm 0.1\,\text{(theo.)}\,\text{fb}\,,$

and is in agreement with the Standard Model expectation of $64\pm
2\,\text{fb}$. Additional cross sections in fiducial regions probing Higgs
boson production from vector-boson fusion or associated with large missing
transverse momentum, leptons or top quarks are reported. The cross section for
the VBF-enhanced region is measured to be

$\displaystyle\sigma_{\mathrm{V}BF-enhanced}=3.7\pm 0.8\,({\mathrm{s}tat.})\pm
0.5\,({\mathrm{e}xp.})\pm 0.2\,\text{(theo.)}\,\text{fb}\,,$

which is to be compared with the Standard Model prediction of $2.3\pm
0.1\,\text{fb}$. The larger measured cross section is consistent with the VBF
signal-strength measurement reported above, if one scales the expected SM
contributions from VBF (about 65%) and ggH (about 35%) in this fiducial region
with the corresponding measured signal strengths. For the remaining fiducial
regions, limits at 95% CL are reported

$\displaystyle\sigma_{N_{\mathrm{l}epton}\geq
1}<1.39\,\mathrm{fb}\,\,,\quad\sigma_{{\mathrm{H}igh}\,E_{\mathrm{T}}^{\mathrm{m}iss}}<1.00\,\mathrm{fb}\,,\quad\mathrm{and}\quad\sigma_{t\bar{t}H{\mathrm{-}enhanced}}<1.27\,\mathrm{fb}\,,$

which can be compared with the Standard Model expectations of $0.57\pm
0.03\,\mathrm{fb}$, $0.30\pm 0.02\,\mathrm{fb}$, and $0.55\pm
0.06\,\mathrm{fb}$, respectively.

The fiducial cross sections for different jet multiplicities is reported and
compared to several theoretical predictions. Eleven differential cross
sections and two double-differential cross sections are reported for events
belonging to the inclusive diphoton fiducial region, as a function of
kinematic variables of the diphoton system or of jets produced in association
with the Higgs boson. The reported cross sections are sensitive to the Higgs
boson production kinematics, the jet kinematics, the spin and CP quantum
numbers of the Higgs boson, and the VBF production mechanism. All measured
differential cross sections are compared to predictions and no significant
deviation from the Standard Model expectation is observed. The full
statistical and systematic correlations between measured distributions are
determined and are available in HepData along with the central values of the
measured fiducial and differential cross sections to allow future comparisons
and interpretations.

The strength and tensor structure of the Higgs boson interactions is
investigated using five differential variables and an effective Lagrangian,
which introduces additional CP-even and CP-odd interactions. No significant
new physics contributions are observed and the reported 68% and 95% limits on
such contributions have improved by a factor of two in comparison to the
previous ATLAS measurement.

The measurements presented in this paper lay the foundation for further
studies. All reported results are statistically limited and their precision
will further improve with the full data set to be recorded during Run 2 of the
LHC.

### Acknowledgments

We thank CERN for the very successful operation of the LHC, as well as the
support staff from our institutions without whom ATLAS could not be operated
efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC,
Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and
FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST
and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech
Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG,
Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China;
ISF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan;
CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT,
Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation;
JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South
Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and
Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC,
United Kingdom; DOE and NSF, United States of America. In addition, individual
groups and members have received support from BCKDF, the Canada Council,
CANARIE, CRC, Compute Canada, FQRNT, and the Ontario Innovation Trust, Canada;
EPLANET, ERC, ERDF, FP7, Horizon 2020 and Marie Skłodowska-Curie Actions,
European Union; Investissements d’Avenir Labex and Idex, ANR, Région Auvergne
and Fondation Partager le Savoir, France; DFG and AvH Foundation, Germany;
Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the
Greek NSRF; BSF, GIF and Minerva, Israel; BRF, Norway; CERCA Programme
Generalitat de Catalunya, Generalitat Valenciana, Spain; the Royal Society and
Leverhulme Trust, United Kingdom.

The crucial computing support from all WLCG partners is acknowledged
gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF
(Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA
(Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan),
RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG
resource providers. Major contributors of computing resources are listed in
Ref. [155].

## Appendix

###  Appendix A Simplified template cross-section framework

As introduced in Section 1.2, this paper includes cross-section measurements
using the so called “stage-1” of the simplified template cross-section
framework [8, 7]. In the full stage-1 proposal, template cross sections are
defined in 31 regions of phase space with $|y_{H}|<\nobreak 2.5$. These
regions have been chosen to minimize the dependence on theoretical
uncertainties and isolate possible BSM effects, while maximizing the
experimental sensitivity.

The 31 regions of particle-level phase space corresponding to the stage 1 of
the template cross-section approach are the following [8, 7]:

  * •

Gluon–gluon fusion (11 regions). Gluon–gluon fusion events, together with
$gg\to ZH$ events followed by hadronic decays of the $Z$ boson, are split
according to the number of jets in the event in 0, 1, and $\geq 2$-jet events.
Jets are reconstructed from all stable particles141414The Higgs boson is
treated as stable and consequently its decay products are removed from the jet
finding. with lifetime greater than 10 ps using the anti-$k_{t}$ algorithm
[77] with a jet radius parameter $R=0.4$ and must have
$p_{\text{T}}>30\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$. The region
containing two or more jets is split into two, with one of the two subregions
(“VBF-like”) containing events with a topology similar to vector-boson fusion
events (invariant mass of the leading-$p_{\text{T}}$ jet pair
$m_{jj}>400\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$, and rapidity
separation between the two jets $|\Delta{y_{jj}|}>2.8$). The one-jet and non-
VBF-like two-jet regions are further split according to the transverse
momentum of the Higgs boson in “low” (0–60 GeV), “medium” (60–120 GeV), “high”
(120–200 GeV) and “BSM” ($>200\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$)
regions. The VBF-like events are further split into exclusive two-jet-like and
inclusive three-jet-like events through a requirement on the transverse
momentum $p_{\mathrm{T}}^{Hjj}$ of the system formed by the two photons and
the two leading-$p_{\text{T}}$ jets
($p_{\mathrm{T}}^{Hjj}<25\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$ or
$p_{\mathrm{T}}^{Hjj}>25\leavevmode\nobreak\ \text{Ge\kern-1.00006ptV}$,
respectively). The separation between events with zero, one, or two or more
jets probes perturbative QCD predictions. Events containing a very high
transverse momentum Higgs-boson of more than 200 GeV are sensitive to BSM
contributions, such as those from loop-induced amplitudes mediated by
hypothetical particles heavier than the top-quark.

  * •

Vector-boson fusion (5 regions). Vector-boson fusion events, and $VH$ events
followed by hadronic $V$-boson decays, are first split according to the
$p_{\text{T}}$ of the leading jet. Events that contain at least one jet with a
transverse momentum greater than 200 GeV, which are sensitive to BSM
contributions, are measured separately in a “VBF BSM” category. The remaining
events are separated into VBF-like events, $VH$-like events, and events that
have a ggH-like topology (referred to as “Rest”). VBF-like events satisfy the
same $m_{jj}$ and $|\Delta{y_{jj}|}$ requirements as for the gluon–gluon
fusion VBF-like category and are similarly split into “two-jet” and “$\geq
3$-jet” events by requiring $p_{\mathrm{T}}^{Hjj}<25$ GeV or
$p_{\mathrm{T}}^{Hjj}>25$ GeV, respectively. $VH$-like events are selected by
requiring that they have at least two jets and an invariant mass of
$60\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}<m_{jj}<120\leavevmode\nobreak\
\text{Ge\kern-1.00006ptV}$.

  * •

Associated production with vector bosons decaying to leptons (11 regions).
$VH$ events are first split according to their production mode
($q\bar{q}^{\prime}\to WH$, $q\bar{q}\to ZH$, or $gg\to ZH$). Events are
separated further into regions of the vector boson transverse momentum
$p_{\mathrm{T}}^{V}$, and of jet multiplicity. For $gg\to ZH$, two regions are
defined with $p_{\text{T}}^{V}$ (“low”: 0–150 GeV, and “high”: > 150 GeV). The
“high-$p_{\text{T}}^{V}$” $gg\to ZH$ region is further split into zero-jet and
$\geq 1$-jet regions. Regions sensitive to BSM contributions with
$p_{\mathrm{T}}^{V}>250$ GeV are defined for the $q\bar{q}\to VH$ production
modes and two further $p_{\text{T}}^{V}$ regions are defined (“low”: 0–150
GeV, and “high”: 150–250 GeV). The “high-$p_{\text{T}}^{V}$” $q\bar{q}\to VH$
region is finally split into zero-jet and $\geq 1$-jet regions.

  * •

Associated production with top and bottom quarks (4 regions). $t\bar{t}H$,
$t$-channel $tH$, $W$-associated $tH$, and $b\bar{b}H$ events are classified
according to their production mode, with no further separation into specific
regions of phase space.

Table LABEL:tab:SMacc summarizes the acceptances for each of the stage-1 STXS
$gg\to H$ regions, and for five $qq\to Hqq$ regions, split into their VBF,
$WH$, and $ZH$ respective contributions. The table also lists the summed
acceptance for the 11 $VH$ leptonic regions, separately for the $gg\to ZH$,
$q\bar{q}^{\prime}\to WH$ and $q\bar{q}\to ZH$ processes. Finally, the
acceptances are shown for the rarer production processes: $t\bar{t}H$,
$t$-channel $tH$, $W$-associated $tH$, and $b\bar{b}H$. All STXS regions
require $|y_{H}|<2.5$ and are determined using the samples summarized in Table
2.

Table 19:  The SM acceptances of stage-1 STXS regions useful to the results presented in this paper. For the $gg\to H$ regions each acceptance is relative to inclusive $gg\to H$ production; for all other regions, each acceptance is relative to the inclusive process shown at the top of the column. All regions require $|y_{H}|<2.5$.  $gg\to H$ regions | 0-jet | 1-jet |  $\geq 2$-jet
---|---|---|---
$p_{\textrm{T}}^{H}<60$ GeV | 0.562 | 0.134 | 0.025
$60\,\text{Ge\kern-1.00006ptV}\leq p_{\textrm{T}}^{H}<120$ GeV | - | 0.093 | 0.038
$120\,\text{Ge\kern-1.00006ptV}\leq p_{\textrm{T}}^{H}<200$ GeV | - | 0.015 | 0.020
$p_{\textrm{T}}^{H}\geq 200$ GeV | - | 0.003 | 0.009
VBF-like |  |  |
$p_{\textrm{T}}^{Hjj}<25$ GeV | - | - | 0.006
$p_{\textrm{T}}^{Hjj}\geq 25$ GeV | - | - | 0.007
$qq\to Hqq$ regions | VBF | $q\bar{q}^{\prime}\to WH$ | $q\bar{q}\to ZH$
$p_{\textrm{T}}^{j}\geq 200$ GeV | 0.043 | 0.027 | 0.029
$p_{\textrm{T}}^{j}<200$ GeV |  |  |
VH-like | 0.023 | 0.189 | 0.224
Rest | 0.556 | 0.368 | 0.363
VBF-like |  |  |
$p_{\textrm{T}}^{Hjj}<25$ GeV | 0.235 | 0.002 | 0.002
$p_{\textrm{T}}^{Hjj}\geq 25$ GeV | 0.074 | 0.007 | 0.008
VH, leptonic region | $gg\to ZH$ | $q\bar{q}^{\prime}\to WH$ | $q\bar{q}\to ZH$
| 0.289 | 0.286 | 0.265
Top region | $t\bar{t}H$ |  $t$-ch. $tH$ |  $W$-assoc. $tH$
| 0.987 | 0.921 | 0.989
Beauty region | $b\bar{b}H$ |  |
| 0.945 |  |

###  Appendix B Minimally merged simplified template cross sections

In this appendix, the measurement for a minimally merged set of fifteen
simplified template cross section regions is presented. The merged regions are
defined in Table LABEL:tab:STXS_WEAK and the extracted cross sections are
summarized in Table 21 and Figure 35.

Table 20: The kinematic regions of the stage 1 of the simplified template cross sections, along with the intermediate (minimally merged set of) regions used for the measurements presented in this appendix. The $VH$-like, VBF-like, and rest regions are defined as in Table LABEL:tab:STXS and Appendix A. All regions require $|y_{H}|<2.5$. The leading jet transverse momentum is denoted by $p_{\text{T}}^{j}$. In total, the cross sections for fifteen kinematic regions are measured. Process | Measurement region | Particle-level stage 1 region
---|---|---
ggH \+ $gg\to Z(\to qq)H$ | 0-jet | 0-jet
|  1-jet, $p_{\textrm{T}}^{H}<60$ GeV |  1-jet, $p_{\textrm{T}}^{H}<60$ GeV
|  1-jet, $60\leq p_{\textrm{T}}^{H}<120$ GeV |  1-jet, $60\leq p_{\textrm{T}}^{H}<120$ GeV
|  1-jet, $120\leq p_{\textrm{T}}^{H}<200$ GeV |  1-jet, $120\leq p_{\textrm{T}}^{H}<200$ GeV
|  1-jet, $p_{\textrm{T}}^{H}>200$ GeV |  1-jet, $p_{\textrm{T}}^{H}>200$ GeV
|  $\geq 2$-jet, $p_{\textrm{T}}^{H}<60$ GeV |  $\geq 2$-jet, $p_{\textrm{T}}^{H}<60$ GeV
|  $\geq 2$-jet, $60\leq p_{\textrm{T}}^{H}<120$ GeV |  $\geq 2$-jet, $60\leq p_{\textrm{T}}^{H}<120$ GeV
|  $\geq 2$-jet, $120\leq p_{\textrm{T}}^{H}<200$ GeV |  $\geq 2$-jet, $120\leq p_{\textrm{T}}^{H}<200$ GeV
|  $\geq 2$-jet, $p_{\textrm{T}}^{H}>200$ GeV |  $\geq 2$-jet, $p_{\textrm{T}}^{H}>200$ GeV
| VBF-like |  VBF-like, $p_{\textrm{T}}^{Hjj}<25$ GeV
|  |  VBF-like, $p_{\textrm{T}}^{Hjj}\geq 25$ GeV
$qq^{\prime}\to Hqq^{\prime}$ (VBF + $VH$) |  $p_{\textrm{T}}^{j}<200$ GeV, VBF-like |  $p_{\textrm{T}}^{j}<200$ GeV, VBF-like, $p_{\textrm{T}}^{Hjj}<25$ GeV
|  |  $p_{\textrm{T}}^{j}<200$ GeV, VBF-like, $p_{\textrm{T}}^{Hjj}\geq 25$ GeV
|  $p_{\textrm{T}}^{j}<200$ GeV, VH+Rest |  $p_{\textrm{T}}^{j}<200$ GeV, VH-like
|  |  $p_{\textrm{T}}^{j}<200$ GeV, Rest
|  $p_{\textrm{T}}^{j}>200$ GeV, BSM-like |  $p_{\textrm{T}}^{j}>200$ GeV
$VH$ (leptonic decays) |  $VH$ leptonic |  $q\bar{q}\to ZH$, $p_{\text{T}}^{Z}<150$ GeV
|  |  $q\bar{q}\to ZH$, $150<p_{\text{T}}^{Z}<250$ GeV, 0-jet
|  |  $q\bar{q}\to ZH$, $150<p_{\text{T}}^{Z}<250$ GeV, $\geq 1$-jet
|  |  $q\bar{q}\to ZH$, $p_{\text{T}}^{Z}>250$ GeV
|  |  $q\bar{q}\to WH$, $p_{\text{T}}^{W}<150$ GeV
|  |  $q\bar{q}\to WH$, $150<p_{\text{T}}^{W}<250$ GeV, 0-jet
|  |  $q\bar{q}\to WH$, $150<p_{\text{T}}^{W}<250$ GeV, $\geq 1$-jet
|  |  $q\bar{q}\to WH$, $p_{\text{T}}^{W}>250$ GeV
|  |  $gg\to ZH$, $p_{\text{T}}^{Z}<150$ GeV
|  |  $gg\to ZH$, $p_{\text{T}}^{Z}>150$ GeV, 0-jet
|  |  $gg\to ZH$, $p_{\text{T}}^{Z}>150$ GeV, $\geq 1$-jet
Top-associated production | top | $t\bar{t}H$
|  | $tHW$
|  | $tHq$
$b\bar{b}H$ |  merged w/ ggH | $b\bar{b}H$
Table 21:  Best-fit values and uncertainties of the simplified template cross sections times branching ratio, as defined in Table LABEL:tab:STXS_WEAK. The SM predictions [7] are shown for each region.  Measurement region | Result | Uncertainty | SM prediction
---|---|---|---
($|y_{H}|<2.5$) | Total |  | Stat. | Syst. |  |
$ggH,\mathrm{0\leavevmode\nobreak\ jet}$ | 38 | ${}^{+16}_{-15}$ | $\Big{(}$ | $\pm 14$ | ${}^{+6}_{-5}$ | $\Big{)}$ | fb | $63\pm 5$ | fb
$ggH,\mathrm{1\leavevmode\nobreak\ jet},p_{\text{T}}^{H}<60$ GeV | 23 | ${}^{+14}_{-13}$ | $\Big{(}$ | $\pm 13$ | ${}^{+5}_{-4}$ | $\Big{)}$ | fb | $15\pm 2$ | fb
$ggH,\mathrm{1\leavevmode\nobreak\ jet},60\leq p_{\text{T}}^{H}<120$ GeV | 11 | $\pm 8$ | $\Big{(}$ | $\pm 7$ | ${}^{+3}_{-2}$ | $\Big{)}$ | fb | $10\pm 2$ | fb
$ggH,\mathrm{1\leavevmode\nobreak\ jet},120\leq p_{\text{T}}^{H}<200$ GeV | 4.0 | ${}^{+2.1}_{-1.9}$ | $\Big{(}$ | $\pm 1.8$ | ${}^{+0.9}_{-0.6}$ | $\Big{)}$ | fb | $1.7\pm 0.3$ | fb
$ggH,\mathrm{1\leavevmode\nobreak\ jet},p_{\text{T}}^{H}\geq 200$ GeV | 2.6 | ${}^{+1.6}_{-1.2}$ | $\Big{(}$ | ${}^{+1.3}_{-1.1}$ | ${}^{+0.8}_{-0.5}$ | $\Big{)}$ | fb | $0.4\pm 0.1$ | fb
$ggH,\geq 2\leavevmode\nobreak\ \mathrm{jet},p_{\text{T}}^{H}<60$ GeV | 0 | $\pm 8$ | $\Big{(}$ | $\pm 8$ | ${}^{+3}_{-2}$ | $\Big{)}$ | fb | $3\pm 1$ | fb
$ggH,\geq 2\leavevmode\nobreak\ \mathrm{jet},60\leq p_{\text{T}}^{H}<120$ GeV | 12 | ${}^{+8}_{-7}$ | $\Big{(}$ | $\pm 7$ | ${}^{+3}_{-2}$ | $\Big{)}$ | fb | $4\pm 1$ | fb
$ggH,\geq 2\leavevmode\nobreak\ \mathrm{jet},120\leq p_{\text{T}}^{H}<200$ GeV | 7.9 | ${}^{+3.5}_{-3.4}$ | $\Big{(}$ | $\pm 3.3$ | ${}^{+1.1}_{-0.9}$ | $\Big{)}$ | fb | $2.3\pm 0.6$ | fb
$ggH,\geq 2\leavevmode\nobreak\ \mathrm{jet},p_{\text{T}}^{H}\geq 200$ GeV | 2.6 | ${}^{+1.6}_{-1.4}$ | $\Big{(}$ | ${}^{+1.5}_{-1.4}$ | ${}^{+0.6}_{-0.5}$ | $\Big{)}$ | fb | $1.0\pm 0.3$ | fb
$ggH,\mathrm{VBF-like}$ | 6.2 | ${}^{+5.0}_{-4.5}$ | $\Big{(}$ | $\pm 4.1$ | $\pm 1.2$ | $\Big{)}$ | fb | $1.5\pm 0.3$ | fb
$qq\rightarrow Hqq,\mathrm{VBF-like}$ | 3.8 | ${}^{+2.5}_{-2.3}$ | $\Big{(}$ | ${}^{+2.2}_{-2.0}$ | $\pm 1.2$ | $\Big{)}$ | fb | $2.7\pm 0.2$ | fb
$qq\rightarrow Hqq,\mathrm{VH+Rest}$ | -19 | $\pm 22$ | $\Big{(}$ | ${}^{+21}_{-20}$ | ${}^{+6}_{-7}$ | $\Big{)}$ | fb | $7.7\pm 0.4$ | fb
$qq\rightarrow Hqq,p_{\text{T}}^{j}>200$ GeV | -3.2 | ${}^{+1.9}_{-2.0}$ | $\Big{(}$ | $\pm 1.7$ | ${}^{+0.7}_{-0.9}$ | $\Big{)}$ | fb | $0.5\pm 0.1$ | fb
VH, leptonic | 0.7 | ${}^{+1.4}_{-1.2}$ | $\Big{(}$ | ${}^{+1.4}_{-1.2}$ | ${}^{+0.4}_{-0.3}$ | $\Big{)}$ | fb | $1.4\pm 0.1$ | fb
Top | 0.7 | ${}^{+0.8}_{-0.7}$ | $\Big{(}$ | ${}^{+0.8}_{-0.7}$ | ${}^{+0.2}_{-0.1}$ | $\Big{)}$ | fb | $1.3\pm 0.1$ | fb
Figure 35: Summary plot of the measured simplified template cross sections
times the Higgs to diphoton branching ratio, as defined in Table
LABEL:tab:STXS_WEAK. For illustration purposes, the central values have been
divided by their SM expectations but no additional SM uncertainties have been
folded into the measurement. The uncertainties in the SM predicted cross
sections are shown in gray in the plot. The fitted value of
$\sigma(\mathrm{top})$ corresponds to the sum of the $t\bar{t}H$, $tHq$, and
$tHW$ production-mode cross sections under the assumption that their relative
ratios are as predicted by the SM. The $\sigma(\mathrm{VH,leptonic})$ cross-
section values are determined under the assumption that the ratio of the $WH$
and $ZH$ production mode cross sections is as predicted by the SM and includes
production from both the quark and gluon initial states. The $b\bar{b}H$
contributions are merged with ggH.

###  Appendix C  Additional unfolded differential cross sections

This appendix presents additional measurements and comparisons to theoretical
predictions to those discussed in Section 9.5.

Figure 36 shows differential cross sections as a function of
$p_{\mathrm{T}t}^{\gamma\gamma}$, the orthogonal component of the diphoton
momentum when projected on the axis given by the difference of the 3-momenta
of the two photons, as well as $|\Delta{y_{\gamma\gamma}|}$, the rapidity
separation of the two photons.

Figure 37 shows differential cross sections as a function of $H_{\text{T}}$,
the scalar sum of all reconstructed jets in a given event with
$p_{\mathrm{T}}>30$ GeV, the absolute value of the azimuthal difference
$|\Delta\phi_{jj}|$ between the leading and subleading jet in events with at
least two jets, and the vectorial sum of the transverse momentum of the
diphoton system and the leading and subleading jet system,
$p_{\mathrm{T}}^{\gamma\gamma{}jj}$, in events with at least two jets.

Figure 38 displays measurements of the beam-thrust-like variables
$\tau_{C,j1}$ and $\sum\tau_{C,j}$. For a given jet, $\tau$ is defined by

$\displaystyle\tau=\frac{m_{\mathrm{T}}}{2\cosh y^{*}}\,,\quad
y^{*}=y-y_{\gamma\gamma}\,,\qquad
m_{\mathrm{T}}=\sqrt{p_{\text{T}}^{2}+m^{2}}\,,$ (4)

where $y$ is the jet rapidity and $m$ is the jet mass. The variable
$\tau_{C,j1}$ refers to the highest-$\tau$ jet, and $\sum\tau_{C,j}$ is the
scalar sum of $\tau$ for all jets with $\tau>8$ GeV. For large jet rapidities,
$\tau$ corresponds to the small light-cone component of the jet,
$p_{\mathrm{j}et}^{+}=E_{\mathrm{j}et}-\left|p_{z,{\mathrm{j}et}}\right|$,
while the sum is closely related to the beam-thrust global event shape [156],
as measured in the diphoton rest frame.

Figure 39 shows the first and second moments of each of the additional
differential distributions. The data are compared to a variety of theoretical
predictions. In general, the SM predictions are in agreement with the measured
distributions.

((a))  ((b))

Figure 36:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $p_{\mathrm{T}t}^{\gamma\gamma}$ and (b)
$|\Delta{y_{\gamma\gamma}|}$ are shown and compared to the SM expectations.
The data are shown as filled (black) circles. The vertical error bar on each
data point represents the total uncertainty in the measured cross section and
the shaded (gray) band is the systematic component. The SM prediction, defined
using the Powheg NNLOPS prediction for gluon–gluon fusion and the default MC
samples for the other production mechanisms, is presented as a hatched (blue)
band, with the width of the band reflecting the total theoretical uncertainty
(see text for details). The small contribution from VBF, $VH$ $t\bar{t}H$ and
$b\bar{b}H$ is also shown as a (green) histogram and denoted by $XH$. The
default MC has been normalized with the N3LO prediction of Refs. [31, 32, 33,
34, 24, 7]. In addition, the Hres and SCETlib+MCFM8 predictions, described in
Section 9.5, are displayed in (a) and (b), respectively.

((a))  ((b))

((c))

Figure 37:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $H_{\text{T}}$, (b) $|\Delta\phi_{jj}|$, and (c)
$p_{\mathrm{T}}^{\gamma\gamma{}jj}$ are shown and compared to the SM
expectations. The data and theoretical predictions are presented in the same
way as in Figure 36. In addition, the NNLOJET prediction is displayed in (a),
and the Sherpa and GoSam predictions are displayed in (b) and (c). More
details of these predictions can be found in Section 9.5.1.

((a))  ((b))

Figure 38:  The differential cross sections for $pp\to H\to\gamma\gamma$ as a
function of (a) $\tau_{C,j1}$ and (b) $\sum\tau_{C,j}$ are shown and compared
to the SM expectations. The data and theoretical predictions are presented in
the same way as in Figure 36. In addition, the NNLOJET prediction is displayed
in (b).

((a))  ((b))

Figure 39:  (a) The ratio of the first moment (mean) of each differential
distribution predicted by the Standard Model to that observed in the data. The
SM moment is calculated by using the Powheg NNLOPS prediction for gluon–gluon
fusion and the default MC samples for the other production mechanisms. (b) The
ratio of the second moment (RMS) of each differential distribution predicted
by the Standard Model to that observed in the data. The intervals on the
vertical axes each represent one of the differential distributions. The band
for the theoretical prediction represents the corresponding uncertainty in
that prediction (see text for details). The error bar on the data represents
the total uncertainty in the measurement, with the gray band representing only
the systematic uncertainty.

###  Appendix D Diphoton acceptance, photon isolation and non-perturbative
correction factors for parton-level gluon–gluon fusion calculations

This appendix presents the diphoton acceptance factors that are applied to
parton-level calculations of Higgs production via gluon–gluon fusion, in order
to correctly account for the diphoton selection criteria applied to the Higgs-
boson decay products, are shown in Table 22 for the fiducial and differential
cross sections presented in Section 9.5 and Appendix C. Multiplicative
isolation efficiency and non-perturbative correction factors that account for
the efficiency of the photon isolation criterion and the impact of
hadronization and underlying-event activity are presented in Tables 23 and 24,
respectively. The isolation efficiency is defined as the fraction of selected
diphoton events (i.e. within the kinematic acceptance) that also satisfy the
isolation criteria, and is determined using samples before including
hadronization and the underlying-event activity. The non-perturbative
correction factors are defined as the ratios of cross sections produced with
and without hadronization and the underlying event. The default non-
perturbative correction is taken as the central value of an envelope formed
from multiple event generators and/or event generator tunes, with the
uncertainty taken to be the maximal deviation observed in the envelope. Table
25 also provides the combined non-perturbative and isolation correction with a
total uncertainty that takes into account the correlations between the
uncertainties of both factors. Note though that no non-perturbative correction
factors are applied to the SM predictions presented in this paper.

A summary of the binning of all differential variables is given in Table 26.

| Bin 1 | Bin 2 | Bin 3 | Bin 4 | Bin 5 | Bin 6 | Bin 7 | Bin 8 | Bin 9 | Bin 10 | Bin 11 | Bin 12 | Bin 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Diphoton fiducial | $51.9\pm 0.4$ | – | – | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$ | 52.3 $\pm 0.5$ | 52.9 $\pm 0.5$ | 52.0 $\pm 0.4$ | 50.8 $\pm 0.4$ | 50.0 $\pm 0.3$ | 48.6 $\pm 0.3$ | 51.0 $\pm 0.3$ | 57.7 $\pm 0.3$ | 65.2 $\pm 0.3$ | – | – | – | – | –
$|y_{\gamma\gamma}|$ | 74.0 $\pm 0.2$ | 73.6 $\pm 0.2$ | 72.2 $\pm 0.2$ | 69.3 $\pm 0.1$ | 67.1 $\pm 0.1$ | 64.8 $\pm 0.1$ | 61.5 $\pm 0.1$ | 56.0 $\pm 0.2$ | 31.4 $\pm 0.1$ | – | – | – | – | –
$p_{\mathrm{T}t}^{\gamma\gamma}$ | 49.5 $\pm 0.6$ | 49.4 $\pm 0.6$ | 49.2 $\pm 0.6$ | 48.8 $\pm 0.6$ | 49.0 $\pm 0.6$ | 49.8 $\pm 0.6$ | 52.8 $\pm 0.7$ | 59.7 $\pm 0.5$ | 69.5 $\pm 0.5$ | 73.2 $\pm 0.5$ | 75.7 $\pm 0.5$ | 78.3 $\pm 0.4$ | 82.9 $\pm 0.4$ | –
$|\cos\theta^{*}|$ | 78.8 $\pm 0.6$ | 74.9 $\pm 0.6$ | 73.3 $\pm 0.6$ | 71.7 $\pm 0.6$ | 69.6 $\pm 0.6$ | 67.6 $\pm 0.7$ | 65.8 $\pm 0.7$ | 60.4 $\pm 0.7$ | 23.6 $\pm 0.5$ | – | – | – | – | –
$|\Delta{y_{\gamma\gamma}|}$ | 80.0 $\pm 0.5$ | 76.1 $\pm 0.5$ | 74.9 $\pm 0.5$ | 73.7 $\pm 0.6$ | 72.4 $\pm 0.6$ | 70.6 $\pm 0.6$ | 68.6 $\pm 0.6$ | 67.4 $\pm 0.6$ | 65.3 $\pm 0.7$ | 50.8 $\pm 0.7$ | – | – | – | –
$N_{\mathrm{j}ets}$, $p_{\mathrm{T}}$$>$ 30 GeV | 51.8 $\pm 0.5$ | 51.8 $\pm 0.4$ | 52.3 $\pm 0.4$ | 54.2 $\pm 0.7$ | – | – | – | – | – | – | – | – | – | –
$N_{\mathrm{j}ets}$, $p_{\mathrm{T}}$$>$ 50 GeV | 51.2 $\pm 0.5$ | 54.2 $\pm 0.4$ | 55.8 $\pm 0.7$ | – | – | – | – | – | – | – | – | – | – | –
$p_{\mathrm{T}}^{j_{1}}$ | 51.8 $\pm 0.5$ | 49.8 $\pm 0.4$ | 56.1 $\pm 0.4$ | 52.7 $\pm 0.4$ | 55.5 $\pm 0.6$ | – | – | – | – | – | – | – | – | –
$p_{\mathrm{T}}^{j_{2}}$ | 51.8 $\pm 0.4$ | 51.9 $\pm 0.4$ | 57.1 $\pm 0.8$ | – | – | – | – | – | – | – | – | – | – | –
$H_{\text{T}}$ | 51.8 $\pm 0.5$ | 51.1 $\pm 0.4$ | 52.1 $\pm 0.4$ | 53.8 $\pm 0.5$ | 57.3 $\pm 0.9$ | – | – | – | – | – | – | – | – | –
$|y_{j_{1}}|$ | 55.2 $\pm 0.4$ | 54.6 $\pm 0.4$ | 53.1 $\pm 0.4$ | 53.0 $\pm 0.4$ | 52.3 $\pm 0.4$ | 50.4 $\pm 0.4$ | 48.2 $\pm 0.4$ | – | – | – | – | – | – | –
$|y_{j_{2}}|$ | 54.1 $\pm 0.5$ | 53.5 $\pm 0.5$ | 52.3 $\pm 0.5$ | – | – | – | – | – | – | – | – | – | – | –
$m_{jj}$ | 52.8 $\pm 0.5$ | 53.3 $\pm 0.6$ | 51.6 $\pm 0.6$ | – | – | – | – | – | – | – | – | – | – | –
$|\Delta{y_{jj}|}$ | 70.2 $\pm 3.7$ | 68.7 $\pm 3.4$ | 67.2 $\pm 3.4$ | – | – | – | – | – | – | – | – | – | – | –
$|\Delta\phi_{jj}|$ | 53.8 $\pm 0.6$ | 53.3 $\pm 0.5$ | 51.6 $\pm 0.4$ | – | – | – | – | – | – | – | – | – | – | –
$\Delta\phi_{jj}$ | 51.9 $\pm 0.4$ | 54.1 $\pm 0.6$ | 53.4 $\pm 0.6$ | 52.0 $\pm 0.4$ | – | – | – | – | – | – | – | – | – | –
$p_{\mathrm{T}}^{\gamma\gamma{}jj}$ | 47.6 $\pm 0.4$ | 54.4 $\pm 0.5$ | – | – | – | – | – | – | – | – | – | – | – | –
$|\Delta\phi_{\gamma\gamma,jj}|$ | 50.9 $\pm 0.6$ | 54.0 $\pm 0.4$ | 54.0 $\pm 0.4$ | – | – | – | – | – | – | – | – | – | – | –
$\tau_{C,j1}$ | 51.0 $\pm 0.5$ | 50.9 $\pm 0.4$ | 55.9 $\pm 0.4$ | 63.0 $\pm 0.5$ | 59.0 $\pm 0.7$ | – | – | – | – | – | – | – | – | –
$\sum\tau_{C,j}$ | 51.0 $\pm 0.5$ | 50.5 $\pm 0.4$ | 52.3 $\pm 0.4$ | 59.5 $\pm 0.4$ | 57.6 $\pm 0.5$ | 61.7 $\pm 0.9$ | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$|\cos\theta^{*}|$$<$ 0.5] | 72.5 $\pm 0.6$ | 71.1 $\pm 0.5$ | 54.0 $\pm 0.3$ | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[0.5 $\leq$ $|\cos\theta^{*}|$$<$ 1.0] | 32.4 $\pm 0.4$ | 30.4 $\pm 0.3$ | 55.1 $\pm 0.6$ | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$=0] | 51.2 $\pm 0.5$ | 52.1 $\pm 0.5$ | 52.2 $\pm 0.5$ | 59.9 $\pm 1.9$ | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$=1] | 58.4 $\pm 0.5$ | 49.6 $\pm 0.4$ | 48.8 $\pm 0.4$ | 51.6 $\pm 0.5$ | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$=2] | 52.5 $\pm 0.4$ | 50.1 $\pm 0.4$ | 63.1 $\pm 0.3$ | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$$\geq$3] | 52.2 $\pm 0.4$ | 63.0 $\pm 0.3$ | – | – | – | – | – | – | – | – | – | – | – | –

Table 22:  Diphoton kinematic acceptances in percent for gluon–gluon fusion
for the diphoton fiducial region and all differential variable bins studied in
this paper, defined as the probability to fulfill the diphoton kinematic
criteria: $p_{\text{T}}/m_{\gamma\gamma}<$ 0.35 (0.25) for the leading
(subleading) photon and $|\eta_{\gamma}|<2.37$. The factors are evaluated
using the Powheg NNLOPSevent generator. Uncertainties are taken from PDF
variations. QCD scale variations have a negligible impact on these factors.
The range of each bin is given in Table 26.

| Bin 1 | Bin 2 | Bin 3 | Bin 4 | Bin 5 | Bin 6 | Bin 7 | Bin 8 | Bin 9 | Bin 10 | Bin 11 | Bin 12 | Bin 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Diphoton fiducial | 97.7 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$ | 98.4 $\pm 0.1$ | 97.6 $\pm 0.1$ | 97.2 $\pm 0.0$ | 96.9 $\pm 0.0$ | 97.0 $\pm 0.0$ | 97.7 $\pm 0.1$ | 98.5 $\pm 0.0$ | 98.7 $\pm 0.1$ | 98.9 $\pm 0.2$ | – | – | – | – | –
$|y_{\gamma\gamma}|$ | 97.6 $\pm 0.1$ | 97.6 $\pm 0.1$ | 97.7 $\pm 0.1$ | 97.6 $\pm 0.2$ | 97.7 $\pm 0.2$ | 97.7 $\pm 0.0$ | 97.7 $\pm 0.1$ | 97.8 $\pm 0.0$ | 98.0 $\pm 0.0$ | – | – | – | – | –
$p_{\mathrm{T}t}^{\gamma\gamma}$ | 97.2 $\pm 0.2$ | 97.4 $\pm 0.0$ | 97.5 $\pm 0.1$ | 97.7 $\pm 0.0$ | 97.9 $\pm 0.0$ | 97.9 $\pm 0.0$ | 98.0 $\pm 0.1$ | 98.0 $\pm 0.1$ | 98.2 $\pm 0.1$ | 98.5 $\pm 0.1$ | 98.9 $\pm 0.0$ | 99.1 $\pm 0.0$ | 99.2 $\pm 0.2$ | –
$|\cos\theta^{*}|$ | 97.9 $\pm 0.0$ | 97.9 $\pm 0.1$ | 97.9 $\pm 0.0$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.0$ | 97.7 $\pm 0.2$ | 97.7 $\pm 0.1$ | 97.6 $\pm 0.1$ | 97.6 $\pm 0.1$ | – | – | – | – | –
$|\Delta{y_{\gamma\gamma}|}$ | 97.9 $\pm 0.1$ | 98.0 $\pm 0.1$ | 97.9 $\pm 0.1$ | 97.9 $\pm 0.1$ | 97.9 $\pm 0.2$ | 97.9 $\pm 0.1$ | 97.8 $\pm 0.0$ | 97.7 $\pm 0.1$ | 97.7 $\pm 0.1$ | 97.4 $\pm 0.1$ | – | – | – | –
$N_{\mathrm{j}ets}$, $p_{\mathrm{T}}$$>$ 30 GeV | 97.7 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | –
$N_{\mathrm{j}ets}$, $p_{\mathrm{T}}$$>$ 50 GeV | 97.7 $\pm 0.1$ | 97.8 $\pm 0.1$ | 98.1 $\pm 0.0$ | – | – | – | – | – | – | – | – | – | – | –
$p_{\mathrm{T}}^{j_{1}}$ | 97.7 $\pm 0.1$ | 97.6 $\pm 0.1$ | 97.8 $\pm 0.0$ | 97.8 $\pm 0.2$ | 98.3 $\pm 0.0$ | – | – | – | – | – | – | – | – | –
$p_{\mathrm{T}}^{j_{2}}$ | 97.8 $\pm 0.1$ | 97.7 $\pm 0.1$ | 98.3 $\pm 0.0$ | – | – | – | – | – | – | – | – | – | – | –
$H_{\text{T}}$ | 97.7 $\pm 0.1$ | 97.7 $\pm 0.1$ | 97.8 $\pm 0.1$ | 98.0 $\pm 0.2$ | 98.2 $\pm 0.0$ | – | – | – | – | – | – | – | – | –
$|y_{j_{1}}|$ | 97.7 $\pm 0.1$ | 97.7 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.7 $\pm 0.4$ | 97.8 $\pm 0.1$ | – | – | – | – | – | – | –
$|y_{j_{2}}|$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | – | –
$m_{jj}$ | 97.7 $\pm 0.0$ | 97.8 $\pm 0.1$ | 98.2 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | – | –
$|\Delta{y_{jj}|}$ | 97.8 $\pm 0.1$ | 97.8 $\pm 0.0$ | 97.8 $\pm 0.3$ | – | – | – | – | – | – | – | – | – | – | –
$|\Delta\phi_{jj}|$ | 98.1 $\pm 0.1$ | 97.9 $\pm 0.1$ | 97.4 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | – | –
$\Delta\phi_{jj}$ | 97.6 $\pm 0.1$ | 98.0 $\pm 0.2$ | 98.1 $\pm 0.0$ | 97.5 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | –
$p_{\mathrm{T}}^{\gamma\gamma{}jj}$ | 98.3 $\pm 0.2$ | 97.7 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | – | – | –
$|\Delta\phi_{\gamma\gamma,jj}|$ | 98.4 $\pm 0.1$ | 97.8 $\pm 0.2$ | 96.4 $\pm 0.2$ | – | – | – | – | – | – | – | – | – | – | –
$\tau_{C,j1}$ | 97.7 $\pm 0.1$ | 97.8 $\pm 0.1$ | 97.7 $\pm 0.1$ | 97.6 $\pm 0.1$ | 97.9 $\pm 0.0$ | 98.1 $\pm 0.2$ | – | – | – | – | – | – | – | –
$\sum\tau_{C,j}$ | 97.7 $\pm 0.2$ | 97.7 $\pm 0.1$ | 97.6 $\pm 0.0$ | 97.7 $\pm 0.1$ | 97.9 $\pm 0.2$ | 98.3 $\pm 0.1$ | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$|\cos\theta^{*}|$$<$ 0.5] | 98.3 $\pm 0.1$ | 97.0 $\pm 0.0$ | 98.4 $\pm 0.2$ | 98.9 $\pm 0.4$ | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[0.5 $\leq$ $|\cos\theta^{*}|$$<$ 1.0] | 97.6 $\pm 0.1$ | 97.4 $\pm 0.1$ | 98.9 $\pm 0.0$ | 99.0 $\pm 1.0$ | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$=0] | 98.6 $\pm 0.1$ | 97.8 $\pm 0.1$ | 96.4 $\pm 0.0$ | 91.2 $\pm 1.3$ | 100 | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$=1] | 97.5 $\pm 0.3$ | 97.6 $\pm 0.2$ | 97.7 $\pm 0.0$ | 98.4 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$=2] | 97.0 $\pm 0.3$ | 98.4 $\pm 0.1$ | 98.8 $\pm 0.1$ | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$[$N_{\mathrm{j}ets}$$\geq$3] | 97.4 $\pm 0.2$ | 98.5 $\pm 0.7$ | – | – | – | – | – | – | – | – | – | – | – | –

Table 23:  Isolation efficiencies in percent for gluon–gluon fusion
$H\to\gamma\gamma$ for the diphoton fiducial region and all differential
variable bins in this analysis. The isolation efficiency is defined as the
probability for both photons to fulfill the isolation criteria (as described
in Section 9.1) for events that satisfy the diphoton kinematic criteria.
Regions of phase space where no reliable estimate could be obtained are listed
as ’100’ without uncertainties. Uncertainties are assigned in the same way as
for the non-perturbative correction factors: by varying the fragmentation and
underlying-event modeling. These factors can be multiplied by the kinematic
acceptance factors (see Table 22) to extrapolate an inclusive gluon–gluon
fusion Higgs prediction to the fiducial volume used in this analysis. The
range of each bin is given in Table 26.

| Bin 1 | Bin 2 | Bin 3 | Bin 4 | Bin 5 | Bin 6 | Bin 7 | Bin 8 | Bin 9 | Bin 10 | Bin 11 | Bin 12 | Bin 13 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Diphoton fiducial | 100 $\pm 2$ | – | – | – | – | – | – | – | – | – | – | – | – | –
$p_{{\mathrm{T}}}^{\gamma\gamma}$ | 99.7 $\pm 0.4$ | 100.3 $\pm 0.3$ | 100.2 $\pm 0.4$ | 99.7 $\pm 0.6$ | 100.0 $\pm 0.7$ | 99.8 $\pm 0.5$ | 100.4 $\pm 0.6$ | 99.9 $\pm 0.9$ | 100.1 $\pm 0.6$ | – | – | – | – | –
$|y_{\gamma\gamma}|$ | 99.8 $\pm 0.4$ | 99.9 $\pm 0.3$ | 100.1 $\pm 0.2$ | 100.0 $\pm 0.5$ | 100.0 $\pm 0.3$ | 100.2 $\pm 0.4$ | 99.9 $\pm 0.5$ | 100.2 $\pm 0.3$ | 100.0 $\pm 0.4$ | – | – | – | – | –
$p_{\mathrm{T}t}^{\gamma\gamma}$ | 100.0 $\pm 0.5$ | 100.1 $\pm 0.3$ | 100.0 $\pm 0.4$ | 100.3 $\pm 0.3$ | 100.0 $\pm 0.8$ | 100.3 $\pm 0.7$ | 99.8 $\pm 0.7$ | 100.0 $\pm 0.3$ | 99.9 $\pm 1.1$ | 99.8 $\pm 0.8$ | 99.8 $\pm 1.1$ | 100.6 $\pm 0.9$ | 100.4 $\pm 1.5$ | –
$|\cos\theta^{*}|$ | 100.1 $\pm 0.5$ | 100.0 $\pm 0.5$ | 99.8 $\pm 0.5$ | 99.7 $\pm 0.4$ | 99.9 $\pm 0.4$ | 100.0 $\pm 0.4$ | 100.2 $\pm 0.5$ | 100.0 $\pm 0.4$ | 100.2 $\pm 0.2$ | – | – | – | – | –
$|\Delta{y_{\gamma\gamma}|}$ | 99.9 $\pm 0.7$ | 100.0 $\pm 0.5$ | 100.0 $\pm 0.9$ | 99.7 $\pm 0.5$ | 99.7 $\pm 0.4$ | 100.1 $\pm 0.4$ | 99.9 $\pm 0.3$ | 100.0 $\pm 0.5$ | 100.1 $\pm 0.7$ | 100.1 $\pm 0.2$ | – | – | – | –
$N_{\mathrm{j}ets}$, $p_{\mathrm{T}}$$>$ 30 GeV | 102 $\pm 4$ | 99.2 $\pm 2.8$ | 98.2 $\pm 7.3$ | 94.4 $\pm 11.9$ | – | – | – | – | – | – | – | – | – | –
$N_{\mathrm{j}ets}$, $p_{\mathrm{T}}$$>$ 50 GeV | 100.7 $\pm 2.2$ | 98.7 $\pm 3.6$ | 96.4 $\pm 6.5$ | – | – | – | – | – | – | – | – | – | – | –