Extra Dimension-Inspired Models: $\mathrm{Z^{\prime}}$, $\mathrm{W^{\prime}}$,
Dijet Resonances, Black Hole Searches

Tobias Pook on behalf of the ATLAS & CMS Collaborations111This work is
supported by the german Federal Ministry of Education and Research

III. Physikalisches Instiut A
Physikzentrum, RWTH Aachen University, 52056 Aachen
t.pook $<$at$>$ cern.ch

> I give a summary of BSM searches performed by the ATLAS and CMS experiments
> with an focus on heavy gauge bosons, extra dimensions and quantum black
> holes. The presented results use data collected during 2012 when the LHC
> operated at an center of mass energy of $\sqrt{s}=8\,\textrm{TeV}$.
>
>
> In memory of Harris Hassan

> PRESENTED AT
>
>
>
>
> the Twelfth Conference on the Intersections of Particle and Nuclear Physics
> (CIPANP15)
> Vail, USA, May 19–24, 2015

##  1 Introduction

The Large Hadron Collider (LHC) operated at a center of mass energy of
$\sqrt{s}=8\,\mathrm{TeV}$ during 2012 and the multi-purpose particle
detectors ATLAS [2] and CMS [1] recorded data with an integrated luminosity of
$20\,\mathrm{fb^{-1}}$. The recorded data presents a unique opportunity to
search for physics beyond the standard model (BSM) and both experiments have
interpreted their measurements in terms of a variety of theories.
This work aims to briefly summarize search results in the dilepton (same and
opposite flavor), lepton$+{\not\mathrel{E}}_{T}$, dijet and ditop channel for
a selected set of related BSM theories which predict the existence of heavy
gauge bosons $\mathrm{Z^{\prime}}$ and $\mathrm{W^{\prime}}$, extra dimensions
or quantum black holes.

##  2 Theories

Extra dimension models summarized in the following describe extensions of our
spacetime with additional compactified dimension. The related theories may
lower the fundamental Planck mass $M_{D}$ to the $\mathrm{TeV}$ region, and
thus solve the higgs mass hierachy problem. This summary focuses on the most
popular theories: Randall Sundrum (RS)[3] and the Arkani-Hamed, Dimopulos,
Dvali (ADD) [4, 5] models. Both models provide no fundamental theory of
quantum gravity, but are built as effective field theories based on classical
assumptions. They use parts of the mathematical framework which was developed
in string theory, or more precisely brane physics to confine SM particles to a
(3+1) dimensional subspace of the ($3+1+n$) dimensional space-time[6]. Extra
dimension theories predict a spectrum of Graviton modes (Kaluza-Klein towers)
or a spectrum of heavier copies of SM particles if they are able to propagate
in the compactified additional dimensions.

The ADD model assumes a flat spacetime. The model parameter under study
depends on the production process. The direct production cross section depends
directly on $M_{D}$, while the virtual graviton exchange is only able to probe
the UV cut-off $M_{s}$, which can be argued to be close to $M_{D}$.

The RS model assumes a warped space-time represented by an exponential term in
the metric $ds^{2}=e^{-2kr\phi}\eta_{\mu\nu}dx^{\mu}dx^{\nu}+r_{c}d\phi^{2}$.
The cross section in these models depends on the ratio $\tilde{k}$ of the warp
factor $k$ and $M_{D}$. Several extensions of this model exist, most notably
the Bulk RS1 scenario [7]. Here the fermion and boson fields localized near to
a TeV or a Planck brane respectively. This allows solving the flavor puzzle
and the higgs mass hierarchy problem without introducing an additional
hierarchy.

Heavy Gauge Bosons $\mathbf{\mathrm{W^{\prime}},\mathrm{Z^{\prime}}}$ refer to
heavier versions of the weak gauge bosons and are predicted in several classes
of theories. The most studied scenario is the sequential standard model (SSM)
[8] where $\mathrm{W^{\prime}}$ and $\mathrm{Z^{\prime}}$ bosons carry exactly
the same quantum numbers and interfere with their SM counterparts. The
$\mathrm{Z^{\prime}}$ is expected to decay flavor violating in several
theories. Relevant with respect to the presented searches are generic
extensions of the SSM with additional flavor violating couplings, which are
expressed as ratios $Q_{ij}\,(i,j=e,\mu,\tau)$ of the SSM same flavor coupling
[9] or extra dimensions where the mass hierachy among SM families is explained
by the overlap of the particle wave functions if fermions and the higgs are
localized on a higher dimensional brane [10]. Technicolor models which suggest
additional gauge couplings are of special interest in decay channels with tops
where the color singlet $\mathrm{Z^{\prime}}$ is leptophobic and couples only
to first and third generation quarks[11].

Quantum Black Holes (QBH) may be produced if LHC collisions take place above a
lowered fundamental Planck scale. All discussed models assume either the ADD
or the RS model as their starting point, but include different sets of
additional assumptions. The main parameters to control the signal shape and
cross section are the additional number of dimensions and the threshold mass
$M_{th}$, which is necessary to produce a QBH. The presented models are often
referred to by the generator which implements it. The generators used for the
summarized searches are:

  * •

CalcHEP for flavor violating QBH decays [12].

  * •

QBH which uses a generic description of gravitational bound two-body states
with an non thermal QBH decay [13].

  * •

BLACKMAX includes a wide range of black hole theories but most relevant for
the presented analyses are models comparable to the QBH generator with
additional model assumptions [14].

QBH theories share an important limitation: black hole production is expected
at scales where gravity becomes strong, and one hopes that the extrapolation
from the classical domain holds.

##  3 Selected Searches with the CMS and ATLAS Experiments

###  3.1 Dilepton (same flavor)

The dilepton channel is theoretical well understood and has been studied by
both experiments [15, 16, 17]. Both analyses try to use a model unspecific
selection which aims to reliably select well reconstructed and isolated pairs
of electrons or muons. No significant deviation from the SM was observed and
two distinct limit strategies have been used to set limits for resonant and
non-resonant BSM signals.

The resonant searches fit smooth functions to both data and background
prediction. A set of signal shape templates with different
$\mathrm{Z^{\prime}}$mass is used to construct a background + signal
hypothesis, which is compared to both data and the background only hypothesis.
The resulting limit on the cross section times efficiency for a SSM
$\mathrm{Z^{\prime}}$dependent on the resonance mass is shown in fig. 1.

Figure 1: 95% CL limits on the cross section $\times$ branching ratio
$\times$efficiency dependent on the resonance mass for the ATLAS [15] (left)
and CMS [17] (right) searches.

Both experiments report observed limits of 2.9 TeV on the
$\mathrm{Z^{\prime}}_{SSM}$ mass. The technique to derive these results
differs between both experiments. The ATLAS collaboration uses the complete
spectrum with a binned likelihood approach, this allows gaining additional
sensitivity for the studied SSM by including interference effects outside the
resonance. The CMS collaboration has chosen a more general strategy using an
unbinned likelihood approach with a narrow width approximation. The results
may be reinterpreted for any model with comparable acceptance by simply
applying a cross section ratio for the SSM $\mathrm{Z^{\prime}}$ and the model
under investigation within a mass window of $\pm 5\%\,\sqrt{\hat{s}}$. This
difference explains stronger fluctuations for CMS results in fig 1.

Possible signals from the lightest Kaluza-Klein Graviton mode in RS models
serve as a benchmark model for spin 2 resonances with a modified signal
acceptance. The ATLAS results show exclusion limits in the $k-M_{Pl}$ plane,
while CMS chose to present results similar to the $\mathrm{Z^{\prime}}$
interpretation, see figure 2. The comparison of both CMS limit plots show that
differences in cross section between $\mathrm{Z^{\prime}}$ and RS Gravitons
are only visible for small resonance masses.

Figure 2: 95% CL exclusion limits in the $k-M_{Pl}$ plane as reported by the
ATLAS collaboration [15] (left) 95% CL exclusion limits on the cross section
times efficiency depending on the resonance mass for spin-2 RS Gravitons by
CMS [17] (right).

QBHs are expected to create an edge like resonance structure in the dilepton
mass range close above the production threshold mass $M_{th}$. The ATLAS
search uses the resonant search strategy to derive 95% CL exclusion limits on
$M_{th}$ of 3.65 TeV for a signal based on an ADD scenario $(n=6)$ and 2.24
TeV for a RS based scenario $(n=1)$ using the QBH generator.

Both experiments performed non-resonant searches using a single bin counting
experiment above a lower mass threshold, which was optimized for the best
exclusion limits on the ADD UV cut-off $M_{s}$ at different number of extra
dimensions as shown in fig. 3, the observed limits reach from 4.9 TeV to 3.3
TeV for 3 to 7 additional dimensions.

Figure 3: Comparision of 95% CL exclusion limits on the UV cutoff $M_{s}$
depending on the number of additional dimensions for different searches by
ATLAS [15], CMS [17, 18, 19] and D0 [20]

###  3.2 Dilepton (mixed flavor)

Dilepton events with opposite flavor were studied by both experiments in the
$e\mu$ channel. ATLAS has performed additional searches in $e\tau$ and
$\mu\tau$ channels. Lepton flavor decays are of special interest because of
the good mass resolution and only small SM background contributions to the
final states.

Both experiments searched for $\mathrm{Z^{\prime}}$ bosons with additional
lepton flavor violating couplings. The ATLAS search chose the coupling
$\mathrm{Z^{\prime}}\rightarrow e\mu,e\tau,\mu\tau$ to be equal to SSM
$\mathrm{Z^{\prime}}$ same flavor coupling. A binned likelihood approach was
used to derive limits on the $\mathrm{Z^{\prime}}$ mass of 2.5 TeV ($e\mu$),
2.2 TeV ($e\tau$) and 2.2 TeV ($\mu\tau$) at 95% CL. The CMS analysis studied
an extra dimension inspired model where the coupling is set to match existing
strong bounds from $K_{L}\rightarrow e\mu$ decays. This search concluded to be
not sensitive to the $\mathrm{Z^{\prime}}$ model under investigation.

The quantum gravitational nature of QBHs suggest the existence of lepton
flavor violating decays. The CMS experiment has interpreted its measurements
in terms of several QBH models implemented in CalcHEP where the threshold mass
is set to be equal to the reduced Planck mass. Limits at 95% CL were set on
$M_{th}$ of 2.4 TeV in a RS based scenario $(n=1)$ and 3.15 TeV to 3.63 TeV
for 2 to 6 extra dimensions in an ADD based scenario.

###  3.3 Lepton+$\not\mathrel{\textbf{E}}_{\small\textbf{T}}$

Both experiments published results for final states with one high
$\mathrm{p_{T}}$ lepton and a significant amount of missing momentum in the
transverse plane ${\not\mathrel{E}}_{T}$ [21, 22]. The high mass tails for
this signature are dominated by off-shell SM $W$ production. Single lepton
triggers with transverse momentum thresholds for electrons (muons) of
$\mathrm{p_{T}}>120\,\textrm{GeV}\,(\mathrm{p_{T}}>40\,\textrm{GeV})$ and
$\mathrm{p_{T}}>80\,\textrm{GeV}\,(\mathrm{p_{T}}>40\,\textrm{GeV})$ have been
used by ATLAS and CMS respectively. Events with additional well reconstructed
same flavor leptons with $\mathrm{p_{T}}>20\,\textrm{GeV}$ are discarded in
the ATLAS analysis while CMS uses $\mathrm{p_{T}}>35\,\textrm{GeV}$ for
electrons and $\mathrm{p_{T}}>25\,\textrm{GeV}$ for muons. The transverse mass
$M_{T}=\sqrt{2\mathrm{p_{T}}^{\mathit{l}}{\not\mathrel{E}}_{T}\left(1-\cos[\Delta\phi(\vec{\mathrm{p_{T}}}^{\mathit{l}},\vec{{\not\mathrel{E}}_{T}})]\right)}$
is used as the main observable for $\mathrm{W^{\prime}}$ searches.

Additional final state specific kinematic cuts distinguish both searches:
ATLAS adjusts the lower threshold for ${\not\mathrel{E}}_{T}$ to the trigger
$\mathrm{p_{T}}$ thresholds for each flavor; CMS applies a back-to-back cut
$\Delta\phi(l,{\not\mathrel{E}}_{T})>2.5$ and requirements on the
$\mathrm{p_{T}}$-${\not\mathrel{E}}_{T}$ ratio:
$0.4<\mathrm{p_{T}}/{\not\mathrel{E}}_{T}<1.5$, both cuts should reflect that
BSM paricles are produced in a balanced recoil at leading order.

ATLAS and CMS report lower limits of 3.2 TeV and 3.3 TeV on the
$\mathrm{W^{\prime}}$ mass at 95 %CL. Different statistical procedures were
used to derive the limits; ATLAS uses a single bin counting experiment above a
varying lower threshold on $M_{T}$. Cross section limits are calculated based
on an optimized threshold for each considered $\mathrm{W^{\prime}}$ mass, see
fig. 4. The CMS analysis used an shape based template fit similar to the
resonant ATLAS search in the dilepton channel, see fig. 4. CMS has also
reported limits based on single bin counting experiments above varying mass
thresholds but did not use this approach for the $\mathrm{W^{\prime}}$
interpretation.

Figure 4: 95% CL exclusion limits on branching ratio times cross section
depending on the $\mathrm{W^{\prime}}$mass for ATLAS [21] (left) and CMS [22]
(right)

###  3.4 Dijet

Final states with two high-$\mathrm{p_{T}}$ jets profit from a large cross
section at hadron colliders like the LHC and enough events were collected to
extract shape information up to several TeV. Both experiments add additional
requirements on the dijet event kinematics in their search [23, 24]. A
separation in (pseudo)-rapidity between the jets with the highest
$\mathrm{p_{T}}$ of $\Delta y<0.6$ and $\Delta\eta<0.65$ is used by ATLAS and
CMS respectively. ATLAS used so called pre-scaled triggers where only a fixed
fraction of all events is saved. This allows collecting data with lowered
trigger requirements and decreases the lower limit for searches in the dijet
mass distribution to $m_{jj}>250\,\textrm{GeV}$ compared to the CMS analysis
with $m_{jj}>890\,\textrm{GeV}$. Both experiments use smooth fit function to
estimate the background expectation from data and compare it to signal
templates using a binned likelihood approach. Lower limits on particle masses
for SSM $\mathrm{Z^{\prime}}$, $\mathrm{W^{\prime}}$ and Kaluza-Klein
Gravitons in the RS model with $n=1$ are listed in table 1.

Dijet events also represent the most sensitive channel for QBH searches, and
many QBH models predict that the produced BH decays primarily to dijet pairs
[25]. Lower limits on $M_{th}$ were set by both experiments using the model
implemented in the QBH generator. ATLAS has set $M_{D}=M_{th}$ and reported
5.7 TeV while CMS kept both variables as free parameters and found a limit of
5.8 TeV for $M_{pl}=5\,\textrm{TeV}$. Additional bounds on a related model
implemented in BLACKMAX were set by the ATLAS experiment of
$M_{th}<5.6\,\textrm{TeV}$ where $M_{th}$ is again set to be equal to the
reduced Planck mass $M_{D}$.

[ TeV ] | $\mathrm{W^{\prime}}$ | $\mathrm{Z^{\prime}}$ |  $G_{KK}$(RS)
---|---|---|---
ATLAS | 2.5 |  |
CMS | 2.2 | 1.7 | 1.6
Table 1: 95% CL lower mass limits on the SSM $\mathrm{W^{\prime}}$,
$\mathrm{Z^{\prime}}$ and $G_{KK}$ (RS $n=1$) as reported by ATLAS [23] and
CMS [24] for the dijet channel.

###  3.5 Ditop

Figure 5:  Graphical representation of the possible decay modes for a single
top quark.

The analysis of ditop final states by ATLAS and CMS [26, 27] has significantly
increased its sensitivity by employing new analysis strategies for the
reconstruction of boosted top decays, and the subsequent top identification
via so called top-tagging techniques. Each of the two tops decays either
leptonically or hadronically, the hadronic decays can be further split into a
resolved and boosted topology, see fig. 5. The combination of these decay
modes for both tops results in the ditop decay modes: leptonic-leptonic,
leptonic-hadronic, leptonic-hadronic(boosted), hadronic-hadronic
hadronic(boosted)-hadronic(boosted). ATLAS restricted its analysis to the most
sensitive combination with one leptonic and one hadronic decay for the models
under investigation, CMS analyzed all possible decay modes and combined the
measurements for the final result.

Limits have been set on the $\mathrm{Z^{\prime}}$ mass based on topcolor
models as described in [11] where the coupling to lighter quarks is
suppressed: ATLAS and CMS found lower limits of 1.8 TeV and 2.4 TeV with a
width of 1.2% and 1% of the $\mathrm{Z^{\prime}}$ mass respectively, see
figure 6.
The Bulk RS1 model expects a suppression in production and decay for lighter
quarks. This leaves $t\overline{t}$ final states as the most promising channel
to probe the production of Kaluza-Klein gluons $g_{KK}$ at the LHC [7]. ATLAS
and CMS report lower limits on the mass of the lightest Kaluza-Klein mode of
the gluon $g_{KK}$ of 2.2 TeV and 2.8 TeV respectively.

Figure 6: 95% CL exclusion limits on the branching ratio$\times$cross section
dependent on the $\mathrm{Z^{\prime}}$mass for ATLAS [26] (left) and CMS [27]
(right)

##  4 Conclusion

ATLAS and CMS have both performed a large number of searches for the presented
theories and it should be emphasized that this summary reports only on a small
subset of all searches. No significant evidence for physics beyond the
standard model has been reported. A comprehensive list of all searches for new
physics related to this talk are constantly updated online ( ATLAS:
ExoticsPublicResults CMS: PhysicsResultsEXO, PhysicsResultsB2G ). The reach
for most of the presented analysis is limited by the probable phase space. The
recent restart of the LHC at a center of mass energy of
$\sqrt{s}=13\,\textrm{TeV}$ will increase the discovery reach for most
theories with a fraction of the recorded integrated luminosity at
$8\,\textrm{TeV}$.

ACKNOWLEDGEMENTS

I am grateful to Serguei Petrouchanko, Johannes Haller, Tobias Golling and
Koji Terashi for their helpful input during the preparation of my conference
contribution. I thank CERN and the ATLAS and CMS collaborations for their
great work operating the LHC and for providing the results for this summary.

## References

  * [1] CMS Collaboration, JINST 3, S08004 (2008).
  * [2] ATLAS Collaboration, JINST 3, S08003 (2008).
  * [3] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999), arXiv:hep-ph/9905221.
  * [4] N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 429, 263 (1998), arXiv:hep-ph/9803315.
  * [5] I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, Phys. Lett. B 436, 257 (1998), arXiv:hep-ph/9804398.
  * [6] I. Antoniadis Phys. Lett. B 246, 317 (1990)
  * [7] K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, Phys. Rev. D 77, 015003 (2008), arXiv:hep-ph/0612015.
  * [8] G. Altarelli, B. Mele and M. Ruiz-Altaba, Z. Phys. C 45, 109 (1989) [Z. Phys. C 47, 676 (1990)].
  * [9] B. Murakami, Phys. Rev. D 65, 055003 (2002), arXiv:hep-ph/0110095.
  * [10] J. M. Frere, M. V. Libanov, E. Y. Nugaev and S. V. Troitsky, JETP Lett. 79, 598 (2004) [Pisma Zh. Eksp. Teor. Fiz. 79, 734 (2004)], arXiv:hep-ph/0404139.
  * [11] R. M. Harris and S. Jain, Eur. Phys. J. C 72, 2072 (2012), arXiv:1112.4928.
  * [12] A. Belyaev, N. D. Christensen and A. Pukhov, Comput. Phys. Commun. 184, 1729 (2013), arXiv:1207.6082.
  * [13] D. M. Gingrich, Comput. Phys. Commun. 181, 1917 (2010), arXiv:0911.5370.
  * [14] D. C. Dai, G. Starkman, D. Stojkovic, C. Issever, E. Rizvi and J. Tseng, Phys. Rev. D 77, 076007 (2008), arXiv:0711.3012.
  * [15] ATLAS Collaboration, Phys. Rev. D 90, no. 5, 052005 (2014), arXiv:1405.4123.
  * [16] ATLAS Collaboration, Eur. Phys. J. C 74, no. 12, 3134 (2014), arXiv:1407.2410.
  * [17] CMS Collaboration, JHEP 1504, 025 (2015), Twiki material, arXiv:1412.6302.
  * [18] CMS Collaboration, Phys. Lett. B 711, 15 (2013), Twiki material, arXiv:1202.3827.
  * [19] CMS Collaboration, Phys. Rev. Lett. 108, 111801 (2012), arXiv:1112.0688.
  * [20] D0 Collaboration, Phys. Rev. Lett. 102, 051601 (2009), arXiv:0809.2813.
  * [21] ATLAS Collaboration, JHEP 1409, 037 (2014), arXiv:1407.7494.
  * [22] CMS Collaboration, Phys. Rev. D 91, no. 9, 092005 (2015) arXiv:1408.2745.
  * [23] ATLAS Collaboration, Phys. Rev. D 91, no. 5, 052007 (2015), arXiv:1407.1376.
  * [24] CMS Collaboration, Phys. Rev. D 91, no. 5, 052009 (2015), arXiv:1501.04198.
  * [25] X. Calmet, W. Gong and S. D. H. Hsu, Phys. Lett. B 668, 20 (2008), arXiv:0806.4605.
  * [26] ATLAS Collaboration, arXiv:1505.07018.
  * [27] CMS Collaboration, CMS-PAS-B2G-13-008.