# Measurements of charged particle spectra and nuclear modification factor in
p+Pb collisions with the ATLAS detector

Petr Balek (for the ATLAS Collaboration)  IPNP, Faculty of Mathematics and
Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Prague, Czech
Republic

###### Abstract

The ATLAS detector at the LHC obtained the sample of p+Pb data at
$\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV with integrated luminosity of 25 nb-1,
which can be compared to the pp data obtained by interpolating pp measurements
at $\sqrt{s}=2.76$ TeV and 7 TeV. Due to the excellent capabilities of the
ATLAS detector, and its stable operation in heavy ion as well as proton–proton
physics runs, the data allow measurements of the nuclear modification factor,
ratio of heavy ion charged particle spectra divided by pp reference, in
different centrality classes over a wide range of rapidity. The charged
particle nuclear modification factor is found to vary significantly as a
function of transverse momentum with a stronger dependence in more peripheral
collisions.

keywords: proton–lead collision, nuclear modification factor

##  1 Introduction

The partonic structure of nuclei has been studied extensively in deep
inelastic scattering experiments [1]. These measurements have established
differences in the parton distribution functions (PDFs) in nuclei from those
expected from an incoherent superposition of nucleons. These differences
include the phenomena of shadowing, anti-shadowing [2] and the EMC effect [3].
These observations have inspired significant theoretical work (e.g. [4, 5,
6]), but to date the underlying physics of these phenomena is not completely
understood. Proton–ion collisions at the LHC are capable of probing the
nucleus at scales that have not been experimentally accessible before. This
includes particle production from hard scattering processes with large
transverse momentum transfer, $q^{2}$, which may provide crucial insight into
the large-$q^{2}$ structure of the nucleus or even reveal previously
unobserved phenomena.

##  2 Analysis

Nuclear modification effects are studied by comparing observables in heavy ion
collisions with the corresponding observables obtained in pp collisions. The
rates of hard scattering processes in heavy ion collisions are enhanced
relative to pp collisions due to the increased flux of partons per collision,
i.e. the nucleus contains many nucleons capable of participating in a hard
scattering. This enhancement depends on the thickness of the target nucleus,
$T_{\mathrm{Pb}}$, and on the impact parameter of the projectile. It can be
inferred from geometric models such as the Glauber model [7]. The particle
yields in p+Pb collisions scaled by the average $T_{\mathrm{Pb}}$ can then be
compared directly to the cross section for the same process obtained in pp
collisions:

$R_{\mathrm{pPb}}(p_{\mathrm{T}})=\frac{1}{\langle
T_{\mathrm{Pb}}\rangle}\frac{1/N_{\mathrm{evt}}\leavevmode\nobreak\
\mathrm{d}^{2}N_{\mathrm{\footnotesize
p+Pb}}/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}}{\mathrm{d}^{2}\mathrm{\sigma}_{\mathrm{\footnotesize
pp}}/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}},$ (1)

where $R_{\mathrm{pPb}}$ is called the nuclear modification factor,
$1/N_{\mathrm{evt}}\leavevmode\nobreak\ \mathrm{d}^{2}N_{\mathrm{\footnotesize
p+Pb}}/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}$ is the per-event charge particle
yield in p+Pb collisions measured differentially in transverse momentum
($p_{\mathrm{T}}$) and rapidity ($y$), and
$\mathrm{d}^{2}\mathrm{\sigma}_{\mathrm{\footnotesize
pp}}/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}$ is the corresponding differential
cross section measured in pp collisions.

This analysis [8] uses p+Pb data collected with the ATLAS detector [9] in 2013
at $\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV with a longitudinal rapidity boost
of 0.465 relative to the ATLAS laboratory frame. Further, the analysis uses pp
data with $\sqrt{s}=2.76$ TeV recorded in 2013 and data with $\sqrt{s}=7$ TeV
recorded in 2010 and 2011. The p+Pb data have integrated luminosity
($L_{\mathrm{int}}$) of 25 nb-1, the pp data with $\sqrt{s}=2.76$ TeV and 7
TeV have $L_{\mathrm{int}}\approx 4.0$ pb-1 and 156 pb-1, respectively.

The events used in this analysis are selected from several triggered samples.
A minimum bias (MB) samples were obtained requiring signal in the Minimum Bias
Trigger Scintilator. For jet triggered samples, jets were reconstructed in
events that passed the MB requirement using the anti-kT algorithm [10] with
the distance parameter $R=0.4$. Events were selected by the jet trigger if
they contained jets with $E_{\mathrm{T}}$ above a certain threshold. Multiple
thresholds were defined. Only a fraction of all events which fired a trigger
was randomly selected to be recorded for further analysis. This fraction was
set differently for each trigger. Total spectra were obtained by merging
spectra from MB and jet triggers, all of them scaled by reciprocal of the
fraction to obtain MB spectra up to high $p_{\mathrm{T}}$.

The p+Pb event centrality classes are defined in terms of percentiles of the
total transverse energy measured by the forward calorimeters in the
pseudorapidity range $3.1<\eta<4.9$ in the lead-going direction. The $\langle
T_{\mathrm{Pb}}\rangle$ values are estimated from the Glauber model [11] for
each of the studied centrality class.

To study the effects of the detector response on the measurement, Monte Carlo
(MC) simulation samples were produced using the PYTHIA event generator [12].
MC samples correspond to p+Pb and pp collisions of the same energy, the same
detector configuration and the same beam direction. The MC samples were
processed with the same algorithm as the data. For p+Pb, a sample of pp
collisions at $\sqrt{s}=5.02$ TeV was simulated, but with the output boosted
to match the boost due to the asymmetry of the collisions. This simulation
output was overlaid onto minimum-bias p+Pb data to get events with generated
jets and correct underlying events. Several samples of events were produced
for different intervals of generator-level $R=0.4$ jet $p_{\mathrm{T}}$,
besides the MB samples, in order to obtain good statistics precision over
large range in charged particle $p_{\mathrm{T}}$. The final pp (p+Pb) results
were obtained by merging all pp (p+Pb) samples, while each sample was scaled
by the cross section of the jet production in the appropriate jet
$p_{\mathrm{T}}$ range.

Charge particle tracks are reconstructed in the ATLAS Inner Detector [13].
Tracks are measured using a combination of silicon pixel detector (Pixel),
silicon microstrip detector (SCT), and a straw tube transition radiation
tracker (TRT), all immersed in a 2 T axial magnetic field. Charged particles
typically traverse 3 layers of silicon pixel detectors, 4 layers of double
sided microstrip detector, and 36 straws.

The minimum $p_{\mathrm{T}}$ of tracks used in this analysis is 4 GeV. Each
track is required to have at least 1 hit in the Pixel detector, a hit in the
innermost layer if such hit is expected by the tracking model, and at least 6
hits in the SCT. Additionally, tracks with $p_{\mathrm{T}}>10$ GeV are
required to produce at least 8 hits in the TRT. These requirements select
tracks with good $p_{\mathrm{T}}$ resolution and suppress the contribution of
poorly reconstructed tracks. Yet they limit the analysis to the coverage of
the TRT detector, thus all tracks are selected with $|\eta|<2$.

To ensure that the tracks originate from the event vertex, the transverse
impact parameter, $d_{0}$, and $z_{0}\sin\theta$ ($z_{0}$ is the longitudinal
impact parameter) are required to be less than 1.5 mm. Tracks selected for the
analysis are also required to satisfy the conditions on the impact parameters
significances: $|d_{0}/\sigma_{d_{0}}|<3$ and
$|z_{0}\sin\theta/\sigma_{z_{0}\sin\theta}|<3$. The $d_{0}$ and
$z_{0}\sin\theta$ parameters and their uncertainties are estimated by a vertex
finding algorithm.

To reduce the amount of fake tracks at high $p_{\mathrm{T}}$, all tracks with
$p_{\mathrm{T}}>15$ GeV are required to match anti-kT jets with the distance
parameter $R=0.4$. The main interest of this analysis are spectra of charged
hadrons. Thus, electrons and muons coming from electroweak decays of heavy
bosons are subtracted from the measured spectra.

The raw charged particle spectra in p+Pb and pp collisions are corrected for
fake tracks and secondary particles, for limited momentum resolution, and for
tracking inefficiency. These corrections are functions of $p_{\mathrm{T}}$ and
rapidity in center-of-mass frame ($y^{\star}$) and are estimated using
corresponding MC samples. First, the raw spectra are corrected for the
fraction of tracks associated to secondary particles and for the fraction of
tracks which cannot be associated to any particles in the MC, i.e. fake
tracks. The fraction of secondary particles is at most 1% at
$p_{\mathrm{T}}=4$ GeV. The fraction of fake tracks strongly depends on
$p_{\mathrm{T}}$ and at the highest measured $p_{\mathrm{T}}$ reaches 13%. It
also depends on rapidity. Next, the resulting spectra are unfolded using the
iterative Bayesian unfolding [14] to correct for the finite detector
$p_{\mathrm{T}}$ resolution. The first iteration is sufficient, further
iterations do not change the results by more than 2% even at the highest
$p_{\mathrm{T}}$. The spectra are then corrected for particle loss in the
reconstruction by the track reconstruction efficiency.

Once the differential pp cross section at $\sqrt{s}=2.76$ and 7 TeV have been
measured, the differential pp cross section at $\sqrt{s}=5.02$ TeV is obtained
by interpolation. The interpolation is proportional to $\ln(\sqrt{s})$ and it
is performed for every $p_{\mathrm{T}}$ bin in each rapidity interval used in
the p+Pb analysis.

Systematic uncertainties are evaluated by varying individual sources within
the ranges of their uncertainties and comparing the results to the results of
the default analysis. Tracking and vertex pointing cuts contribute up to 5%.
The uncertainties on the correction for fake tracks and on the correction for
track reconstruction efficiency contribute up to 10% and 15% at the highest
$p_{\mathrm{T}}$, respectively. Uncertainty on the momentum resolution of the
Inner Detector tracking system adds a significant contribution of 12% to the
systematic uncertainties at high $p_{\mathrm{T}}$. Difference up to 5% was
found between parts of the run with opposite directions of the p and Pb beams
in the LHC due to different jet trigger performance. The calculation of
$y^{\star}$ is made with the assumption that all particles are pions, this
introduces an uncertainty of 1%. The uncertainty related to the description of
the inactive detector material is found to vary between 1–7% depending on
$\eta$.

The uncertainty on the event selection is accounted for in the uncertainty of
the corresponding $\langle T_{\mathrm{Pb}}\rangle$ values. The luminosities of
the pp data samples have an uncertainty of 3.2% and 4% for the measurements at
$\sqrt{s}=2.76$ and 7 TeV respectively. Possible distortion introduced by the
interpolation algorithm reaches up to 12%. It is estimated as the difference
between $\sqrt{s}$ and $\ln(\sqrt{s})$ interpolations. For $R_{\mathrm{pPb}}$,
most of the systematic uncertainties between p+Pb and pp contribute to the
final ratio, since the $y^{\star}$ variable corresponds to different areas in
the detector, as the two systems are in two different centre-of-mass frames.

##  3 Results

Figure 1: The $R_{\mathrm{pPb}}$ distributions as a function of
$p_{\mathrm{T}}$ in the 0–90% centrality class. Left: $R_{\mathrm{pPb}}$
measured for the $|y^{\star}|<1$. Right: $R_{\mathrm{pPb}}$ with interpolated
pp reference (black points) and with simulated pp reference (red squares).
Vertical bars indicate the statistical uncertainty of the measurement.
Systematic uncertainties are plotted with step lines encompassing each point,
the systematic uncertainties of $\langle T_{\mathrm{Pb}}\rangle$ are not
included in the bands and shown with the gray-shaded bands at unity. Figure 2:
The $R_{\mathrm{pPb}}$ distributions as a function of $p_{\mathrm{T}}$
measured for the 60–90% (left), 20–30% (middle) and 0–10% (right) centrality
class. Vertical bars indicate the statistical uncertainty of the measurement.
Systematic uncertainties are plotted with step lines encompassing each point,
the systematic uncertainties of $\langle T_{\mathrm{Pb}}\rangle$ are not
included in the bands and shown with the gray-shaded bands at unity.

The final charged particle spectra are MB spectra (including scaled jet
triggered spectra). The p+Pb yield is normalized per event, while the pp
yields are normalized by corresponding luminosity and interpolated to the same
center-of-mass energy as p+Pb sample.

Left panel of Fig. 1 shows $R_{\mathrm{pPb}}$ in the rapidity interval
$-1<y^{\star}<1$ for centrality class 0–90%. The figure shows unexpected
increase of $R_{\mathrm{pPb}}$ with increasing $p_{\mathrm{T}}$, compared to
the lower $p_{\mathrm{T}}$ values. The $R_{\mathrm{pPb}}$ distribution reaches
the maximum of approximately 1.4. This result is comparable with the CMS
measurement [15] and both measurements show the same trend at high
$p_{\mathrm{T}}$.

Right panel of Fig. 1 shows comparison of $R_{\mathrm{pPb}}$ with the
interpolated pp reference and with a reference obtained by pure simulation at
$\sqrt{s}=5.02$ TeV. The increase of $R_{\mathrm{pPb}}$ at high
$p_{\mathrm{T}}$ is similar for these two distributions.

Figure 2 shows the $R_{\mathrm{pPb}}$ distributions for 3 centrality classes
(0–10%, 20–30% and 60–90%) and for the rapidity interval $-2<y^{\star}<1.5$.
Especially in the 60–90% centrality class, there is a clear trend of
increasing enhancement towards higher $p_{\mathrm{T}}$. In the more central
classes the enhancement is presented as well.

## Acknowledgements

This research is supported by Charles University in Prague (projects UNCE
204020/2012, GAUK 500912 and GAUK 713612) and by INGO LG13009.

## References

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f-p_{J_{n}}\left(e^{-t\mathcal{L}}f_{0}\right)\right\rVert_{L^{\infty}\left(\nu\right)}\leqslant
ch_{n}^{\beta}\ln N\right|J_{n},h_{n}\right]\geqslant$
$\displaystyle\Pi\left[\max_{1\leqslant j\leqslant N}\left\lvert
z_{j}-\left\langle
u_{j}|e^{-t\mathcal{L}}f_{0}\right\rangle_{L^{2}\left(\nu\right)}\right\rvert\leqslant\frac{ch_{n}^{\beta}\ln
N}{N}\right]$ $\displaystyle\geqslant$
$\displaystyle\prod_{j=1}^{J_{n}}\Pi\left[\left\lvert z_{j}-\left\langle
u_{j}|e^{-t\mathcal{L}}f_{0}\right\rangle_{L^{2}\left(\nu\right)}\right\rvert\leqslant\frac{ch_{n}^{\beta}\ln
N}{N}\right]$ $\displaystyle\geqslant$
$\displaystyle\left(\frac{2ch_{n}^{\beta}\ln
N}{N}\inf_{[-K,K]}\Psi\right)^{J_{n}}\text{vol}(B_{J_{n}}(0,1)),$

where

$K\geqslant\max_{1\leqslant j\leqslant J_{n}}\left\lvert\left\langle
u_{j}|e^{-t\mathcal{L}}f_{0}\right\rangle_{L^{2}\left(\nu\right)}\right\rvert+\frac{ch_{n}^{\beta}\ln
N}{N}\lesssim 1+\underbrace{\left\lVert
e^{-t\mathcal{L}}\right\rVert_{\mathcal{L}\left(L^{\infty}\left(\nu\right)\right)}}_{=1}\left\lVert
f_{0}\right\rVert_{L^{\infty}\left(\mathcal{M}\right)}<+\infty.$

Hence

$-\ln\Pi\left[\left.\left\lVert
f-p_{J}\left(e^{-t\mathcal{L}}f_{0}\right)\right\rVert_{L^{\infty}\left(\nu\right)}\leqslant
ch_{n}^{\beta}\ln N\right|J_{n},h_{n}\right]\lesssim J_{n}\ln N$

Therefore

$\begin{split}\varmathbb P_{0}&\left(\Pi\left[\left.\left\lVert
f-p_{J}\left(e^{-t\mathcal{L}}f_{0}\right)\right\rVert_{L^{\infty}\left(\nu\right)}\leqslant\varepsilon_{n}\right|J_{n},h_{n}\right]<\exp\left(-n\varepsilon_{n}^{2}\right)\right)\\\
&\leqslant\varmathbb P_{0}\left(\left\lVert
f_{0}-p_{J_{n}}\left(e^{-t\mathcal{L}}f_{0}\right)\right\rVert_{L^{\infty}\left(\nu\right)}>\varepsilon_{n}/2\right)\leqslant
n^{-H}\end{split}$

for any $H>0$, by choosing $J_{0}$ large enough.

  2. 2.

The case $\beta>2$ is similar, the only difference being that we use the bound

$\left\lvert\left\langle
u_{j}|e^{-t\mathcal{L}}f_{t}\right\rangle_{L^{2}\left(\nu\right)}\right\rvert\leqslant\left\lVert\sum_{l=0}^{k}\frac{\left(t\mathcal{L}\right)^{l}e^{-t\mathcal{L}}}{l!}\right\rVert_{\mathcal{L}\left(L^{2}\left(\nu\right)\right)}\left\lVert
f_{0}\right\rVert_{L^{2}\left(\nu\right)}\leqslant\left\lVert
f_{0}\right\rVert_{L^{\infty}\left(\mathcal{M}\right)}\sup_{s>0}\sum_{l=0}^{k}\frac{s^{l}e^{-s}}{l!}<+\infty$

∎

######  Lemma D.3.

For some $z\geqslant 1$ and $J\in\left\\{1,\ldots,N\right\\}$ let

$\mathcal{F}_{z,J}=\left\\{\sum_{j=1}^{J}a_{j}u_{j}:\left\lvert
a_{j}\right\rvert\leqslant z\right\\},\quad z>0$

Then

$\Pi\left[\mathcal{F}_{z,J}^{c}|J,h\right]\leqslant Je^{-b_{1}z^{b_{2}}}$

and, there exists $\varepsilon_{1},C_{1}>0$ such that for any
$\varepsilon\leqslant\varepsilon_{1}$

$N\left(\varepsilon,\mathcal{F}_{z,J},\left\lVert\cdot\right\rVert_{L^{\infty}\left(\nu\right)}\right)\leqslant\left(\frac{C_{1}zN}{\varepsilon}\right)^{2J}$

###### Proof.

Proof of lemma D.3
Using the representation $f=\sum_{j=1}^{J}Z_{j}u_{j}$, the upper bound

$\Pi\left[\mathcal{F}_{z,J}^{c}|J,h\right]\leqslant\sum_{j=1}^{J}\Pi\left[\left\lvert
Z_{j}\right\rvert>z|J,h\right]\leqslant J\Psi\left([-z,z]^{c}\right)\leqslant
Je^{-b_{1}z^{b_{2}}}$

follows by the assumption on the tails of $\Psi$. Moreover by proposition B.2,
if $\mathcal{E}$ is an $\frac{\varepsilon}{JN}$-net of $[-z,z]^{J}$ then

$\left\\{\sum_{j=1}^{J}f_{j}u_{j}:f\in\mathcal{E}\right\\}$

is an $\varepsilon$-net of $\mathcal{F}_{z,J}$ (in $L^{\infty}(\nu)$). Since
we can always take

$\\#\mathcal{E}\leqslant\left(\frac{C_{1}zJN}{\varepsilon}\right)^{J}\leqslant\left(\frac{C_{1}zN^{2}}{\varepsilon}\right)^{J}\leqslant\left(\frac{C_{1}^{1/2}z^{1/2}N}{\varepsilon^{1/2}}\right)^{2J}\leqslant\left(\frac{C_{1}^{1/2}cN}{\varepsilon}\right)^{2J}$

for $\varepsilon\leqslant\varepsilon_{1}$ and some $C_{1},\varepsilon_{1}>0$
this gives the result by changing $C_{1}^{1/2}$ into a new $C_{1}$. ∎