11institutetext: Istituto Nazionale di Fisica Nucleare, Sezione di Bologna

# Small systems at the LHC

Roberto Preghenella on behalf of ALICE, ATLAS and CMS Collaborations ()11
<EMAIL_ADDRESS>
###### Abstract

In these proceedings, I report on a selection of recent LHC results in small
systems from ALICE Aamodt:2008zz , ATLAS Aad:2008zzm  and CMS
Chatrchyan:2008aa  experiments. Due to the fact that the investigation of QCD
in small systems at high multiplicity is becoming an increasingly large
subject, interesting the heavy-ion community and more in general the high-
energy physics community, not all the related topics can be discussed in this
paper. The focus will be given to some of the measurements addressing the
physics of collective phenomena in small systems and to the recent results on
strangeness enhancement in proton-proton collisions. The reader must be
informed that a large number of interesting results did not find space in the
discussion reported here.

##  1 Introduction

There was a time when small collision systems, like proton-proton and proton-
nucleus, where almost excusively employed in heavy-ion physics as a reference
to compute the nuclear modification factors of particle production and as a
proxy to disentangle initial state, cold nuclear matter effects (i.e. due to
the nuclear PDF of the target/projectile) from genuine final state, hot
nuclear matter effects. As a matter of fact, results based on the analysis of
particle production in small systems provided the evidence that the
characteristic phenomena observed in heavy-ion collisions, most notably the
high-$p_{\rm T}$ and jet suppression Adler:2003ii ; Adams:2003im , were
actually due to the formation of a hot state of QCD matter, the Quark-Gluon
Plasma.

With the advent of the LHC, pioneering studies of pp collisions in high-
multiplicity events revealed the presence of unexpected phenomena in small
systems. The discovery of the “ridge” in pp collisions by the CMS
Collaboration was the first of a long list of such results Khachatryan:2010gv
. Long-range, near-side angular correlations in particle production emerged in
pp and subsequently in p–Pb collisions CMS:2012qk  and paved the way for a
systematic investigation of the existence of collective phenomena, known since
long in heavy-ion collisions Abelev:2009af , in the much smaller pp and p–Pb
collision systems. A wealth of new, unexpected phenomena have been observed so
far with striking similarities to heavy-ion phenomenolgy. In this report, only
a few of them can be discussed because of the lack of space. The focus will be
given to a selection of recent LHC results aiming at studying collective
phenomena and the chemistry of hadron production in small systems.

##  2 Collective phenomena

The observation of the ridge in pp Khachatryan:2010gv  and subsequently in
p–Pb collisions CMS:2012qk  promptly triggered further investigations. Studies
of two-particle correlations in p–Pb collisions reported by the ALICE
Collaboration have shown that, when taking the difference between the yields
per trigger particle in high-multiplicity and low-multiplicity events, two
nearly identical long-range ridge-like excess structures on the near-side and
away-side, the so-called “double ridge”, arise Abelev:2012ola ; Aad:2012gla .
Results on two-particle correlations of identified hadrons Khachatryan:2016txc
; ABELEV:2013wsa ; Khachatryan:2014jra ; Abelev:2014pua  and of Bose-Einstein
(HBT) correlations ATLAS:2017jts ; Adamova:2017opl  further stressed the
initial observations, showing striking similarities between pp, p–Pb and Pb–Pb
collisions, consistent with the hydrodynamic picture of a particle-production
source expanding more explosively along the collision event plane.

Figure 1: Second-order azimuthal anisotropy Fourier harmonics $v_{2}$ measured
by CMS in pp, p–Pb and Pb–Pb collisions based on correlations among multiple
charged particles Khachatryan:2015waa ; Khachatryan:2016txc .

Figure 2: Four-particle cumulants $c_{2}\\{4\\}$ measured by ATLAS in p–Pb
collisions (left) and in pp collisions (right) using different multiplicity
selection methods Aaboud:2017acw .

Figure 3: Four-particle cumulants $c_{2}\\{4\\}$ measured by ATLAS in p–Pb
collisions (left) and in pp collisions (right) with the “standard”, “two-
subevent” and the “three-subevent” methods Aaboud:2017blb .

###  2.1 Multi-particle correlations

A fundamental question is whether the two-particle azimuthal correlation
structures observed at large relative pseudorapidity in pp and p–Pb collisions
result from correlations exclusively between particle pairs, or if it is a
multi-particle, genuine collective effect. A strong hint, originally named as
evidence by the CMS Collaboration, for collective multi-particle correlations
in pp and p–Pb pp collisions was reported already Khachatryan:2015waa ;
Khachatryan:2016txc . Figure 1 shows the second-order azimuthal anisotropy
Fourier harmonics $v_{2}$ measured in pp, p–Pb and Pb–Pb collisions over a
wide pseudorapidity range based on correlations among up to eight particles.
The $v_{2}$ values obtained with correlations among more than four particles
are consistent with four-particle results and with comparable magnitude to
those from two-particle correlations. These observations support the
interpretation of a collective origin for the observed long-range correlations
in high-multiplicity pp and p–Pb collisions.

There is a note of care that must be taken seriously into account. While
multi-particle correlation measurements have the advantage of suppressing
short-range two-particle correlations such as jets and resonance decays, they
are not totally insensitive to such or other so-called “non-flow” effects.
This has been stressed in a publication by the ATLAS Collaboration
Aaboud:2017acw , where it is shown how different multiplicity selection
methods may yield different four-particle cumulants ($c_{2}\\{4\\}$) results.
The measurements of $c_{2}\\{4\\}$ are shown in Figure 2 for pp and p–Pb
collisions. The results confirm the evidence for collective phenomena in p–Pb
and low-multiplicity Pb–Pb collisions (not reported in Figure 2). On the other
hand, the pp results for $c_{2}\\{4\\}$ do not demonstrate collective
behaviour, indicating that they may be biased by contributions from non-flow
correlations.

Reliably suppressing non-flow correlations in pp collision is a central issue
that needs to be solved in order to be able to unveil the actual underlying
collectivity. Fortunately, several new methods have been recently developed
which aim at tackling this issue. As an example, the ATLAS Collaboration has
reported on the measurement of multi-particle correlations in pp and p–Pb
collisions with the so-called “two-subevent” and the “three-subevent” methods
ATLAS:2017tqk . Figure 3 shows $c_{2}\\{4\\}$ measured in pp and p–Pb
collisions with such methods. $c_{2}\\{4\\}$ from the standard method is
sensitive to the choice of particles used to form the event classes. The
sensitivity is greatly reduced in the two-subevent method and is almost fully
removed in the three-subevent method, suggesting that the three-subevent
method is much more robust against non-flow effects. The three-subevent method
shows significant flow in pp collisions in a broad $N_{\rm ch}$ range.

Figure 4: Ratios of $p_{\rm T}$ spectra of $\Lambda$/2${\rm K}^{0}_{S}$
measured by CMS in pp (left), p–Pb (middle), and Pb–Pb collisions (right)
Khachatryan:2016yru .

Figure 5: Multiplicity dependence of the $T_{\rm kin}$ and $\beta_{\rm T}$
Blast-Wave Schnedermann:1993ws  parameters fitted to pion, kaon and proton
$p_{\rm T}$ spectra measured by ALICE in pp, p–Pb and Pb–Pb collisions.

###  2.2 Identified hadron spectra

The $p_{\rm T}$ distributions of identified hadrons are another tool to probe
the collective behaviour of particle production. If collective radial flow
develops, this would result in a characteristic dependence of the shape of the
transverse momentum distribution on the particle mass. The $p_{\rm T}$
distributions in pp and p–Pb collisions show a clear evolution, becoming
harder as the multiplicity increases, with a change which is most pronounced
for protons and lambdas. The stronger multiplicity dependence of the spectral
shapes of heavier particles is evident when looking at the $p_{\rm
T}$-dependent ratios, such as the $\Lambda$/${\rm K}^{0}_{S}$ ratio measured
by the CMS Collaboration Khachatryan:2016yru , shown in Figure 5. The ratios
in pp and p–Pb collisions show a significant enhancement at intermediate
$p_{\rm T}$ ($\sim$3 GeV/$c$), quantitatively similar to that measured in
Pb–Pb collisions at similar multiplicity. Results from the ALICE Collaboration
show that the modification of the $p_{\rm T}$-depentent ratios of $\rm
p$/${\pi}$ and of $\Lambda$/${\rm K}^{0}_{S}$ follows a rather smooth
evolution at low and mid $p_{\rm T}$ across different systems, pointing
towards a universal soft mechanism driven by final state ${\rm d}N_{\rm
ch}/{\rm d}\eta$ Abelev:2013haa . The high-$p_{\rm T}$ part of the ratio,
which is dominated by hard fragmentation, is unchanged.

The Blast-Wave model Schnedermann:1993ws  is a useful tool to characterize the
spectral shapes of identified hadrons and test data against the radial flow
picture. A simultaneous fit to pions, kaons and protons is performed by the
ALICE Collaboration following the approach discussed in Abelev:2013haa . The
best fit describes the data with good accurancy in the low-$p_{\rm T}$ domain,
stressing the consistency of particle production from a thermal source
expanding with a common transverse velocity. The results of the fit to pp,
p–Pb and Pb–Pb data are shown in Figure 5 as a function of ${\rm d}N_{\rm
ch}/{\rm d}\eta$. In the context of the Blast-Wave model, when comparing the
parameters of different systems at similar ${\rm d}N_{\rm ch}/{\rm d}\eta$,
$T_{\rm kin}$ values are similar, whereas $\beta_{\rm T}$ is larger for small
systems. This might be an indication of a larger radial flow in small systems
as consequence of stronger pressure gradients. The ALICE results also show
that both $T_{\rm kin}$ and $\beta_{\rm T}$ parameters obtained from pp and
p–Pb fits are consistent for similar ${\rm d}N_{\rm ch}/{\rm d}\eta$. One has
to acknowledge that a different conclusion emerges from similar fits reported
by CMS Khachatryan:2016yru , where pp collisions appear as more explosive than
p–Pb collisions, with a larger $\beta_{\rm T}$ for similar ${\rm d}N_{\rm
ch}/{\rm d}\eta$.

##  3 Strangeness production

The study of the production of strange hadrons in high-energy hadronic
interactions provides an important means to investigate the properties of QCD.
Unlike up ($u$) and down ($d$) quarks, which form ordinary matter, strange
($s$) quarks are not present as valence quarks in the initial state. Yet they
are sufficiently light to be abundantly created by non-perturbative (soft)
processes in the course of the collisions. String fragmentation, as an example
of non-perturbative QCD process, dominates the production of strange hadrons
at low $p_{\rm T}$. As a matter of fact, given that the mass of the strange
quark is larger than the one of up and down quarks, production of strange
hadrons in fragmentation is suppressed relative to hadrons containing only
light quarks.

Figure 6: (left) $p_{\rm T}$-integrated yield ratios of strange and multi-
strange hadrons to pions as a function of ${\rm d}N_{\rm ch}/{\rm d}\eta$
measured by ALICE in pp, p–Pb and Pb–Pb collisions ALICE:2017jyt ;
Abelev:2013haa ; Adam:2015vsf ; ABELEV:2013zaa . Figure 7: (top right)
Particle yield ratios $\Lambda$/${\rm K}^{0}_{S}$ and $\rm p$/${\pi}$ as a
function of ${\rm d}N_{\rm ch}/{\rm d}\eta$ measured by ALICE in pp and p–Pb
collisions. (bottom right) Particle yield ratios to pions normalised to the
values measured in the inclusive pp sample.

###  3.1 Strangeness enhancement

An enhanced production of strange hadrons was one of the earliest proposed
indicators for the formation of a Quark-Gluon Plasma (QGP) state
Rafelski:1982pu ; Koch:1982ij ; Koch:1986ud , as higher rates for strange
quark production are expected in a highly-excited state of QCD matter. This
strangeness enhancement is expected to be more pronounced for multi-strange
baryons, and was indeed observed in collisions of heavy nuclei at the SPS,
RHIC and LHC Andersen:1998vu ; Andersen:1999ym ; Antinori:2004ee ;
Afanasiev:2002he ; Anticic:2003ux ; Adams:2003fy ; Adams:2006ke ;
Abelev:2007xp ; Antinori:2010jm ; ABELEV:2013zaa .

The ALICE Collaboration has recently reported on the multiplicity dependence
of the production of primary strange and multi-strange hadrons in pp
collisions ALICE:2017jyt . Similar measurements have been previously performed
by ALICE p–Pb collisions Abelev:2013haa ; Adam:2015vsf  and in Pb–Pb
collisions Abelev:2013xaa ; ABELEV:2013zaa . Figure 7 shows the measured
ratios of the $p_{\rm T}$-integrated yields of ${\rm K}^{0}_{S}$, $\Lambda$,
$\Xi$ and $\Omega$ to the pion yield as a function of ${\rm d}N_{\rm ch}/{\rm
d}\eta$ in pp collisions ALICE:2017jyt  compared to p–Pb and Pb–Pb results at
the LHC Abelev:2013haa ; Adam:2015vsf ; ABELEV:2013zaa . A significant
enhancement of strange to non-strange hadron production is observed with
increasing charged-particle multiplicity in pp collisions. The behaviour
observed in pp collisions resembles that of p–Pb collisions at a slightly
lower centre-of-mass energy Adam:2015vsf , both in the values of the ratios
and in their evolution with ${\rm d}N_{\rm ch}/{\rm d}\eta$, suggesting that
strangeness production is driven by the event activity of the event rather
than by the initial-state collision system or energy. Figure 7 shows that the
$p_{\rm T}$-integrated yield ratios $\Lambda$/${\rm K}^{0}_{S}$ and $\rm
p$/${\pi}$ do not change significantly with multiplicity, demonstrating that
the observed enhanced production rates of strange hadrons with respect to
pions is not due to the difference in the hadron masses.

The results in Figures 7 and 7 are compared to calculations from Monte Carlo
models commonly used for pp collisions at the LHC: PYTHIA8 Sjostrand:2007gs ,
EPOS LHC Pierog:2013ria  and DIPSY Flensburg:2011kk ; Bierlich:2014xba ;
Bierlich:2015rha . The observation of a multiplicity-dependent enhancement of
the production of strange hadrons along with the constant production of
protons relative to pions cannot be simultaneously reproduced by any of the
Monte Carlo event generators commonly used at the LHC.

Figure 8: (left) Ratios of several particle species measured by ALICE as a
function of the midrapidity pion yields for pp, p–Pb and Pb–Pb collisions
compared to the THERMUS strangeness canonical suppression model prediction
Vislavicius:2016rwi . Figure 9: (top right) $p_{\rm T}$-integrated $\phi$/K
ratio in pp collisions as a function of ${\rm d}N_{\rm ch}/{\rm d}\eta$.
(bottom right) $p_{\rm T}$-integrated $\Xi$/$\phi$ ratio in pp, p–Pb
Adam:2015vsf ; Adam:2016bpr  and Pb–Pb collisions as a function of ${\rm
d}N_{\rm ch}/{\rm d}\eta$.

###  3.2 Canonical suppression

The abundances of strange particles in heavy-ion collisions are compatible
with those of a hadron gas in thermal and chemical equilibrium and can be
described using a grand canonical statistical model Cleymans:2006xj ;
Andronic:2008gu . Extensions of the statistical description, like the ones
employed in the strangeness canonical suppression Redlich:2001kb  and the
core-corona superposition Becattini:2008yn ; Aichelin:2008mi  models, can
effectively produce a suppression of strangeness production in small systems.

The authors in Vislavicius:2016rwi  have studied the multiplicity dependence
of light flavour hadron production at LHC energies in the strangeness
canonical suppression picture using THERMUS Wheaton:2004vg . The details can
be found therein. As can be observed from Figure 9, the study shows that the
model provides a good description of the experimental data, except for the
$\phi$ meson. As a matter of fact, the strangeness canonical suppression model
is only sensitive to the strangeness quantum number of the hadron. The
observation of an enhancement (suppression) of $\phi$ meson production with
increasing (decreasing) multiplicity clearly signals that the particle
production rate is not consistent with the one expected from a hadron with
zero strangeness quantum number. This can be observed also in Figure 9, which
shows the ratio of $\phi$/K and $\Xi$/$\phi$ as a function of ${\rm d}N_{\rm
ch}/{\rm d}\eta$. It is evident that $\phi$ meson (S = 0) production increases
faster than K meson (S = 1) production. When compared to the $\Xi$, the
$\Xi$/$\phi$ is constant within uncertainties for ${\rm d}N_{\rm ch}/{\rm
d}\eta$ $>$ 10\. This is an indication that the $\phi$ meson behaviour is
closer to the behaviour expected from a hadron formed by two strange quarks.
The increase of the relative $\phi$ meson production with ${\rm d}N_{\rm
ch}/{\rm d}\eta$ constitues a notable crack in the canonical suppression
interpretation of the observed strangeness enhancement in high-multiplicity pp
and p–Pb collisions.

##  4 Conclusions

Several effects, like near-side long-range correlations and mass-dependent
hardening of $p_{\rm T}$ distributions, which in nuclear collisions are
typically attributed to the formation of a strongly-interacting collectively-
expanding quark-gluon medium, have been observed in high-multiplicity pp and
p–Pb collisions at the LHC Khachatryan:2010gv ; CMS:2012qk ; Abelev:2012ola ;
Aad:2012gla ; Aad:2013fja ; Chatrchyan:2013nka ; Abelev:2013haa ;
ABELEV:2013wsa ; Adam:2015vsf ; Khachatryan:2016yru ; Khachatryan:2016txc . An
enhanced production of strange particles as a function of the charged-particle
multiplicity density (${\rm d}N_{\rm ch}/{\rm d}\eta$), originally considered
to be another signature of QGP formation in nuclear collisions Rafelski:1982pu
; Koch:1982ij ; Koch:1986ud , has also been recently observed in pp collisions
ALICE:2017jyt .

The study of small collision systems at high multiplicity is undoubtedly of
considerable interest. Further studies are essential to assess whether the
combination of these observations can be interpreted as signal of the
progressive onset of a QGP medium, which starts developing already in small
systems.

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