### Forward-backward correlations between mean transverse momenta in Pb–Pb collisions with ALICE

#### 1. Introduction

Studies of Forward-Backward (FB) correlations are performed
between observables in two separated
pseudo-rapidity intervals
ΔηF
and
ΔηB
, which are conventionally
referred to as forward and backward windows.
The FB correlations are created predominantly at the early stages of the collision [1]
and arise in such initial state models as Color Glass Condensate [2]
and String Fusion [3].
The FB correlations are sensitive to event-by-event fluctuations
of number and properties of particle-emitting sources elongated in rapidity,
and in later stages of the system evolution the correlations
can be modified by medium and final state effects.

The strength of the FB correlation is usually characterized by the correlation coefficient
b corr
, which is obtained from a linear regression analysis of the event-averaged quantity
measured in the backward rapidity hemisphere (
〈B〉F
) as a function of the quantity measured in the forward hemisphere (
F
): Alternatively, the
b corr
can be determined using the Pearson correlation coefficient:

(2)
where angular brackets denote averaging over events.
Different dynamical variables can be chosen in
F
and
B
windows in order to study correlations between them.
In conventional FB measurements, multiplicities of charged particles
nF
and
nB
within the windows are chosen.
We refer to this kind of FB correlations as
𝑛--𝑛
correlations, and
formulae 1 and 2 for them as

(3)
The forward-backward multiplicity correlations have been previously studied
in a large number of colliding systems, for instance, in
pp¯
[4],
pp [5]
and Au–Au [6] collisions.

Charged particle multiplicity is an *extensive* quantity,
therefore the strength of the FB
𝑛--𝑛
correlations is affected by
the so-called “volume fluctuations" (i.e., in Glauber-like models, by
event-by-event fluctuations of the number of
participating nucleons),
which complicates the interpretation of the experimental values of this observable.
To suppress this contribution,
one may consider other, *intensive* observables within the observation windows.
In particular,
the mean transverse momentum of particles in a given event can be determined within each of the
F
and
B
windows,
given by the expressions
F≡pF¯=∑j=1nFpT(j)/nF
and
B≡pB¯=∑i=1nBpT(i)/nB
[7].
Then the formulae 1 and 2 for
the correlation strength are expressed as

(4)

In this work,
FB correlations between charged primary particles
have been measured with the ALICE detector in Pb–Pb collisions
at
s NN =
2.76 and 5.02 TeV.
We first show an analysis
of FB multiplicity correlations and after that present
results on FB correlations between mean-
pT
.

#### 2. Forward-backward correlations between multiplicities

In the ALICE setup,
charged particles are reconstructed using combined information from the Inner Tracking System (ITS) and the Time Projection Chamber (TPC). Both detectors are located inside the ALICE solenoid with a field of 0.5 T and have full azimuthal coverage for track reconstruction within a pseudo-rapidity window of
|η|<0.8
[8].
Centrality of Pb–Pb collisions is determined using the signals from the V0 detectors –
two forward scintillator arrays with coverage
-3.7<η<-1.7
and
2.8<η<5.1
.
Alternatively, centrality can be estimated using the signal from spectators in the Zero-Degree Calorimeters coupled with the response from a small electromagnetic calorimeter ZEM (ZDCvsZEM estimator),
as well as using the number of clusters counted in the second layer of the Silicon Pixel Detector covering
|η|<1.4
(CL1 estimator) [9].
Centrality classes are defined as percentiles of the multiplicity distributions.

##### Figure 1

Strength of the FB multiplicity correlations
as a function of centrality in Pb–Pb collisions at
s NN =2.76
TeV.
Centrality classes of different width are determined by the V0 (a) and by the ZDCvsZEM (b). Systematic uncertainties are shown as rectangles (widths correspond to the sizes of centrality classes),
statistical uncertainties are smaller than marker sizes.

(a) a,

(b) a,

A pair of
η
intervals chosen for this FB correlation analysis are (-0.8, -0.4) and (0.4, 0.8),
which have a width
δη=0.4
and pseudorapidity separation
η gap =0.8
.
Such a separation allows short-range effects from (mini-)jets and resonance decays to be reduced.
A “soft”
pT
-range of 0.2-2.0 GeV/
c
was chosen for the study.
The numbers of Pb–Pb events selected for analysis
are
12×106
at
s NN =2.76
TeV
and
49×106
at
5.02
TeV.

Figure figfor_approval_nn shows the centrality dependence of the FB correlation strength
b corr 𝑛--𝑛
between multiplicities in the two windows.
The centrality estimator used for panel (a) is the V0 detector.
For wide centrality classes of 10% width (red filled circles), the correlation strength grows towards more central collisions, as it was observed by the STAR collaboration for Au–Au collisions [6]. However, for smaller
class widths (5, 2, 1 and 0.5%) the values of
b corr 𝑛--𝑛
drop and the centrality trend flattens,
because the contribution from
the volume fluctuations is suppressed for narrower centrality classes.

Panel (b) shows values of
b corr 𝑛--𝑛
in classes of centrality determined by the ZDCvsZEM estimator.
It can be seen that the trends
are very different in comparison with the V0-based results.
This is
because acceptance and resolution of the ZDCvsZEM estimator is distinct from those of the V0,
therefore, volume fluctuations inside centrality classes are different.
Moreover, a cross-correlation between ZDC with the central-barrel region is
also not the same as in case of the V0,
and it is known also that resolution of the ZDC
worsens towards more peripheral collisions [9]. All these effects contribute to
b corr 𝑛--𝑛
. Therefore, in view of a dramatic dependence of FB multiplicity correlation strength on centrality class determination, theoretical interpretation of the experimental results
should be done with care.

#### 3. Forward-backward correlations between event-mean transverse momenta

Instead of multiplicities, correlations between event-mean
pT
have been studied
for the same FB window pair.
Figure figHIST2D_FB_CORR (a)
shows an event-by-event distribution of
pF¯
versus
pB¯
for centrality class 0–5% (centrality is determined by the V0 estimator).
For a linear regression analysis,
event-averaged values in the backward window
(
〈pB¯〉
) are calculated for each
pF¯
bin: panel (b) demonstrates this for several centrality classes of 5% width.
One may note that correlation functions are linear in narrow centrality classes,
therefore each function can be quantified by the correlation
strength
b corr pt-pt
, which corresponds to the slope of the linear fit line.
Note, that for too wide classes the linearity of the
correlation functions may be broken: an extreme case is shown in
panel (c) for the 0–80% class.
Therefore, to interpret the meaning of
b corr pt-pt
,
it is important to look at the correlation functions themselves.

##### Figure 2

Mean
pT
in Backward window
vs
mean
pT
in Forward window (with corresponding profile) in class 0–5% (a),
profiles with linear fits for several centrality classes of 5% width (b)
and profile for wide centrality class 0–80% (c). Centrality is determined by the V0 detector.

(a) a,

(b) a,

(c) a,

The centrality dependence of
b corr pt-pt
is presented in
Figure figptpt_centr_dep_cWidths (a).
Since mean-
pT
is an intensive observable,
the results are independent of volume fluctuations
and therefore are robust to changes of the centrality class width, if the classes are not too wide (points
for 10, 5 and 2% classes are shown).
Moreover, different centrality estimators also provide consistent results
(panel b).
The small deviations in the centrality range 20–40% for the ZDC-based results
can be attributed to a reduced centrality resolution of the ZDC in this centrality range,
mentioned above.
The correlation strength
b corr pt-pt
rises
from peripheral to mid-central and
drops towards central collisions.
This characteristic shape persists also at
s NN =5.02
TeV energy of Pb–Pb collisions (Figure figptpt_eta_gaps_energy, a).
Also, the same behavior is seen for windows of smaller width
δη=0.2
with different gaps between them (panel b): the results for
η gap =1.2
and
0.6
are on top
of each other, while values for adjacent FB windows (
η gap =0
, blue squares) are slightly higher due to short-range correlations. The short-range contribution is most pronounced for peripheral events and decreases
towards central events.

##### Figure 3

Dependence of
b corr pt-pt
on centrality
for classes of 10, 5 and 2% widths, determined by the V0 (a).
Results for centrality classes of 5% width determined
by the V0, ZDCvsZEM and CL1 estimators (b).

(a) a,

(b) a,

##### Figure 4

Centrality dependence of
b corr pt-pt
(a) at two energies of Pb–Pb collisions
s NN =
2.76 and 5.02 TeV,
and (b) for three
η
gaps between
F
and
B
windows
η gap =
1.2, 0.6 and 0.
Lines correspond to calculations with AMPT event generator.
Centrality by the V0 detector.

(a) a,

(b) a,

The positive values of
b corr pt-pt
seen above
are related to the event-by-event fluctuations of the
event-averaged transverse momentum of particles. The origin of these mean-
pT
fluctuations can be attributed, for example,
to event-by-event fluctuations of the initial size of the fireball,
which is reflected in pressure gradients
at a later stage of a collision [10].
What is more difficult, however,
is to capture correctly the *shape* of the centrality dependence of the
b corr pt-pt
.
Qualitatively,
the same shape was obtained in the Monte Carlo implementation of the
string fusion model [11],
where fluctuations of initial densities provide different
patterns of overlapping strings, and changes of tension of fused strings affect
pT
of particles emitted when the strings break.

Figure figptpt_models_HIJING_AMPT compares
the FB mean-
pT
correlation strength with
calculations in Monte Carlo generators. HIJING demonstrates weak correlations with no dependence on centrality.
Small positive values of
b corr pt-pt
in this generator can be attributed to back-to-back jets,
which hit both
F
and
B
windows.
AMPT generally reproduces the shape of the centrality dependence,
however, it does not reproduce the magnitude.
Switching off rescattering or string melting mechanisms
leads to a rise of
b corr pt-pt
, the underlying reasons for this
need to be investigated further.
Calculations of the mean-
pT
correlations in some other event generators are given in
[12].

##### Figure 5

Correlation strength
b corr pt-pt
between the FB windows (-0.8, -0.4) and (0.4, 0.8)
in comparison with event generators:
HIJING (blue solid line) and tunes of the AMPT (dashed lines).

#### 4. Summary

In summary,
it is shown that the strength of forward-backward correlations
between multiplicities
heavily depends on the centrality determination procedure
(type of centrality estimator and class width),
therefore, any physics conclusions should be made very carefully.
The FB correlations between mean-
pT
have been
measured for the first time in ALICE in Pb–Pb collisions.
Correlations of this type
are robust against volume fluctuations and thus the centrality determination methods,
and, therefore, provide higher sensitivity to the properties of the initial state and evolution of the medium created in A-A collisions.
The correlation strength rises from peripheral to mid-central and
drops towards central collisions.
This evolution with centrality is described by some models qualitatively, but not quantitatively.

#### Acknowledgements

This work is supported by the Russian Science Foundation, grant 17-72-20045.