Forward-backward multiplicity correlations in proton-proton col- lisions from several GeV to LHC energies

Forward-backward multiplicity correlations in pp collisions at LHC energies are studied with the quark-gluon string model. Comparison with experimental data and with model calculations for lower energies is performed. The model correctly reproduces the linear slope of the correlations, �nB(nF )� = a + bcorrnF , in the whole energy interval. Positive correlations arise because of mixing of sub-processes with different mean multiplicities. The increase of bcorr with rising collision energy is linked to the increase of the variety of sub-processes going via the soft and hard multi-Pomeron exchanges. For the events with fixed amount of Pomerons the correlation slope bcorr is shown to be essentially zero.


Introduction
The first observation of significant positive correlations between the multiplicity of charged particles emitted in forward and backward hemispheres in pp collisions at ISR energies was considered as evidence of long range correlations between the "clusters" of fragmenting system [1].This phenomenon has attracted a lot of attention, see e.g.[2][3][4][5][6][7][8] and references therein.Positive forward-backward (FB) correlations in multiplicity were found in hadronic interactions at energies from several GeV to √ s = 1.8 TeV [9][10][11][12].In contrast, no significant FB correlations were observed in e + e − annihilation at energies up to √ s = 93 GeV [13] and 133 GeV [14].It appeared soon that the FB multiplicity correlations possessed the following properties: -the linear dependence of the averaged multiplicity of charged particles emitted in forward (or backward) hemisphere on the multiplicity of charged particles emitted in the opposite hemisphere, i.e., �n B (n The slope parameter b corr is defined as where n F and n B represent multiplicities of charged particles in forward and backward hemispheres, respectively. -the correlations reveal positive slope b corr for particles from the central region |x F | < 0.1, whereas for particles from the fragmentation regions |x F | > 0.1 the slope is consistent with zero -the strength of the correlations increases with rising collision energy -for events with very high particle multiplicity the correlation strength is weakened.On a phenomenological level these features were explained by mixture of emitting clusters with different mean multiplicity [4].To provide a linear dependence given by Eq. ( 1) the clusters should obey the Poisson distribution [8].
We would like to present here our study of forward-backward multiplicity correlations within the quark-gluon string model (QGSM) [15] and its Monte Carlo version [16,17].The details of the model can be found in these Proceedings in [18].QGSM was successfully applied for the description of FB correlations in pp and pp collisions at p lab = 32 GeV/c [10], and recently in pp collisions at LHC energies 900 GeV ≤ √ s ≤ 13 TeV [19].Results of the both studies are presented below.

FB correlations in pp and pp interactions at intermediate energies
In [10] the FB multiplicity correlations were studied in both pp and pp collisions at p lab = 32 GeV/c.The experiments were carried out on the big bubble chamber "Mirabelle" (ITEP, Serpukhov). Figure 1 shows the �n F �(n B ) dependence of charged particles measured in inelastic and in nondiffractive pp and pp interactions.Calculations of QGSM are plotted onto the experimental results as well.The model correctly reproduces the data.One can see that the slope b corr of the distributions in pp collisions is steeper than that in pp collisions.For both reactions, the FB multiplicity correlations seem to be stronger in inelastic collisions compared to non-single diffractive (NSD) ones.
International Conference on New Frontiers in Physics (ICNFP 2016)   To present this more distinctly, we list the slope parameters in Table 1 for inelastic and NSD events.The data were also extracted for central ( For better understanding of the reason why the FB correlations in pp collisions are stronger at this energy than the FB correlations in pp collisions, we plot in Fig. 2 the set of diagrams employed in QGSM for treatment of both types of collisions at intermediate energies.Obviously, the variety of sub-processes in pp interactions is richer compared to that in pp ones, because, e.g., the planar diagrams (a) and annihilation diagrams (g)-(i) are absent in pp processes.Since more sub-processes with different mean multiplicities contribute to particle production in pp collisions, the correlation slope is steeper, i.e. b pp corr > b pp corr .Similarly, because of the lack of single diffraction diagrams the correlation strength in non-single diffractive (NSD) processes is smaller compared to that in inelastic ones.Figure 3 displays the FB correlations for different sub-processes shown in Fig. 2, namely, cylinder diagram, undeveloped cylinder, single diffraction, pp annihilation and planar diagram.Only the planar sub-processes demonstrate weak positive FB correlations, whereas the correlation slopes for cylinder and diffractive diagrams are slightly negative.
The cross section of annihilation process drops rapidly with rising energy of the collisions.Therefore, the slopes of FB multiplicity correlations in pp and pp interactions become similar after some collision energy threshold.The strength of the correlations continues to increase, as shown in Fig. 4.
Here QGSM calculations of FB correlations in pp interactions are displayed for energies ranging from √ s = 20 GeV to √ s = 14 TeV.Comparison with the UA5 data on pp collisions at √ s = 546 GeV and 900 GeV [3,11] demonstrates a good agreement between the model calculations and the experimental data.For all reactions the slope of the FB correlations remains almost linear.We have mentioned already the vanishing of annihilation diagrams, as well as other so-called pre-asymptotic diagrams, with the increase of collision energy.However, the only reason of enlargement of the correlation strength b corr in the model is the rise of the variety of different sub-processes with different mean multiplic-   ity.These sub-processes and their role in formation of FB multiplicity correlations at ultra-relativistic energies are discussed in 3.

FB correlations at LHC energies
The set of diagrams describing the pp interactions at ultra-relativistic energies is shown in Fig. 5.
The first two diagrams represent (a) the soft (multi)Pomeron exchanges and (b) processes going via the formation of hard Pomerons.Other diagrams deal with the processes of single diffraction, (c) and (d), and double diffraction, (e)-(g).The main contribution to particle multiplicity comes from the processes with soft and hard Pomeron exchanges.Their numbers increase with rising collision energy, as it can be seen in Fig. 6.This figure displays the relative amounts of soft and hard Pomerons in a single pp-event at energies √ s = 900 GeV, 2.76 TeV, 7 TeV and 13 TeV, respectively.At √ s = 900 GeV the number of soft Pomerons exceeds the number of hard Pomerons by factor 4, whereas at √ s = 13 TeV their ratio drops to 1.4.As it follows from Fig. 6, the maximum number of both soft and hard Pomerons in a single event gradually increases with collision energy.The variety of sub-processes containing all possible combinations of soft and hard Pomerons becomes more extensive.Since these processes have different mean multiplicities of produced hadrons, the strength of the FB correlations measured for the whole sample of events increases, as shown in Fig. 7.One can see that the FB correlations are not very strong at low multiplicity area, n ch ≤ 15.The slopes of the distributions are also becoming less steep after a certain multiplicity threshold.Figure 8 displays the �n B �(n F ) dependencies calculated in QGSM for pp events at √ s = 7 TeV which proceed only via the soft Pomeron exchanges.The FB correlations for the sub-processes with fixed amount of soft Pomerons, varying from 1 to 7, are also plotted in Fig. 8.It is worth noting that FB correlations within each of the selected sample of events have zero slope, although the charged particle multiplicity measured on event-by-event basis changes from few hadrons up to one hundred.Not all topologies contribute to event with very small and very big multiplicity.This circumstance leads to reduction of the correlation strength in both multiplicity intervals.
At LHC energies the FB correlations in pp interactions were studied by the ALICE [21] and ATLAS [22] Collaborations.The analysis is performed in terms of gaps in pseudorapidity, η gap , between the hadrons in forward and backward hemispheres, and widths of pseudorapidity bins, δη. Figure 9 presents the comparison of model calculations of the b corr as a function of δη at zero rapidity gap with the ALICE data for √ s = 900 GeV, 2.76 TeV and 7 TeV.The slope b corr increases with broadening of δη for all three energies.Note, that the strength of FB correlations drops with rising midrapidity gap [19].
ALICE Collaboration has also studied the FB correlations between different azimuthal sectors.Parameters of the study are as follows.The azimuthal angle of the sectors is ϕ = π/4 and the width of the bin is δη = 0.2.The data obtained for pp interactions at 900 GeV and 7 TeV are shown in Fig. 10 in comparison with the QGSM calculations.The correlations at √ s = 7 TeV are twice stronger than that at 900 GeV; other characteristics are pretty similar.

Conclusions
We apply the quark-gluon string model, based on Reggeon Field Theory, for the description of forward-backward multiplicity correlations in proton-proton collisions at ultrarelativistic energies.It is shown that positive FB correlations arise in QGSM because of addition of different sub-processes with different mean multiplicities.For the individual sub-processes, their �n B �(n F ) distributions are remarkably flat, although the event-by-event multiplicity can vary from few particles up to more than one hundred.
At c.m. energies about 10 GeV the number of diagrams describing pp collisions is larger than that for pp interactions.Therefore, FB correlations are stronger in pp case.At c.m. energies higher than 100 GeV the sets of diagrams for pp and pp collisions are similar.The further rise of the correlation strength occurs due to increasing number of soft and hard Pomerons allowed for a single event.
The correlation dependence is linear, �n B �(n F ) = a + b corr n F , for pp and pp collisions at all energies in question.However, for low and for very high multiplicities n F the slopes b corr are not so steep.Finally, the FB correlations take place mainly in the region |x F | < 0.1, whereas for |x F | > 0.1 the correlations are almost absent.

Figure 1 .
Figure 1.(a): Dependence �n F �(n B ) of charged particles in inelastic (solid circles) and nondiffractive (open circles) pp collisions at 32 GeV/c.Solid curve denotes the QGSM calculations.(b): The same as (a) but for pp interactions at 32 GeV/c.

Figure 2 .
Figure 2. Diagrams taken into account in QGSM in the modeling of pp and pp interactions at intermediate energies: (a) planar, (b) cylinder, (c) undeveloped cylinder, (d) binary, (e)-(f) single diffraction with low-mass and high-mass excitation, (g)-(j) annihilation diagrams.

Figure 5 .
Figure 5. Diagrams taken into account in QGSM in the modeling of pp interactions at ultrarelativistic energies: (a) multi-Pomeron exchange, (b) (semi)hard gluon-gluon interaction and soft Pomeron exchange, (c)-(d) single diffraction with high-mass and low-mass excitation, (e)-(f) double diffraction with low-mass and high-mass excitation, (g) central diffraction.

Table 1 .
Slope parameters b corr of the forward-backward correlations in inelastic and NSD pp and pp collisions at 32 GeV/c.