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two - particle correlations in azimuthal angle and pseudorapidity ( @xmath10 ) is an valuable tool to study the space - time dynamics of the heavy ion collisions .
one important recent result is the observation of the long - range ridge correlation in @xmath3 and @xmath1 collisions , with a magnitude comparable to those observed in pb+pb collisions at similar multiplicity  @xcite .
there are presently significant debates on the origin of the apparent collectivity in small collision systems , whether this is a final state effect signifying a qgp - like matter or this is a initial state effect associated with strong qcd field .
to clarify the situation , it is crucial to understand the nature of the sources of particle production that seed these long - range collective ridges : what are these sources made of and how many ?
what are their sizes and distribution in the transverse direction ?
forward - backward ( fb ) multiplicity correlation provides a handle on these questions . due to quantum fluctuations of the nuclear wavefunction ,
the number of colliding objects , participating nucleons or in general colliding partons , in the target and those in the projectile are not the same on the event - by - event ( ebye ) basis  @xcite .
this asymmetry leads to correlation of particles with large pseudorapidity separation ( long - range correlations or lrc ) .
the colliding objects also serve as the sources for particle production which drive the transverse flow dynamics : the eccentricity of a collision depends on the distribution of the sources in the transverse plane , and it usually decreases with the number of sources @xmath11 as @xmath12 . therefore measuring the lrc also provides important information on the initial condition for the transverse collective dynamics in @xmath3 , @xmath1 and pb+pb collisions  @xcite .
many previous studies in this direction are based on fb correlations of particle multiplicity in two @xmath10 ranges symmetric around the centre - of - mass of the collision system .
this study is based on measuring a simple 2-d correlation function in @xmath10  @xcite : @xmath13 where @xmath14 is the multiplicity density distribution in a single event and @xmath15 is the average distribution for a given event - multiplicity class .
the correlation function is directly related to a single - particle quantity @xmath16 , which characterizes the fluctuation of multiplicity in a single event relative to the average shape of the event class .
the @xmath17 is constructed using the usual event - mixing method , and a renormalization procedure is used to remove the residual centrality dependence in @xmath18 , with the resulting correlation function denoted by @xmath19  @xcite .
figure  [ fig:1 ] shows the @xmath16 in three typical pb+pb events in the 10 - 15% centrality interval  @xcite .
the apparent non - uniform structures reflect both the statistical fluctuations and dynamical fluctuations of interest .
the advantage of the correlation function is that the statistical fluctuations natrually drop out after the averaging ( eq .  [ eq:1 ] ) and only the dynamical fluctuations remain .
the multiplicity distributions of three typical events in 15-20% centrality interval .
they are divided by the average distribution of all events in the same centrality interval .
the dashed lines indicate fits to a third - order polynorminal function . taken from ref .
@xcite . ]
r0.45     the @xmath20 is measured in @xmath21=2.76 tev pb+pb , @xmath22=5.02 tev @xmath1 and @xmath2=13 tev @xmath3 collisions , using the atlas detector  @xcite .
events are classified according to the total number of reconstructed charged particles , @xmath23 , with @xmath6 and transverse momentum @xmath7 gev .
the magnitudes of the fb fluctuations are compared for the three systems at similar event multiplicity . as shown by fig .
[ fig:2 ] , the range of @xmath23 distribution is much broader in pb+pb collisions than that in @xmath1 collisions which in turn is much broader than that in the @xmath3 collisions .
therefore , the probability for events with large @xmath23 in @xmath3 collisions is much smaller than that in pb+pb collisions .
one interesting question is whether the long - range multiplicity correlation is controlled by @xmath23 similar to the ridge phenomena or it also depends on other quantities .
figure  [ fig:3 ] shows charge dependent pb+pb correlation functions in @xmath24 multiplicity range .
the correlation functions show a broad peak along @xmath25 associated with short - range correlations ( src ) , and a depletion at large @xmath26 associated with lrc .
the src reflects correlations within the same source , while the lrc reflects fb - asymmetry of the number of sources .
the magnitude of src differs by more than factor of three between same - charge and opposite - charge pairs , while the lrc are nearly identical between the two charge combinations .
based on this , a data - driven method was developed to separate the src from lrc .
the resulting src denoted by @xmath27 and lrc denoted by @xmath28 are shown in the middle and right columns , respectively .
the src extends nearly @xmath29 in @xmath30 independent of @xmath31 , and its magnitude is quantified by : @xmath32 the saddle - like shape of the lrc is found to be well approximated by : @xmath33 suggesting that the dynamical fluctuation of @xmath16 is linear in @xmath10 .
the pb+pb correlation function @xmath34 ( left column ) , its short - range component ( middle column ) and long - range component ( right column ) in @xmath24 multiplicity range for opposite - charge pairs ( top ) and same - charge pairs ( bottom ) .
taken from ref .
@xcite.,title="fig : " ] +   the pb+pb correlation function @xmath34 ( left column ) , its short - range component ( middle column ) and long - range component ( right column ) in @xmath24 multiplicity range for opposite - charge pairs ( top ) and same - charge pairs ( bottom ) . taken from ref .  @xcite.,title="fig : "
]    figure  [ fig:4 ] compares the strength of src in terms of @xmath35 and lrc in terms of @xmath36 between the three collision systems as a function of @xmath37 ( the efficiency corrected @xmath23 ) .
all distributions follow a simple power law dependence on @xmath37 .
however , the magnitude of src is much stronger in @xmath3 collisions than in pb+pb collisions ; in contrast the lrc signal is found to be similar between the three collision systems .
this is a nontrivial result as the distribution of @xmath37 as well as the sizes of the overlap region are very different between the three collision systems .
the estimated magnitude of the src @xmath38 ( left panel ) and lrc and @xmath36 ( right panel ) as a function of @xmath37 for all - charge pairs in pb+pb ( solid circles ) , @xmath1 ( open circles ) and @xmath3 ( open squares ) collisions . taken from ref .
@xcite . ]    the strength of the src and lrc is related to the number of sources @xmath11 contributing to the final multiplicity @xmath37 , which is the sum of the number of sources from the projectile and target nucleon or nucleus , @xmath39 .
the lrc is expected to be related to the asymmetry between @xmath40 and @xmath41 : @xmath42 .
the sources may be consists of participating nucleons @xmath43 , sub - nucleonic degrees of freedom such as the fragmentation of scattered partons , or resonance decays . in an independent cluster model scenario
@xcite , each source emits the same number of pairs and the number of sources follows a poisson distribution . in this picture , the strength of src and lrc should scale approximately as the inverse of the number of sources .
therefore , assuming @xmath44 , the @xmath38 and @xmath36 in fig .
[ fig:4 ] are expected to follow a simple power - law function in @xmath37 : @xmath45 a power index that is less than 0.5 , @xmath46 , would suggest that @xmath11 grows slower than @xmath23 , and vice versa .    to test this idea , the data in fig .
[ fig:4 ] are fit to a power - law function : @xmath47 .
the extracted power index values are summarized in table  [ tab : fit ] .
the values of @xmath48 for src are found to be smaller for smaller collision systems , they are close to 0.5 in pb+pb collisions and are significantly smaller than 0.5 in @xmath3 collisions .
in contrast , the values of @xmath48 for @xmath36 agree within uncertainties between the three colliding systems and are slightly below 0.5 .
.[tab : fit ] the power index and associated total uncertainty from a power - law fit of the @xmath37 dependence of @xmath38 and @xmath36 . taken from ref .
@xcite . [ cols="^,^,^,^",options="header " , ]
two - particle pseudorapidity correlations are measured in @xmath21 = 2.76 tev pb+pb , @xmath21 = 5.02 tev @xmath1 and @xmath2 = 13 tev @xmath3 collisions .
the correlation function @xmath20 is measured using charged particles in the pseudorapidity range @xmath4 with transverse momentum @xmath5 gev , and is decomposed into a short - range component ( src ) and a long - range component ( lrc ) .
the src is centered around @xmath25 with a width of 1 - 2 units , while lrc has an approximate functional form @xmath8 .
the magnitudes of the src and lrc are compared between the three collision systems as a function of @xmath37 .
large differences are observed for the src , but the strength of the lrc agrees within @xmath4920% at the same @xmath37 .
the @xmath37 dependences of both src and @xmath9 follow an approximate power - law shape .
the power index for @xmath9 is approximately the same between the three collision systems .
in contrast , the power - law index for the src is smaller for smaller collision systems .
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two - particle pseudorapidity correlations are measured in @xmath0  =  2.76  tev pb+pb , @xmath0  =  5.02  tev @xmath1 and @xmath2  =  13 tev @xmath3 collisions  @xcite . 
 correlation function is measured using charged particles in the pseudorapidity range @xmath4 with transverse momentum @xmath5 gev , and it is measured as a function of event multiplicity , defined by number of charged particles with @xmath6 and @xmath7 gev . the correlation function is decomposed into a short - range component ( src ) and a long - range component ( lrc ) . 
 the src differs significantly between the opposite - charge pairs and same - charge pairs , and between the three collision systems at similar multiplicity . 
 the lrc is described approximately by @xmath8 in all collision systems over the full multiplicity range . 
 the values of @xmath9 are consistent between the opposite - charge and same - charge pairs , and are similar for the three collision systems at similar multiplicity . 
 the values of @xmath9 and the magnitude of the src both follow a power - law dependence on the event multiplicity .    
 heavy ion , pseudorapidity correlation , short - range correlation , long - range correlation