Measurement of twoÂ-particle pseudorapidity correlations in Pb+Pb collisions at = 2.76 TeV with the ATLAS detector
Two-particle pseudorapidity correlations, measured using charged particles with 0.5 GeV and 2.4, from = 2.76 TeV Pb+Pb collisions collected in 2010 by the ATLAS experiment at the LHC are presented. The correlation function is measured for different centrality intervals as a function of the pseudorapidity of the two particles, and . The correlation function shows an enhancement along 0 and a suppression at large values. The correlation function also shows a quadratic dependence along the + direction. These structures are consistent with a strong forward-backward asymmetry of the particle multiplicity that fluctuates event to event. The correlation function is expanded in an orthonormal basis of Legendre polynomials, , and corresponding coefficients are measured. These coefficients are related to mean-square values of the Legendre coefficients, , of the single particle longitudinal multiplicity fluctuations: . Significant values are observed for the diagonal terms and mixed terms . Magnitude of is the largest and the higher order terms decrease quickly with increase in . The centrality dependence of the leading coefficient is compared to that of the mean-square value of the asymmetry of the number of participating nucleons between the two colliding nuclei, and also to the calculated from HIJING.
keywords:Heavy-ion collisions, forward-backward correlations, multiplicity fluctuations
Ultra relativistic heavy-ion collisions at RHIC and LHC create hot dense matter of deconfined quarks and gluons. The initial density distributions in the collisions fluctuate event to event and so a proper understanding of these fluctuations is necessary to describe and study the subsequent evolution of the produced matter. Study of the multiplicity correlations in the transverse direction and its fluctuations event by event have helped place important constraints on the transverse density fluctuations in the initial state phnx_vn:2011 (); atl_ebe:2013 (); atl_epc:2014 (). Multiplicity correlations in the longitudinal direction are sensitive to the initial density fluctuations in pseudorapidty (). These density fluctuations influence the early time entropy production and generate long-range correlations (LRC) which appear as correlations of the multiplicity of produced particles separated by large difference bia_bzd_zal:2012 (); bzd_tea:2013 (); jia_huo:2014 (). For example, EbyE differences between the number of nucleon participants in the target and the projectile may lead to a long-range asymmetry in the longitudinal multiplicity distribution bzd_tea:2013 (). Longitudinal multiplicity correlations can also be generated during the final state, such as from resonance decays, jet fragmentation and Bose-Einstein correlations, which are typically localized over a smaller range of difference, and are commonly referred to as short-range correlations (SRC).
Previous studies of the longitudinal multiplicity correlations have focussed on the forward-backward correlations of the particle multiplicity in two symmetric windows around the center of mass of the collision system bia_zal:2010 (); star_lrc:2009 (). Recently, a more general method which uses on the correlation function in the full , space has been proposed bzd_tea:2013 (); jia_rad_zho:2015 (). The orthogonal modes of the correlation function provides information on the orthogonal modes in EbyE single particle longitudinal multiplicity fluctuations and their magnitudes. The method had been applied to HIJING gyu_wan:1994 () and AMPT lin_ko_li_zha_pal:2005n () models to extract different shape components of the multiplicity fluctuation. In this proceedings, the correlation functions and the extracted magnitudes of the shape components of longitudinal multiplicity fluctuation, measured in Pb+Pb collisions at 2.76 TeV at the LHC using the ATLAS atl_inst:2008 () detector are presented.
2 Method and analysis procedure
The two particle correlation function in pseudorapidity is defined as vechvlad:2013 ():
where is the multiplicity density at in a single event and is the average multiplicity at for a given event class.
In principle, the averages in Eq. 1 should be calculated over event-classes defined using narrow centrality intervals, so that it contains only dynamical fluctuations that decouple from any residual centrality dependence of the average shape, , which would lead to a modulation of the projections of the correlation function along the or axes. But due to experimental limitations and finite statistics, this modulation from the change of average shape cannot be completely removed in as defined in Eq.1. However, these modulations can be removed by a simple redefinition of the correlation function jia_rad_zho:2015 ():
where , with being the maximum value of and . The resulting distribution is then renormalized such that the average value of in the and plane is one.
where and are the Legendre polynomials. The coefficients in the expansion are related to the magnitudes of the shape fluctuations in the EbyE distribution, where are the coefficients in the expansion of the single particle ratio, .
In the analysis the correlation functions are calculated in 5% centrality bins atl_cent:2012 (), defined using the transverse energy distribution in the ATLAS Forward Calorimeters (FCal). The analysis uses charged particle tracks reconstructed in the ATLAS inner detector to construct the correlation functions. The tracks are required to have 0.5 GeV and 2.4. The correlation function is constructed as the ratio of distributions of same-event pairs ( and mixed-event pairs (), . The events used for constructing the mixed event pairs are required to have similar total number of reconstructed tracks, , (matched within 0.5%) and -coordinate of the collision vertex (matched within 2.5 mm). The events are also required to be close to each other in time to account for possible time-dependent variation of the detector conditions. To correct and for detector inefficiencies, the tracks are weighted by the inverse of their tracking efficiencies. Remaining detector effects largely cancel in the same to mixed event ratio. The systematic uncertainties in the correlation function are evaluated to be in the range 28.5% depending on the centrality interval. These uncertainties are propagated into and other derived quantities, as the . More details of the analysis and systematic uncertainties along with a complete set of results can be found in this reference atl_lrc:2015 ().
The top panels of Figure.1 shows the correlation function in a mid-central and a peripheral event class. The correlation functions show a broad ”ridge-like” shape along , and a depletion in the large region around . The magnitude of the ridge structure is larger in peripheral event classes than in central event classes and could have a significant contribution from SRC. The depletion in the large region reflects the contribution from the LRC. The lower panels of Figure.1 shows the extracted coefficients for the two centrality classes. Non-zero values are observed for the diagonal terms, and also for mixed coefficients of the form . The first six diagonal terms and first five mixed terms are shown in the figure. Magnitude of is much larger than the other coefficients and the magnitude of higher order terms decrease quickly with increasing . The magnitudes of the coefficients are larger in the peripheral event classes. Also the magnitude of the higher order coefficients decrease less rapidly with increasing in the peripheral event class compared to the central event class. A significant contribution to , particularly the higher order terms, could be from short-range correlations which contribute to coefficients of all orders.
To further analyse the features of the correlation function, the correlation function is expressed in terms of and . The resulting correlation function, is then projected onto the () axis in narrow ranges of (). The shape of the projections along are more sensitive to the SRC as the SRC have a strong dependence on . The shape of the projections along on the other hand is more sensitive to the long-range correlations. If the first-order coefficient is dominating, then the correlation function in and can be written as
Since the SRC are expected to have a weak dependence on , a quadratic dependence of the projection, , on can be expected.
The projections, and , are shown in Figure.2 for different and slices respectively for the two centrality classes. Along the direction, the projections for all slices peak at = 0 and decrease quickly for 1, followed by a much weaker decrease beyond that. The quick decrease in 1 is consistent with the dominance of short-range correlations, which are mostly centred around 0. The weaker decrease at large could be related to the term in Eq. 4.
The projections along direction show a clear quadratic dependence on for all slices used for projection. This reflects the dominant component of the long-range correlation. The quadratic dependence is quantified by fitting the data with the function , where is a constant. The function fits the data quite well and are shown as solid lines in the figure. The values are extracted from the fit for each window used for projection.
Figure.3 shows the centrality dependence (in terms of the total number of participating nucleons, ) of the RMS value of the first order coefficient, . The values calculated from the Legendre expansion (Eq. 3) as well as those obtained from the fit to projections in Figure.2 are shown. The magnitude of increase towards peripheral event classes. The values from the fits are always smaller than those from direct calculation by 2 20% depending on the centrality interval and slice used for projection. This could be due to the contribution from the SRC to the values calculated using Legendre expansion.
Figure.3 also shows the centrality dependence of the RMS value of the asymmetry between number of forward going and backward going participants, defined as
where and denote the number of forward going and backward going participants respectively. The values are calculated from a Monte-Carlo Glauber model glaub:2007 (). The RMS values, , are scaled down by an arbitrary factor of 0.4 to approximately match the values. The centrality dependence of the RMS values of quite well match the centrality dependence of the RMS values of in the mid-central classes, but show a stronger decrease in the most central event classes and a weaker increase in the more peripheral event classes. The good match between the centrality dependence of the RMS values of and over a large centrality range suggest that modulations are driven by and is consistent with the observation in jia_rad_zho:2015 () that EbyE, is strongly correlated with . Also shown in the figure are values calculated from HIJING. The values from HIJING over-estimate the data except in the most peripheral event classes.
4 Summary and conclusions
Two-particle pseudorapidity correlation functions are measured as a function of centrality for charged particles with 0.5 GeV and 2.4, for Pb+Pb collisions at 2.76 TeV. The correlation function shows a ”ridge like” enhancement along the , and suppression at . These structures are further investigated by projecting the 2-D correlation function as function of and in narrow ranges of and respectively. The projections show strong contribution from the short-range correlations, particularly in the region 1, where the magnitude of the correlation decrease quickly with increase in . The distribution shows a clear quadratic dependence, characteristic of a forward-backward asymmetry induced by the asymmetry in the number of participating nucleons in the two colliding nuclei.
The correlation function is decomposed into a sum of products of Legendre polynomials those describe the different shape components, and the coefficients are calculated. Significant values are observed for and . Magnitude of is much larger than that of other coefficients and the magnitude of higher order terms decrease with increase in . These coefficients are observed to increase for peripheral collisions, consistent with the increase of the multiplicity fluctuation for smaller collision systems. The centrality dependence of is compared with the centrality dependence of the coefficient of the quadratic term in the fits to . The fit results are 220% smaller than that obtained from a Legendre expansion, which could be due to the stronger influence of short-range correlations on the values calculated directly from the Legendre expansion.
This research is supported by NSF under grant number PHY–1305037
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