Kavli Affiliate: Tom Melia
| First 5 Authors: Andrew J. Larkoski, Tom Melia, , ,
| Summary:
Despite being the overwhelming majority of events produced in hadron or heavy
ion collisions, minimum bias events do not enjoy a robust first-principles
theoretical description as their dynamics are dominated by low-energy quantum
chromodynamics. In this paper, we present a novel expansion scheme of the cross
section for minimum bias events that exploits an ergodic hypothesis for
particles in the events and events in an ensemble of data. We identify power
counting rules and symmetries of minimum bias from which the form of the
squared matrix element can be expanded in symmetric polynomials of the phase
space coordinates. This expansion is entirely defined in terms of observable
quantities, in contrast to models of heavy ion collisions that rely on
unmeasurable quantities like the number of nucleons participating in the
collision, or tunes of parton shower parameters to describe the underlying
event in proton collisions. The expansion parameter that we identify from our
power counting is the number of detected particles $N$ and as $Ntoinfty$ the
variance of the squared matrix element about its mean, constant value on phase
space vanishes. With this expansion, we show that the transverse momentum
distribution of particles takes a universal form that only depends on a single
parameter, has a fractional dispersion relation, and agrees with data in its
realm of validity. We show that the constraint of positivity of the squared
matrix element requires that all azimuthal correlations vanish in the
$Ntoinfty$ limit at fixed center-of-mass energy, as observed in data. The
approach we follow allows for a unified treatment of small and large system
collective behavior, being equally applicable to describe, e.g., elliptic flow
in PbPb collisions and the "ridge" in pp collisions.
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