Particle momentum spectra, correlations, and maximum entropy principle in high-multiplicity collision events

TL;DR

Understanding multiplicity-selected observables in high-multiplicity $pp$ collisions at fixed energy, the paper develops a maximum-entropy quantum state at kinetic freeze-out to describe central-collision conditions. The approach yields a density operator $\rho$ with constraint $f(x,p)=\mathrm{Tr}[\hat f(x,p)\rho]$ and derives $\rho=\frac{1}{Z}\exp\left(- \int_{\sigma} d\sigma'_{\mu}\int d^{3}p' \frac{p'^{\mu}}{p'_{0}} \lambda(x',p') \hat f(x',p')\right)$, with $\lambda(x,p)\approx \ln \left[ 1+ \frac{1}{(2\pi)^3 f(x,p)} \right]$. By computing $p_{0}\frac{d^{3}\langle N\rangle}{d^{3}p}$ and the two-particle spectrum $\langle a^{\dag}(\mathbf p_{1})a^{\dag}(\mathbf p_{2}) a(\mathbf p_{1})a(\mathbf p_{2}) \rangle_{N}$, the paper links the observables to the Wigner function and the homogeneity-region structure, yielding a two-particle correlation function $C_{N}(\mathbf p_{1},\mathbf p_{2})$ that reflects source geometry. A key result is that, at very large multiplicities, the extracted radii become nearly independent of multiplicity, offering a quantum-consistent explanation for the observed constancy of HBT radii in high-multiplicity $pp$ data and guiding hydrodynamic-model interpretations.

Abstract

In this paper, we utilize the maximum entropy prescription to determine a quantum state of a small collision system at the kinetic freeze-out. We derive expressions for multiplicity-selected particle momentum spectra and correlation functions by applying a fixed particle number constraint to this state. The results of our analysis can be useful for interpreting the multiplicity dependence of the particle momentum spectra and correlations in high-multiplicity $pp$ collision events at a fixed LHC energy.