Quasi equilibrium state of expanding quantum fields and two-pion Bose-Einstein correlations in pp collisions at the LHC

Abstract

We argue that the two-particle momentum correlation functions of high-multiplicity p + p collisions at the LHC provide a signal for a ground state structure of a quasi equilibrium state of the longitudinally boost-invariant expanding quantum field which lies in the future light cone of a collision. The physical picture is that pions are produced by the expanding quantum emitter with two different scales approximately attributed to the expanding ideal gas in local equilibrium state and ground-state condensate. Specifically, we show that the effect of suppressing the two-particle Bose-Einstein momentum correlation functions increases with increasing transverse momentum of a like-sign pion pair due to different momentum-dependence of the corresponding particle emission regions.It is firmly established now that collective phenomena in relativistic heavy ion collisions are associated with hydrodynamics [1][2][3]. Surprisingly, similar collective phenomena have been observed recently in high-multiplicity p + p collisions at the CERN Large Hadron Collider (LHC) [4]. It is not clear however whether such collective phenomena can be attributed to hydrodynamic evolution like in A + A collisions [5,6]. Also, while there is some evidence that hydrodynamics can be successfully applied to describe flow-like features in high-multiplicity p + p collisions, see e.g. refs. [7-10] (for discussions on whether hydrodynamics is applicable in small systems see e.g. refs. [11,12]), till now there is no united description of one-particle momentum spectra and multi-particle momentum correlations in p + p collisions in any detail dynamical model.Many-particle correlations play an important role in the understanding of multiparticle production mechanisms. In particular, the correlation femtoscopy method (commonly referred to as femtoscopy, or HBT interferometry) uses momentum correlations of two identical particles at low relative momenta to extract information about the space-time evolution and properties of the expanding matter in high energy nucleon and nuclear collisions, for reviews see e.g. refs. [13][14][15][16][17][18][19]. Because in such collisions most of produced particles are pions, the Bose-Einstein correlations of two identical pions are usually analyzed. The measured Bose-Einstein correlations of particles with some fixed momentum of a particle pair are typically described by a function with two sort of parameters: the effective radius parameters R i (sometimes called "HBT radii"), which can be interpreted as mean (statistically averaged) distance between centers of particle emissions, and the "correlation strength" parameter λ, the latter is also called the incoherence or chaoticity parameter. The interpretation of the latter is not unambiguous, because under the real experimental conditions λ-parameter can be affected by particle misidentifications, decays of long-lived resonances 1 , and non-Gaussian features of the particle distributions. Practically, the values of λ-parameter obtained fitting experimental data are moment...

Relativistic quantum fluid with boost invariance

“…In this work, we extend the results of Ref. [11] and study the stress-energy tensor with longitudinal boost-invariant symmetry. We find that, even for the simplest case of a free scalar field, there are relevant quantum corrections related to its renormalization by subtraction of the vacuum expectation value.…”

“…This symmetry and the solution found in Ref. [11] also offers a special opportunity to explore in detail some essential features of quantum relativistic hydrodynamics in a non-equilibrium arXiv:2102.09016v1 [hep-th] 17 Feb 2021 situation and, in particular, to determine the pure quantum corrections to classical hydrodynamics and kinetic equations, including those to the stress-energy tensor and to the entropy current. In other words, this solution provides a benchmark test of a relativistic quantum fluid.…”

“…Indeed, it can be shown that if the subgroup G transform Σ(τ 0 ) into itself and if the fields β and ζ are also symmetric under G, namely they fulfill Eqs. (9) or (11), this is the case. Indeed, by definition, ρ LE (τ ) is the solution of maximizing a function which is invariant under any unitary transformation, the entropy, with the constraint (4).…”

“…A very interesting feature of a relativistic quantum fluid with the four-temperature field (12) is that the spectrum of Π(τ 0 ), and particularly the lowest-lying eigenvector, the Π vacuum, may depend on τ , as it is clear from Ref. [11]. This τ -dependent vacuum |0 τ is in general also different from the vacuum of a quantum field theory -even for free fields -in flat space-time obtained by quantizing in Cartesian coordinates, the so-called Minkowski vacuum |0 M .…”

“…Beyond this approximation, quantum corrections appear, which have been estimated by means of a perturbative expansion only in the global-equilibrium case [10]. Recently, S. Akkelin [11,12] has derived an exact solution of a particular non-equilibrium problem, a free neutral scalar field with the density operator:…”