Jet quenching and gluon to hadron fragmentation function in non-equilibrium QCD at RHIC and LHC

Abstract

Theoretical understanding of the observed jet quenching measurements at RHIC and LHC is challenging in QCD because it requires understanding of parton to hadron fragmentation function in non-equilibrium QCD. In this paper, by using closed-time path integral formalism, we derive the gauge invariant definition of the gluon to hadron fragmentation function in non-equilibrium QCD which is consistent with factorization theorem in non-equilibrium QCD from first principles.

Proof of factorization of $$\chi _{\text{cJ}}$$ χ cJ production in non-equilibrium QCD at RHIC and LHC in color singlet mechanism

“…This result in QED agrees with classical mechanics [41,49,50]. Hence we find that the infrared divergences at all orders in coupling constant due to the real photons'' emission from the light-like electron in quantum field theory can be studied by using the path integral formulation of the background field method of quantum field theory in the presence of pure gauge background field [1,33,34,51,52].…”

“…where the light-like gauge link or the light-like eikonal line in the fundamental representation of SU (3) is given by [1,33,34]…”

“…Now let us discuss the hadroproduction of v cJ from color singlet c c pair at high-energy colliders. If the factorization theorem is valid [1,33,34,[37][38][39][40][41][42][43][44][45][46] then the v cJ production from the color singlet c c pair at high energy colliders is given by…”

“…(32) [1,33,34]. Note that the path integral technique is suitable to study the properties of the non-perturbative quantities in QCD.…”

Correct definition of color singlet P-wave non-perturbative matrix element of heavy quarkonium production

“…Hence we find that since the light-like eikonal current produces pure gauge field, the study of infrared divergence due to soft photon (eikonal photon) emission due to the presence of light-like eikonal line can be simplified in quantum field theory by using pure gauge without modifying the finite value of the cross section. Since the light-like eikonal current produces pure gauge field in classical mechanics and in quantum field theory, the factorization of infrared divergence due to the presence of light-like eikonal line can be studied by using path integral formulation of the background field method of quantum field theory in the presence of pure gauge background field [1,[31][32][33].…”