Deep inelastic scattering on the quark-gluon plasma

Abstract

We provide an interpretation of the structure functions of a thermal medium such as the quark-gluon plasma in terms of the scattering of an incoming electron on the medium via the exchange of a spacelike photon. We then focus on the deep-inelastic scattering (DIS) regime, and formulate the corresponding moment sum rules obeyed by the structure functions. Accordingly, these moments are given by the thermal expectation value of twist-two operators, which is computable from first principles in lattice QCD for the first few moments. We also show how lattice QCD calculations can be used to probe how large the photon virtuality needs to be in order for the Bjorken scaling of structure functions to set in. Finally, we provide the parton-model interpretation of the structure functions in the Bjorken limit and test its consistency. As in DIS on the proton, the kinematic variable x is proportional to the longitudinal momentum carried by the partons, however x ranges from zero to infinity. Choosing the parton momentum parametrization to be xT u where u is the fluid four-velocity and T its temperature in the rest frame, the parton distribution function for a plasma of non-interacting quarks is proportional to x log(1 + e−x/2).

Vacuum correlators at short distances from lattice QCD

“…As we discussed in some detail the OPE-based expansion of the electromagnetic-current correlator in a recent publication ( [30]), we largely refer to that for setting the notation and for the introduction of the main observables. More specifically, we make reference to the first few paragraphs of section 3 for the definition of the Wilson coefficients and of the tower of local twist-two operators, and to the beginning of section 3.1 for the operator mixing in the dimension-four sector.…”

“…(3.3) in ref. [30]) must be taken into account. To write explicitly the contribution from the dimension-four operators to NLO precision, we follow closely the sections 3 and 3.1 of ref.…”

“…To write explicitly the contribution from the dimension-four operators to NLO precision, we follow closely the sections 3 and 3.1 of ref. [30] and refer to those for any unexplained notation. Going back to eq.…”

“…As already pointed out in ref. [30] relative to the structure functions of the quark-gluon plasma, the free-theory prediction of eqs. (A.9), (A.10) is not recovered in the short-distance limit x 3 → 0, contrary to the intuition coming from the property of asymptotic freedom.…”

“…In this case, the expectation value of the dimension-four operator reads (see appendix B of ref. [30])…”