Quark and gluon contributions to the QCD trace anomaly

Abstract

We show that, in dimensional reguralization in the minimal subtraction scheme, the QCD trace anomaly can be unambiguously decomposed into two parts coming from the renormalized quark and gluon energy momentum tensors. We carry out this decomposition at the two-loop level. The result can be used to constrain the renormalization group properties of the nucleon's twist-four gravitational form factorCq,g.

Revisiting the mechanical properties of the nucleon

“…We are only interested in the mechanical interpretation of particular components of the static EMT, defined in a quantum theory as the expectation value of the EMT operator in a specified state [9,10]. estimates in [76],C q (0) seems to be negative and sizeable [67,77], in agreement with the MIT Bag Model prediction [78] and recent Lattice estimates [6]. In contrast, it has been suggested based on the instanton picture of the QCD vacuum thatC q (0) at low scale may be small and positive [69].…”

Mechanical properties of particles

“…The quark form factorc Q (t) = ∑ a=u,d,s,...c a (t) = −c g (t), describes the non-conservation of EMT for individual quark and gluon pieces. This form factor is important to determine the pressure forces distribution in a hadron individually for quarks and gluons, and to study the forces between quark and gluon subsystems in hadrons ¶ (see recent discussions in [17,18,8,9]). The form factors in eq.…”

“…• The comprehensive perturbative QCD analysis of the trace anomaly for quark EMT was performed in Refs. [8,9]. This analysis is very important for the discussion of the nucleon mass decomposition in QCD.…”

Mass sum rules of the electron in quantum electrodynamics

“…Understanding the internal structure of hadrons is intimately related to understanding the origin of its mass from the mass and energies of the partons. Different mass decompositions (sum rules) related to the EMT have been proposed in the literature [21][22][23][24][25]. It has also been argued that photo-and electro-production of quarkonia close to the kinematical threshold can add to the understanding of the nucleon mass [26][27][28][29][30][31][32].…”

“…Here we explore the proposed mass decompositions by Ji [21], Lorcé [24], and Hatta, Rajan, Tanaka [25] for an electron in quantum electrodynamics (QED) by using perturbation theory up to one-loop order. Normally, it is not common to talk about a decomposition of the electron mass in QED.…”