Proton Mass Decomposition from the QCD Energy Momentum Tensor

Abstract

We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of N f = 2 + 1 DWF configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully non-perturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 33(4)(4)% and 37(5)(4)% respectively in the M S scheme at µ = 2 GeV. A quarter of the trace anomaly gives a 23 (1)(1)% contribution to the proton mass based on the sum rule, given 9(2)(1)% contribution from the u, d, and s quark scalar condensates. The u, d, s and glue momentum fractions in the M S scheme are in good agreement with global analyses at µ = 2 GeV.Introduction: In the standard model, Higgs boson provides the origin of quark masses. But how it is related to the proton mass and thus the masses of nuclei and atoms is another question. The masses of the valence quarks in the proton are just ∼3 MeV per quark which is directly related to the Higgs boson, while the total proton mass is 938 MeV. The percentage of the quark and gluon contributions to the proton mass can only be provided by solving QCD non-perturbatively, and/or with information from experiment. With phenomenological input, the first decomposition was carried out by Ji [1]. As in Refs. [1,2], the Hamiltonian of QCD can be decomposed asin the rest frame of the hadron state where M is the hadron mass, T µν is the energy momentum tensor of QCD with T 44 as its expectation value in the hadron, and the trace anomaly gives

Revisiting the mechanical properties of the nucleon

“…We set B q (0) ≈ −0.07 as suggested by the AdS/QCD correspondence [62,63] and which agrees in magnitude with recent estimates from Lattice QCD [7,64]. We also use the values C q (0) = d q 1 (0)/5 with d q 1 (0) ≈ −1.59 obtained in a dis- [65] which is close to a recent experimental extraction reported in [66],C q (0) ≈ −0.11 given by a phenomenological estimate [67] supported by a recent Lattice calculation [6], and D q (0) = −G q A (0) ≈ −0.33 obtained from a leading twist NNLO analysis by the HERMES collaboration [68]. The quark multipole masses F q with F = A, B, C,C are motivated 3 by results obtained in the chiral quark-soliton model [26,69], and D q = G q A is taken from a recent Lattice estimate [70].…”

“…The GFFs have been studied in a variety of theoretical approaches, see e.g. [41] and references therein, and also using Lattice QCD simulations [4][5][6][7][42][43][44].…”

“…Since the corresponding cross-sections are small, these processes are studied in high-luminosity setups like Jefferson Laboratory or COMPASS at CERN, and constitute an important aspect of the experimental program to be conducted in a near future in a U.S.-based Electron-Ion Collider [3]. The nucleon EMT is also intensively studied using Lattice QCD, see [4][5][6][7][8] for recent developments.…”

Pion constituent quark couplings strong form factors: A dynamical approach

“…This momentum dependent constituent quark mass emerges therefore by means of a different mechanism from the usual DChSB. This might be in agreement with recent calculations [30]. The resulting couplings and form factors therefore correspond to tree level pion-constituent quark vertices.…”

Complete matching for quasidistribution functions in large momentum effective theory

“…In the RI/MOM scheme, the renormalization of local composite operators is done by demanding that the counterterm cancels all loop contributions to their matrix element between off-shell external states at specific momenta [18,31] (for the application to quark and glue momentum fractions see Ref. [92].) For multiplicatively renormalizable nonlocal correlators such as the quasi-PDFs given above, the renormalization is similar but now one requires calculating the renormalization factors at each z.…”