Operator relations for gravitational form factors of a spin-0 hadron

Self Cite

In the QCD energy-momentum tensor T µν , the terms that contribute to physical matrix elements are expressed as the sum of the gauge-invariant quark part and gluon part. Each part undergoes the renormalization due to the interactions among quarks and gluons, although the total tensor T µν is not renormalized thanks to the conservation of energy and momentum. Recently it has been shown that, through the renormalization, each of the quark and gluon parts of T µν receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly, T µ µ = (β/2g)F µν F µν + m(1 + γ m )ψψ, and the corresponding formulas have been derived up to two-loop order. We extend this result to the three-loop order, working out all the relevant three-loop renormalization structure for the quark and gluon energy-momentum tensors in the (modified) minimal subtraction scheme in the dimensional regularization. We apply our three-loop formula of the quark/gluon decomposition of the trace anomaly to calculate the anomaly-induced mass structure of nucleons as well as pions. * kztanaka@juntendo.ac.jp

“…Before ending this section, we mention an immediate consequence of our three-loop results, combined with the exact operator identities in QCD, which read [10,46,47]…”

Section: Results At Three Loopsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Three-loop formula for quark and gluon contributions to the QCD trace anomaly

Tanaka

2019

Self Cite

“…The relations ofc Q (t) to twist-4 generalised parton distributions (GPDs) were derived in Refs. [5,6,9].…”

Section: Introductionmentioning

confidence: 99%

“…Using the QCD equation of motion one can easily relate (see e.g. [7][8][9]) the quark form factorc Q (t) to the matrix element of the flavour singlet twist-4 quark-gluon operator…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nucleon gravitational form factors from instantons: forces between quark and gluon subsystems

Polyakov

Son

2018

Using the instanton picture of the QCD vacuum we compute the nucleonc Q (t) form factor of the quark part of the energy momentum tensor (EMT). This form factor describes the non-conservation of the quark part of EMT and contributes to the quark pressure distribution inside the nucleon. Also it can be interpreted in terms of forces between quark and gluon subsystems inside the nucleon. We show that this form factor is parametrically small in the instanton packing fraction. Numerically we obtain for the nucleon EMT a small value ofc Q (0) ≃ 1.4 · 10 −2 at the low normalisation point of ∼ 0.4 GeV 2 . This smallness implies interesting physics picture -the forces between quark and gluon mechanical subsystems are smaller than the forces inside each subsystem. The forces from side of gluon subsystem squeeze the quark subsystem -they are compression forces. Additionally, the smallness ofc Q (t) might justify Teryaev's equipartition conjecture.We estimate that the contribution ofc Q (t) to the pressure distribution inside the nucleon is in the range of 1 − 20% relative to the contribution of the quark D-term.

A note on quark and gluon energy-momentum tensors

Ahmed

Chen

Czakon

2023

We discuss the constraints on quark and gluon energy-momentum tensors in QCD that follow from the requirement of Renormalisation-Group invariance of the traces of these operators. Our study covers the most general form of the latter traces, while the energy-momentum tensors themselves are only subjected to very mild constraints. We derive Renormalisation-Group equations for the two finite independent functions of the strong coupling constant and renormalisation scale of minimal subtraction which completely define the energy-momentum tensors. We demonstrate that previously proposed definitions of the renormalized quark and gluon energy-momentum tensors are special cases of our results assuming no explicit dependence on the renormalisation scale. Finally, we present $$ \overline{\textrm{MS}} $$ MS ¯ -renormalised quark and gluon energy-momentum tensors at four-loop order.