Twist-four gravitational form factor at NNLO QCD from trace anomaly constraints

TL;DR

This paper calculates the twist-four gravitational form factor $ar{C}_{q,g}$ at NNLO in QCD using trace anomaly constraints, providing model-independent results for nucleons and pions with high precision.

Contribution

It derives the NNLO quark/gluon trace anomaly formulas and applies them to determine the forward gravitational form factor $ar{C}_{q,g}$ for hadrons.

Findings

NNLO formulas for trace anomaly in QCD derived.

Model-independent predictions for nucleon and pion $ar{C}_{q,g}$.

Predictions for nucleon $ar{C}_{q,g}$ with a few percent accuracy.

Abstract

It is known that the trace anomaly in the QCD energy-momentum tensor $T^{\mu \nu}$ can be attributed to the anomalies for each of the gauge-invariant quark part and gluon part of $T^{\mu \nu}$, and their explicit three-loop formulas have been derived in the $\overline{\rm MS}$ scheme in the dimensional regularization. The matrix elements of this quark/gluon decomposition of the QCD trace anomaly allow us to derive the QCD constraints on the hadron's gravitational form factors, in particular, on the twist-four gravitational form factor, $\bar{C}_{q,g}$. Using the three-loop quark/gluon trace anomaly formulas, we calculate the forward (zero momentum transfer) value of the twist-four gravitational form factor $\bar{C}_{q,g}$ at the next-to-next-to-leading-order (NNLO) accuracy. We present quantitative results for nucleon as well as for pion, leading to a model-independent determination of the forward value of $\bar{C}_{q,g}$. We find quite different pattern in the obtained results between the nucleon and the pion. In particular, for the nucleon, the present information from experiment and lattice QCD on the nonperturbative matrix elements arising in our NNLO formula allows us to obtain a prediction of the forward value of $\bar{C}_{q,g}$ at the accuracy of a few percent level.