Renormalization of Gauge-Invariant Operators for the Structure Function g2(x, Q2)

Hadron spin physics is now one of the most active fields of physics. Especially in the last ten years, great progress has been made both theoretically and experimentally that has considerably improved our knowledge of the spin structure of nucleons. We review the nucleon's polarized structure functions from the viewpoint of factorization theorems and the gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton distribution functions, which are relevant to inclusive lepto- and hadro-production. We give a detailed analysis of these spin-dependent distribution functions at the twist-2 and twist-3 level, and present various properties and relations satisfied by the parton distributions, which can be derived directly from QCD. We emphasize unique features of higher twist distributions, and the role of the QCD equations of motion to derive their sensitivity to the quark-gluon correlation and their anomalous dimensions for Q^2-evolution.Comment: 58 pages, PTPTEX, 4 Postscript figures, psfig.sty and here.sty are required; typos fixed and minor changes in the text. Final version to be published in Prog. Theor. Phy

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“…* * ) An explicit calculation is given for the n = 3 case in Ref. 49), and the result is again consistent with the general argument in §4.…”

Section: The Structure Functionsupporting

confidence: 82%

Polarized Structure Functions in QCD

Kodaira

Tanaka

1999

Progress of Theoretical Physics

117

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“…Here, for simplicity, we do not explicitly show the mixing with the equations-of-motion operators as well as the BRST-exact operators; their matrix elements sandwiched between physical states vanish (see e.g., [4,[33][34][35]…”

Section: Operator Mixing In Renormalization Of Energy-momentum Tementioning

confidence: 99%

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

Tanaka

2019

J. High Energ. Phys.

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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

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“…using the gluon EOM, where j is summed over the transverse components, and the final form is given as an integral of the twist-three bilocal gluon correlation which could be eventually re-expressed by the gluonic three-body operators using the technique as in [37,[45][46][47].…”

Section: Unravelling In the Light-cone Gauge Fixingmentioning

confidence: 99%

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

Tanaka

2018

Phys. Rev. D

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The gravitational form factors for a hadron, the form factors for the hadron matrix element of the QCD energy-momentum tensor, not only describe the coupling of the hadron with a graviton, but also serve as unique quantities for describing the shape inside the hadron reflecting dynamics of quarks and gluons, such as the internal shear forces acting on the quarks/gluons and their pressure distributions. We consider the quark contribution to the gravitational form factors for a (pseudo)scalar hadron, and derive and clarify the relations satisfied by them as direct consequences of the symmetries and the equations of motion in QCD, and connections to the generalized parton distributions. Our results reveal the connections between the gravitational form factors and the higher-twist quark-gluon correlation effects inside the hadrons.

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Renormalization of Gauge-Invariant Operators for the Structure Function g2(x, Q2)

Cited by 17 publications

References 7 publications

Polarized Structure Functions in QCD

Polarized Structure Functions in QCD

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

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

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