2,328 research outputs found
Three-loop formula for quark and gluon contributions to the QCD trace anomaly
In the QCD energy-momentum tensor , 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 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 receives a definite amount of anomalous trace
contribution, such that their sum reproduces the well-known QCD trace anomaly,
, 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.Comment: 26 pages, text improved and references adde
Transverse-spin gluon distribution function
We introduce the spin-operator representation for the gluon as well as quark
distribution functions as nucleon matrix element of the gauge-invariant bilocal
light-cone operators in QCD. To identify the relevant spin operators for quarks
and gluons in a unified manner, we rely on the transformation properties of the
quark and gluon fields in the coordinate space under the action of the
generator of the Lorentz group. In particular, this approach allows us to
define the transverse-spin gluon distribution function , which is the
genuine counterpart of the transverse-spin quark distribution function
relevant to the transverse-spin structure function in the deep
inelastic scattering. We show that is given by the sum of the
chromoelectric and chromomagnetic correlators associated with helicity-flip by
one unit, and the treatment of the latter correlator completes the
classification of the collinear parton distribution functions up to twist
three. We show that receives the three-gluon and quark-gluon
correlation effects and discuss the operator product expansion for . We
also discuss the relevance of the first moment of for the partonic
decomposition of the transverse nucleon spin.Comment: 6 pages, Proceedings of the XXII. International Workshop on
Deep-Inelastic Scattering and Related Subjects (DIS2014) 28 April - 2 May
2014, Warsaw, Poland. Reference: PoS DIS2014 (2014) 22
Operator Relations for Gravitational Form Factors
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 as the
``gravitational form factors'', 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 gravitational form factors for a
hadron, in particular, for a (pseudo)scalar hadron and for the nucleon. We
derive and clarify the relations satisfied by the gravitational form factors as
direct consequences of the symmetries and the equations of motion in QCD, and
connections to the generalized parton distributions. Our results reveal that
the gravitational form factors are related to the higher-twist quark-gluon
correlation effects inside the hadrons and also to QCD trace anomaly.Comment: 4 pages. To appear in the proceedings of 8th International Conference
on Quarks and Nuclear Physics (QNP2018), November 13-17, 2018, Tsukuba, Japa
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