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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., Comment: 40 pages, 5 figures; v3: typos corrected, published version

In the QCD energy-momentum tensor $T^{\mu\nu}$, 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 $T^{\mu\nu}$ is not renormalized thanks to conservation of energy and momentum. We show that, through the renormalization, each of the quark and gluon parts of $T^{\mu\nu}$ receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly. We provide a procedure to derive such anomalous trace contribution for each quark/gluon part to all orders in perturbation theory, and obtain the corresponding explicit formulas up to three-loop order in the $\overline{\rm MS}$ scheme in the dimensional regularization. We apply our three-loop formulas of the quark/gluon decomposition of the trace anomaly to calculate the anomaly-induced mass structure of nucleons as well as pions. Another application of our three-loop formulas is a quantitative analysis for the constraints on the twist-four gravitational form factors of the nucleon, $\bar{C}_{q,g}$., Comment: 5 pages, 2 figures. Contribution to the 24th International Spin Symposium (SPIN2021). JPS Conference Proceedings

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, Japan

In the QCD energy-momentum tensor $T^{\mu\nu}$, 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 $T^{\mu\nu}$ 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 $T^{\mu\nu}$ receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly, $T^\mu_\mu= (\beta/2g)F^{\mu\nu}F_{\mu\nu}+ m (1+\gamma_m)\bar{\psi}\psi$, 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 added

We show that, in dimensional reguralization in the minimal subtraction scheme, the QCD trace anomaly can be unambiguously decomposed into two parts coming from the renormalized quark and gluon energy momentum tensors. We carry out this decomposition at the two-loop level. The result can be used to constrain the renormalization group properties of the nucleon's twist-four gravitational form factor $\bar{C}_{q,g}$., Comment: 13 pages

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., Comment: 20 pages, typos corrected, version published in Phys. Rev. D

Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is shown to be the exclusive pion-induced Drell-Yan process, $\pi^- p \to \mu^+ \mu^- n$, as demonstrated by recent theoretical advances on describing this process in terms of QCD factorization as the partonic subprocess convoluted with the nucleon GPDs and the pion distribution amplitudes, and by the feasibility study for its measurement via a spectrometer at the High Momentum Beamline being constructed at J-PARC in Japan. We also discuss the possible soft partonic mechanisms beyond the QCD factorization framework, and present an estimate of the soft mechanisms at J-PARC kinematics, making use of dispersion relations and quark-hadron duality. Realization of the measurement of the exclusive pion-induced Drell-Yan process at J-PARC will provide a new test of QCD descriptions of a novel class of hard exclusive reactions, and also offer the possibility of experimentally accessing nucleon GPDs at large timelike virtuality., Comment: 5 pages, 3 figures. Contribution to the proceedings of the XXV International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2017), 3-7 April 2017, University of Birmingham, UK. arXiv admin note: substantial text overlap with arXiv:1703.02190

Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is the exclusive pion-induced Drell-Yan process. We discuss recent theoretical advances on describing this process in terms of the partonic subprocess convoluted with the nucleon GPDs and the pion distribution amplitudes. Furthermore, we mention the feasibility study for measuring the exclusive pion-induced Drell-Yan process, $\pi^- p \to \mu^+ \mu^- n$, via a spectrometer at the High Momentum Beamline being constructed at J-PARC in Japan. We also point out the possible soft partonic mechanisms beyond the QCD factorization framework, which could give important contributions at J-PARC kinematics, and present an estimate of the soft mechanisms making use of dispersion relations and quark-hadron duality. Realization of the measurement of the exclusive pion-induced Drell-Yan process at J-PARC will provide a new test of QCD descriptions of a novel class of hard exclusive reactions. It will also offer the possibility of experimentally accessing nucleon GPDs at large timelike virtuality., Comment: 6 pages, 5 figures. To appear in proceedings of 22nd International Symposium on Spin Physics (SPIN 2016), University of Illinois, Champaign, Illinois, USA, September 25-30, 2016

Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is the exclusive pion-induced Drell-Yan process. In this paper, we discuss recent theoretical advances on describing this process in terms of nucleon GPDs and pion distribution amplitudes. Furthermore, we address the feasibility of measuring the exclusive pion-induced Drell-Yan process $\pi^- p \to \mu^+\mu^- n$ via a spectrometer at the High Momentum Beamline being constructed at J-PARC in Japan. Realization of such measurement at J-PARC will provide a new test of perturbative QCD descriptions of a novel class of hard exclusive reactions. It will also offer the possibility of experimentally accessing nucleon GPDs at large timelike virtuality., Comment: 35 pages and 16 figures. Replaced with published version. Added the journal reference and DOI

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 $G_T(x)$, which is the genuine counterpart of the transverse-spin quark distribution function $g_T(x)$ relevant to the transverse-spin structure function $g_2(x, Q^2)$ in the deep inelastic scattering. We show that $G_T(x)$ 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 $G_T(x)$ receives the three-gluon and quark-gluon correlation effects and discuss the operator product expansion for $G_T(x)$. We also discuss the relevance of the first moment of $G_T(x)$ 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) 229

We derive exact relations among the polarized gluon and three-gluon distributions in the transversely polarized nucleon which are relevant to single and double spin asymmetries in various hard processes. We also discuss the partonic decomposition of the transverse nucleon spin and point out a potential problem with frame-independence., Comment: 18 pages; v2: revised version, references added, to appear in JHEP

A new spectrometer system was designed and constructed at the secondary beam line K1.8BR in the hadron hall of J-PARC to investigate $\bar K N$ interactions and $\bar K$-nuclear bound systems. The spectrometer consists of a high precision beam line spectrometer, a liquid $^3$He/$^4$He/D$_2$ target system, a Cylindrical Detector System that surrounds the target to detect the decay particles from the target region, and a neutron time-of-flight counter array located $\sim$15 m downstream from the target position. Details of the design, construction, and performance of the detector components are described., Comment: 33 pages, 25 figures

We discuss the single transverse-spin asymmetry (SSA) to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive deep inelastic scattering, $e p^\uparrow \rightarrow e D X$. This contribution is embodied as a twist-3 mechanism in the collinear factorization, which is induced by purely gluonic correlation inside the transversely-polarized nucleon, in particular, by the three-gluon correlation effects. The complete formula for the corresponding SSA in the leading-order QCD is expressed in terms of the four independent gluonic correlation functions and reveals the five independent structures with respect to the dependence on the azimuthal angle for the produced $D$-meson. We present the numerical calculations of the SSA formula at the kinematics relevant to a future Electron Ion Collider., Comment: 16 pages, 7 figures

We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters, $\lambda_E$ and $\lambda_H$, which correspond to matrix elements representing quark-gluon three-body components in the $B$-meson wavefunction. We derive the sum rules for $\lambda_{E,H}$ calculating the new higher-order QCD corrections, i.e., the order $\alpha_s$ radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensates, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve the stability of the corresponding Borel sum rules and lead to the reduction of the values of $\lambda_{E,H}$. We also discuss the renormalization-group improvement for the sum rules and present update on the values of $\lambda_{E,H}$., Comment: 28 pages, 20 figures, version to appear in Nuclear Physics B

We discuss the single transverse-spin asymmetry (SSA) to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $e p^\uparrow \rightarrow e D X$. This contribution is embodied as a twist-3 mechanism in the collinear factorization, which is induced by purely gluonic correlation inside the transversely-polarized nucleon, in particular, by the three-gluon correlation effects. We derive the first complete formula for the corresponding SSA in the leading-order QCD, revealing the five independent structures with respect to the dependence on the azimuthal angle for the produced $D$-meson. Our result obeys universal structure behind the SSAs in a variety of hard processes. We present the numerical calculations of our SSA formula for the $D$-meson production at the kinematics relevant to a future Electron Ion Collider., Comment: 4 pages, 2 figures. To appear in the proceedings of the XIX International Workshop on Deep-Inelastic Scattering and Related Subjests(DIS2011), Newport News, USA, Apr.11-15, 2011

We derive a "master formula" for the contribution of the three-gluon correlation function in the nucleon to the twist-3 single-spin-dependent cross section for semi-inclusive deep-inelastic scattering, ep^\uparrow\to eDX. This is an extension of the similar formula known for the so-called soft-gluon-pole contribution induced by the quark-gluon correlation function in a variety of processes. Our master formula reduces the relevant interfering partonic subprocess with the participation of the three gluons to the Born cross sections for the \gamma^*g\to c\bar{c} scattering, which reveals the new structure behind the twist-3 single spin asymmetry and simplifies the actual calculation greatly. A possible extension to higher order corrections is also discussed., Comment: 23 pages, 4 figures. Final version to appear in Phys. Rev. D. Presentation changed slightly

We study the single spin asymmetry (SSA) induced by purely gluonic correlation inside a nucleon, in particular, by the three-gluon correlation functions in the transversely polarized nucleon, $p^\uparrow$. This contribution is embodied as a twist-3 mechanism in the collinear factorization framework and controls the SSA to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $ep^\uparrow \rightarrow eDX$. We define the relevant three-gluon correlation functions in the nucleon, and determine their complete set at the twsit-3 level taking into account symmetry constraints in QCD. We derive the single-spin-dependent cross section for the $D$-meson production in SIDIS, taking into account all the relevant contributions at the twist-3 level. The result is obtained in a manifestly gauge-invariant form as the factorization formula in terms of the three-gluon correlation functions and reveals the five independent structures with respect to the dependence on the azimuthal angle for the produced $D$ meson. We also demonstrate the remarkable relation between the twist-3 single-spin-dependent cross section and twist-2 cross sections for the $D$-meson production, as a manifestation of universal structure behind the SSA in a variety of hard processes., Comment: 8 pages, 2 figures. To appear in the proceedings of the 19th International Spin Physics Symposium (SPIN2010), Juelich, Germany, Sept.27 - Oct.2, 2010

As a possible source of the single transverse spin asymmetry, we study the contribution from purely gluonic correlation represented by the twist-3 ``three-gluon correlation" functions in the transversely polarized nucleon. We first define a complete set of the relevant three-gluon correlation functions, and then derive its contribution to the twist-3 single-spin-dependent cross section for the $D$-meson production in semi-inclusive deep inelastic scattering, which is relevant to determine the three-gluon correlations. Our cross-section formula differs from the corresponding result in the literature, and the origin of the discrepancy is clarified., Comment: 29 pages, 3 figures minor corrections; version to appear in Phys. Rev. D

The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the "quasilocal" kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate-space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation $t$ in terms of the DA at a lower renormalization scale $\mu$ with smaller interquark separations $zt$ ($z \leq 1$). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale $\sim \sqrt{m_b \Lambda_{\rm QCD}}$ for $t$ less than $\sim 1$ GeV^{-1}, using the recently obtained operator product expansion of the DA as the input at $\mu \sim 1$ GeV. We also derive the master formula, which reexpresses the integrals of the DA at $\mu \sim \sqrt{m_b \Lambda_{\rm QCD}}$ for the factorization formula by the compact integrals of the DA at $\mu \sim 1$ GeV., Comment: 19 pages, 4 figures; typos corrected, version to appear in Phys. Rev. D

We discuss the single-spin asymmetry in semi-inclusive DIS, $e p^\uparrow \to e \pi X$, based on the twist-3 mechanism in the collinear factorization relevant for the pion production with the large transverse-momentum. This updates our previous study by including, in particular, the contributions induced by the novel partonic subprocesses, and allows us to derive the entire formula for the corresponding single-spin asymmetry associated with a complete set of the twist-3 quark-gluon correlation functions in the transversely polarized nucleon. We discuss the correspondence with the results obtained by the transverse-momentum-dependent factorization relevant for the pion production with the low transverse-momentum., Comment: 5 pages, 2 figures. To appear in the proceedings of the XVII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2009), Madrid, Spain, 26-30 April, 2009

The $B$-meson light-cone distribution amplitude (LCDA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory (HQET) and is a building block of QCD factorization formula for exclusive $B$-meson decays. When the corresponding bilocal HQET operator has a light-like distance $t$ between the quark and antiquark fields, the scale $\sim 1/t$ separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat the bilocal HQET operator based on the operator product expansion (OPE), disentangling the singularities from the IR and UV regions systematically. The matching at the next-to-leading order $\alpha_s$ is performed in the $\overline{\rm MS}$ scheme with a complete set of local operators of dimension $d \le 5$, through a manifestly gauge-invariant calculation organizing all contributions in the coordinate space. The result exhibits the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This OPE yields the $B$-meson LCDA for $t$ less than $\sim 1$ GeV$^{-1}$, in terms of $\bar{\Lambda}= m_B - m_b$ and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive $B$ decays, $\lambda_B$, is also discussed., Comment: 7 pages, 1 figure; to appear in the proceedings of the International Workshop on Effective Field Theories: from the pion to the upsilon (EFT09), February 2-6, 2009, Valencia, Spain

We discuss the double-spin asymmetries in transversely polarized Drell-Yan process, calculating all-order gluon resummation corrections up to the next-to-leading logarithmic accuracy. This resummation is relevant when the transverse-momentum $Q_T$ of the produced lepton pair is small, and reproduces the (fixed-order) next-to-leading QCD corrections upon integrating over $Q_T$. The resummation corrections in $p\bar{p}$-collision behave differently compared with $pp$-collision cases, and are small at the kinematics in the proposed GSI experiments. This fact allows us to predict large value of the double-spin asymmetries at GSI, using recent empirical information on the transversity., Comment: 4 pages, 2 figures; to appear in the proceedings of the 18th International Symposium on Spin Physics (SPIN20008), October 6 - 11, 2008, Charlottesville, Virginia, USA

The longitudinal-transverse spin asymmetry $A_{LT}$ in the polarized Drell-Yan process depends on twist-3 quark distributions of nucleon. In addition to the contributions associated with the twist-3 operators, these distributions contain the "Wandzura-Wilczek (WW)" part, which is determined by a certain integral of twist-2 distributions. The recently obtained empirical information on the transversity allows a realistic estimate of the WW contribution to $A_{LT}$ for the polarized $p\bar{p}$ collisions. Our results indicate that rather large $A_{LT}$ ($\sim 10$%) can be observed in the proposed spin experiments at GSI, with novel pattern as a function of dilepton mass compared with $A_{TT}$ and $A_{LL}$., Comment: 4 pages, 2 figures; to appear in the proceedings of the 18th International Symposium on Spin Physics (SPIN20008), October 6 - 11, 2008, Charlottesville, Virginia, USA

We derive the complete twist-3 single-spin-dependent cross section for semi-inclusive DIS, $ep^\uparrow\to e\pi X$, associated with the complete set of the twist-3 quark-gluon correlation functions in the transversely polarized nucleon, extending our previous study. The cross section consists of five independent structure functions with different azimuthal dependences, consistently with the transverse-momentum-dependent (TMD) factorization approach in the low $q_T$ region. Correspondence with the inclusive DIS limit and comparison with the TMD approach are briefly discussed., Comment: 4 pages, 2 figures; to appear in the proceedings of the 18th International Symposium on Spin Physics (SPIN2008), October 6 - 11, 2008, Charlottesville, Virginia, USA