arXiv subjects

S. Kumano

Publications and source records attributed to S. Kumano.

At least 19 recordsLinked to original sources

arXiv2026

Tensor-polarized parton distribution functions of the deuteron by a convolution model

Tensor-polarized parton distribution functions (PDFs) are calculated for the deuteron by using a convolution formalism, where the tensor-polarized PDFs are given by the corresponding nucleon's unpolarized PDFs convoluted with the tensor-polarized nucleon momentum distribution in the deuteron. These distributions are obtained at $Q^2=2.5$ GeV$^2$ in order to compare with the tensor-polarized PDFs which were determined by HERMES $b_1$ data. The obtained distributions are very different from the ones determined from the HERMES data, which indicates further studies are needed to clarify the difference, possibly by considering a new mechanism beyond the simple bound system of a proton and a neutron. The obtained PDFs $\delta_T q $ and $\delta_T \bar q$ are converted to the PDFs of the Trento convention $f_{1LL}^{\, q}$ and $f_{1LL}^{\, \bar q}$, and they are used for estimating the twist-3 PDFs $f_{LT}^{\, q}$ and $f_{LT}^{\, \bar q}$ by using a Wandzura-Wilczek-like relation. Because deep-inelastic-scattering experiments are under preparation for structure functions with a tensor-polarized deuteron target at the Thomas Jefferson National Accelerator Facility, and a Drell-Yan experiment will be possible at hadron accelerator facilities, such as the Fermi National Accelerator Laboratory, the obtained tensor-polarized PDFs will be tested experimentally.

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arXiv2026

Twist-2 relations for the twist-3 tensor-polarized distribution function $f_{LT}$ of a spin-1 hadron by the operator-product-expansion method

In a spin-1 hadron, tensor-polarized parton distribution functions (PDFs) exist. The twist-2 function is $f_{1LL}$ and a twist-3 one is $f_{LT}$. Because an experiment is under preparation at the Thomas Jefferson National Accelerator Facility (JLab) to measure the cross section of electron-deuteron deep inelastic scattering with the tensor-polarized deuteron target, these PDFs need to be understood theoretically. Especially, measurements will be done in a relatively low-$Q^2$ region at JLab, so that twist-3 contributions could become sizable in the cross section. In a previous work, a twist-2 relation was derived for $f_{LT}$ in terms of $f_{1LL}$ by using a nonlocal operator, and it corresponds to the Wandzura-Wilczek (WW) relation between $g_1$ and $g_2$. In addition, another relation similar to the Burkhardt-Cottingham (BC) sum rule was obtained. It is known that a formal way to derive the WW relation and the BC sum rule is to use the operator product expansion (OPE) with local operators. In this work, the WW-like relation and the BC-like sum rule for $f_{LT}$ are derived by using the local OPE method as a reliable independent way to establish these relations.

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arXiv2026

Generalizing the Soffer Bound: Positivity Constraints on Parton Distributions of Spin-3/2 Particles

We derive the complete set of positivity bounds for the leading-twist parton distribution functions (PDFs) of a spin-3/2 hadron for the first time. This work generalizes the Soffer bound, a fundamental constraint for spin-1/2 nucleons, to quark and gluon distribution functions in higher-spin systems. Expressing the antiparton-hadron scattering amplitudes in terms of the PDFs and the spin density matrix, we establish the connections between the PDFs and the scattering amplitudes in the tensor product space of the parton and hadron spins. Moreover, we obtain the definitions of the PDFs in terms of the helicity amplitudes. Positive definiteness of the scattering amplitude matrix yields a set of inequalities that define the physically allowed parameter space for the helicity amplitudes and a set of constraints for the PDFs. The Cauchy-Schwartz inequality determines the constrains between the PDFs and generalized parton distributions.

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arXiv2026

Tensor-polarized parton distribution functions for spin-1 hadrons

Spin-1 hadrons contain different aspects of spin physics from the ones of the spin-1/2 nucleon because of the existence of tensor-polarized structure functions. In the charged-lepton deep inelastic scattering from a spin-1 hadron or nucleus, such as the deuteron, there are leading-twist structure functions $b_1$ and $b_2$. In addition, there exists a gluon transversity which does not exist in the spin-1/2 nucleon. In the deuteron, these observables could probe interesting dynamical aspects beyond a simple bound system of a proton and a neutron. In addition, there are recent theoretical studies on higher-twist distributions. Tensor-polarized deuteron experiments are now under preparation at the Thomas Jefferson National Accelerator Facility, so that the topic of polarized deuteron is expected to become one of exciting fields in hadron physics. This paper is a brief overview on the tensor-polarized parton distribution functions, including transverse-momentum-dependent parton distributions and fragmentation functions up to twist 4.

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arXiv2026

Nuclear effects on longitudinal-transverse structure function ratio in the deuteron

Nuclear modifications of the nucleon's structure function $F_2^N$ have been investigated mainly since the discovery of the EMC nuclear effect in 1983, and there were many experimental measurements from the deuteron to a heavy nucleus. Now, the details of the modifications of $F_2^N$ are known from small $x$ to large $x$. On the other hand, it is taken as granted that a nuclear modification does not exist for the longitudinal-transverse structure function ratio $R_N=F_L^N/(2xF_1^N)$. However, such a nuclear modification does exist theoretically. A nucleon in a nucleus moves in any space direction, which is not necessary the longitudinal direction along the virtual-photon momentum in charged-lepton scattering. Because of this transverse Fermi motion, the longitudinal and transverse structure functions mix with the mixture probability proportional to the nucleon's transverse-momentum squared $\vec p_T^{\,\, 2}/Q^2$. In this paper, the nuclear modifications are shown numerically for the deuteron by using a standard convolution description. The magnitude of the modifications is of the order of a few percent in the deuteron; however, they should be large in large nuclei. In handling high-energy nuclear data, such nuclear modifications need to be taken into account for a precise determination of physical quantities. Now, the longitudinal-transverse structure-function ratio and tensor-polarized experiments are under preparation for the deuteron at JLab. We hope that such effects will be confirmed experimentally for not only for the deuteron but also for larger nuclei.

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arXiv2025

First determination of fragmentation functions in an exotic-hadron candidate

In recent years, there are experimental reports on exotic-hadron candidates, which have different quark configurations from ordinary $q\bar q$ and $qqq$ constituents. However, it is not easy to confirm their exotic nature from global observables such as masses, spins, parities, and decay widths. At high energies, internal quark and gluon configurations could become more apparent because hadrons should be described by fundamental degrees of freedom of quarks and gluons in quantum chromodynamics. One of such possibilities is to use the fragmentation functions (FFs). In this work, accurate FFs of an exotic hadron candidate $f_0$(980) are determined for the first time by an global analysis of experimental data on $e^+ + e^- \to f_0 (980)+X$ with recent precise measurements of the Belle collaboration. From the global analysis, we found that their second moments have a relation $M_u = M_d \ll M_s \sim M_g $ for up-quark, down-quark, strange-quark, and gluon FFs. Furthermore, the function $D_s^{f_0}(z)$ is distributed in the larger-$z$ region in comparison with the functions $D_{u}^{f_0}(z)$, $D_{d}^{f_0}(z)$, and $D_g^{f_0}(z)$. These facts support that the $f_0 (980)$ has the $s\bar s$ configuration at high energies. This is a new finding that $f_0 (980)$ should be considered mainly as the $s\bar s$ state, which is different from our usual understanding as a tetraquark (or $K\bar K$) hadron from low-energy studies. Our results could indicate the transition of the internal configuration picture that $f_0 (980)$ looks like a $q\bar q$ state at high energies although it is described by tetra-quark or $K\bar K$ molecule state at low energies. It sheds light on a new direction in exotic hadron physics.

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arXiv2025

Tensor-polarized twist-3 parton distribution functions $f_{LT}(x)$ for the spin-1 deuteron by using twist-2 relations

Tensor-polarized twist-3 parton distribution functions (PDFs) $f_{LT}(x)$ are calculated for the spin-1 deuteron by using twist-2 relations, which are similar to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule in the spin-1/2 nucleon, together with tensor-polarized twist-2 PDFs $f_{1LL}(x)$. The PDFs are shown for $f_{LT}(x)$ at $Q^2 =2.5$ GeV$^2$, where the tensor-polarized PDFs $f_{1LL}(x)$ are provided. The $x$-dependence of $f_{LT}(x)$ is similar to $f_{1LL}(x)$, and the magnitude of $f_{LT}(x)$ is roughly of the order of $f_{1LL}(x)$. In experiments at the Thomas Jefferson National Accelerator Facility (JLab), higher-twist effects could be sizable because $Q^2$ values are not very large in comparison with the hadronic scale of 1 GeV$^2$. Therefore, the JLab experiments could provide a good opportunity to investigate the twist-3 distributions $f_{LT}(x)$ in addition to the twist-2 ones $f_{1LL}(x)$. Furthermore, these tensor-polarized PDFs could be investigated at future Electron-Ion Colliders (EICs) and hadron accelerator facilities such as the Fermi National Accelerator Laboratory (Fermilab), the Nuclotron-based Ion Collider fAcility (NICA), and the Large Hadron Collider (LHC).

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arXiv2025

Transversity Generalized Parton Distributions of $\Delta$ with the Diquark Spectator Model

We show quark transversity generalized parton pistributions (GPDs) of $\Delta^+$ isobar by using the diquark spectator model for the first time. First, this model is tested by electric charge, magnetic-dipole and axial charge form factors, and it is used for calculating the transversity GPDs $H^{qT}_{1,3,5,7}$ of $\Delta^+$. The quark transversity distribution $h_1$ is then obtained from the transversity GPDs in the forward limit. Then, helicity-flip amplitudes are shown numerically by using relations between the helicity amplitudes and the GPDs. Finally, by taking first moments of the GPDs, tensor form factors are obtained and we predict the tensor charge. Experimentally, $N$-$\Delta$ transition GPDs are investigated in deeply virtual Compton scattering and virtual meson-production processes, and generalized distribution amplitudes, which correspond to the $s$-channel GPDs, could be investigated by the two-photon processes $\gamma^* \gamma \to \Delta \bar\Delta$ at the electron-positron colliders. Therefore, the spin-3/2 $\Delta$ GPDs could become interesting quantities experimentally in future.

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arXiv2025

Existence of nuclear modifications on longitudinal-transverse structure-function ratio

It has been assumed that nuclear modification does not exist in the longitudinal-transverse structure-function ratio $R_N=F_L^N/(2xF_1^N)$ in lepton deep inelastic scattering. This assumption is widely used in obtaining structure functions of the "nucleon" from nuclear data such as the deuteron ones. However, nuclear modifications do exist theoretically at least in medium- and large-$x$ regions because nucleons in a nucleus move in any direction, which is not necessarily the longitudinal direction of the virtual-photon or weak-boson momentum in lepton scattering. Because of this transverse motion, the nucleon's transverse and longitudinal structure functions should mix with each other in nuclei with the mixture probability proportional to the nucleon's transverse momentum squared $\vec p_T^{\,\, 2}/Q^2$. In this work, numerical results are explicitly shown regarding such nuclear modifications in the deuteron. These nuclear modifications are important for determining precise structure functions of the nucleon. Furthermore, modifications of $R_N$ should be investigated also at small $x$ by the future electron-ion collider to find interesting gluon dynamics in nuclei. Hopefully, this nuclear effect of $R_N$ could be found by future experimental measurements at lepton accelerator facilities.

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arXiv2024

Parton distribution functions and fragmentation functions of spin-1 hadrons

Structure functions of the spin-1 deuteron will be investigated experimentally from the late 2020's at various facilities such as Thomas Jefferson National Accelerator Facility, Fermi National Accelerator Laboratory, nuclotron-based ion collider facility, and electron-ion colliders. We expect that a new high-energy spin-physics field could be created by these projects. In this paper, the current theoretical status is explained for the structure functions of spin-1 hadrons, especially on parton distribution functions, transverse-momentum dependent parton distributions, and fragmentation functions. Related multiparton distribution functions are also shown.

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arXiv2024

Transversity generalized parton distributions in spin-3/2 particles

The definitions of the quark and gluon transversity generalized parton distributions (GPDs) in spin-3/2 particles are obtained in the light-cone gauge. It is found that they contain 16 independent components for each parton. Their even or odd property is found in terms of skewness variable, and the odd transversity GPDs vanish in the forward limit. There are 16 amplitudes with helicity flip of quark or gluon. We conclude that all the amplitudes, unpolarized, polarized, and transversity amplitudes, have a common factor $F(\zeta)$ carrying all the complex part. Here, the variable $\zeta$ is the helicity difference $\zeta=(\lambda' -\lambda)-(\mu' - \mu)$ for the amplitude $\mathcal{A}_{\lambda' \mu',\lambda\mu}$. This kinematical factor is associated with the transfer of the orbital angular momentum in the quark- and gluon-spin-3/2 particle scattering amplitudes. We also derive another main physical quantity, transversity distribution, from the transversity GPDs in the forward limit for the spin-3/2 particles.

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arXiv2024

Pion-production cross sections in neutrino reactions for studying generalized parton distributions of the nucleon

Gravitational form factors of hadrons provide information on mass and pressure distributions in the hadrons, and they have been investigated by generalized parton distributions (GPDs). The GPDs also contain information on internal compositions of hadron spins. Understanding on the origin of hadron masses, pressures, and spins is an important topic not only in hadron physics but also as fundamental physics, and it should be clarified by the GPD studies. The spacelike and timelike GPDs have been measured at charged-lepton accelerator facilities, for example, by the virtual Compton scattering and the two-photon process, respectively. In this work, we show the $\pi^\pm$ and $\pi^0$ production cross sections in neutrino (antineutrino) reactions $\nu \,(\bar\nu) + N \to \ell + \pi + N'$ for measuring the GPDs of the nucleon by using the theoretical formalism of Pire, Szymanowski, and Wagner. The $\pi^\pm$-production cross sections are useful for determining gluon GPDs, whereas the $\pi^0$ production probes quark GPDs. In particular, we show the roles of the pion- and rho-pole terms, the contribution from each GPD term ($H$, $E$, $\tilde H$, $\tilde E$), the effects of the gluon GPDs $H_g$ and $E_g$, and the effects of the reaction energy on the neutrino cross sections. The $\pi^0$-production cross section is sensitive to the quark GPDs including the pion- and rho-pole GPD terms in the Efremov-Radyushkin-Brodsky-Lepage region. These cross sections could be measured at Fermilab in future. The neutrino GPD studies will play a complementary role to the projects of charged-lepton and hadron reactions for determining the accurate GPDs.

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arXiv2022

J-PARC hadron physics and future possibilities on color transparency

The J-PARC is a hadron-accelerator facility to provide secondary beams of kaons, pions, neutrinos, muons, and the others together with the primary proton beam for investigating a wide range of science projects. High-energy hadron physics can be studied by using high-momentum beams of unseparated hadrons, which are essentially pions, and also primary protons. In this report, possible experiments are explained on color transparency and generalized parton distributions (GPDs). These projects are complementary to lepton-scattering experiments at JLab, COMPASS/AMBER, and future electron-ion colliders. Because of hadron-beam energies up to 30 GeV, the J-PARC is a unique facility to investigate the transition region from the hadron degrees of freedom to the quark-gluon one. It is suitable for finding mechanisms of the color transparency. Such color-transparency studies are also valuable for clarifying factorization of hadron-production processes in extracting the GPDs from actual measurements. These studies will lead to the understanding of basic high-energy hadron interactions in nuclear medium and to clarifications on the origins of hadron spins, masses, and internal pressure mechanisms.

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arXiv2022

Possible studies on generalized parton distributions and gravitational form factors in neutrino reactions

Spacelike and timelike generalized parton distributions (GPDs) have been investigated in charged-lepton scattering and electron-positron collisions via deeply virtual Compton scattering and two-photon processes, respectively. Furthermore, we expect that hadron-accelerator-facility measurements will be performed in future. The GPDs will play a crucial role in clarifying the origins of hadron spins and masses in terms of quarks and gluons. It is also possible to probe internal pressure within hadrons for understanding their stability. Gravitational form factors of hadrons used to be considered as a purely academic subject because gravitational interactions are too weak to be measured in microscopic systems. However, due to the development of hadron-tomography field, it became possible to extract the gravitational form factors from the actual GPD measurements without relying on direct gravitational interactions. Neutrino reactions can also be used for GPD studies in future, for example, by using the Long-Baseline Neutrino Facility at Fermilab. The neutrino GPD measurements are valuable especially for finding the flavor dependence of the GPDs in a complementary way to the charged-lepton experiments. We give an overview of the GPDs and discuss possible neutrino GPD measurements using the single-pion production processes $ν+ N \to \ell^- + N' + π$ and $\barν+ N \to \ell^+ + N' + π$.

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arXiv2022

Equation-of-motion and Lorentz-invariance relations for tensor-polarized parton distribution functions of spin-1 hadrons

Structure functions of polarized spin-1 hadrons will be measured at various accelerator facilities in the near future. Recently, transverse-momentum-dependent and collinear parton distribution functions were theoretically proposed at twist 3 and twist 4 in addition to the twist-2 ones, so that full investigations became possible for structure functions of spin-1 hadrons in the same level with those of the spin-1/2 nucleons. Furthermore, twist-3 tensor-polarized multiparton distribution functions were also recently found for spin-1 hadrons. In this work, we show relations among the collinear parton- and multiparton-distribution functions for spin-1 hadrons by using equation of motion for quarks. These relations are valuable in constraining the distribution functions and learning about multiparton correlations in spin-1 hadrons.

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arXiv2022

Useful relations and sum rules for PDFs and multiparton distribution functions of spin-1 hadrons

There are two types of polarizations in spin-1 hadrons, and they are vector and tensor polarizations. The latter is a unique one since it does not exist in the spin-1/2 proton. The vector-polarized PDFs are the same for both the proton and spin-1 hadrons; therefore, we mainly investigate the unique PDFs in tensor-polarized hadrons. By using the operator product expansion, the twist-3 PDF $f_{LT}$ can be expressed by two terms in the same way with $g_T$ of the proton. The first term is determined by the twist-2 PDF $f_{1LL}$ (or $b_1$) which was measured by an experiment, and the second term is expressed by twist-3 quark-gluon distributions. If we neglect the higher-twist effects, $f_{LT}$ is simply given by $f_{1LL}$, and this relation is similar to the Wandzura-Wilczek relation of $g_T$. Furthermore, a new sum rule is also obtained for $f_{2LT}=2/3 f_{LT}- f_{1LL}$, which is analogous to the Burkhardt-Cottingham sum rule, in the tensor-polarized spin-1 hadrons. In future, these interesting relations could be studied at accelerator facilities, such as the Jefferson Laboratory, the Fermilab, the nuclotron-based ion collider facility in Russia, the proposed electron-ion colliders in US and China.

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arXiv2022

TMDs for spin-1 hadrons

Transverse-momentum-dependent parton distribution functions (TMDs) were investigated at the twists 3 and 4 for spin-1 hadrons in addition to the twist-2 ones. They were found by studying all the possible decomposition of a quark correlation function in a Lorentz-invariant way with the Hermiticity and parity invariance. The time-reversal invariance was not imposed for the TMDs due to an active role of gauge links; however, they were used for collinear parton distribution functions (PDFs) by integrating the TMDs over the transverse momentum. We found that 30 TMDs exist in the tensor-polarized spin-1 hadron at the twists 3 and 4, whereas there are 10 TMDs at the twist 2. We also showed that there are 3 collinear PDFs at the twists 3 and 4. The corresponding TMD fragmentation functions exist sat the twists 2, 3, and 4 simply by changing function names and variables. Since the time-reversal invariance is valid in the collinear PDFs, the integrals of time-reversal-odd TMDs over the transverse momentum should vanish. It leads to the sum rules $ \int d^2 k_T \, h_{1LT} (x, k_T^{\, 2}) = \int d^2 k_T g_{LT} (x, k_T^{\, 2}) = \int d^2 k_T h_{LL} (x, k_T^{\, 2}) = \int d^2 k_T h_{3LL}(x, k_T^{\, 2}) =0$ on the time-reversal odd TMDs at the twists 3 and 4.

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arXiv2022

Gluon transversity and TMDs for spin-1 hadrons

We explain a gluon transversity, transverse-momentum-dependent parton distribution functions (TMDs), and parton distribution functions (PDFs) for spin-1 hadrons. The gluon transversity exists in hadrons with spin more than or equal to one, and it does not exist in the spin-1/2 nucleons. Since there is no direct contribution from the nucleons, it is an appropriate quantity to probe an exotic component in the spin-1 deuteron beyond a simple bound system of the nucleons. We show how the gluon transversity can be measured at hadron accelerator facilities by the Drell-Yan process in addition to lepton-accelerator experiments. Next, possible TMDs are explained for the spin-1 hadrons at the twists 3 and 4 in addition to twist-2 ones by considering tensor polarizations. We found that 30 TMDs exist in the tensor-polarized spin-1 hadron at the twists 3 and 4 in addition to 10 TMDs at the twist 2. There are 3 collinear PDFs at the twists 3 and 4. We also indicate that the corresponding TMD fragmentation functions exist at the twists 3 and 4. Due to the time-reversal invariance in the collinear PDFs, there are new sum rules on the time-reversal odd TMDs. In addition, we obtained a useful twist-2 relation, a sum rule, and relations with multiparton distribution functions by using the operator product expansion and the equation of motion for quarks. These findings are valuable for experimental investigations on polarized deuteron structure functions in 2020's and 2030's at world accelerator facilities.

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