arXiv subjects

S. Kumano

Publications and source records attributed to S. Kumano.

At least 37 records · Page 2Linked to original sources

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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arXiv2021

Twist-2 relation and sum rule for tensor-polarized parton distribution functions of spin-1 hadrons

Sum rules for structure functions and their twist-2 relations have important roles in constraining their magnitudes and $x$ dependencies and in studying higher-twist effects. The Wandzura-Wilczek (WW) relation and the Burkhardt-Cottingham (BC) sum rule are such examples for the polarized structure functions $g_1$ and $g_2$. Recently, new twist-3 and twist-4 parton distribution functions were proposed for spin-1 hadrons, so that it became possible to investigate spin-1 structure functions including higher-twist ones. We show in this work that an analogous twist-2 relation and a sum rule exist for the tensor-polarized parton distribution functions $f_{1LL}$ and $f_{LT}$, where $f_{1LL}$ is a twist-2 function and $f_{LT}$ is a twist-3 one. Namely, the twist-2 part of $f_{LT}$ is expressed by an integral of $f_{1LL}$ (or $b_1$) and the integral of the function $f_{2LT} = (2/3) f_{LT} -f_{1LL}$ over $x$ vanishes. If the parton-model sum rule for $f_{1LL}$ ($b_1$) is applied by assuming vanishing tensor-polarized antiquark distributions, another sum rule also exists for $f_{LT}$ itself. These relations should be valuable for studying tensor-polarized distribution functions of spin-1 hadrons and for separating twist-2 components from higher-twist terms, as the WW relation and BC sum rule have been used for investigating $x$ dependence and higher-twist effects in $g_2$. In deriving these relations, we indicate that four twist-3 multiparton distribution functions $F_{LT}$, $G_{LT}$, $H_{LL}^\perp$, and $H_{TT}$ exist for tensor-polarized spin-1 hadrons. These multiparton distribution functions are also interesting to probe multiparton correlations in spin-1 hadrons.

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arXiv2021

Transverse-momentum-dependent parton distribution functions for spin-1 hadrons

We show transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions by taking the decomposition of a quark correlation function in the Lorentz-invariant way with the conditions of Hermiticity and parity invariance. We found 30 new TMDs in the tensor-polarized spin-1 hadron at twists 3 and 4 in addition to 10 TMDs at twist 2. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtained new sum rules for the time-reversal-odd structure functions, $\bm{\int d^2 k_T g_{LT} = \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL}}$$\bm{=0}$, at twists 3 and 4. We also indicated that transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs can probe color degrees of freedom, so that they are valuable in providing unique opportunities for creating interdisciplinary physics fields such as gluon condensate, color Aharonov-Bohm effect, and color entanglement. We also found three new collinear PDFs at twists 3 and 4, and a twist-2 relation and a sum rule were derived in analogy to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule on the structure function $\bm{g_2}$.

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arXiv2021

Possible studies of gluon transversity in the spin-1 deuteron at hadron-accelerator facilities

Chiral-odd gluon transversity distribution could shed light on a new aspect of hadron physics. Although we had much progress recently on quark transversity distributions, there is no experimental measurement on the gluon transversity. The gluon trasversity does not exist in the spin-1/2 nucleons and it exists in the spin-1 deuteron. Therefore, it could probe new hadron physics in the deuteron beyond the basic bound system of a proton and a neutron because the nucleons cannot contribute directly. Here, we explain that the gluon transversity can be measured at hadron accelerator facilities, such as Fermilab and NICA, in addition to charged-lepton scattering measurements at lepton accelerator facilities by showing cross sections of the proton-deuteron Drell-Yan process as an example.

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arXiv2021

On the physics potential to study the gluon content of proton and deuteron at NICA SPD

The Spin Physics Detector (SPD) is a future multipurpose experiment foreseen to run at the NICA collider, which is currently under construction at the Joint Institute for Nuclear Research (JINR, Dubna, Russia). The physics program of the experiment is based on collisions of longitudinally and transversely polarized protons and deuterons at $\sqrt{s}$ up to 27 GeV and luminosity up to 10$^{32}$ cm$^{-2}$ s$^{-1}$. The SPD will operate as a universal facility for comprehensive study of unpolarized and polarized gluon content of the nucleon, using different complementary probes such as: charmonia, open charm, and prompt photon production processes. The aim of this work is to make a thorough review of the physics objectives that can potentially be addressed at the SPD, underlining related theoretical aspects and discussing relevant experimental results when available. Among different pertinent phenomena particular attention is drawn to the study of the gluon helicity, gluon Sivers and Boer-Mulders functions in the nucleon, as well as the gluon transversity distribution in the deuteron, via the measurement of specific single and double spin asymmetries.

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arXiv2021

Transverse-momentum-dependent parton distribution functions up to twist 4 for spin-1 hadrons

We show possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions in addition to the leading twist-2 ones by investigating all the possible decomposition of a quark correlation function in the Lorentz-invariant way. The Hermiticity and parity invariance are imposed in the decomposition; however, the time-reversal invariance is not used due to an active role of gauge links in the TMDs. Therefore, there exist time-reversal-odd functions in addition to the time-reversal even ones in the TMDs. We list all the functions up to twist-4 level because there were missing terms associated with the lightcone vector $n$ in previous works on the twist-2 part and there was no correlation-function study in the twist-3 and 4 parts for spin-1 hadrons. We show that 40 TMDs exist in the tensor-polarized spin-1 hadron in twists 2, 3, and 4. Some expressions of twist-2 structure functions are modified from previous derivations due to the new terms with $n$, and we find 30 new structure functions in twists 3 and 4 in this work. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtain new sum rules for the time-reversal-odd structure functions, $ \int d^2 k_T h_{LT}= \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL} =0$. In addition, we indicate that new transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs are rare observables to find explicit color degrees of freedom in terms of color flow, which cannot be usually measured because the color is confined in hadrons.

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arXiv2020

Deuteron polarizations in the proton-deuteron Drell-Yan process for finding the gluon transversity

The gluon transversity distribution in the deuteron is defined by the matrix element between linearly-polarized deuteron states, and it could be investigated in proton-deuteron collisions in addition to lepton-deuteron scattering. The linear polarization of photon is often used, whereas it is rarely used for the spin-1 deuteron. Therefore, it is desirable to express deuteron-reaction cross sections in term of conventional deuteron spin polarizations for actual experimental measurements. In this work, we investigate how proton-deuteron Drell-Yan cross sections are expressed by the conventional polarizations for finding the gluon transversity distribution. In particular, we show that the gluon transversity can be measured in the proton-deuteron Drell-Yan process by taking the cross-section difference between the deuteron spin polarizations along the two-transverse axes. Since the gluon transversity does not exist for the spin-1/2 nucleons, a finite gluon transversity of the deuteron could indicate an "exotic" mechanism beyond the simple bound system of the nucleons in the deuteron. Therefore, the gluon transversity is an interesting and appropriate observable to shed light on a new hadronic mechanism in nuclei.

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arXiv2020

Gluon transversity in polarized proton-deuteron Drell-Yan process

Nucleon spin structure functions have been investigated mainly by longitudinally-polarized ones for finding the origin of the nucleon spin. Other types of spin structure functions are transversely-polarized ones. In particular, quark transversity distributions in the nucleons have very different properties from the longitudinally-polarized quark distribution functions, especially in scaling violation, because they are decoupled from the gluon transversity, due to the fact that they are helicity-flip (chiral-odd) distributions. Such studies are valuable for finding not only the origin of the nucleon spin but also a signature on physics beyond the standard model, because the electric dipole moment of the neutron is proportional to the transversity distributions. Now, there is experimental progress on the quark transversity distributions; however, there is no experimental information on gluon transversity. In fact, the gluon transversity does not exist for the spin-1/2 nucleon due to the helicity-conservation constraint. One needs a hadron with spin more than or equal to one, so that the helicity flip of two units is allowed. A stable spin-1 target is, for example, the deuteron for studying the gluon transversity. In this work, we propose a possibility for finding the gluon transversity at hadron-accelerator facilities, especially in the proton-deuteron Drell-Yan process with the linearly-polarized deuteron, by showing theoretical formalism and numerical results. We show the dependencies of the Drell-Yan cross section on the dimuon-mass squared $M_{μμ}^{\,2}$, the dimuon transverse-momentum $q_T$, the dimuon rapidity $y$ in the center-of-momentum frame, and the magnitude of the gluon transversity $Δ_T g$.

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arXiv2019

Conference Summary of QNP2018

This report is the summary of the Eighth International Conference on Quarks and Nuclear Physics (QNP2018). Hadron and nuclear physics is the field to investigate high-density quantum many-body systems bound by strong interactions. It is intended to clarify matter generation of universe and properties of quark-hadron many-body systems. The QNP is an international conference which covers a wide range of hadron and nuclear physics, including quark and gluon structure of hadrons, hadron spectroscopy, hadron interactions and nuclear structure, hot and cold dense matter, and experimental facilities. First, I introduce the current status of the hadron and nuclear physics field related to this conference. Next, the organization of the conference is explained, and a brief overview of major recent developments is discussed by selecting topics from discussions at the plenary sessions. They include rapidly-developing field of gravitational waves and nuclear physics, hadron interactions and nuclear structure with strangeness, lattice QCD, hadron spectroscopy, nucleon structure, heavy-ion physics, hadrons in nuclear medium, and experimental facilities of EIC, GSI-FAIR, JLab, J-PARC, Super-KEKB, and others. Nuclear physics is at a fortunate time to push various projects at these facilities. However, we should note that the projects need to be developed together with related studies in other fields such as gravitational physics, astrophysics, condensed-matter physics, particle physics, and fundamental quantum physics.

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arXiv2019

Theoretical predictions on polarization asymmetry for Drell-Yan process with spin-one deuteron and tensor-polarized structure function $b_1$

We report recent theoretical progress on a polarization asymmetry in the proton-deuteron Drell-Yan process with a polarized-deuteron target and the tensor-polarized structure function $b_1$. Experimental measurements are possible at JLab for $b_1$ and at Fermilab for the Drell-Yan process. First, we show a theoretical estimate for the proton-deuteron Drell-Yan asymmetry in the Fermilab-E1039 experiment. We evolved tensor-polarized parton distribution functions, which explain existing HERMES $b_1$ data, at $Q^2=2.5$ GeV$^2$ to the $Q^2$ range of the Fermilab Drell-Yan measurements. Then, we predicted that the asymmetry is of the order of a few percent. The Drell-Yan experiment has an advantage to probe the tensor-polarized antiquark distributions, which were suggested by the HERMES experiment as a finite sum for $b_1$ ($\int dx b_1 (x) \ne 0$). Second, we predicted $b_1$ for the JLab experiment by the standard convolution model of the deuteron. Our theoretical $b_1$ structure function seems to be much different from the HERMES data. Furthermore, a significant distribution exists at very large $x$ ($>1$) beyond the kinematical limit $x_{max}=1$ for the proton. Because the standard deuteron-model estimate is much different from the HERMES data, there could be an interesting development as a new hadron-physics field if future JLab data will be much different from our conventional prediction.

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arXiv2019

Hadron tomography in meson-pair production and gravitational form factors

Generalized parton distributions (GPDs) are 3-dimensional (3D) structure functions for hadrons, and they are important for solving the proton spin puzzle including partonic orbital-angular-momentum contributions. The $s$-$t$ crossed quantities of the GPDs are generalized distribution amplitudes (GDAs). Here, $s$ and $t$ are Mandelstam variables. The GDAs can be studied in two-photon processes ($γ^* γ\to h \bar h$) at KEKB. A GDA describes the amplitude from quark and antiquark to the hadron pair $h \bar h$. In 2016, the Belle collaboration reported measurements for pion-pair production in electron-positron collision, and the pion GDAs were determined in this work by analyzing the Belle data. In our analysis, the pion GDAs are expressed by a few parameters, which are determined by analyzing the Belle data. From the obtained GDAs, form factors of energy-momentum tenor, so called gravitational form factors, are calculated for pion in the timelike region. The spacelike gravitational form factors are calculated from the timelike ones by using the dispersion relation. Then, the mass radius is calculated as 0.32-0.39 fm and the mechanical radius, defined by the slope of the form factor $Θ_1$, is calculated as 0.82-0.88 fm for the pion by using the spacelike form factors. This is the first study on gravitational form factors and radii of hadrons from actual experimental measurements. In 2019, the Belle II collaboration will start collecting data by the higher luminosity Super KEKB, so that the GDAs of other hadrons should also be investigated in the near future. Our studies are valuable in understanding 3D structure and gravitational properties of hadrons.

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arXiv2019

Hadron tomography by generalized distribution amplitudes in pion-pair production process $γ^* γ\rightarrow π^0 π^0 $ and gravitational form factors for pion

Hadron tomography can be investigated by three-dimensional structure functions such as generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions, and generalized distribution amplitudes (GDAs). Here, we extract the GDAs, which are $s$-$t$ crossed quantities of the GPDs, from cross-section measurements of hadron-pair production process $γ^* γ\rightarrow π^0 π^0$ at KEKB. This work is the first attempt to obtain the GDAs from the actual experimental data. The GDAs are expressed by a number of parameters and they are determined from the data of $γ^* γ\rightarrow π^0 π^0$ by including intermediate scalar- and tensor-meson contributions to the cross section. Our results indicate that the dependence of parton-momentum fraction $z$ in the GDAs is close to the asymptotic one. The timelike gravitational form factors $Θ_1$ and $Θ_2$ are obtained from our GDAs, and they are converted to the spacelike ones by the dispersion relation.From the spacelike $Θ_1$ and $Θ_2$, gravitational densities of the pion are calculated. Then, we obtained the mass (energy) radius and the mechanical (pressure and shear force) radius from $Θ_2$ and $Θ_1$, respectively. They are calculated as $\sqrt {\langle r^2 \rangle _{\text{mass}}} =0.32 \sim 0.39$ fm, whereas the mechanical radius is larger $\sqrt {\langle r^2 \rangle _{\text{mech}}} =0.82 \sim 0.88$ fm. This is the first report on the gravitational radius of a hadron from actual experimental measurements. It is interesting to find the possibility that the gravitational mass and mechanical radii could be different from the experimental charge radius $\sqrt {\langle r^2 \rangle _{\text{charge}}} =0.672 \pm 0.008$ fm for the charged pion.

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arXiv2018

High-energy neutrino-nucleus interactions

High-energy neutrino-nucleus interactions are discussed by considering neutrino-oscillation experiments and ultra-high-energy cosmic neutrino interactions. The largest systematic error for the current neutrino oscillation measurements comes from the neutrino-nucleus interaction part, and its accurate understanding is essential for high-precision neutrino physics, namely for studying CP violation in the lepton sector. Depending on neutrino beam energies, quasi-elastic, resonance, Regge, or/and deep inelastic scattering (DIS) processes contribute to the neutrino cross section. It is desirable to have a code to calculate the neutrino-nucleus cross section in any kinematical range by combining various theoretical descriptions. On the other hand, the IceCube collaboration started obtaining cross section data up to the $10^{15}$ eV range, so that it became necessary to understand ultra-high-energy neutrino interactions beyond the artificial lepton-accelerator energy range. For future precise neutrino physics including the CP measurement, it is also necessary to understand accurate nuclear corrections. The current status is explained for nuclear corrections in DIS structure functions. The possibility is also discussed to find gravitational sources within nucleons and nuclei, namely matrix elements of quark-gluon energy-momentum tensor. They could be probed by neutrino interactions without replying on direct ultra-weak "gravitational interactions" with high-intensity neutrino beams, possibly at a future neutrino factory, by using techniques of hadron tomography.

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arXiv2018

Theoretical perspective for the future experiments on parton densities

I explain the current status of parton-distribution-function (PDF) studies and future experimental prospects on their determinations. First, unpolarized PDFs of the nucleon are introduced as a field of precision QCD physics including higher-order $α_s$ corrections. Second, nuclear PDFs and polarized nucleonic PDFs are discussed. Third, the determination of fragmentation functions is explained. Forth, the three-dimensional (3D) structure functions are discussed in connection with the origin of the nucleon spin and gravitational form factors of hadrons. By the 3D structure functions, gravitational sources and the origin of nucleon mass could be clarified in the microscopic level of quarks and gluons. Furthermore, 3D structure studies of hadrons could be used for clarifying internal structure of exotic hadron candidates, nuclear composition of ultra-high-energy cosmic rays, and color-entanglement phenomena. The PDF field will be developed further along with progress in other fields of science.

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arXiv2018

Hadron tomography and its application to gravitational radii of hadrons

Hadron tomography has been investigated by three-dimensional structure functions, such as generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs). The GDAs are $s$-$t$ crossed quantities of the GPDs, and both functions probe gravitational form factors for hadrons. We determined the pion GDAs by analyzing Belle data on the differential cross section for the two-photon process $γ^* γ\to π^0 π^0$. From the determined GDAs, we calculated timelike gravitational form factors of the pion and they were converted to the spacelike form factors by using the dispersion relation. These gravitational form factors $Θ_1$ and $Θ_2$ indicate mechanical (pressure, shear force) and gravitational-mass (or energy) distributions, respectively. Then, gravitational radii are calculated for the pion from the form factors, and they are compared with the pion charge radius. We explain that the new field of gravitational physics can be developed in the microscopic level of quarks and gluons.

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arXiv2018

Tomography and gravitational radii for hadrons by three-dimensional structure functions

Three-dimensional tomography of hadrons can be investigated by generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions (TMDs), and generalized distribution amplitudes (GDAs). The GDA studies had been only theoretical for a long time because there was no experimental measurement until recently, whereas the GPDs and TMDs have been investigated extensively by deeply virtual Compton scattering and semi-inclusive deep inelastic scattering. Here, we report our studies to determine pion GDAs from recent KEKB measurements on the differential cross section of $γ^* γ\to π^0 π^0$. Since an exotic-hadron pair can be produced in the final state, the GDAs can be used also for probing internal structure of exotic hadron candidates in future. The other important feature of the GDAs is that the GDAs contain information on form factors of the energy-momentum tensor for quarks and gluons, so that gravitational form factors and radii can be calculated from the determined GDAs. We show the mass (energy) and the mechanical (pressure, shear force) form factors and radii for the pion. Our analysis should be the first attempt for obtaining gravitational form factors and radii of hadrons by analysis of actual experimental measurements. We believe that a new field of gravitational physics is created from the microscopic level in terms of elementary quarks and gluons.

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