We show possible transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and twist-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 light cone vector n in previous works on the twist-2 part and there was no correlation-function study in the twist-3 and twist-4 parts for spin-1 hadrons. We show that 40 TMDs exist in the tensor-polarized spin-1 hadron in twists 2–4. 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, ∫ d2 kT hLT = ∫ d2 kT hLL = ∫ d2 kT h3LL = 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. Furthermore, the studies of TMDs enable us not only to find three-dimensional structure of hadrons, namely, hadron tomography including transverse structure, but also to provide unique opportunities for creating interesting interdisciplinary physics fields such as gluon condensates, color Aharonov-Bohm effect, and color entanglement. The tensor structure functions may not be easily measured in experiments. However, high-intensity facility such as the Thomas Jefferson National Accelerator Facility, the Fermilab Main Injector, and future accelerators like electron-ion collider may probe such observables. In addition, since the Nuclotron-based Ion Collider fAcility focuses on spin-1 deuteron structure functions, there is a possibility to study the details of polarized structure functions of the deuteron at this facility.
Tensor-polarized parton distribution functions are new quantities in spin-1 hadrons such as the deuteron, and they could probe new quark-gluon dynamics in hadron and nuclear physics. In ...charged-lepton deep inelastic scattering, they are studied by the twist-2 structure functions b1 and b2. The HERMES Collaboration found unexpectedly large b1 values compared to a naive theoretical expectation based on the standard deuteron model. The situation should be significantly improved in the near future by an approved experiment to measure b1 at Thomas Jefferson National Accelerator Facility (JLab). There is also an interesting indication in the HERMES result that finite antiquark tensor polarization exists. It could play an important role in solving a mechanism on tensor structure in the quark-gluon level. The tensor-polarized antiquark distributions are not easily determined from the charged-lepton deep inelastic scattering; however, they can be measured in a proton-deuteron Drell-Yan process with a tensor-polarized deuteron target. In this article, we estimate the tensor-polarization asymmetry for a possible Fermilab Main-Injector experiment by using optimum tensor-polarized parton distribution functions to explain the HERMES measurement. We find that the asymmetry is typically a few percent. If it is measured, it could probe new hadron physics, and such studies could create an interesting field of high-energy spin physics. In addition, we find that a significant tensor-polarized gluon distribution should exist due to Q2 evolution, even if it were zero at a low Q2 scale. The tensor-polarized gluon distribution has never been observed, so it is an interesting future project.
A
bstract
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
1
LL
and
f
LT
, where
f
1
LL
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
1
LL
(or
b
1
) and the integral of the function
f
2
LT
= (2
/
3)
f
LT
− f
1
LL
over
x
vanishes. If the parton-model sum rule for
f
1
LL
(
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
⊥
, 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. In the near future, we expect that physics of spin-1 hadrons will become a popular topic, since there are experimental projects to investigate spin structure of the spin-1 deuteron at the Jefferson Laboratory, the Fermilab, the nuclotron-based ion collider facility, the electron-ion colliders in US and China in 2020’s and 2030’s.
We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones (F1, F2, g1, g2) which exist for the spin-1/2 nucleon, associated with its tensor ...structure. The new structure functions are b1, b2, b3, and b4 in deep inelastic scattering of a charged-lepton from a spin-one hadron such as the deuteron. Among them, twist- two functions are related by the Callan-Gross type relation b2 2xb1 in the Bjorken scaling limit. First, these new structure functions are introduced, and useful formulae are derived for projection operators of b1-4 from a hadron tensor Wμν. Second, a sum rule is explained for b1, and possible tensor-polarized distributions are discussed by using HERMES data in order to propose future experimental measurements and to compare them with theoretical models. A proposal was approved to measure b1 at the Thomas Jefferson National Accelerator Facility (JLab), so that much progress is expected for b1 in the near future. Third, formalisms of polarized proton-deuteron Drell-Yan processes are explained for probing especially tensor- polarized antiquark distributions, which were suggested by the HERMES data. The studies of the tensor-polarized structure functions will open a new era in 2020's for tensor-structure studies in terms of quark and gluon degrees of freedom, which are very different from ordinary descriptions in terms of nucleons and mesons.
We investigated the possibility of determining the internal structure of exotic hadrons by using high-energy reaction processes, where quarks and gluons are appropriate degrees of freedom. In ...particular, it should be valuable to investigate the high-energy exclusive processes that include generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs). The GPDs and GDAs contain momentum distributions of partons and form factors. We found that the exotic nature appears in momentum distributions of quarks as suggested by the constituent-counting rule and in the form factors associated with exotic hadron sizes and the number of constituents. We also propose that these exotic signatures should be found in the exclusive production processes of exotic hadrons from gamma * gamma in electron-positron annihilation. For example, the GDAs contain information on a timelike form factor of the energy-momentum tensor of a hadron h. We show that the cross section of e gamma arrow right e + hh is sensitive to the exotic signature by looking at the hh invariant-mass dependence by taking light hadrons, h = functionof sub(0)(980) and a sub(0)(980). From such GDA measurements, the tomography of exotic hadrons becomes possible, for example, with Belle and BABAR experiments and a future linear collider.
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.
We analyze the CLAS data on the photoproduction of hyperon resonances, as well as the available data for the ground state Lambda and capital sigma super(0) of the CLAS and SLAC-E84 collaborations, by ...considering a constituent-counting rule suggested by perturbative QCD. The counting rule emerges as a scaling behavior of cross sections in hard exclusive reactions with large scattering angles, and it enables us to determine the number of elementary constituents inside hadrons. Therefore, it could be used as a new method for identifying internal constituents of exotic hadron candidates. From the analyses of the gamma p arrow right K+Lambda and K+ capital sigma super(0) reactions, we find that the number of elementary constituents is consistent with n sub( gamma )=1, n sub(p)=3, n sub()K2, and n sub(Lambda)=n sub( capital sigma 0)=3. Then, an analysis is made for the photoproductions of the hyperon resonances Lambda(1405), capital sigma (1385) super(0), and Lambda(1520), where Lambda(1405) is considered to be a KN molecule, and hence its constituent number could be 5. However, we find that the current data are not enough to conclude the numbers of their constituents. It is necessary to investigate the higher-energy region at radicals>2.8GeV experimentally beyond the energy of the available CLAS data to count the number of constituents clearly. We also mention that our results indicate energy dependence in the constituent number, especially for Lambda(1405). If an excited hyperon is a mixture of three-quark and five-quark states, the energy dependence of the scaling behavior could be valuable for finding its composition and mixture.
Violation of the Gottfried sum rule was suggested by the New Muon Collaboration in measuring proton and deuteron
F
2 structure functions. The finding triggered many theoretical studies on physics ...mechanisms for explaining the antiquark flavor asymmetry
u
̄
−
d
̄
in the nucleon. Various experimental results and proposed theoretical ideas are summarized. Possibility of finding the flavor asymmetry in Drell–Yan experiments is discussed together with other processes, which are sensitive to the
u
̄
/
d
̄
asymmetry.
We propose to use hard exclusive production of an exotic hadron for finding its internal quark-gluon configuration by the constituent-counting rule in perturbative QCD. In particular, the cross ...section for the exclusive process pi super(-) + p arrow right K super(0) + Lambda(1405) is estimated at the scattering angle straighttheta = 90degrees in the center-of-mass frame by using current experimental data. In comparison, the cross section for the ground-state Lambda production pi super(-) + p arrow right K super(0) + Lambda is also shown. We suggest that the internal quark configuration of Lambda(1405) should be determined by the asymptotic scaling behavior of the cross section. If it is an ordinary three-quark baryon, the scaling of the cross section is s super(8)dsigma/dt = constant, whereas it is s super(10)dsigma/dt = constant if Lambda(1405) is a five-quark hadron, where s and t are Mandelstam variables. Such a measurement will be possible, for example, by using the high-momentum beam line at Japan Proton Accelerator Research Complex. In addition, another exclusive process gamma +p arrow right K super(+) + Lambda(1405) could be investigated at laser electron photon beam line at SPring-8 and JLab for finding the nature of Lambda(1405). We indicate that the constituent-counting rule could be used as a valuable quantity in determining internal structure of exotic hadrons by high-energy exclusive processes, where quark-gluon degrees of freedom explicitly appear. Furthermore, it is interesting to investigate the transition from hadron degrees of freedom to quark-gluon ones for exclusive exotic-hadron production processes.
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