Proton-deuteron Drell-Yan Processes Research Articles

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.

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.

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 $M_{\mu\mu}^{\,2}$, the dimuon transverse-momentum $q_T$, the dimuon rapidity $y$ in the center-of-momentum frame, and the magnitude of the gluon transversity $\Delta_T g$.

Theoretical estimate on tensor-polarization asymmetry in proton-deuteron Drell-Yan process

Tensor-polarized parton distribution functions are new quantities in spin-one hadrons such as the deuteron, and they could probe new quark-gluon dynamics in hadron and nuclear physics. In charged-lepton deep inelastic scattering (DIS), they are studied by the twist-two structure functions $b_1$ and $b_2$. The HERMES collaboration found unexpectedly large $b_1$ values than 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 $b_1$ at JLab (Thomas Jefferson National Accelerator Facility). 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 DIS; 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 PDFs 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 $Q^2$ evolution, even if it were zero at a low $Q^2$ scale. The tensor-polarized gluon distribution has never been observed, so that it is an interesting future project.

Tensor-polarized structure functions: Tensor structure of deuteron in 2020'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.

Nuclear effects in the proton-deuteron Drell-Yan process

We compute the nuclear corrections to the proton-deuteron Drell-Yan cross section for inclusive dilepton production, which, when combined with the proton-proton cross section, is used to determine the flavor asymmetry in the proton sea, $\overline{d}\ensuremath{\ne}\overline{u}$. In addition to nuclear smearing corrections that are known to be important at large values of the nucleon's parton momentum fraction ${x}_{N}$, we also consider dynamical off-shell nucleon corrections associated with the modifications of the bound nucleon structure inside the deuteron, which we find to be significant at intermediate and large ${x}_{N}$ values. We also provide estimates of the nuclear corrections at kinematics corresponding to existing and planned Drell-Yan experiments at Fermilab and J-PARC which aim to determine the $\overline{d}/\overline{u}$ ratio for $x\ensuremath{\lesssim}0.6$.

Pion-exchange and Fermi-motion effects on the proton-deuteron Drell-Yan process

Within a nuclear model where the deuteron has $NN$ and $\ensuremath{\pi}NN$ components, we derive a convolution formula for investigating the Drell-Yan process in proton-deuteron ($pd$) reactions. The contribution from the $\ensuremath{\pi}NN$ component is expressed in terms of a pion momentum distribution that depends sensitively on the $\ensuremath{\pi}NN$ form factor. With a $\ensuremath{\pi}NN$ form factor determined by fitting the $\ensuremath{\pi}N$ scattering data up to invariant mass $W=1.3\text{ }\text{ }\mathrm{GeV}$, we find that the pion-exchange and nucleon Fermi-motion effects can change significantly the ratios between the proton-deuteron and proton-proton Drell-Yan cross sections, ${R}_{pd/pp}={\ensuremath{\sigma}}^{pd}/(2{\ensuremath{\sigma}}^{pp})$, in the region where the partons emitted from the target deuteron are in the Bjorken ${x}_{2}\ensuremath{\gtrsim}0.4$ region. The calculated ratios ${R}_{pd/pp}$ at 800 GeV agree with the available data. Predictions at 120 GeV for analyzing the forthcoming data from Fermilab are presented.

Nuclear Effects in Polarized Proton–Deuteron Drell–Yan Processes

The longitudinally polarized Drell–Yan process is one of the most powerfultools to probe the structure of hadrons. By means of the recentformalism of the polarized proton–deuteron (pd) Drell–Yan, we calculatethe ratio of the proton–deuteron Drell–Yan cross section to theproton–proton (pp) one Δσpd/2Δσpp in thepolarized case. The theoretical results can be compared with futureexperimental data to confirm the nuclear effect due to the six-quarkcluster in deuteron.

Polarized proton-deuteron Drell-Yan processes and parton distributions

We show in general that there are 108 structure functions in the proton-deuteron Drell-Yan processes. However, there exist only 22 finite ones after integrating the cross section over the virtual-photon transverse momentum Q T or after taking the limit Q T → 0. There are 11 new structure functions in comparison with the ones of the proton-proton reactions, and they are related to the tensor structure of the deuteron. Parton-model analyses indicate an important tensor structure function V T UQo , which can be measured by a quadrupole spin asymmetry. The Drell-Yan process has an advantage over lepton reactions in finding tensor polarized antiquark distributions. We hope that our studies will be realized in the next-generation RHIC-Spin project and other ones.

Structure functions in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. I. General formalism

We discuss general formalism for the structure functions which can be investigated in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. To be specific, the formalism can be applied to the proton-deuteron Drell-Yan processes. Because of the spin-1 nature, there are new structure functions which cannot be studied in the proton-proton reactions. Imposing Hermiticity, parity conservation, and time-reversal invariance, we find that 108 structure functions exist in the Drell-Yan processes. However, the number reduces to 22 after integrating the cross section over the virtual-photon transverse momentum Q_T or after taking the limit Q_T->0. There are 11 new structure functions in addition to the 11 ones in the Drell-Yan processes of spin-1/2 hadrons. The additional structure functions are associated with the tensor structure of the spin-1 hadron, and they could be measured by quadrupole spin asymmetries. For example, the structure functions exist for "intermediate" polarization although their contributions vanish in the longitudinal and transverse polarization reactions. We show a number of spin asymmetries for extracting the polarized structure functions. The proton-deuteron reaction may be realized in the RHIC-Spin project and other future ones, and it could be a new direction of next generation high-energy spin physics.