Target Fragmentation Region Research Articles

The connection between nucleon energy correlators and fracture functions

We establish a sum rule that connects fracture functions to nucleon energy-energy correlators (NEECs) in a one-to-one correspondence. Using this sum rule, we study the energy pattern in the target fragmentation region of deep inelastic scatterings. Through investigations up to twist-3, we express all eighteen energy-pattern structure functions in terms of associated NEECs, elucidating various azimuthal and spin asymmetries critical for nucleon tomography. Additionally, we investigate the perturbative matching of the twist-2 quark NEECs. We demonstrate that the Sivers-type and worm-gear-type quark NEECs match onto twist-3 multi-parton distributions. Our work provides a framework for examining energy-weighted observables through hadron production processes in the target fragmentation region, offering new insights into nucleon tomography.

Gluonic contributions to semi-inclusive DIS in the target fragmentation region

We study one-loop contributions to semi-inclusive deep inelastic scattering in the target fragmentation region for a polarized lepton beam and nucleon target. Complete one-loop results at leading twist are derived, with a particular focus on the gluonic channel. It shows that four structure functions are generated uniquely by the gluon fracture functions starting at one-loop. Additionally, we obtain two structure functions associated with the longitudinal polarization of the virtual photon, and they are contributed by both gluon and quark channels. By combining existing twist-3 results, all eighteen structure functions for the studied process are predicted in terms of fracture functions convoluted with perturbative coefficient functions.

Bjorken x weighted energy-energy correlators from the target fragmentation region to the current fragmentation region

We present the complete spectrum for the Bjorken x weighted energy-energy correlation in the deep inelastic scattering (DIS) process, from the target fragmentation region to the current fragmentation region, in the Breit frame. The corresponding collinear and transverse momentum-dependent logarithms are resummed to all orders with the accuracy of NLL and N3LL, respectively. The results in the full region are matched with an O(αs2) fixed-order calculation. The final numerical predictions are presented for both Electron-Ion Collider and Continuous Electron Beam Accelerator Facility kinematics. Published by the American Physical Society 2024

Twist-3 contributions in semi-inclusive DIS in the target fragmentation region

Twist-3 contributions in semi-inclusive DIS in the target fragmentation region

Production of Δ0 resonances in the target and projectile fragmentation regions in p+12C and d+12C collisions at 4.2 GeV/c per nucleon

Production of Δ0 resonances in the target and projectile fragmentation regions in p+12C and d+12C collisions at 4.2 GeV/c per nucleon

Search for a three-proton resonance state in d+12C, α+12C and 12C+12C collisions at 3.37AGeV

The new experimental results on the search and study of formation of a possible three-proton resonance state in a target fragmentation region in the total ensemble of collisions of deuterons (2H), [Formula: see text]-particles (4He), and carbon-12 nuclei with target carbon-12 nuclei at incident kinetic energy 3.37[Formula: see text]GeV per nucleon are presented. The narrow peak structure of a possible three-proton resonance state was observed with a four-sigma statistical significance in the spectrum of invariant masses of three protons in the analyzed ensemble of collisions in the collision events with four protons in the final state. The peak structure was not visible in the other channels with the number of protons equal 3, 5, and [Formula: see text]. The mass and width of this possible three-proton resonance state were estimated to be [Formula: see text][Formula: see text]MeV/[Formula: see text] and [Formula: see text][Formula: see text]MeV/[Formula: see text]. The inclusive cross-section of formation of this possible resonance state was estimated to be [Formula: see text][Formula: see text]mb. It was deduced that the three-proton resonances could possibly be formed as a result of capture by a two-proton resonance (with mass [Formula: see text][Formula: see text]MeV/[Formula: see text]) of one more proton with a close velocity. The observed three-proton as well as two-proton resonances are likely to be the hadronic molecules. Taking into account an alpha cluster structure of carbon-12 nuclei, one of the possible mechanisms of formation of three-proton resonances could be the effective fusing of pair of protons with opposite spins, from one fragmenting alpha cluster, with a proton, originating from the second fragmenting alpha cluster.

First Measurement of Λ Electroproduction off Nuclei in the Current and Target Fragmentation Regions.

We report results of Λ hyperon production in semi-inclusive deep-inelastic scattering off deuterium, carbon, iron, and lead targets obtained with the CLAS detector and the Continuous Electron Beam Accelerator Facility 5.014GeV electron beam. These results represent the first measurements of the Λ multiplicity ratio and transverse momentum broadening as a function of the energy fraction (z) in the current and target fragmentation regions. The multiplicity ratio exhibits a strong suppression at high z and an enhancement at low z. The measured transverse momentum broadening is an order of magnitude greater than that seen for light mesons. This indicates that the propagating entity interacts very strongly with the nuclear medium, which suggests that propagation of diquark configurations in the nuclear medium takes place at least part of the time, even at high z. The trends of these results are qualitatively described by the Giessen Boltzmann-Uehling-Uhlenbeck transport model, particularly for the multiplicity ratios. These observations will potentially open a new era of studies of the structure of the nucleon as well as of strange baryons.

Observation of Correlations between Spin and Transverse Momenta in Back-to-Back Dihadron Production at CLAS12.

We report the first measurements of deep inelastic scattering spin-dependent azimuthal asymmetries in back-to-back dihadron electroproduction in the deep inelastic scattering process. In this reaction, two hadrons are produced in opposite hemispheres along the z axis in the virtual photon-target nucleon center-of-mass frame, with the first hadron produced in the current-fragmentation region and the second in the target-fragmentation region. The data were taken with longitudinally polarized electron beams of 10.2 and 10.6GeV incident on an unpolarized liquid-hydrogen target using the CLAS12 spectrometer at Jefferson Lab. Observed nonzero sinΔϕ modulations in ep→e^{'}pπ^{+}X events, where Δϕ is the difference of the azimuthal angles of the proton and pion in the virtual photon and target nucleon center-of-mass frame, indicate that correlations between the spin and transverse momenta of hadrons produced in the target- and current-fragmentation regions may be significant. The measured beam-spin asymmetries provide a first access in dihadron production to a previously unexplored leading-twist spin- and transverse-momentum-dependent fracture function. The fracture functions describe the hadronization of the target remnant after the hard scattering of a virtual photon off a quark in the target particle and provide a new avenue for studying nucleonic structure and hadronization.

Matching of fracture functions for SIDIS in target fragmentation region

In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of ΛQCD, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than ΛQCD but much smaller than Q which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be factorized with collinear parton distributions and fragmentation functions. We study the factorization up to twist-3 level and obtain gauge invariant results. They will be helpful for modeling fracture functions and useful for resummation of large logarithm of the transverse momentum appearing in collinear factorization.

Δ0 (1232) production in n+12C collisions at 4.2GeV/c

For the first time, the production of [Formula: see text] (1232) resonances has been analyzed in minimum bias [Formula: see text]C collisions at 4.2[Formula: see text]GeV/[Formula: see text]. The value of the mass and width of the [Formula: see text] resonances as well as the fraction of the negative pions coming from [Formula: see text] decay obtained in this work in [Formula: see text]C collisions coincide within the uncertainties with those extracted earlier in [Formula: see text]C collisions at 4.2[Formula: see text]GeV/[Formula: see text] per nucleon. The inclusive cross-section for production of [Formula: see text] (1232) resonances in [Formula: see text]C collisions at 4.2[Formula: see text]GeV/[Formula: see text] is estimated to be [Formula: see text][Formula: see text]mb. Production of [Formula: see text] resonances in [Formula: see text]C collisions at 4.2[Formula: see text]GeV/[Formula: see text] has been investigated separately in regions of fragmentation of the target and projectile. The mass of the [Formula: see text] (1232) proved to be the same within the statistical errors in the target and projectile fragmentation regions. The width of the invariant mass spectrum of [Formula: see text] excited in the projectile region proved to be considerably larger than that in the target fragmentation region, coinciding within statistical errors with that obtained in collisions of free nucleons. The results of the previous experiments, in which production of [Formula: see text] resonances is investigated in the whole phase space (without separating the target and projectile fragmentation regions), can be approximately regarded as the mean values of [Formula: see text] parameters, averaged over those in the target and projectile fragmentation regions.

Deep inelastic scattering in the target fragmentation region

Deep inelastic scattering is one of the best place to study hadron structures. In this paper we consider the target fragmentation region deep inelastic scattering process at leading twist. The calculations are carried out by applying the collinear expansion. In the collinear expansion formalism the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. Quantum chromodynamics is a non-Abelian gauge theory of strong interactions in which parity symmetry can be violated by the nontrivial [Formula: see text]-vacuum tunneling effects. As a result, the axial vector current is induced. By defining and decomposing the parity-odd correlator we calculate both the parity-even and parity-odd contributions to the cross-section of the target fragmentation region deep inelastic scattering. We also present the positivity bounds for these fracture functions.

Gluon radiation from a classical point particle. II. Dense gluon fields

The goal of this paper is to extend the results of Ref. [1], where formulae were derived for gluonic radiation for a high energy nucleus colliding with a classical colored particle. In Ref. [1], we computed the amplitudes for radiation in the fragmentation region of the particle for a dilute gluonic field. In this paper, we compute the radiation by solving the fluctuation equations of the dense background field in a specific gauge which makes it simple to solve the asymptotic radiation from an initial condition immediately after the passage of the nucleus. We identify and compute two components of gluon radiation, a bulk component which extends to the central region and bremsstrahlung, which may give rise to an experimentally observable intensity peak in the target fragmentation region.

Vorticity and Particle Polarization in Relativistic Heavy-Ion Collisions

We review studies of vortical motion and the resulting global polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons in heavy-ion collisions, in particular, within 3FD model. 3FD predictions for the global midrapidity polarization in the FAIR-NICA energy range are presented. The 3FD simulations indicate that energy dependence of the observed global polarization of hyperons in the midrapidity region is a consequence of the decrease of the vorticity in the central region with the collision energy rise because of pushing out the vorticity field into the fragmentation regions. At high collision energies this pushing-out results in a peculiar vortical structure consisting of two vortex rings: one ring in the target fragmentation region and another one in the projectile fragmentation region with matter rotation being opposite in these two rings.

Particle Polarization and Structure of Vortical Field in Relativistic Heavy-Ion Collisions

We review studies of vortical motion and the resulting global polarization of Λ and hyperons in heavy-ion collisions within 3FD model. The 3FD simulations indicate that energy dependence of the observed global polarization of hyperons in the midrapidity region is a consequence of the decrease of the vorticity in the central region with the collision energy rise because of pushing out the vorticity field into the fragmentation regions. At high collision energies this pushing-out results in a peculiar vortical structure consisting of two vortex rings: one ring in the target fragmentation region and another one in the projectile fragmentation region with matter rotation being opposite in these two rings.

Study of azimuthal correlations in the target fragmentation region in p, d, He, C+C, Ta and C+Ne, Cu collisions at momenta of 4.2, 4.5 and 10 A GeV/c

Azimuthal correlations between the same type of particles (protons or pions) in the target fragmentation region was studied in d, He, C+C, Ta (4.2A GeV/c, C+Ne, Cu (4.5A GeV/c) and p+C, Ta (10 GeV/c) interactions. The data were obtained from the SKM-200-GIBS streamer chamber and from the Propane Bubble Chamber (PBL-500) systems utilized at JINR. Study of multiparticle azimuthal correlations offers unique information about space-time evolution of the interactions. Azimuthal correlations were investigated by using correlation function $ C(\Delta\phi) = \mathrm{d} N/\mathrm{d} (\Delta\phi)$ , where $ \Delta\phi$ represents the angle between the sums of transverse momenta vectors for particles emitted in the forward and backward hemispheres. For protons “back-to-back” (“negative”) azimuthal correlations were observed in the above-mentioned interactions. The absolute values of the correlation coefficient $ \vert\xi\vert$ --the slope parameter of $ C(\Delta\phi)$, strongly depend on the mass number of the target ($ A_{T}$) nuclei in the nucleon-nucleus and nucleus-nucleus collisions. Namely, $ \vert\xi\vert$ decreases with increase of $ A_T$ in p+C and p+Ta collisions, while $ \vert\xi\vert$ initially decreases from d+C to C+Ne and then almost does not change with increase of $ A_P$, $ A_T$ in (d+He)Ta, C+Cu and C+Ta collisions. For pions “back-to-back” correlations were obtained for light targets (C, Ne), and “side-by-side” (“positive”) correlations for heavy targets (Cu, Ta). The $ \vert\xi\vert$ insignificantly changes with increase of the momenta per nucleon and almost does not change with increase of $ A_P$ and $ A_T$. Models used for description of the data, the Ultra relativistic Quantum Molecular Dynamic (UrQMD) and Quark-Gluon String Model (QGSM), satisfactorily describe the obtained experimental results.

Vortex rings in fragmentation regions in heavy-ion collisions at sNN=39 GeV

Vorticity generated in heavy-ion collisions at energy of $\sqrt{s_{NN}}=$ 39 GeV is studied. Simulations are performed within a model of the three-fluid dynamics. A peculiar structure consisting of two vortex rings is found: one ring in the target fragmentation region and another one in the projectile fragmentation region. These rings are also formed in central collisions. The matter rotation is opposite in this two rings. These vortex rings are already formed at the early stage of the collision together with primordial fragmentation regions. The average vorticity, responsible for the global polarization of the observed $\Lambda$ and $\bar{\Lambda}$, is also studied. In the semi-central collisions the average vorticity in the midrapidity region turns out to be more than an order of magnitude lower than the total one. The total vorticity is dominated by the contributions of the fragmentation regions and is produced because of asymmetry of the vortex rings in noncentral collisions. This suggests that in semi-central collisions the global polarization in the fragmentation regions should be at least an order of magnitude higher than that observed by the STAR collaboration in the midrapidity. This polarization should be asymmetrical in the reaction plain and correlate with the corresponding directed flow.

Electron-deuteron deep-inelastic scattering with spectator nucleon tagging and final-state interactions at intermediate x

We consider electron-deuteron deep-inelastic scattering (DIS) with detection of a proton in the nuclear fragmentation region ("spectator tagging") as a method for extracting the free neutron structure functions and studying their nuclear modifications. Such measurements could be performed at a future Electron-Ion Collider (EIC) with suitable forward detectors. The measured proton recoil momentum (~< 100 MeV in the deuteron rest frame) specifies the deuteron configuration during the high-energy process and permits a controlled theoretical treatment of nuclear effects. Nuclear and nucleonic structure are separated using methods of light-front quantum mechanics. The impulse approximation (IA) to the tagged DIS cross section contains the free neutron pole, which can be reached by on-shell extrapolation in the recoil momentum. Final-state interactions (FSI) distort the recoil momentum distribution away from the pole. In the intermediate-x region 0.1 < x < 0.5 FSI arise predominantly from interactions of the spectator proton with slow hadrons produced in the DIS process on the neutron (rest frame momenta ~< 1 GeV, target fragmentation region). We construct a schematic model describing this effect, using final-state hadron distributions measured in nucleon DIS experiments and low-energy hadron scattering amplitudes. We investigate the magnitude of FSI, their dependence on the recoil momentum (angular dependence, forward/backward regions), their analytic properties, and their effect on the on-shell extrapolation. We comment on the prospects for neutron structure extraction in tagged DIS with EIC. We discuss possible extensions of the FSI model to other kinematic regions (large/small x). In tagged DIS at x << 0.1 FSI resulting from diffractive scattering on the nucleons become important and require separate treatment.

A combined model for pseudorapidity distributions in p-p collisions at center-of-mass energies from 23.6 to 7000 GeV**Supported by Hujiang Foundation of China (B14004) and Shanghai Key Lab of Modern Optical System

In p-p collisions, the charged particles produced consist of two leading particles and those frozen out from the hot and dense matter created in the collisions. The two leading particles are in the projectile and target fragmentation regions, respectively, which, in this paper, are conventionally supposed to have Gaussian rapidity distributions. The hot and dense matter is assumed to expand according to unified hydrodynamics, a hydrodynamic model which unifies the features of the Landau and Hwa-Bjorken models, and freeze out into charged particles from a space-like hypersurface with a fixed proper time of τFO. The rapidity distribution of these charged particles can be derived analytically. The combined contribution from both leading particles and unified hydrodynamics is then compared against experimental data from a now available center-of-mass energy region from 23.6 to 7000 GeV. The model predictions are consistent with experimental measurements.

Studies of the 3D Structure of the Nucleon at JLab

Studies of the 3D structure of the nucleon encoded in transverse momentum dependent distribution and fragmentation functions of partons and generalized parton distributions are among the key objectives of the JLab 12 GeV upgrade and the electron ion collider. Main challenges in extracting 3D partonic distributions from precision measurements of hard scattering processes include clear understanding of leading twist QCD fundamentals, higher twist effects, and also correlations of hadron production in target and current fragmentation regions. In this contribution we discuss some ongoing studies and future measurements of spin-orbit correlations at Jefferson Lab.

Lambda production in the DIS target fragmentation region

By using a recently obtained set of Lambda fracture functions, we present predictions for Lambda production in the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering in CLAS@12 GeV kinematics, supplemented with a conservative error estimates. We discuss a number of observables sensitive to the assumptions of the underlying theory and many of the assumptions of the proposed phenomenological model.