Impact Parameter Space Research Articles

Chiral-odd generalized parton distributions of sea quarks at ξ=0 in the light-cone quark model

We study the chiral-odd generalized parton distributions (GPDs) of the u¯ and d¯ quarks inside the proton at zero skewness using the overlap representation within the light-cone formalism. Utilizing the light-cone wave functions of the proton obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we provide expressions for the GPDs H˜Tq¯/P(x,0,t), HTq¯/P(x,0,t), and ETq¯/P(x,0,t) where q¯=u¯ and d¯. Numerical results for these GPDs in momentum space as well as in impact parameter space are presented. Additionally, we investigate specific combinations of the chiral-odd GPDs in impact parameter space, focusing on the spin-orbit correlation effect of the sea quarks. Published by the American Physical Society 2024

Wigner distributions of sea quarks in the light-cone quark model

We investigate the Wigner distributions of u¯ and d¯ quarks in a proton using the overlap representation within the light cone formalism. Using the light-cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we calculate the Wigner distributions for the unpolarized/longitudinally polarized sea quarks in an unpolarized/longitudinally polarized proton. The Wigner distributions can be obtained through a Fourier transform on the generalized transverse-momentum dependent parton distributions (GTMDs). We also calculate the GTMDs of u¯ and d¯ quarks in the intermediate step. Numerical results for the Wigner distributions of u¯ and d¯ quarks in transverse momentum space, impact parameter space and the mixed plane are presented. We also study the orbital angular momentum and the spin-orbit correlations of the sea quarks. Published by the American Physical Society 2024

Algebraic model to study the internal structure of pseudoscalar mesons with heavy-light quark content

The internal structure of all lowest-lying pseudoscalar mesons with heavy-light quark content is studied in detail using an algebraic model that has been applied recently, and successfully, to the same physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based of the meson’s Bethe-Salpeter amplitude (BSA) and quark’s propagator in such a way that the Bethe-Salpeter wave function (BSWF) can then be readily computed algebraically. Its subsequent projection onto the light front yields the light front wave function (LFWF) whose form allows us a simple access to the valence-quark parton distribution amplitude (PDA) by integrating over the transverse momentum squared. We exploit our current knowledge of the PDAs of lowest-lying pseudoscalar heavy-light mesons to compute their generalized parton distributions (GPDs) through the overlap representation of LFWFs. From these three dimensional knowledge, different limits/projections lead us to deduce the related parton distribution functions (PDFs), electromagnetic form factors (EFFs), and impact parameter space GPDs (IPS-GPDs). When possible, we make explicit comparisons with available experimental results and earlier theoretical predictions. Published by the American Physical Society 2024

Light-by-light scattering in ultraperipheral collisions of heavy ions at two future detectors

We discuss possible future studies of photon-photon (light-by-light) scattering using a planned FoCal and ALICE 3 detectors. We include different mechanisms of γγ→γγ scattering such as double-hadronic photon fluctuations, t/u-channel neutral pion exchange or resonance excitations (γγ→R) and deexcitation (R→γγ). The broad range of (pseudo)rapidities and lower cuts on transverse momenta open a necessity to consider not only dominant box contributions but also other subleading contributions. Here we include low mass resonant R=π0, η, η′ contributions. The resonance contributions give intermediate photon transverse momenta. However, these contributions can be eliminated by imposing windows on diphoton invariant mass. We study and quantify individual box contributions (leptonic, quarkish). The electron/positron boxes dominate at low Mγγ<1 GeV diphoton invariant masses. The PbPb→PbPbγγ cross section is calculated within equivalent photon approximation in the impact parameter space. Several differential distributions are presented and discussed. We consider four different kinematic regions. We predict a cross section in the (mb-b) range for typical ALICE 3 cuts, a few orders of magnitude larger than for the current ATLAS or CMS experiments. We also consider the two-π0 background which can, in principle, be eliminated at the new kinematical range for the ALICE 3 measurements by imposing dedicated cuts on diphoton transverse momentum and/or so-called vector asymmetry. Published by the American Physical Society 2024

A Systematic Survey of Moon-forming Giant Impacts. I. Nonrotating Bodies

In the leading theory of lunar formation, known as the giant impact hypothesis, a collision between two planet-size objects resulted in a young Earth surrounded by a circumplanetary debris disk from which the Moon later accreted. The range of giant impacts that could conceivably explain the Earth–Moon system is limited by the set of known physical and geochemical constraints. However, while several distinct Moon-forming impact scenarios have been proposed—from small, high-velocity impactors to low-velocity mergers between equal-mass objects—none of these scenarios have been successful at explaining the full set of known constraints, especially without invoking controversial post-impact processes. In order to bridge the gap between previous studies and provide a consistent survey of the Moon-forming impact parameter space, we present a systematic study of simulations of potential Moon-forming impacts. In the first paper of this series, we focus on pairwise impacts between nonrotating bodies. Notably, we show that such collisions require a minimum initial angular momentum budget of approximately 2 J EM in order to generate a sufficiently massive protolunar disk. We also show that low-velocity impacts (v ∞ ≲ 0.5 v esc) with high impactor-to-target mass ratios (γ → 1) are preferred to explain the Earth–Moon isotopic similarities. In a follow-up paper, we consider impacts between rotating bodies at various mutual orientations.

Generalized parton distributions of gluon in proton: A light-front quantization approach

We solve for the gluon generalized parton distributions (GPDs) inside the proton at zero skewness, focusing specifically on leading twist chiral-even GPDs. We obtain and employ the light-front wavefunctions (LFWFs) of the proton from a light-front quantized Hamiltonian with Quantum Chromodynamics input using basis light-front quantization (BLFQ). Our investigation incorporates the valence Fock sector with three constituent quarks and an additional Fock sector, encompassing three quarks and a dynamical gluon. We examine the GPDs within impact parameter space and evaluate the x-dependence of the transverse square radius. We find that the transverse size of the gluon at lower-x is larger than that of the quark, while it exhibits opposite behavior at large-x. Using the proton spin sum rule, we also determine the relative contributions of quarks and the gluon to the total angular momentum of the proton.

Generalized parton distributions of sea quark at zero skewness in the light-cone model

We study the chiral-even generalized parton distributions (GPDs) of {bar{u}} and {bar{d}} quarks at zero skewness using the overlap representation within the light cone formalism. The GPDs of {bar{u}} and {bar{d}} quarks can be expressed as the convolution of the light cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |q{bar{q}}Brangle Fock states. We present the numerical results for H^{{bar{u}}/P}(x,xi ,Delta ^2), H^{{bar{d}}/P}(x,xi ,Delta ^2), E^{{bar{u}}/P}(x,xi ,Delta ^2) and E^{{bar{d}}/P}(x,xi ,Delta ^2). We apply the model resulting GPDs to calculate the orbital angular momentum of the {bar{u}} and {bar{d}} quarks, showing that L^{{bar{u}}/P}, L^{{bar{d}}/P} are positive and L^{{bar{u}}/P} is smaller than L^{{bar{d}}/P}. The sea quark OAM distributions in the impact parameter space L_{{bar{q}}}(x,{varvec{b}}_{varvec{T}}) are also calculated.

Bethe-Salpeter equation for classical gravitational bound states

The Bethe-Salpeter equation is a non-perturbative, relativistic and covariant description of two-body bound states. We derive the classical Bethe-Salpeter equation for two massive point particles (with or without spin) in a bound gravitational system. This is a recursion relation which involves two-massive-particle-irreducible diagrams in the space of classical amplitudes, defined by quotienting out by symmetrization over internal graviton exchanges. In this context, we observe that the leading eikonal approximation to two-body scattering arises directly from unitarity techniques with a coherent state of virtual gravitons. More generally, we solve the classical Bethe-Salpeter equation analytically at all orders by exponentiating the classical kernel in impact parameter space. We clarify the connection between this classical kernel and the Hamilton-Jacobi action, making manifest the analytic continuation between classical bound and scattering observables. Using explicit analytic resummations of classical (spinless and spinning) amplitudes in momentum space, we further explore the relation between poles with bound state energies and residues with bound state wavefunctions. Finally, we discuss a relativistic analogue of Sommerfeld enhancement which occurs for bound state cross sections.

Spin-orbital coupling in strong interaction and global spin polarization

In non-central relativistic heavy ion collisions, the colliding nuclear system possesses a huge global orbital angular momentum in the direction opposite to the normal of the reaction plane. Due to the spin-orbit coupling in strong interaction, such a huge orbital angular momentum leads to a global spin polarization of the quark matter system produced in the collision process. The global polarization effect in high energy heavy ion collisions was first predicted theoretically and confirmed by STAR experiments at the Relativistic Heavy Ion Collider in Brookhaven National Laboratory. The discovery has attracted much attention to the study of spin effects in heavy ion collision and leads to a new direction in high energy heavy ion physics—Spin Physics in Heavy Ion Collisions. In this paper, we briefly review the original ideas, the calculation methods, the main results and recent theoretical developments in last years. First, we present a short discussion of the spin-orbit coupling which is an intrinsic property for a relativistic fermionic quantum system. Then we review how the global orbital angular momentum can be generated in non-central heavy ion collisions and how the global orbital angular momentum can be transferred to the local orbital angular momentum distribution in two limit model---Landan fireball model and Bjorken scaling model. After that, we review how we can describe the scattering process with initial local orbital angular momentum in the formalism of scattering cross section in impact parameter space and how we calculate the polarization of the quarks and antiquarks in quark gluon plasma produced in non-central heavy ion collisions after single or multiple scattering. We also give a brief review on how the global polarization can be predicted from the formalism of relativistic hydrodynamics with the generalized Cooper-Frye formula with spin. Finally, we discuss how the quark's polarization can be transferred to the final hadron's polarization. We focus on the hyperon's polarization and vector meson's spin alignment produced in heavy-ion collisions.

Electromagnetic interaction of low transverse momentum charged leptons with heavy nuclei in ultra-peripheral ultra-relativistic heavy-ion collisions

The photon–photon interaction in ultra-relativistic heavy-ion collision is a source of the charged lepton pairs. The photon-photon fusion leads to the lepton creation in broad configuration space around the “collision” point. Those created close to heavy nuclei may undergo strong electromagnetic interaction with them. The impact parameter space distributions of electrons/positrons and charged muons are calculated within the b-space EPA model of such collisions. The evolution of e^+/e^- and mu ^+/mu ^- distributions due to the electromagnetic interaction of leptons with nuclei is studied, and the distortion of rapidity and transverse momentum distributions are shown. A part of the analysis is independent of the production model. We show the first exploratory results for the reaction Pb + Pb at sqrt{s_{NN}} = 17.3 GeV (SPS) and 200 GeV (RHIC) energies. We provide results for selected creation points and when integrating over their positions as dictated by the b-space EPA model. We observe sizeable effects for e^+ / e^- and much smaller effects for mu ^+ / mu ^-. We predict a possible sizeable accumulation of leptons with rapidities close to the beam rapidity. The EM effects lead to asymmetry in the production of e^+ and e^- or mu ^+ and mu ^-.

Generalized parton distributions through universal moment parameterization: zero skewness case

We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions (PDFs) from phenomenology and generalized form factors from lattice calculations, and show that the parameterization is flexible enough to accommodate these constraints. In addition, we can also fit direct lattice calculations of GPDs from large-momentum effective theory. In this work we focus on the analysis of t-dependent PDFs which correspond to GPDs in the ξ → 0 limit. The strategy also applies to the ξ ≠ 0 region with extra parameters, and therefore can be fitted to experimental observables in the future. With a demonstrative example of fitted GPDs, we exhibit the quark transverse angular momentum densities of the proton as well as the impact parameter space distributions of quarks in both unpolarized and transversely polarized protons.

Evolution equation for elastic scattering of hadrons

We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which has a form of the complex nonlinear reaction–diffusion equation, with time being played by the logarithm of energy. The initial conditions are provided by the data-driven models for the real and imaginary parts of the amplitude. Numerical calculations of pp differential cross sections and forward quantities for LHC energies agree very well with experimental data extending up to, and including the diffractive cone. Furthermore, we show that at current accessible energies the non-linear effects play an important role, as the impact parameter space profiles approach the unitarity bound. The equation also predicts some other effects discussed in the literature, like the hollowness of nuclear matter or existence of stationary points in momentum transfer t.

Pseudoscalar mesons: Light front wave functions, GPDs, and PDFs

We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia (${\ensuremath{\eta}}_{c}$ and ${\ensuremath{\eta}}_{b}$). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this three-dimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PDFs for mesons formed with light quarks are then evolved from the hadronic scale of around 0.3 to 5.2 GeV, probed in experiments. We make explicit comparisons with experimental results available and with earlier theoretical predictions.

Backward timelike Compton scattering to decipher the photon content of the nucleon

The exclusive photoproduction off nucleon of a large invariant mass lepton pair in the backward region specified by the small Mandelstam variable -u is discussed in the framework of collinear QCD factorization. The amplitude is factorized in terms of photon-to-nucleon Transition Distribution Amplitudes (TDAs). These new non-perturbative objects, complementary to the “photon-inside-the-nucleon PDF”, lead to a tomographic picture of the nucleon’s photon content after Fourier transforming to the impact parameter space. This allows to address the question of where in the transverse plane the nucleon emits a photon. A simplistic model-estimate of photon-to-nucleon TDAs is used to estimate the magnitude of the corresponding cross sections. The background due to the electromagnetic Bethe–Heitler process is shown to be negligible in the kinematical regime of interest.

Proton gravitational form factors and mechanical properties in a light-front quark-diquark model

We present our recent calculation of the gravitational form factors (GFFs) of proton using the light-front quark-diquark model constructed by the soft-wall AdS/QCD. We extract the four quark GFFs by calculating the matrix elements of the symmetric energy momentum tensor. Using the D-term we calculate the pressure and shear distributions of quarks inside the proton in the impact parameter space. The GFFs, A(Q2) and B(Q2) are found to be consistent with the lattice QCD, while the qualitative behavior of the D-term form factor is in agreement with the extracted data from the deeply virtual Compton scattering (DVCS) experiments at JLab, the lattice QCD, and the predictions of different phenomenological models.

Regularization dependence of pion generalized parton distributions * *Supported by the National Natural Science Foundation of China (11775118)

Pion generalized parton distributions are calculated within the framework of the Nambu–Jona-Lasinio model using different regularization schemes, including the proper time regularization scheme, the three-dimensional (3D) momentum cutoff scheme, the four-dimensional momentum cutoff scheme, and the Pauli-Villars regularization scheme. Furthermore, we check the theoretical constraints of pion generalized parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes. The diagrams of pion parton distribution functions are plotted, in addition, we evaluate the Mellin moments of generalized parton distributions, which are related to the electromagnetic and gravitational form factors of pion. Pion generalized parton distributions are continuous but not differential at , when considering the effect of the contact contribution term, generalized parton distributions become not continuous at in all the four regularization schemes. Generalized parton distributions in impact parameter space are considered, the width distribution of u quark in the pion and the mean-squared are calculated. The light-front transverse-spin distributions are studied when quark polarized in the light-front-transverse direction, the transverse-spin density is no longer symmetric around , the peaks shift to , we compare the average transverse shift and in different regularization schemes. The light-cone energy radius and the light-cone charge radius are also evaluated, we found that in the proper time regularization scheme the values of these quantities were the largest, in the 3D momentum cutoff scheme they were the smallest.

Splitting rates in QCD plasmas from a nonperturbative determination of the momentum broadening kernel C(q⊥)

We exploit a recent non-perturbative determination of the momentum broadening kernel $C(b_{\bot})$ in impact parameter space \cite{Moore:2021jwe}, to determine the momentum space broadening kernel $C(q_{\bot})$ in high-temperature QCD plasmas. We show how to use the non-pertubatively determined kernel $C(q_{\bot})$ to compute the medium-induced splitting rates in a QCD plasma of finite size. We compare the resulting in-medium splitting rates to the results obtained with leading-order and next-to-leading order perturbative determinations of $C(q_{\bot})$, as well as with various approximations of the splitting employed in the literature. Generally, we find that the differences in the splitting rates due to the momentum broadening kernel are larger than the errors associated with approximations of the splitting rate.

Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD

We present a calculation of the scalar, vector, and tensor form factors for the pion and kaon in lattice QCD. We use an ensemble of two degenerate light, a strange and a charm quark (${N}_{f}=2+1+1$) of maximally twisted mass fermions with clover improvement. The corresponding pion and kaon masses are about 265 MeV and 530 MeV, respectively. The calculation is done in both rest and boosted frames obtaining data for four-vector momentum transfer squared up to $\ensuremath{-}{q}^{2}=2.5\text{ }\text{ }{\mathrm{GeV}}^{2}$ for the pion and $3\text{ }\text{ }{\mathrm{GeV}}^{2}$ for the kaon. The excited-states effects are studied by analyzing six values of the source-sink time separation for the rest frame (1.12--2.23 fm) and for four values for the boosted frame (1.12--1.67 fm). The lattice data are renormalized nonperturbatively and the results for the scheme- and scale-dependent scalar and tensor form factors are presented in the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. We apply different parametrizations to describe ${q}^{2}$-dependence of the form factors to extract the scalar, vector, and tensor radii, as well as the tensor anomalous magnetic moment. We compare the pion and kaon form factors to study SU(3) flavor symmetry breaking effects. By combining the data for the vector and tensor form factors we also obtain the lowest moment of the densities of transversely polarized quarks in the impact parameter space. Finally, we give an estimate for the average transverse shift in the $y$ direction for polarized quarks in the $x$ direction.

Photon escape in the extremal Kerr black hole spacetime

We consider necessary and sufficient conditions for photons emitted from an arbitrary spacetime position of the extremal Kerr black hole to escape to infinity. The radial equation of motion determines the necessary conditions for photons emitted from $r=r_*$ to escape to infinity, and the polar angle equation of motion further restricts the allowed region of photon motion. From these two conditions, we provide a method to visualize a two-dimensional photon impact parameter space that allows photons to escape to infinity, i.e., the escapable region. Finally, we completely identify the escapable region for the extremal Kerr black hole spacetime. This study has generalized our previous result [K.~Ogasawara and T.~Igata, Phys. Rev. D \textbf{103}, 044029 (2021)], which focused only on light sources near the horizon, to the classification covering light sources in the entire region.

Exponentiation of the leading eikonal phase with spin

We initiate a study into the eikonal exponentiation of the amplitude in impact-parameter space when spinning particles are involved in the scattering. Considering the gravitational scattering of two spin-1/2 particles, we demonstrate that the leading eikonal exhibits exponentiation up to $\mathcal{O}(G^{2})$ in the limit where the spacetime dimension $D\rightarrow4$. We find this to hold for general spin orientations. The exponentiation of the leading eikonal including spin is understood through the unitarity properties at leading order in $\hbar$ of momentum-space amplitudes, allowing the extension of our results to arbitrary-spin scattering.