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Gluon gravitational form factors at large momentum transfer
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Diffractive photoproduction of J / ψ and ϒ using holographic QCD: Gravitational form factors and GPD of gluons in the proton
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J / ψ near threshold in holographic QCD: A and D gravitational form factors
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Updated analysis of near-threshold heavy quarkonium production for probe of proton’s gluonic gravitational form factors
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Pion gravitational form factors in the QCD instanton vacuum. I
The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q 2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024
Application of novel computational techniques for the determination of the proton’s gravitational form factors and mechanical properties
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Impossibility of obtaining time-independent, three-dimensional, spherically symmetric densities of confined systems of relativistically moving constituents
The quantum-mechanical definition of probability, the uncertainty principle, and Poincaré invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of confined systems of relativistically moving constituents. Despite this, many papers ignore one or more of these restrictions. Here I show how to obtain time-independent , two-dimensional densities that are consistent with the stated restrictions. This is done using the light-front, infinite momentum frame formalism. Two-dimensional density interpretations of the axial-vector form factor and all three gravitational form factors is obtained. The resulting mass radius is smaller than the charge radius. Additionally, an expression of a two-dimensional mass density related to the trace of the energy momentum tensor is obtained. I also show that all known methods for finding three-dimensional densities—using the Breit frame, Abel transformations, Wigner distributions, and spherically symmetric wave packets with vanishing spatial extent—violate the basic restrictions in different ways. Furthermore, the use of the latter leads to densities that vanish almost everywhere in space as time increases from an initial value.
Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory
Abstract We compute the gravitational form factorsA i ,D i and$$ {\overline{c}}_i $$ c ¯ i of the scalar Yukawa theory using both the light-cone and covariant perturbation theory at the one-loop level. The light-cone formalism provides a potential approach to access these form factors beyond the perturbative regime. However, unlike the covariant formulation, the Poincaré symmetry on the light cone is not manifest. In this work, we use perturbation theory as a benchmark to extract the gravitational form factors from the light-front energy-momentum tensor. By comparing results on and off the light cone, we identifyT ++ ,T +a ,T +− ,T 12 as the “good currents” that are properly renormalized and can be used to extract the gravitational form factors.
Violation of energy conditions and the gravitational radius of the proton
The energy-momentum tensor (EMT) of the proton encodes fundamental information about its mass, pressure, and shear distributions. Using recent lattice QCD data for the gravitational form factors, we show that the Breit-frame Wigner EMT may be of Hawking-Ellis type IV in the proton’s core. Such EMT violates all pointwise energy conditions and lacks a causal rest frame so that the usual mechanical picture fails at short distances. We define the —a new hadronic observable—marking the scale where the EMT becomes ordinary (type I) and the classical interpretation is restored. We also derive from the averaged null energy condition nonperturbative, model-independent quantum field theory constraints on gravitational form factors.
An experimental program with high duty-cycle polarized and unpolarized positron beams at Jefferson Lab
Positron beams, both polarized and unpolarized, are identified as important ingredients for the experimental programs at the next generation of lepton accelerators. In the context of the hadronic physics program at Jefferson Lab (JLab), positron beams are complementary, even essential, tools for a precise understanding of the electromagnetic structure of nucleons and nuclei, in both the elastic and deep-inelastic regimes. For instance, elastic scattering of polarized and unpolarized electrons and positrons from the nucleon enables a model independent determination of its electromagnetic form factors. Also, the deeply-virtual scattering of polarized and unpolarized electrons and positrons allows unambiguous separation of the different contributions to the cross section of the lepto-production of photons and of lepton-pairs, enabling an accurate determination of the nucleons and nuclei generalized parton distributions, and providing an access to the gravitational form factors of the energy-momentum tensor. Furthermore, positron beams offer the possibility of alternative tests of the Standard Model of particle physics through the search of a dark photon, the precise measurement of electroweak couplings, and the investigation of charged lepton flavor violation. This document discusses the perspectives of an experimental program with high duty-cycle positron beams at JLab.
Dissecting a strongly coupled scalar nucleon
We continue our investigation of the stress within a strongly coupled scalar nucleon, and now dissect the gravitational form factors into contributions from its constituents, the (mock) nucleon and the (mock) pion. The computation is based on a nonperturbative solution of the scalar Yukawa model in the light-front Hamiltonian formalism with a Fock sector expansion, including up to one nucleon and two pions. By employing the “good currents” T i + + , T i + − and T i 12 , we extract the full set of gravitational form factors A i , D i , c ¯ i without the contamination of the spurious form factors and free of uncanceled UV divergences. With these results, we decompose the mass of the system into its constituents and compute the matter and mechanical radii, gaining insights into the strongly coupled system. Published by the American Physical Society 2024
Spatial and momentum imaging of the pion and kaon
We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: ( b T 2 ) u π = 0.11 fm 2 , ( b T 2 ) s K = 0.08 fm 2 , and ( b T 2 ) u K = 0.13 fm 2 , and therefore the s quark in the kaon is much closer to the center of transverse momentum than the u quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.
String-based parametrization of nucleon GPDs at any skewness: A comparison to lattice QCD
We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) valid at all skewness values. The conformal moments of the GPDs are expressed as sums of the spin-j nucleon A-form factor and the skewness-dependent spin-j nucleon D-form factor. This representation, which fulfills the polynomiality condition (due to Lorentz invariance) and does not rely on model-specific assumptions, is derived from t-channel string exchanges in anti-de Sitter spaces. The spin-j nucleon D-form factor is closely related to the spin-j nucleon A-form factor. We use the Mellin moments from empirical parton distributions to model the spin-j nucleon A-form factors. Using only five Regge slope parameters, fixed from the electromagnetic and gravitational form factors, our string-based parametrization generates accurate singlet, nonsinglet, isovector, and flavor-separated nucleon quark GPDs, along with symmetric nucleon gluon GPDs from their Mellin-Barnes integral representations. Our isovector nucleon quark GPD is in agreement with existing lattice data. Our string-based parametrization should facilitate the empirical extraction and global analysis of nucleon GPDs in exclusive processes, bypassing the deconvolution challenge.
Threshold charmonium photoproduction with GlueX
We report the total and differential cross sections for J/ψ photoproduction obtained using the large acceptance GlueX spectrometer at the 12 GeV JLab accelerator over the full near-threshold kinematic region. The GlueX experiment uses tagged linearly-polarized photon beam from coherent Bremsstrahlung off a thin diamond. Charmonium photoproduction near threshold, under certain assumptions including gluon exchange and factorization, can be used to study important aspects of the gluon structure of the proton, such as the gluon GPD, the gravitational form factors, the mass radius of the proton, and the anomalous contribution to the proton mass. In the measured cross sections we find evidence for possible contributions beyond gluon exchange. The results are compared to a wide range of theoretical predictions including GPD calculations and models with open-charm intermediate states. Photoproduction near threshold of charmonium states with opposite-to-photon parity offer another opportunity, complementary to the J/ψ, to understand the reaction mechanism of the charmonium photoproduction. While we see some evidence for such states, comprehensive studies of such higher-mass charmonia can be done only with the proposed JLab energy upgrade. An electron beam energy of up to 22 GeV significantly increases the photon flux and polarization in the corresponding threshold regions allowing for precise cross section and polarization measurements there.