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Ismail Zahed

Publications and source records attributed to Ismail Zahed.

At least 55 records · Page 3Linked to original sources
arXiv2024

Bridging hadronic and vacuum structure by heavy quarkonia

We discuss the central and, mostly, spin-dependent potentials in heavy quarkonia $\bar b b, \bar c c$, with two goals in mind. The first is phenomenological: using the splitting between the 1S and 2S pairs, as well as the 1P and 2P quartet masses, we obtain very accurate values of all matrix elements of the spin-depepdent potentials. The second is theoretical: using standard wave functions, we compute these matrix elements, from perturbative, nonperturbative and ``string" contributions. The model for nonperturbative effects is a ``dense instanton liquid model", in which the QCD vacuum is made of (strongly color correlated) instanton-antiinstanton pairs or "molecules". We calcuate their effect via standard Wilson lines, with or without extra powers of gauge fields. We find that this model provides a reasonable description of all central, spin-spin and spin-orbit forces at distances $r= 0-0.7 \, fm $, relevant for $\bar b b $ and $\bar c c$ quarkonia.

hep-ph↗
arXiv2024

Hadronic structure on the light-front VIII. Light scalar and vector mesons

We use the QCD instanton vacuum model to discuss the emergence of the light scalar and vector mesons on the light front. We take into account both the instanton and anti-instanton single and molecular interactions on the light quarks, in the form of non-local effective interactions. Although the molecular induced interactions are suppressed by a power of the packing fraction, they are still sufficient to bind the vector mesons, while keeping most of the scalar spectrum relatively unchanged. We explicitly derive the light front distribution amplitudes (DAs) and partonic functions (PDFs) for the scalar and vector mesons, and compare them after pertinent QCD evolution, to the available empirical and lattice measured counterparts. The Dirac electric form factors for both the pion and rho meson are derived, and shown to compare well with current data.

hep-ph↗
arXiv2024

Holographic Odderon at TOTEM ?

We consider the contribution of the Odderon to diffractive $pp$ and $p\bar p$ elastic scattering at large center of mass energy. We identify the Odderon and Pomeron with the Reggeized $1^{\pm-}$ and $2^{++}$ glueballs in the bulk, respectively. We use for the gravity dual description the repulsive wall model, to account for the proper Gribov diffusion for off-forward scattering. The eikonalized and unitarized amplitudes exhibit a vanishingly small rho-parameter, and a slope parameter fixed by twice the closed string slope. The results for the differential and total cross sections are compared to the empirical results reported recently by the TOTEM collaboration.

hep-ph↗
arXiv2024

Entanglement in massive Schwinger model at finite temperature and density

We evaluate the entanglement entropy and entropic function of massive two dimensional QED (Schwinger model) at finite temperature, density, and $θ$-angle. In the strong coupling regime, the entropic function is dominated by the boson mass for large spatial intervals, and reduces to the CFT result for small spatial intervals. We also discuss the entanglement spectrum at finite temperature and a finite $θ$-angle.

hep-th↗
arXiv2024

Deuteron gravitational form factors: exchange currents

Following on our recent analysis of the energy momentum tensor (EMT) of light nuclei in the impulse approximation, we evaluate the leading exchange corrections also upto momenta of the order of the nucleon mass. The exchange contributions to the EMT, are composed of the pair interaction, plus the seagull and the pion exchange interactions, modulo the recoil correction. The exchange contributions are shown to satisfy the current conservation requirement. These contributions are small compared to those from the impulse approximation for most of the deuteron gravitational form factors (GFFs), for momenta smaller than half of the nucleon mass. For larger momenta, the exchange contributions are significant for the deuteron A- and D-GFFs. We suggest that the pion GFFs can be extracted from the exchange contributions of select deuteron GFFs.

nucl-th↗
arXiv2023

Entanglement entropy in a time-dependent holographic Schwinger pair creation

We analyze the entanglement of a Schwinger pair created by a time-dependent pulse. In the semi-classical approximation, the pair creation by a pulse of external electric field is captured by a periodic worldline instanton. At strong gauge coupling, the gauge-gravity dual worldsheet instanton exhibits a falling wormhole in AdS. We identify the tunneling time at the boundary with the inverse Unruh temperature, and derive the pertinent entanglement entropy between the created pair using thermodynamics. The entanglement entropy is enhanced by the sub-barrier tunneling process, and partly depleted by the radiation in the post-barrier process.

hep-th↗
arXiv2023

The Nambu-Goto string in QCD: Dipole interactions, scattering and entanglement

We revisit some aspects of the stringy approach to dipole-dipole interactions, scattering and entanglement in QCD, using the Nambu-Goto (NG) string, without recourse to holography. We first show that the potential between two static dipoles exchanging closed NG strings is attractive at all separations. Underlining the exchange there is an emergent entropy, that is dominated by the tachyon at large separation, and vanishes at short separation, a measure of the confinement-deconfinement transition. The same tachyon is dominant in the scattering amplitude, as a correlator of two Wilson loops for two fixed dipole-like hadrons separated at large rapidity gap, where the contribution of the worldsheet fermions is included. While the tachyon causes the mean string bit density to grow exponentially with the rapidity, the total scattering cross section still satisfies the Froissart bound by quantum shadowing. The stringy scattering exchange also carries an entanglement entropy, that saturates when the bound is reached. For hadrons with varying dipole sizes, the tachyon exchange takes place in hyperbolic space in the conformal limit. The result for the full S-matrix is reminiscent of the one from Mueller$^\prime$s evolved dipole wavefunction, for the total dipole-dipole cross section in perturbative QCD.

hep-ph↗
arXiv2023

Hadronic structure on the light-front IX . Orbital-spin-isospin wave functions of baryons

This paper which is part of a series, is devoted to several technical issues. In the first part of the paper, we discuss the usual wavefunctions in the CM frame for baryons, by clarifying the representations of the three-quark permutation group $S_3$. We extend the analysis for up to five ``spinors" with $ρ,λ$-symmetry, and derive explicitly the totally symmetric wavefunctions modulo color. They are explicitly used to describe the excited nucleons $N^*$ states, in the P- and D-shell. We also show how to use symbolic operations in Mathematica, in spin-tensor notations to make explicit these states. For the S- and P-shells, the totally antisymmetric wavefunctions are given, and the pertinent matrix elements for the spin-dependent operators calculated, including the mixing between states with different total spin $S$. In the second part of the paper we turn to the light front wavefunctions, with an emphasis on the longitudinal wavefunctions, with a novel basis set. We also discuss their symmetries under permutations, and select the proper combinations for the transverse and longitudinal excitations for $N^*$ on the light front.

hep-ph↗
arXiv2023

Baryons and tetraquarks using instanton-induced interactions

We analyze some aspects of the perturbative and non-perturbative interactions in the composition of heavy quarkonia, heavy and light baryons ($ccc$ and $uuu$ ones), as well as all charm tetraquarks ($cc\bar c\bar c$). Using the hyper-spherical approximation and effective radial potentials (in 6 and 9 dimensions, respectively) we derive their spectra and wave functions. In all of the cases, we focus on the splittings between the s-shell levels, which are remarkably insensitive to the quark masses, but proportional to the effective interaction potentials. We use the traditional Cornell-like potentials, and the non-perturbative instanton-induced static potentials, from correlators of two, three and four Wilson lines, and find rather satisfactory description of spectra in all cases.

hep-ph↗
arXiv2023

Mueller's dipole wave function in QCD: emergent KNO scaling in the double logarithm limit

We analyze Mueller's QCD dipole wave function evolution in the double logarithm approximation (DLA). Using complex analytical methods, we show that the distribution of dipole in the wave function (gluon multiplicity distribution) asymptotically satisfies the Koba-Nielsen-Olesen (KNO) scaling, with a non-trivial scaling function $f(z)$ with $z=\frac n{\bar n}$. The scaling function decays exponentially as $2(2.55)^2ze^{-\frac{z}{0.3917}}$ at large $z$, while its growth is log-normal as $e^{-\frac{1}{2}\ln^2 z}$ for small-$z$. A detailed analysis of the Fourier-Laplace transform of $f(z)$, allows for performing the inverse Fourier transform, and access the non-asymptotic bulk-region around the peak. The bulk and asymptotic results are shown to be in good agreement with the measured hadronic multiplicities in DIS, as reported by the H1 collaboration at HERA in the region of large $Q^2$. A numerical tabulation of $f(z)$ is included. Remarkably, the same scaling function is found to emerge in the resummation of double logarithms in the evolution of jets. Using the generating function approach, we show why this is the case. The absence of KNO scaling in non-critical and super-renormalizable theories is briefly discussed. We also discuss the universal character of the entanglement entropy in the KNO scaling limit, and its measurement using the emitted multiplicities in DIS and $e^+e^-$ annihilation.

hep-ph↗
arXiv2023

Quark and gluon GPDs at finite skewness from strings in holographic QCD: evolved and compared to experiment

We present a framework for constructing Generalized Parton Distributions (GPDs) using holographic QCD in the large $N_c$ limit, with a focus on low-x and finite skewness. Our approach utilizes holographic amplitudes for exclusive electroproduction processes to extract the spin-j conformal (Gegenbauer) moments of GPDs, which are then evolved to higher resolution scales using QCD evolution equations. Our evolved GPDs (reconstructed from their evolved conformal moments) are applied to analyze the electroproduction of $ρ^{0,+}$ and $ϕ$ mesons, and we account for non-perturbative contributions in the $s+u$ - channel using holographic QCD. The results compare well with the existing experimental data. Our GPDs provide detailed information about partonic distributions and are useful for future experimental studies and global data analyses.

hep-ph↗
arXiv2023

Entanglement in a holographic Schwinger pair with confinement

We revisit the entanglement of a Schwinger pair created by external fields of arbitrary strength, using a holographic dual description of QCD. When external fields are strong in comparison to the string tension, the entanglement is geometrically tied to the Einstein-Rosen (ER) bridge in the bulk, and disappears when the pair production is not exponentially suppressed at the boundary. For moderate external fields, the entanglement is shown to follow from the geometrical interplay between the position of the ER bridge and the confining wall in the bulk. We clarify the physical nature of quantum entanglement in pair production, and connect it to the entropy of entanglement between the left- and right-moving fermions. In particular, we clarify the effect of real radiation off the produced particles on quantum entanglement of the pair.

hep-th↗
arXiv2023

Hadronic structure on the light-front VII. Pions and kaons and their partonic distributions

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. The spontaneous breaking of chiral symmetry on the light front, is shown to parallel that in the rest frame, where the non-local instanton induced $^\prime$t Hooft interaction plays a central role. By rewriting this interaction solely in terms of the good component of the fermionic field, a scalar chiral condensate emerges in the mean-field approximation, which is identical to the one obtained in the rest frame. The pions and kaons emerge as deeply bound Goldstone modes in the chiral limit, with the scalar-isoscalar sigma meson mode as a threshold state with zero binding. We explicitly derive the light front distribution amplitudes (DAs) and partonic functions (PDFs) for these mesons. The DAs and PDFs are in good agreement with those extracted from the QCD instanton vacuum in the rest frame, using the large momentum effective theory (LaMET). The QCD evolved DAs and PDFs compare well with available measurements, as well as recent lattice results.

hep-ph↗
arXiv2023

Universality of Koba-Nielsen-Olesen scaling in QCD at high energy and entanglement

Using Mueller's dipole formalism for deep inelastic scattering in QCD, we formulate and solve the evolution for the generating function for the multiplicities of the produced particles, in hadronic processes at high energy. The solution for the multiplicities satisfies Koba-Nielsen-Olesen (KNO) scaling, with good agreement with the recently re-analyzed data from the H1 experiment at HERA (DESY), and the old ALEPH data for hadronic $Z$ decay at LEP (CERN). The same scaling function with KNO scaling, carries to the hadronic multiplicities from jets in electron-positron annihilation. This agreement is {\it a priori} puzzling, since in Mueller's dipole evolution, one accounts for virtual dipoles in a wave function, whereas in electron-positron annihilation, one describes cross-sections of real particles. We explain the origin of this similarity, pointing at a particular duality between the two processes. Finally, we interpret our results from the point of view of quantum entanglement between slow and fast degrees of freedom in QCD, and derive the entanglement entropy pertinent to electron-positron annihilation into hadronic jets.

hep-ph↗
arXiv2023

Hadronic structure on the light-front VI. Generalized parton distributions of unpolarized hadrons

We discuss the generalized parton distributions (GPDs) for unpolarized hadrons, as a continuation of our recent work on hadronic structure on the light front. We analyze the unpolarized GPDs for the light nucleon and delta, as well as generic mesons, using the lowest Fock states. We use these GPDs to reconstruct the charge and gravitational form factors, and discuss their relative sizes. The results are also compared to reported QCD lattice results.

hep-ph↗
arXiv2022

Meson structure on the light-front III : The Hamiltonian, heavy quarkonia, spin and orbit mixing

This is the third paper on hadronic light front wave functions (LFWFs). We derive a light front Hamiltonian from first principles using the key features of the QCD vacuum at low resolution. In the first approximation, it gives transverse oscillator and longitudinal harmonic modes and yields the correct Regge trajectories. For heavy quarkonia, we compare its spectrum to that obtained from the usual Schroedinger equation in the rest frame. We use the same approach for light quarks, and investigate the role of confinement and chiral symmetry breaking in the quark-antiquark sector. We then study spin-spin and spin-orbit mixing, resulting in e.g. quadrupole moments of vector mesons. For the light mesons, we show how to extend the famed t$^\prime$Hooft interaction to the light front, which solves the U(1) problem and helps produce a light pion. We use the ensuing light front wavefunctions, to derive the pertinent parton distribution functions, parton amplitudes and low energy constants.

hep-ph↗
arXiv2022

Hadronic structure on the light-front IV: Heavy and light Baryons

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front. The chief focus of this paper is the quantum-mechanical solution of the three-quark model Hamiltonian, describing baryons. In Jacobi coordinates, we use a harmonic oscillator basis for the transverse directions. For the longitudinal momentum fractions $x_i$, the pertinent basis follows from quantum mechanics in a "triangular cup" potential, which we solve exactly. We calculate the masses and light front wave functions for the flavor symmetric $\frac 32^+$ baryons $bbb,ccc,sss,uuu$.

hep-ph↗