Hadronic Wave Functions Research Articles

Wave functions of multiquark hadrons from representations of the symmetry groups Sn

Construction of the wave functions of multiquark hadrons by a traditional method based on the tensor products of colors, flavors, spins (and orbital) parts becomes quite complex when quark numbers grow n=5,6…12, as it gets difficult to satisfy the requirements of Fermi statistics. Our novel approach is focused directly on representations of the permutation symmetry generators. After showing how C3 is manifested in the wave functions of (excited) baryons, we use it to construct the wave functions for a set of pentaquarks and hexaquarks (n=5,6). We also have some partial results for larger systems, with n=9 and 12, and even beyond that as far as n=24. Published by the American Physical Society 2024

Universal rapidity scaling of entanglement entropy inside hadrons from conformal invariance

When a hadron is probed at high energy, a nontrivial quantum entanglement entropy inside the hadron emerges due to the lack of complete information about the hadron wave function extracted from this measurement. In the high-energy limit, the hadron becomes a maximally entangled state, with a linear dependence of entanglement entropy on rapidity, as has been found in a recent analysis based on parton description. In this paper, we use an effective conformal field theoretic description of hadrons on the light cone to show that the linear dependence of the entanglement entropy on rapidity found in parton description is a general consequence of approximate conformal invariance and does not depend on the assumption of weak coupling. Our result also provides further evidence for a duality between the parton and string descriptions of hadrons. Published by the American Physical Society 2024

Probing the spatial distribution of gluons within the proton in the coherent vector meson production at large-|t|

The coherent production of vector mesons in photon–hadron interactions is considered one of the most promising observables to probe the QCD dynamics at high energies and the transverse spatial distribution of the gluons in the hadron wave function. In this paper, we perform an exploratory study about the dependence of the transverse momentum distributions, dσ/dt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\sigma /dt$$\\end{document}, on the model assumed for the proton density profile. We consider a set of non-Gaussian profiles and include them in the forward dipole–proton scattering amplitude associated with the IP-sat model. We demonstrate that the predictions for dσ/dt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\sigma /dt$$\\end{document} are similar in the HERA kinematical range, but are very distinct for values of t that will be probed in future colliders. In particular, the presence of diffractive dips in the t-distributions associated with the production of J/Ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J/\\Psi $$\\end{document} and ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} mesons is strongly dependent on the model assumed for the density profile. Similar conclusions are also derived when the non-linear effects on the dipole–target interaction are disregarded. Our results indicate that a future study of the coherent vector meson production at large-t will be useful to constrain the spatial distribution of gluons within the proton.

Flavor-independent yield of high- pT hadrons from nuclear collisions

Data on high-pT hadron production in heavy ion collisions at Feynman xF=0 indicate at universality of the observed nuclear suppression. Our analysis of the production mechanisms demonstrates important role of the color transparency effects which make the survival probability of a quark-antiquark dipole independent of the quark flavor, provided that the hadron wave function is formed outside the medium. The latter condition imposes restrictions on the range of pT, which should be sufficiently high to make the nuclear suppression universal. We also found that the in-medium broadening rate q^ (frequently called transport coefficient) significantly depends on the quark flavor, diminishing for heavy quarks. Published by the American Physical Society 2024

QGSJET-III model of high energy hadronic interactions: The formalism

The physics content of the QGSJET-III Monte Carlo generator of high energy hadronic collisions is described. In particular, a phenomenological implementation of higher twist corrections to hard parton scattering processes is discussed in some detail. Additionally addressed is the treatment of the so-called “color fluctuation” effects related to a decomposition of hadron wave functions into a number of Fock states characterized by different spatial sizes and different parton densities. Selected model results regarding the energy dependence of the total, elastic, and diffractive proton-proton cross sections are presented. Published by the American Physical Society 2024

Hadronic structure on the light front. II. QCD strings, Wilson lines, and potentials

This is the second paper on hadronic wave functions in the light-front formulation. We first consider only confinement effects, using the classical Nambu-Gotto string with massive end points in the light-cone gauge. We derive the light-front Hamiltonian and show how to solve it, using an expansion in suitable basis functions. We next discuss the correlators of Wilson lines on the light front, leading to an effective Hamiltonian that includes spin effects. At the end, we consider a separate problem of instanton-induced interactions, at the origin of the pion as a massless Goldstone mode on the light front.

Chasing QCD Signatures in Nuclei Using Color Coherence Phenomena

Over the last few decades, several experiments have used atomic nuclei as unique laboratories to probe the internal structure of the strongly interacting particles, namely hadrons. Indeed, the nucleus could be used as a revealing medium of the time evolution of elementary configurations of the hadron wave function. One of the ordinary approaches used to probe this picture involves searching for the onset of various phenomena which are naturally predicted by Quantum Chromo-Dynamics (QCD), the theory of strong interactions. One such phenomenon is the color transparency (CT), which refers to the production and propagation of a small size hadron-like configuration that, under specific conditions, stays intact in a transparent nuclear medium. In this paper, I will briefly review the status of the experimental search for CT effects and highlight the upcoming Jefferson Laboratory (JLab) 12 GeV experiment that will study CT at higher momentum transfer using the CLAS12 spectrometer.

Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model

To study quantum properties of the hadron wavefunction at small x, we derived the reduced density matrix for soft gluons in the CGC framework. We explicitly showed that the reduced density matrix is not diagonal in the particle number basis. The off-diagonal components are usually ignored in the conventional parton model. We thus defined the density matrix of ignorance by keeping only the part of the reduced density matrix which can be probed in a limited set of experimental measurements. We calculated Von Neumann entropy for both the reduced and ignorance density matrices. The entropy of ignorance is always greater than the entanglement entropy (computed drom the reduced density matrix) of gluons. Finally, we showed that the CGC reduced density matrix for soft gluons can be diagonalized in a thermal basis with Boltzmann weights suggesting thermalization of new quasi-particle states which we dubbed entangolons.

Perturbative QCD Core of Hadrons and Color Transparency Phenomena

In the current paper, we argue that the ground state of a hadron contains a significant perturbative quantum chromodynamics (pQCD) core as the result of color gauge invariance and the values of chiral and gluon vacuum condensates. The evaluation within the method of dispersion sum rules (DSR) of the vacuum matrix elements of the correlator of local currents with the proper quantum numbers leads to the value of the radius of the pQCD core of a nucleon of about 0.4–0.5 fm. The selection of the initial and final states allows to select processes in which the pQCD core of the projectile gives the dominant contribution to the process. It is explained that the transparency of nuclear matter for the propagation of a spatially small and color-neutral wave packet of quarks and gluons—a color transparency (CT) phenomenon—for a group of hard processes off nuclear targets can be derived in the form of the QCD factorization theorem accounting for the color screening phenomenon. Based on the success of the method of DSR, we argue that a pQCD core in a hadron wave function is surrounded by the layer consisting of quarks interacting with quark and gluon condensates. As a result, in the quasi-elastic processes e+A→e′+N+(A−1)∗, the quasi-Feynman mechanism could be dominating in a wide range of the momentum transfer squared, Q2. In this scenario, a virtual photon is absorbed by a single quark, which carries a large fraction of the momentum of the nucleon and dominates in a wide range of Q2. CT should reveal itself in these processes at extremely large Q2 as the consequence of the presence of the Sudakov form factors, which squeeze a nucleon.

Probing Gluon Bose Correlations in Deep Inelastic Scattering.

We study correlations originating from the quantum nature of gluons in a hadronic wave function. Bose-Einstein correlation between identical particles lead to the enhancement in the number of pairs of gluons with the same quantum numbers and small relative momentum. We show that these preexisting correlations can be probed in deep inelastic scattering experiments at high energy. Specifically, we consider diffractive dijet plus a third jet production. The azimuthal dependence displays a peak at the zero relative angle between the transverse momentum imbalance of the photon-going dijet and the transverse momentum of the hadron-going jet. Our calculations explicitly show that the peak originates from Bose enhancement. Comparing electron-proton to electron-nucleus collisions, we demonstrate that the nuclear target enhances the relative strength of the peak. With the future high luminosity electron-ion collider the proposed measurements of gluon Bose enhancement become experimentally feasible.

Spin alignment of vector mesons as a probe of spin hydrodynamics and freeze-out

We argue that a detailed analysis of the spin alignment of vector mesons can serve as a probe of two little-understood aspects of spin dynamics in a vortical fluid: The degree of relaxation between vorticity and particle spin polarization, and the degree of coherence of the hadron wave function at freeze-out. We illustrate these with a coalescence model.

Sum rule for the partial decay rates of bottom hadrons based on the dynamical supersymmetry of the s¯ quark and the ud diquark

We investigate the weak decays of ${\overline{B}}_{s}^{0}$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}$ to charm hadrons based on the dynamical supersymmetry between the $\overline{s}$ quark and the $ud$ diquark. We derive a new sum rule relating the decay rates of the processes ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{+}{P}^{\ensuremath{-}}$, ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{*+}{P}^{\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{P}^{\ensuremath{-}}$, where ${P}^{\ensuremath{-}}$ is a negatively charged meson, such as ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{\ensuremath{-}}$. It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the $\overline{s}$ quark and the $ud$ diquark is also seen in the wave functions of the heavy hadrons and suggests that the $ud$ diquark can be regarded as a valid effective constituent for heavy hadrons.

Gluon quasiparticles and the CGC density matrix

We revisit and extend the calculation of the density matrix and entanglement entropy of a color glass condensate (CGC) by including the leading saturation corrections in the calculation. We show that the density matrix is diagonal in the quasiparticle basis, where it has the Boltzmann form. The quasiparticles in a wide interval of momenta behave as massless two-dimensional bosons with the temperature proportional to the typical semihard scale $T={Q}_{s}/\sqrt{{\ensuremath{\alpha}}_{s}{N}_{c}}$. Thus, the semihard momentum region ${Q}_{s}<k<{Q}_{s}/\sqrt{{\ensuremath{\alpha}}_{s}{N}_{c}}$ arises as a well-defined intermediate regime between the perturbatively hard momenta and the nonperturbative soft momenta $k<{Q}_{s}$ in the CGC description of a hadronic wave function.

Quark Mass Effects in JIMWLK Evolution

Quark mass effects in the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) evolution appear at the next to leading order (NLO) of QCD, i.e., at 𝒪(α2s) of the QCD coupling for the JIMWLK evolution kernels. Based on the light-cone hadronic wave function approach, we obtain the analytic expressions for the JIMWLK evolution kernels, which are expressed in terms of one dimensional integrals that in principle can be numerically useful for future phenomenological applications. In comparison to the situation with massless quarks, a new divergence arises. We illustrate the origin of this divergence and how the divergence is canceled within the renormalization procedures of light-cone quantization.

Quantum information approach to high energy interactions.

High energy hadron interactions are commonly described by using a probabilistic parton model that ignores quantum entanglement present in the light-cone wave functions. Here, we argue that since a high energy interaction samples an instant snapshot of the hadron wave function, the phases of different Fock state wave functions cannot be measured-therefore the light-cone density matrix has to be traced over these unobservable phases. Performing this trace with the corresponding [Formula: see text] Haar integration measure leads to 'Haar scrambling' of the density matrix, and to the emergence of entanglement entropy. This entanglement entropy is determined by the Fock state probability distribution, and is thus directly related to the parton structure functions. As proposed earlier, at large rapidity [Formula: see text] the hadron state becomes maximally entangled, and the entanglement entropy is [Formula: see text] according to QCD evolution equations. When the phases of Fock state components are controlled, for example in spin asymmetry measurements, the Haar average cannot be performed, and the probabilistic parton description breaks down. This article is part of the theme issue 'Quantum technologies in particle physics'.

Hadron wave functions in high-energy scattering, form factors and strong decays: The effects of the Lorentz contracted form

In this paper, we study the class of the processes, where dynamics depends essentially on the properties of the hadron wave functions involved in the reactions. In this case, the momentum dependence of the form of the wave functions, imposed by the Lorentz invariance and in particular by the Lorentz contraction, can be tested in the experiment and may strongly influence the resulting cross-sections. One example of such observables is given by the hadron form factors in the case when the large [Formula: see text] behavior is mostly frozen, while the Lorentz contraction of the hadron wave functions is taken into account. Another example, considered earlier, is the strong hadron decay with high-energy emission. In this paper, we study the role of the Lorentz contraction in the high-energy hadron–hadron scattering process at large momentum transfer. For the [Formula: see text] and [Formula: see text] scattering at large [Formula: see text], it is shown that at small [Formula: see text], the picture of two exponential slopes in the differential cross-section, explained previously by the author, remains stable, while the backward scattering cross-section is strongly increased by the Lorentz contraction.

E1 and M1 radiative transitions involving heavy-light axial, pseudoscalar, and vector quarkonia in the framework of the Bethe-Salpeter equation

This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\rightarrow 1^{--} \gamma$, and E1 transitions involving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}\gamma$, and $0^{-+}\rightarrow 1^{+-} \gamma $ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work, we make use of leading Dirac structures in the hadronic Bethe-Salpeter wave functions of the involved hadrons, which makes the formulation more rigorous. We evaluate the decay widths for both the above mentioned $M1$ and $E1$ transitions. We have used algebraic forms of Salpeter wave functions obtained through analytic solutions of mass spectral equations for ground and excited states of $1^{--}$,$0^{-+}$ and $1^{+-}$ heavy-light quarkonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. We have compared our results with experimental data, where ever available, and other models.

Forces within hadrons on the light front

In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.

Evolution of Colour in QCD and Informational Approach to Quantum Measurement

Quantum chromodynamics (QCD) introduces the quantum characteristic of colour in order to satisfy the Pauli exclusion principle and symmetric considerations for wavefunctions of hadrons. However, the particles that possess colour charge (quarks and gluons) are not directly observed in experiment – the effect which is often referred to as confinement. Confinement of quarks and gluons represents a theoretical challenge, as the dynamics of underlying fields is non-perturbative and therefore is problematic to be described analytically. One possible way is to use non-perturbative approaches and derive analogies with other well-established branches of physics. In this work we describe the use of the method of vacuum correlators – to analyze the confinement and other non-perturbative dynamics of quarks. The discussion of the acquired results is then given on the basis of quantum information and measurement description. It is shown that the confinement of quarks might be associated with the decoherence of colour state due to the interaction of colour charges with the environment of colour fields (QCD stochastic vacuum).

The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional

We introduce the notion of the Color Glass Condensate (CGC) density matrix widehat{rho} . This generalizes the concept of probability density for the distribution of the color charges in the hadronic wave function and is consistent with understanding the CGC as an effective theory after integration of part of the hadronic degrees of freedom. We derive the evolution equations for the density matrix and show that the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of ρ in the color charge density basis. We analyze the behavior of this density matrix under high energy evolution and show that its purity decreases with energy. We show that the evolution equation for the density matrix has the celebrated Kossakowsky-Lindblad form describing the non-unitary evolution of the density matrix of an open system. Additionally, we consider the dilute limit and demonstrate that, at large rapidity, the entanglement entropy of the density matrix grows linearly with rapidity according to frac{d}{dy}{S}_e=gamma , where γ is the leading BFKL eigenvalue. We also discuss the evolution of widehat{rho} in the saturated regime and relate it to the Levin-Tuchin law and find that the entropy again grows linearly with rapidity, but at a slower rate. By analyzing the dense and dilute regimes of the full density matrix we are able to establish a duality between the regimes. Finally we introduce the Wigner functional derived from this density matrix and discuss how it can be used to determine the distribution of color currents, which may be instrumental in understanding dynamical features of QCD at high energy.