Soft-wall Model Research Articles

Holographic spin alignment of J/ψ meson in magnetized plasma

We study the mass spectra and spin alignment of vector meson J/ψ in a thermal magnetized background using a generalized theoretical framework based on gauge/gravity duality. Utilizing a soft wall model for the QGP background and a massive vector field for the J/ψ meson, we delve into the meson’s spectral function and spin parameters (λθ, λφ, λθφ) for different cases, assessing their response to variations in magnetic field strength, momentum, and temperature. We initially examine scenarios where a meson’s momentum aligns parallel to the magnetic field in helicity frame. Our results reveal a magnetic field-induced positive λθH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{\ heta}^{\ extrm{H}} $$\\end{document} for low meson momentum, transitioning to negative with increased momentum. As a comparison, we also study the case of momentum perpendicular to the magnetic field and find the direction of magnetic field does not affect the qualitative behavior for the eB-dependence of λθH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\lambda}_{\ heta}^{\ extrm{H}} $$\\end{document}. Moreover, we apply our model to real heavy-ion collisions for three different spin quantization directions. Further comparisons with experimental data show qualitative agreement for spin parameters λθ and λφ in the helicity and Collins-Soper frames.

Effect of charm quark on chiral phase transition in Nf=2+1+1 holographic QCD

We investigate the effect of the charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark-flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark-flavor symmetry breaking which is associated with the violation of the U(1) axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, and then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark-mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm-quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark-flavor system. The critical exponents related to the chiral phase transition are also addressed. Published by the American Physical Society 2024

Hybrid spectroscopy within the graviton soft-wall model

In this analysis, the so-called holographic graviton soft-wall (GSW) model, first developed to investigate the glueball spectrum, has been adopted to predict the masses of hybrids with different quantum numbers. Results have been compared with other models and lattice calculations. We have extended the GSW model by introducing two modifications based on anomalous dimensions in order to improve our agreement with other calculations and to remove the initial degeneracy not accounted for by lattice predictions. These modifications do not involve new parameters. The next step has been to identify which of our calculated states agree with the PDG data, leading to experimental hybrids. The procedure has been extended to include hybrids made of heavy quarks by incorporating the quark masses into the model. Published by the American Physical Society 2024

Hadronic light-by-light scattering contributions to (g−2)μ from axial-vector and tensor mesons in the holographic soft-wall model

We compute the light axial-vector and tensor meson two-photon transition form factors in the soft-wall holographic model of quantum chromodynamics (QCD) in the flavor-symmetric case. They are used to evaluate the axial-vector and tensor meson contributions to the anomalous magnetic moment of the muon via the hadronic light-by-light scattering process. As expected, these contributions are smaller than the one from pseudoscalar mesons. The result for axial-vector mesons is higher than the value found in other approaches. Published by the American Physical Society 2024

D(s)− mesons semileptonic form factors in four-flavor holographic QCD

We investigate semileptonic form factors of a D(s) meson from a modified soft-wall 4-flavor holographic model. The model successfully reproduces the masses and decay constants of various mesons, including ρ, K*, D*, Ds*, a1, K1, f1, D1, Ds1, π, K, η, D, and Ds. Moreover, we study the semileptonic decay processes D+→(π,K,η)l+νl and Ds+→(K,η)l+νl, associated with the vector meson exchange, as well as D(s)+→Kl+νl, associated with the vector and axial vector meson exchange. The form factors f+(q2) for D→π and D(s)→K decays agree excellently with experimental and lattice data, outperforming other theoretical approaches. The f+(q2) form factor for D+→η is compatible with experimental data, while a slight discrepancy is observed for Ds+→η at large q2. Additionally, we predict the vector form factors V(q2) and A1(q2) for D→K and Ds→K decays, respectively. The results agree well with other approaches and lattice data at maximum recoil (q2=0). Published by the American Physical Society 2024

Axial-vector form factor of nucleons at finite temperature from the AdS/QCD soft-wall model

The axial-vector form factor of the nucleons is studied at a finite temperature using the holographic soft-wall model with the thermal dilaton field. We use the bulk interaction action known from the zero temperature case and apply the profile functions of fields thermalized by the interaction with the thermal dilaton field. The dependence of the axial form factor on the square of the transferred momentum and the temperature is plotted for the ground and excited states of the nucleons.

On incorporation of heavy-quark mass into soft-wall holographic models

In this paper, we consider the soft-wall holographic model with the linear dilaton background. The model leads to a Hydrogen-like meson spectrum which can be interpreted as the static limit with very large quark masses when the Coulomb interaction dominates. The mass scale introduced by the linear dilaton is matched to the quark mass. The resulting model is analyzed for the scalar, vector and tensor cases. The electromagnetic coupling constants predicted by the model are decreasing with the radial number in contrast to the soft-wall model with quadratic dilaton where these couplings represent a universal constant. The given prediction is qualitatively consistent with the corresponding experimental data in vector quarkonia. The proposed model can thus be used as a constituent part of more elaborated holographic models for heavy quarkonia. A particular example of such a model is put forward.

Vector meson gravitational form factors and generalized parton distributions at finite temperature within the soft-wall AdS/QCD model

We investigate the vector meson’s gravitational form factors (GFFs) and generalized parton distributions (GPDs) at finite temperatures within the soft-wall AdS/ QCD model. The plotted soft-wall GFFs graphs at zero temperature are close to the hard-wall results (Abidin and Carlson in Phys. Rev. D 77:095007, arXiv:0801.3839 [hep-th], 2008). The dependence on temperature of the GFFs and GPDs is studied using the thermal dilaton approach in the soft-wall model. Plots of thermal GFFs show that they decrease in temperature increase. Also, the gravitational radius of rho meson decreases in temperature growth and becomes zero around the critical temperature T_c=0.2 mathrm{ GeV}. GPDs at zero skewness are plotted and analyzed at zero and finite temperature cases.

Information entropy of nuclear electromagnetic transitions in AdS/QCD

Electromagnetic transitions involving nucleons and their resonances are here presented in the fermionic sector of the AdS/QCD soft-wall model, using the differential configurational entropy (DCE) as a measure of information entropy. The DCE is employed to derive adjustable parameters that define the minimal and nonminimal couplings in the nuclear interaction with a gauge vector field, in the nucleonic γN→N⁎(1535) transition. The values obtained comply with phenomenological data with good accuracy.

A second Higgs near 0.5 TeV from bottom-up holographic modeling of beyond the Standard Model strong sector

One of the simplest extensions of the Standard Model (SM) consists in adding a scalar singlet. This second Higgs boson is able to solve several fundamental problems of SM. Additional scalar particles arise naturally in composite Higgs scenarios in which some confining “strong sector” beyond the SM drives the electroweak symmetry breaking. The underlying strongly coupled gauge theory may be similar to QCD and could be modeled holographically. We construct a bottom-up holographic model for description of the spectrum of composite Higgs particles. The model is based on the holographic Soft Wall model and the Wilson confinement criterion. The constructed model predicts the existence of a second Higgs boson with a mass of about 515 GeV.

π0,η,η′ two-photon transition form factors in the holographic soft-wall model and contributions to (g−2)μ

We compute the two-photon transition form factors of the light pseudoscalar π0, η and η′ mesons in a soft-wall holographic model of QCD with a solution of the U(1)A problem. We compare the results with the experimental data in different ranges of photon virtualities. The obtained transition form factors are used to determine the π0, η and η′ pole terms in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.

Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum

It is well known that the soft-wall holographic model for QCD successfully reproduces not only the linear Regge spectrum, but also, via the holographic Wilson confinement criterion, the “linear plus Coulomb” confinement potential, which is similar to the Cornell potential. This property could be interpreted as a holographic counterpart of the hadron string picture, where the linearly rising potential and Regge-like spectrum are directly related. However, such a relation does not exist in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up holographic models. The standard soft-wall model is merely a particular representative of this class. This fact is relatively unknown, so we provide a comprehensive discussion of the point. As an example, we consider a soft-wall-like model with linear dilaton background in the metric. This model leads to a hydrogen-like spectrum. A “linear plus Coulomb” confinement potential within this model is calculated. The calculation of renormalized potential at short distances turns out to be complicated by a new subtlety that was skipped in general discussions of the issue existing in the literature. However, the confinement potential of the model is shown to be not very different from the potential obtained in the standard soft-wall model with a quadratic background.

Axial-Vector Form Factor of Nucleons at Finite Temperature from The Ads/Qcd Soft-Wall Model

Axial-Vector Form Factor of Nucleons at Finite Temperature from The Ads/Qcd Soft-Wall Model

Pion dynamics in a soft-wall AdS-QCD model

Pseudo-Goldstone modes appear in many physical systems and display robust universal features. First, their mass m obeys the so-called Gell-Mann-Oakes-Renner (GMOR) relation f2m2 = Hoverline{sigma} , with f the Goldstone stiffness, H the explicit breaking scale and overline{sigma} the spontaneous condensate. More recently, it has been shown that their damping Ω is constrained to follow the relation Ω = m2Dφ, where Dφ is the Goldstone diffusivity in the purely spontaneous phase. Pions are the most paradigmatic example of pseudo-Goldstone modes and they are related to chiral symmetry breaking in QCD. In this work, we consider a bottom-up soft-wall AdS-QCD model with broken SU(2)L × SU(2)R symmetry and we study the nature of the associated pseudo-Goldstone modes — the pions. In particular, we perform a detailed investigation of their dispersion relation in presence of dissipation, of the role of the explicit breaking induced by the quark masses and of the dynamics near the critical point. Taking advantage of the microscopic information provided by the holographic model, we give quantitative predictions for all the coefficients appearing in the effective description. In particular, we estimate the finite temperature behavior of the kinetic parameter mathfrak{r} 2 defined as the ratio between the Goldstone diffusivity Dφ and the pion attenuation constant DA. Interestingly, we observe important deviations from the value mathfrak{r} 2 = 3/4 computed in chiral perturbation theory in the limit of zero temperature.

Deuteron electromagnetic form factors and tensor polarization observables in the framework of the hard-wall AdS/QCD model

We study the electromagnetic form factors and tensor polarization observables of the deuteron in the framework of the hard-wall AdS/QCD model. We find a profile function for the bulk twist vector field, which describes the deuteron on the boundary and fix the infrared boundary cut-off of AdS space in accordance with the ground state mass of the deuteron. We obtain the deuteron charge monopole, quadrupole, and magnetic dipole form factors and tensor polarization observables from the bulk Lagrangians for the deuteron and photon field interactions. We plot the momentum transfer dependence of the form factors and tensor polarization observables and compare our numerical results with those in the soft-wall model and experimental data.

Meson and glueball spectroscopy within the graviton soft-wall model

In this contribution we present results of the calculations of several hadronic spectra within the holographic graviton soft-wall (GSW) model. In particular, we studied and compared with data for the ground state and excitations of: glueballs, scalar, vector, axial and pseudo-scalar mesons. The GSW model is found to be capable to describe these observable with only few parameters.

The pion in the graviton soft-wall model: phenomenological applications

The holographic graviton soft-wall model, introduced to describe the spectrum of scalar and tensor glueballs, is improved to incorporate the realization of chiral-symmetry as in QCD. Such a goal is achieved by including the longitudinal dynamics of QCD into the scheme. Using the relation between AdS/QCD and light-front dynamics, we construct the appropriate wave function for the pion which is used to calculate several pion observables. The comparison of our results with phenomenology is remarkably successful.

Gluon string breaking and meson spectrum in the holographic Soft Wall model

We propose a general method for finding a string-like meson spectrum which is based on a certain condition for the breaking of closed gluon string. A model is constructed that successfully realizes the proposed method. The model is based on the holographic Soft Wall model for QCD and the use of the Wilson confinement criterion. We applied our approach to the vector and scalar cases and obtained numerical predictions for the intercepts of corresponding Regge like radial meson spectra. A good agreement is obtained both with the existing experimental data and with some other known phenomenological approaches. Remarkably, our closed string breaking condition has two branches. We argue that they should correspond to states of opposite parity. The Wilson confinement criterion leads then to a natural mass splitting between parity partners. The constructed model represents thus the first example of bottom-up holographic model in which the effects of chiral symmetry breaking can emerge automatically, i.e., without additional assumptions taken outside of the holographic approach.

Partonic behavior of string scattering amplitudes from holographic QCD models

We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s. In the fixed angle approximation we find in the hard and soft wall models that mathcal{A} ∼ s2−∆/2 whereas in Witten’s model mathcal{A} ∼ s3−∆/2 and mathcal{A} ∼ s7/3−2∆/3 for the 11D and 10D formulations, respectively. In the Regge regime mathcal{A} ∼ s2t−2+α (log s/t)−1+α where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [ mathcal{A} ] ∼ s−1, Im [ mathcal{A} ] ∼ sα. We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.

Gravitational waves of the QCD phase transition in a 5D soft wall model with Gauss-Bonnet correction

In this paper, we study the gravitational wave energy density spectrum of cosmological de/confinement phase transition at finite baryon chemical potential within a soft wall model of AdS/QCD with Gauss-Bonnet correction. Focusing on the approach of dilaton/radion dominance approximation, we find the dual bounce action and the duration of the phase transition at the nucleation temperature. We also consider the possibility of a supercooling period during the transition, obtain the quantities characterizing the gravitational wave spectrum through this approach, and discuss the detectability prospect of generated gravitational wave signals by gravitational wave experiments.