Within the AdS/CFT correspondence, for description of $\mathcal{N}=4$ super Yang-Mills theory in four dimensions one needs not only low-energy supergravity on AdS$_5$ but also the whole infinite tower of massive Kaluza-Klein (KK) states on AdS$_5\times$S$_5$ which appear after the KK-compactification on five-dimensional sphere. The latter aspect is usually ignored in phenomenological AdS/QCD models. The emerging massive 5D fields on AdS$_5$ are dual to higher-dimensional operators in 4D gauge theory, with masses being known polynomial functions of canonical dimensions of these operators. Motivated by this observation, we propose to calculate the spectrum of radially excited hadrons in bottom-up holographic QCD models as spectrum of zero KK modes of massive 5D fields dual to higher dimensional operators in QCD. A relevant physical motivation is suggested. The radial states with growing masses are then enumerated by growing dimensions of interpolating QCD operators. We tested the proposal in the Soft Wall and Hard Wall holographic models in the sector of light mesons. The spectrum of Soft Wall model turns out to be unchanged in the new description. But in the Hard Wall model, our approach is shown to lead to a much better phenomenological spectrum of vector radial excitations than the traditional description.
We discuss a derivation of the quadratic in fields part of action of bottom-up holographic models from some general properties of the large-Nc limit in QCD.
Recent progress in constructing holographic models for QCD is discussed, concentrating on the bottom-up models which implement holographically the renormalization group flow of QCD. The dynamics of gluons can be modeled by using a string-inspired model termed improved holographic QCD, and flavor can be added by introducing space filling branes in this model. The flavor fully backreacts to the glue in the Veneziano limit, giving rise to a class of models which are called V-QCD. The phase diagrams and spectra of V-QCD are in good agreement with results for QCD obtained by other methods.
Within the bottom-up holographic approach to QCD, the highly excited hadrons are identified with the bulk normal modes in the fifth "holographic" dimension. We show that additional states in the same mass range can appear also from taking into consideration the 5D fields dual to higher dimensional QCD operators. The possible effects of these operators were not taken into account in almost all phenomenological applications. Using the scalar case as the simplest example, we demonstrate that the additional higher dimensional operators lead to a large degeneracy of highly excited states in the Sof…
We advance in constructing a bottom-up holographic theory of linear meson Regge trajectories that generalizes and unites into one logical framework various bottom-up holographic approaches proposed in the past and scattered in the literature. The starting point of the theory is a quadratic in fields holographic five-dimensional action in which the Poincaré invariance along the holographic coordinate is violated in the most general way compatible with the linear Regge behavior of the discrete spectrum in four dimensions. It is further demonstrated how different Soft Wall (SW) like holographic m…
We consider the photo-excitation of charm and bottom pentaquarks with the holographic assignments $[\frac 12\frac 12^-]_{S=0,1}$ and $[\frac 12\frac 32^-]_{S=1}$, in the photo-production of heavy vector mesons such as charmonia and bottomonia near threshold. We use a Witten diagram to combine the s-channel photo-excitation of holographic pentaquarks with a massive t-channel graviton or tensor glueball exchange, to extract the scattering amplitude for heavy meson photo-production in the threshold region. The pentaquark signal is too weak to be detected at current electron facilities.
We analyze the decay modes of the three $[\frac 12\frac 12^-]_{S=0,1}$ and $[\frac 12\frac 32^-]_{S=1}$ non-strange pentaquarks with hidden charm and bottom, predicted by holographic QCD in the heavy quark limit. In leading order, the pentaquarks %are composed of heavy-light mesons in bulk bound to an instanton core. They are degenerate and stable by heavy quark symmetry. At next to leading order, the spin interactions lift the degeneracy and cause the pentaquarks to decay. We show that the open charm (bottom) decay modes dwarf the hidden charm (bottom) ones, with total widths that are consist…
A holographic dual of hadrons at finite density is considered. We use the zero black-hole mass limit of Reisner-Nordstrom (RN) AdS background with hard wall to describe a confining background with finite quark density. We calculate density-dependence of meson masses and decay constants. In our model, pion decay constant and its velocity go down but all the meson masses go up as density grows.
We propose a five-dimensional framework for modeling the background geometry associated to ordinary Yang-Mills (YM) as well as to nonsupersymmetric gauge theories possessing an infrared fixed point with fermions in various representations of the underlying gauge group. The model is based on the improved holographic approach, on the string theory side, and on the conjectured all-orders beta function for the gauge theory one. We first analyze the YM gauge theory. We then investigate the effects of adding flavors and show that, in the holographic description of the conformal window, the geometry …
Confining potential in holographic bottom-up QCD from WKB
School of Nuclear Science and Technology, University of South China（南华大学核科学与技术学院）；Key Laboratory of Advanced Nuclear Energy Design and Safety, Ministry of Education（教育部先进核能设计与安全重点实验室）；Instituto de Física y Astronomía, Universidad de Valparaíso（瓦尔帕莱索大学物理与天文学研究所）
We evaluate the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon with two light flavors in minimal hard-wall and soft-wall holographic QCD models, as well as in simple generalizations thereof, and compare with the rather precise results available from dispersive and lattice approaches. While holographic QCD cannot be expected to shed light on the existing small discrepancies between the latter, this comparison in turn provides useful information on the holographic models, which have been used to evaluate hadronic light-by-light contributions …
Bottomonium and charmonium, representing quarkonia states, are scrutinized under the point of view of the information theory, in the AdS/QCD holographic setup. A logarithmic measure of information, comprised by the configurational entropy, is here employed to quantitatively study quarkonia radially excited S-wave states. The configurational entropy provides data regarding the relative dominance and the abundance of the bottomonium and charmonium states, whose underlying information is more compressed, in the Shannon's theory meaning. The derived configurational entropy, therefore, identifies t…
String theory's holographic QCD duality makes predictions for hadron physics by building models that live in five-dimensional (5D) curved space. In this pedagogical note, we explain how finding the hadron mass spectrum in these models amounts to finding the eigenvalues of a time-independent, one-dimensional Schroedinger equation. Changing the structure of the 5D curved space is equivalent to altering the potential in the Schroedinger equation, which in turn alters the hadron spectrum. We illustrate this concept with three holographic QCD models possessing exact analogs in basic quantum mechani…
We compute the spectrum of light hadrons in a holographic dual of QCD defined on $AdS_5 \times S^5$ which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale $Λ_{QCD}$, is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio…
We explore the effect of magnetic field on chiral condensation in QCD via a simple bottom up holographic model which inputs QCD dynamics through the running of the anomalous dimension of the quark bilinear. Bottom up holography is a form of effective field theory and we use it to explore the dependence on the coefficients of the two lowest order terms linking the magnetic field and the quark condensate. In the massless theory, we identify a region of parameter space where magnetic catalysis occurs at zero temperature but inverse magnetic catalysis at temperatures of order the thermal phase tra…
We revisit the three non-strange pentaquarks $[\frac 12\frac 12^-]_{S=0,1}$ and $[\frac 12\frac 32^-]_{S=1}$ predicted using the holographic dual description, where chiral and heavy quark symmetry are manifest in the triple limit of a large number of colors, large quark mass and strong $^\prime$t Hooft gauge coupling. In the heavy quark limit, the pentaquarks with internal heavy quark spin $S$ are all degenerate. The holographic pentaquarks are dual to an instanton bound to heavy mesons in bulk, without the shortcomings related to the nature of the interaction and the choice of the hard core i…
This work explores a holographic proposal to describe light nuclide spectroscopy by considering extensions to the well-known bottom-up AdS/QCD proposals, the hardwall and softwall models. We also propose an alternative description inspired by the Woods-Saxon potential. We find the static dilaton associated with this potential in this Wood-Saxon-like model. We compute the nuclide spectra finding that, despite their pure AdS/QCD origin, hardwall and softwall, as monoparametric models, have good accuracy and precision since the RMS error is near 11 $\%$ and 4 $\%$ respectively. In the case of the…
We estimate the thermalization time in two colliding shock waves holographic model of heavy-ion collisions. For this purpose we model the process by the Vaidya metric with a horizon defined by the trapped surface location. We consider two bottom-up AdS/QCD models that give, within the colliding shock waves approach, the dependence of multiplicity on the energy compatible with RHIC and LHC results. One model is a bottom-up AdS/QCD confining model and the other is related to an anisotropic thermalization. We estimate the thermalization time and show that increasing the confining potential decrea…
S-wave states of charmonium and bottomonium are described using bottom-up AdS/QCD. We propose a holographic model that unifies the description of masses and decay constants, leading to a precise match with experimental data on heavy quarkonia. Finite temperature effects are considered by calculating the current-current spectral functions of heavy vector mesons. The identification of quasi-particle states as Breit-Wigner resonances in the holographic spectral function was made. We develop a prescription to subtract background contributions from the spectral function to isolate the Breit-Wigner …
We apply recent techniques to construct geometries, based on local Calabi-Yau manifolds, leading to warped throats with 3-form fluxes in string theory, with interesting structure at their bottom. We provide their holographic dual description in terms of RG flows for gauge theories with almost conformal duality cascades and infrared confinement. We describe a model of a throat with D-branes at its bottom, realizing a 3-family Standard Model like chiral sector. We provide the explicit holographic dual gauge theory RG flow, and describe the appearance of the SM degrees of freedom after confinemen…
We show how the string amplitude $Φ(z)$ defined on the fifth dimension in AdS$_5$ space can be precisely mapped to the light-front wavefunctions of hadrons in physical spacetime. We find an exact correspondence between the holographic variable $z$ and an impact variable $ζ$, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schrödinger equations for the bound states of massless quarks and gluons which exactly reproduce the AdS/CFT results and give a realistic description of the light-quark meson and b…
Within the framework of AdS/QCD models, the spectra of radially excited hadrons are identified with towers of Kaluza-Klein (KK) states in a putative dual theory. The infinite number of KK states is indispensable to provide correct high energy asymptotics of correlation functions in QCD. It is known, however, that the KK modes of dual theory must be qualitatively different from real hadrons. And what is more important, the radially excited states appear in lattice calculations not as "excitations" of some ground state, but rather as independent states coupled to higher dimensional QCD operators…
We provide a method to study hadronic matter at finite density in the context of the Sakai-Sugimoto model. We introduce the baryon chemical potential through the external $U(1)_v$ in the induced (DBI plus CS) action on the D8-probe-brane, where baryons are skyrmions. Vector dominance is manifest at finite density. We derive the baryon density effect on the energy density, the dispersion relations of pion and vector mesons at large $N_c$. The energy density asymptotes to a constant at large density suggesting that dense matter at large $N_c$ freezes, with the pion velocity dropping to zero. Hol…
We present a no-go theorem that it is impossible in general to construct a holographic description of each meson with the quark-antiquark valence degree of freedom only with fixed (conserved) quantum number L in 3+1 dimensions and that would satisfy at the same time manifest chiral symmetry in the ultraviolet and would not violate unitarity.
One of the most fundamental problems in Quantum Chromodynamics is to understand the origin of the mass scale which controls the range of color confinement and the hadronic spectrum. We show that a mass gap and a fundamental color confinement scale arise when one extends the formalism of de Alfaro, Fubini and Furlan to frame-independent light-front Hamiltonian theory. Remarkably, the resulting light-front potential has a unique form of a harmonic oscillator in the light-front invariant impact variable if one requires that the action remains conformally invariant. The result is a single-variable…
In this paper we will show some applications achieved within type IIB superstring backgrounds since the emergence of the AdS/CFT correspondence. This correspondence relates a super Yang-Mills (SYM) theory, with strong coupling, and a type IIB superstring theory, with weak coupling. The use of the AdS/CFT correspondence allows us to investigate many aspects of hadronic physics described by QCD outside the perturbative regime, for example, glueball masses and the Regge trajectories related to the pomeron and the odderon. Throughout the text we will deal with the AdS/CFT correspondence within the…
We discuss the recent progress made in using bottom-up holographic QCD models in calculating hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where holographic QCD naturally satisfies the Melnikov-Vainshtein constraint by an infinite series of axial vector meson contributions.
We study pion condensation at zero temperature in a hard-wall holographic model of hadrons with isospin chemical potential. We find that the transition from the hadronic phase to the pion condensate phase is first order except in a certain limit of model parameters. Our analysis suggests that immediately across the phase boundary the condensate acts as a stiff medium approaching the Zel'dovich limit of equal energy density and pressure.
We review the recent progress made in using holographic QCD to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models. This requires the summation of an infinite tower of axial vector mesons, which is naturally present in holographic QCD models, and indeed takes care of the longitudinal short-distance constraint due to Melnikov and Vainshtein. Numerically the results of simple hard-w…
The properties of scalar mesons and glueballs at finite temperature are analyzed through a {\it bottom-up} holographic approach. We focus on the spectral functions and mass spectra. A discussion on hadron dissociation and deconfinement phase transition is also put forward.
We consider a new approach towards constructing approximate holographic duals of QCD from experimental hadron properties. This framework allows us to derive a gravity dual which reproduces the empirically found linear square-mass trajectories of universal slope for radially and orbitally excited hadrons. Conformal symmetry breaking in the bulk is exclusively due to infrared deformations of the anti-de Sitter metric and governed by one free mass scale proportional to Lambda_QCD. The resulting background geometry exhibits dual signatures of confinement and provides the first examples of holograp…
We revisit the predictions for the pseudoscalar-photon transition form factors in bottom-up and top-down holographic QCD models which only use the pion decay constant and the $ρ$ meson mass as input. We find remarkable agreement with the available experimental data for the single-virtual $π^0$ form factor that have recently been extended to lower momenta by BESIII, down to 0.3 GeV$^2$. The bottom-up models moreover turn out to be roughly consistent with recent experimental results obtained by BaBar for the double-virtual $η'$ form factor at large momenta as well as with a recent lattice extrap…
We extend our previous calculations of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment in holographic QCD to models with finite quark masses and a tower of massive pions. Analysing the role of the latter in the Wess-Zumino-Witten action, we show that the Melnikov-Vainshtein short-distance constraint is satisfied solely by the summation of contributions from the infinite tower of axial vector meson contributions. There is also an enhancement of the asymptotic behavior of pseudoscalar contributions when their infinite tower of excitations is summed, but …
Some problems with theoretical foundations of bottom-up holographic models are briefly discussed. It is pointed out that the spectroscopic aspects of these models in principle do not require the AdS/CFT prescriptions and may be interpreted as just an alternative language expressing the phenomenology of QCD sum rules in the large-Nc limit. A general recipe for incorporation of the chiral symmetry breaking scale into the soft-wall holographic models is proposed.
We study hadronization of the final state in a particle-antiparticle annihilation using a holographic gravity dual description of QCD. At the point of hadronization we match the events to a simple (Gaussian) energy distribution in the five dimensional theory. The final state multiplicities are then modelled by calculating the overlap between the Gaussian and a set of functions in the fifth dimension which represent each hadron. We compare our results to those measured in e+e- collisions at LEP and PEP-PETRA. Hadron production numbers, which differ in range by four orders of magnitude, are repr…
A holographic model of probe vector mesons (quarkonia) is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The vector meson action is modified to account for various quark masses. We focus on the $Φ$, $J/ψ$ and $Υ$ meson melting in agreement with hadron phenomenology in heavy-ion collisions at LHC, that is the formation of hadrons at the observed freeze-out temperature of 155 MeV.
We compute the complete next-to-leading order (NLO) SUSY-QCD corrections for the associated production of a pseudoscalar Higgs boson with a bottom quark via bottom-gluon fusion at the CERN Large Hadron Collider (LHC) and the Fermilab Tevatron. We find that the NLO QCD correction in the MSSM reaches $40%\sim50%$ at the LHC and $45%\sim80%$ at the Tevatron in our chosen parameter space.
The holographic description of Pomeron exchange in a strongly-coupled gauge theory with an AdS dual is extended to the case of two to three scattering. We study the production event of a central particle via hadron-hadron scattering in the double Regge kinematic regime of large center-of-momentum energy and fixed momentum transfer. The computation reduces to the overlap of a holographic wave function for the central particle with a source function for the Pomerons. The formalism is applied to scalar glueball production and the resulting amplitude is studied in various kinematic limits.
We use a variant of the $D4$-$D8$ construction that includes two chiral and one heavy meson, to describe heavy-light baryons and their exotics as heavy mesons bound to a flavor instanton in bulk. At strong coupling, the heavy meson is shown to {\it always bind} in the form of a flavor instanton zero mode in the fundamental representation. The ensuing instanton moduli for the heavy baryons exhibits both chiral and heavy quark symmetry. We detail how to quantize it, and derive model independent mass relations for heavy bayons with a single-heavy quark in leading order, in overall agreement with …
We present results for the production cross section of a Higgs Boson with a pair of bottom/anti-bottom quarks, including next-to-leading order (NLO) QCD corrections.
Parity violation induced by the chromo-anapole form factor of the bottom quark, generated from weak corrections, is studied in polarized hadron collisions. The forward-backward asymmetry in the bottom quark pair production at polarized $pp$ and $p\bar{p}$ colliders is evaluated in the Standard Model and in a Two Higgs Doublet Model to examine the effects of parity violation. In the models studied, promising results are found for polarized $p\bar{p}$ colliders.
We propose a five-dimensional framework for modeling low-energy properties of QCD. In the simplest three parameter model we compute masses, decay rates and couplings of the lightest mesons. The model fits experimental data to within 10%. The framework is a holographic version of the QCD sum rules, motivated by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. The model naturally incorporates properties of QCD dictated by chiral symmetry, which we demonstrate by deriving the Gell-Mann-Oakes-Renner relationship for the pion mass.
We present total rates and kinematic distributions for the associated production of a single bottom quark and a Higgs boson at the Tevatron and the LHC. We include next-to-leading order QCD corrections and compare the results obtained in the four and five flavor number schemes for parton distribution functions.
Chiral symmetry can be applied to many-body nonleptonic decays of heavy hadrons. We establish the chiral effective Hamiltonian for some typical many-body nonleptonic decays of bottom hadrons. We discuss the lowest-order contributions coming from such a Hamiltonian and present, as an example, a calculation of decay distributions of $B^-\to D^+ D^-_s π^-$ and $B^-\to D^{\ast +} D^-_s π^-$. We emphasize that wide applications of this method are possible.
Several physical quantities of light hadrons are examined by a new holographic model of QCD, which is the modified version of the one proposed by Erlich et al. defined on AdS${}_5$. In our model, AdS${}_5$ is deformed by a non-trivial bulk scalar, this is corresponding to adding the mass term of the adjoint fermions to the 4d SYM theory dual to the gravity on AdS${}_5$. We find that this deformation should be taken to be rather small, but its important effects are also seen.
We compute a shift of baryon mass spectra due to quark masses in perturbation, in Sakai-Sugimoto model of holographic QCD. We find the shift for the ground state nucleons to be δM = 4.1 m_π^2 [GeV^{-1}], which is consistent with the current lattice QCD result. We predict the same value of the shift for N(1535) and Delta, while a larger value 7.7 m_π^2 [GeV^{-1}] for Roper N(1440). We also present some evidences that the shifts of the vector meson masses are suppressed in the large 't Hooft coupling limit.
A new contribution from pair-production of light gluinos, of mass 12 to 16 GeV, with two-body decays into bottom quarks and light bottom squarks, helps to obtain a bottom-quark production rate in better agreement with hadron collider data. The masses of the gluino and bottom squark are further restricted by the ratio of like-sign to opposite-sign leptons at hadron colliders. Constraints on this scenario from other data are examined and predictions are made.
Higgs-boson production in association with bottom quarks is an important discovery channel for supersymmetric Higgs particles at the Tevatron and the LHC. We present higher-order QCD predictions for inclusive cross sections and for the production of a Higgs boson in association with high-p_T bottom quarks. We compare calculations performed in a four-flavour scheme based on the parton processes gg,qqbar -> b bbar H with five-flavour scheme calculations based on bottom-quark scattering.
We present the results of a study of the semileptonic decays of the $B_c$-meson and the lowest lying doubly heavy baryons using the relativistic quark model. We do not employ a heavy quark mass expansion but keep the masses of the heavy quarks and hadronss finite. We calculate all relevant form factors and decay rates.
We calculate the branching ratio of a bottom hadron decaying into a charmed hadron and a charged $ρ$ meson within the QCD factorization approach. We consider the effect of the finite width correction of the $ρ$ meson. Our numerical calculation shows an obvious correction because of this effect. We find that the finite width effect of the $ρ$ meson reduces the branching ratios by about 9% to 11% for bottom meson decay channels: $B^+\to\bar{D^0}ρ^+$, $B^0\to D^-ρ^+$, and $B^0_s\to D^-_sρ^+$, and increases the branching ratio by about 10% for $Λ_b^0\toΛ_c^+ρ^-$.
We present predictions for the inclusive productions of the D meson originating from bottom hadrons at the CERN LHC in the general-mass variable-flavour-number scheme at next-to-leading order. We present results using two methods to describe the transition for $b\rightarrow D$: a two-step transition $b\rightarrow B \rightarrow D$, based on the $b\rightarrow B$ fragmentation functions and the spectra for $B\rightarrow D$ as measured by CLEO and a one-step transition based on the fragmentation functions for $b\rightarrow D$. The results of both approaches are compared.
Light-front holographic QCD provides a successful first approximation to hadron spectroscopy in the chiral limit of $(3+1)$-dim light-front QCD, where a holographic Schrödinger-like equation, with an emerging confining scale, $κ$, governs confinement in the transverse direction. In its supersymmetric formulation, light-front holography predicts that each baryon has two superpartners: a meson and a tetraquark, with their degenerate masses being generated by the same scale, $κ$. In nature, this mass degeneracy is lifted by chiral symmetry breaking and longitudinal confinement. In this paper, we …
In this paper we present a short overview on the dynamical holographic QCD method for hadron physics and QCD matter. The 5-dimensional dynamical holographic QCD model is constructed in the graviton-dilaton-scalar framework with the dilaton background field $Φ$ and the scalar field $X$ dual to the gluon condensate and the chiral condensate operator thus can represent the gluodynamics (linear confinement) and chiral dynamics (chiral symmetry breaking), respectively. The dilaton background field and the scalar field are a function of the 5th dimension, which plays the role of the energy scale, in…
We study the scalar glueball and vector meson spectral functions in a hot and dense medium by means of the soft-wall holographic model of QCD. Finite temperature and density effects are implemented through the AdS/RN metric. We analyse the behaviour of the hadron masses and widths in the $(T,μ)$ plane, and compare our results with the experimental ones and with other theoretical determinations.
We apply the soft wall holographic model from hadron physics to a description of the high-$T_c$ superconductivity. In comparison with the existing bottom-up holographic superconductors, the proposed approach is more phenomenological. On the other hand, it is much simpler and has more freedom for fitting the conductivity properties of the real high-$T_c$ materials. We demonstrate some examples of emerging models and discuss a possible origin of the approach.
