H. G. Dosch, S. J. Brodsky, G. F. de Téramond, M. Nielsen, Liping Zou
Supersymmetric Light Front Holographic QCD is a holographic theory, which not only describes the spectroscopy of mesons and baryons, but also predicts the existence and spectroscopy of tetraquarks. A discussion of the limitations of the theory is also presented.
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The aim of these lectures is to convey a working knowledge of Light Front Holographic QCD and Supersymmetric Light Front Holographic QCD. We first give an overview of holographic QCD in general and then concentrate on the application of the holographic methods on QCD quantized in the light front form. We show how the implementation of the supersymmetric algebra fixes the interaction and how one can obtain hadron mass spectra with the minimal number of parameters. We also treat propagators and compare the holographic approach with other non-perturbative methods. In the last chapter we describe …
Starting from the Hamiltonian equation of motion in QCD we find a single variable light-front equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space.
We describe the observed light-baryon spectrum by extending superconformal quantum mechanics to the light front and its embedding in AdS space. This procedure uniquely determines the confinement potential for arbitrary half-integer spin. To this end, we show that fermionic wave equations in AdS space are dual to light-front supersymmetric quantum mechanical bound-state equations in physical space-time. The specific breaking of conformal invariance explains hadronic properties common to light mesons and baryons, such as the observed mass pattern in the radial and orbital excitations, from the s…
We provide a holographic description of non-strange multiquark exotics as compact topological molecules by binding heavy-light mesons to a tunneling configuration in D8-D$\bar 8$ that is homotopic to the vacuum state with fixed Chern-Simons number. In the tunneling process, the heavy-light mesons transmute to fermions. Their binding is generic and arises from a trade-off between the dipole attraction induced by the Chern-Simons term and the U(1) fermionic repulsion. In the heavy quark limit, the open-flavor tetraquark exotics $QQ\bar q\bar q$ and $\bar Q\bar Q qq$, emerge as bound Efimov state…
In this article a systematic quantitative analysis of the isoscalar bosonic states is performed in the framework of supersymmetric light front holographic QCD. It is shown that the spectroscopy of the $η$ and $h$ mesons can be well described if one additional mass parameter -- which corresponds to the hard breaking of chiral $U(1)$ symmetry in standard QCD -- is introduced. The mass difference of the $η$ and $η'$ isoscalar mesons is then determined by the strange quark mass content of the $η'$. The theory also predicts the existence of isoscalar tetraquarks which are bound states of diquarks a…
In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essenti…
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…
We derive a light-front Schrodinger-type equation of motion for the quark-antiquark wave function of heavy quarkonia imposing constraints from the holographic soft-wall model.
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…
Holographic QCD model for heavy and exotic mesons at finite density: A self-consistent dynamical approach
本研究提出自洽动力学全息QCD模型，通过求解耦合场方程替代特设输入，研究有限温密下重介子与奇特介子的质谱和熔化行为，揭示了序贯熔化规律及化学势的影响，明确了相变线特征。
We construct an effective QCD light-front Hamiltonian for both mesons and baryons in the chiral limit based on the generalized supercharges of a superconformal graded algebra. The superconformal construction is shown to be equivalent to a semi-classical approximation to light-front QCD and its embedding in AdS space. The specific breaking of conformal invariance inside the graded algebra uniquely determines the effective confinement potential. The generalized supercharges connect the baryon and meson spectra to each other in a remarkable manner. In particular, the $π/b_1$ Regge trajectory is i…
Anti-de Sitter space in five dimensions provides an exact geometrical representation of the conformal group. Remarkably, gravity in AdS$_5$ space is holographically dual to frame-independent light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time $τ= x^0+x^3$. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension $z$ of AdS space and the variable $ζ$, where $ζ^2 = b^2_\perp x(1-x)$ is the argument of the boost-invariant light-front wavefunctions describing the internal structure of…
We report that the pion radius, decay constant, EM and transition form factors can simultaneously and accurately be predicted in light-front holographic QCD with a universal AdS/QCD mass scale, provided dynamical spin effects are taken into account.
The breaking of chiral symmetry in holographic light-front QCD is encoded in its longitudinal dynamics with its chiral limit protected by the superconformal algebraic structure which governs its transverse dynamics. The scale in the longitudinal light-front Hamiltonian determines the confinement strength in this direction: It is also responsible for most of the light meson ground state mass consistent with the Gell-Mann-Oakes-Renner constraint. Longitudinal confinement and the breaking of chiral symmetry are found to be different manifestations of the same underlying dynamics as found in 't Ho…
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 consider the light-front holographic QCD with the light-front wave functions for mesons, modified for massive quarks. We evaluate the wave functions, distribution amplitudes, and form factors for $π$, $ρ$, $K$, and $J/ψ$ mesons and photon-to-meson transition form factors for $π$, $η$, and $η^\prime$ mesons. The results are compared with the experimental data, wherever available.
Using light-front holography, we predict simultaneously the pion decay constant and the pion charge radius by taking into account (higher twist) dynamical spin effects whose relative importance is constrained by QCD.
The light-front wavefunction for mesons predicted by holographic light-front QCD is used to obtain the light-cone distribution amplitudes for the light vector mesons and the transition form factors for B and $B_s$ decays to $ρ$, $K^*$ and $ϕ$ mesons. Here, I present some of our predictions as compared to lattice QCD, OCD sum rules and the available experimental data.
Light front holographic QCD theory in the generalized uncertainty principle framework
本文将广义不确定性原理引入光前全息QCD，推导出GUP修正的强子质量谱方程，发现质量增大项显著提升了理论与实验的一致性。
Using the light-front holographic model, we study the transverse momentum dependent parton distributions (TMDs) for the case of pion. At leading twist, the unpolarized parton distribution function $ f_{1π}(x,\bfk^{2}) $ and the Boer-Mulders function $ h_{1π}^{\bot}(x,\bfk^{2}) $ are obtained for pion. We calculate both the functions using the light-front holographic model with spin improved wave function and compare the predicted results with available results of other models. In order to provide inputs in predicting future experimental data, a LO evolution is performed from model scale to exp…
Stress inside the pion in holographic light-front QCD
本研究提出利用半经典光前QCD与五维卷绕时空半经典场论的对应关系，在全息QCD中计算引力形状因子$D(Q^2)$的方法，通过光前全息术衔接不同$Q^2$区域物理，并计算π介子$D$项与格点模拟结果对比。
In this paper we review the hadroproduction mechanisms of double-charm baryons for the different experimental environments and reinterpret the SELEX and LHCb results.
Mesons with quantum numbers $J^{PC}=1^{-+}$ cannot be represented as simple quark-antiquark pairs. We explore hybrid configurations in the light meson sector comprising a quark, an antiquark and an excited gluon, studying the properties of such states in a phenomenological model inspired by the gauge/gravity correspondence. The computed mass, compared to the experimental mass of the $1^{-+}$ candidates $π_1(1400)$, $π_1(1600)$ and $π_1(2015)$, favous $π_1(1400)$ as the lightest hybrid state. An interesting result concerns the stability of hybrid mesons at finite temperature: they disappear fro…
We show that the holographic Schrödinger equation of light-front chiral QCD, together with the 't Hooft equation of (1+1)-dimensional QCD in the large $N_c$ limit, can simultaneously describe pion spectroscopy as well as the pion decay constant, charge radius, electromagnetic form factor, photon-to-pion transition form factor, Parton Distribution Function (PDF) and Distribution Amplitude (DA). Furthermore, the chiral-limit constraints, as encoded in the Gell-Mann-Oakes-Renner (GMOR) relation, are satisfied.
We present the leading-twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 target, such as the $ρ$-meson, in the light-front framework. Specifically, we predict the TMDs in the light-front holographic model and compare with the light-front quark model predictions. We obtain the TMDs using the overlap of the light-front wave functions. We evaluate the ${\bf k}_\perp$ moments upto second order and compare with the available theoretical predictions. Further, we analyze the leading-twist parton distribution functions (PDFs) of the $ρ$-meson in the light-fr…
Flavor-Dependent Entanglement Entropy in the Veneziano Limit from Light-Front Holographic QCD
本文利用轻前端反胶子QCD计算QCD子系统的味依赖熵，在Veneciano极限下探讨量子相关性，通过引入味修改的稀顿势和味特定标量场，揭示味驱动的纠缠不对称性。
The spin asymmetries in SIDIS associated with $T$-odd TMDs are presented in a light-front quark-diquark model of a proton. To incorporate the effects of the final state interaction, the light front wave functions are modified to have a phase factor which is essential to have Sivers or Boer-Mulders functions. The Sivers and Boer-Mulder asymmetries are compared with HERMES and COMPASS data.
We obtain the gluon parton distribution functions (PDFs) in the proton within the extended light-front holographic QCD framework, where the proton couples with the spin-two Pomeron in Anti-de Sitter space, together with constraints imposed by the Veneziano model. The gluon helicity asymmetry, after satisfying the perturbative QCD constraints at small and large longitudinal momentum regions, agrees with existing experimental measurements. The polarized gluon distribution is consistent with global analyses. We predict the gluon helicity contribution to the proton spin, $ΔG=0.221^{+0.056}_{-0.044…
We investigate the properties of octet and decuplet baryons in a light-front holographic model. By taking into account the effect of nonvanishing quark mass, we obtain the modified light-front wave functions which are applicable at both low and high energy scales. We calculate the spectra, form factors, magnetic moments and electromagnetic radii of octet and decuplet baryons with the results all matching the experiments well. The axial charge, which describes the contribution of quark helicity to the proton spin in the quark-parton model at the high energy scale, is also consistent with the ex…
We account for dynamical spin effects in the holographic light-front wavefunction of the pion in order to predict its mean charge radius, decay constant, spacelike electromagnetic form factor, twist-2 Distribution Amplitude and the photon-to-pion transition form factor. Using a universal fundamental AdS/QCD scale of 523 MeV and a constituent quark mass of 330 MeV, we find a remarkable improvement in describing all observables.
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 …
We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $ρ$ and $ϕ$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $ρ$ and $ϕ$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $ρ$ and $ϕ$ production data provided we use a set of light quark masses …
Holographic spectral functions of exotic spin-1 mesons
研究通过开发通用全息框架计算奇异自旋-1介子热谱函数，在软壁模型中测试该框架用于π₁和Zc通道，结果表明两通道解离温度低于相变温度，增加c延迟解离，且Zc共振在相同环境下更低温度解离。
We show the 't Hooft Equation and the light-front holographic Schrödinger Equation are complementary to each other in governing the transverse and longitudinal dynamics of colour confinement in quark-antiquark mesons. Together, they predict remarkably well the light, heavy-light and heavy-heavy meson spectroscopic data. The universal emerging hadronic scale of light-front holography, $κ\approx 0.5$ GeV, controls the transverse dynamics of confinement in all mesons. In heavy-heavy mesons, it also coincides numerically with the 't Hooft coupling which governs longitudinal confinement, thus refle…
We predict the twist-2 Transverse Momentum Dependent parton distribution functions (TMDs) of the pion, namely the unpolarized quark TMD, $f_{1}(x, k_\perp)$, and the transversely polarized quark TMD, also known as the Boer-Mulders function, $h^\perp_{1}(x, k_\perp)$, using a holographic light-front pion wavefunction with dynamical spin effects. These spin effects, in conjunction with gluon rescattering, are crucial to predict a non-zero holographic Boer-Mulders function. We investigate the use of a non-perturbative SU(3) gluon rescattering kernel, thus going beyond the usual approximation of p…
We predict the $\mathcal{V} \to \mathcal{P} γ$ decay widths and the $\mathcal{V} \to \mathcal{P} γ^{*}$ transition form factors, where $\mathcal{V}=(ρ, ω, K^*, ϕ)$ and $\mathcal{P}= (π,K, η,η^\prime)$, using spin-improved holographic light-front wavefunctions for the mesons. We find excellent agreement with the available data for both the decay widths and the timelike transition form factors extracted from the leptonic conversion decays $\mathcal{V} \to \mathcal{P} l^+ l^-$.
Gravitational form factors of the pion in light-front holographic QCD
该研究针对量子色动力学中π介子内部结构这一基本挑战，结合全息QCD与光前QCD，通过引入有效光前波函数计算π介子引力形状因子及半径，结果与格点QCD吻合良好，支持了现象学模型。
Non-equilibrium real-time dynamics and transport coefficients in Light-Front Holographic QCD
本研究扩展光前全息QCD框架，引入温度密度效应与度量涨落，计算强耦合QCD物质的关键输运系数，实现预平衡与热化动力学的实时建模，为重离子碰撞研究提供可检验预测。
The light-front holographic QCD approach is used to describe baryon spectroscopy and the systematics of nucleon transition form factors.
We construct a Schrodinger-like equation for the longitudinal wave function of a meson in the valence qq-bar sector, based on the 't Hooft model for large-N two-dimensional QCD, and combine this with the usual transverse equation from light-front holographic QCD, to obtain a model for mesons with massive quarks. The computed wave functions are compared with the wave function ansatz of Brodsky and De Teramond and used to compute decay constants and parton distribution functions. The basis functions used to solve the longitudinal equation may be useful for more general calculations of meson stat…
Using ideas from Light Front Holography, we discuss the calculation of the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case.
Holographic light-front QCD
本文综述了光前全息量子色动力学（HLFQCD）的核心要素，重点介绍在超共形代数中引入色禁闭尺度，并概述其在谱学、形状因子、部分子分布及纠缠熵与高能散射关系等方面的应用。
We generalize the soft-wall and hard-wall models to a light-front holographic QCD model with a generic dilaton profile. The effective potential induced by a higher power dilaton profile is interpreted as a stronger color confinement at long distance, and it gradually evolves to the hard-wall model when the power increases to infinity. As an application, we investigate the exotic meson states recently discovered in experiments in the generic soft-wall model with a higher power dilaton profile, and the results are in agreement with the spectra of the exotic mesons. Our calculation indicates a we…
We construct spin-improved holographic light front wavefunctions for the nucleons (viewed as quark-diquark systems) and use them to successfully predict their electromagnetic Sachs form factors, their electromagnetic charge radii, as well as the axial form factor, charge and radius of the proton. The confinement scale is the universal mass scale of light-front holography, previously extracted from spectroscopic data for light hadrons. With the Dirac and Pauli form factors normalized using the quark counting rules and the measured anomalous magnetic moments respectively, the masses of the quark…
The application of light front holographic QCD to B physics
本研究利用Brodsky和de Téramond发展的光前全息方法得到的强子波函数，计算轻矢量介子分布振幅，进而得到B介子跃迁形状因子及辐射衰变的相关贡献，并与实验数据对比。
We calculate the Standard Model (SM) predictions for the differential branching ratio of the rare $B_s \to ϕμ^+ μ^-$ decays using $B_s \to ϕ$ transition form factors (TFFs) obtained using holographic light-front QCD (hQCD) instead of the traditional QCD sum rules (QCDSR) . Our predictions for the differential branching ratio is in better agreement with the LHCb data. Also, we find that the hQCD prediction for $R_{K^*ϕ}$, the ratio of the branching fraction of $B \to K^* μ^+ μ^-$ to that of $B_s \to ϕμ^+ μ^-$ , is in excellent agreement with both the LHCb and CDF results in low $q^2$ range.
We investigate the quark Wigner distributions of the pion to reveal the multidimensional picture of pion. We have used the spin improved wave functions of pion deduced from the light-front holographic model of mesons. By using the Fock-state overlap representation, the Wigner distributions of an unpolarized, longitudinally polarized and transversely polarized quark inside the pion are calculated. We have presented the results of transverse Wigner distributions in impact-parameter space as well as in momentum space. In order to understand the role of skewness which gives the longitudinal moment…
Color transparency, the reduction of initial- or final-state interactions in coherent nuclear processes, is a natural prediction of QCD provided that small-sized or point-like configurations (PLCs) are responsible for high-momentum transfer, high-energy, semi-exclusive processes. I use the FMS criteria for the existence of PLCs to show that the wave functions of light front holographic QCD, as currently formulated, do not contain a PLC.
A complementary approach, derived from (a) higher dimensional anti--de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group and SO(2,1). This…
In this paper we show that the intrinsic heavy-quark QCD mechanism for the hadroproduction of heavy hadrons at large $x_F$ can resolve the apparent conflict between measurements of double-charm baryons by the SELEX fixed-target experiment and the LHCb experiment at the LHC collider. We show that both experiments are compatible, and that both results can be correct. The observed spectroscopy of double-charm hadrons is in agreement with the predictions of supersymmetric light front holographic QCD.
Pion parton distribution functions and pion-nucleus induced $J/ψ$ production in extended light-front holographic QCD
本文通过轻前波函数确定介子部分子分布函数，并利用其与核部分子分布函数计算介子-核碰撞中$J/ψ$产生截面，结果与实验数据一致。
Flavor-Dependent Dynamical Spin-Orbit Coupling in Light-Front Holographic QCD: A New Approach to Baryon Spectroscopy
本文提出一种新的轻前 holographic QCD 方法，通过引入依赖味的动态自旋-轨道势来研究自旋-轨道耦合对重子光谱的影响，预测了味依赖的质量分裂和 Regge 轨道，改进了轻和重重子光谱的描述。
In this paper the dynamical spin effects of the light-front holographic wavefunctions for light pseudoscalar mesons are studied using two different assumptions. These improved wavefunctions are then confronted with a number of sensitive hadronic observables: the decay constants of $π$ and $K$ mesons, their $ξ$-moments, the pion-to-photon transition form factor, and the pure annihilation $\bar{B}_{s}\to π^+ π^-$ and $\bar{B}_{d}\to K^+K^-$ decays. Taking $f_π$, $f_{K}$ and their ratio $f_{K}/f_π$ as constraint conditions, the $χ^2$ analyses for holographic parameters, including the mass scale p…
A phenomenological analysis of the scalar glueball and scalar meson spectra is carried out by using the AdS/QCD framework in the bottom-up approach. The resulting spectra are in good agreement for glueballs with lattice QCD results and for mesons with PDG data. We make use of the relation between the mode functions in AdS/QCD and the wave functions in Light-Front $QCD$ to discuss the mixing of glueballs and mesons. The results of our investigation point out that above 2 GeV scalar particles will appear in almost degenerate pairs of unmixed glueball and mesons states leading to an interesting p…
We show that (a) the conformal properties of Anti-de Sitter (AdS) space, (b) the properties of a field theory in one dimension under the full conformal group found by de Alfaro, Fubini and Furlan, and (c) the frame-independent single-variable light-front Schrödinger equation for bound states all lead to the same result: a relativistic nonperturbative model which successfully incorporates salient features of hadronic physics, including confinement, linear Regge trajectories, and results which are conventionally attributed to spontaneous chiral symmetry breaking.
We summarize the light-front coupled-cluster (LFCC) method for the solution of field-theoretic bound-state eigenvalue problems and indicate the connection with light-front holographic QCD. This includes a sample application of the LFCC method and leads to a relativistic quark model for mesons that adds longitudinal dynamics to the usual transverse light-front holographic Schrodinger equation.
The valence-quark distribution function of the pion has been of interest for decades; particularly, the profile it should adopt when $x\to1$ (the large-$x$ behavior) is subject of a long-standing debate. In the light-front holographic QCD (LFHQCD) approach, this behavior is controlled by the so called reparametrization function, $w_τ(x)$, which is not fully determined from first principles. We show that, owing to the flexibility of $w_τ(x)$, the large-$x$ profile $u^π(x)\sim (1-x)^{2}$ can be contained within the LFHQCD formalism. This is in contrast with a previous LFHQCD study~(Guy F. de Ter…
We study the photon-to-meson transition form factors (TFFs) F_{M γ}(Q^2) for gamma gamma^* \to M using light-front holographic methods. The Chern-Simons action, which is a natural form in 5-dimensional anti-de Sitter (AdS) space, leads directly to an expression for the photon-to-pion TFF for a class of confining models. Remarkably, the predicted pion TFF is identical to the leading order QCD result where the distribution amplitude has asymptotic form. The Chern-Simons form is local in AdS space and is thus somewhat limited in its predictability. It only retains the q \bar q component of the pi…
The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function $w(x)$ which incorporates Regge behavior at small $x$ and inclusive counting rules at $x \to 1$. A simple ansatz for $w(x)$ which fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory …
A remarkable holographic feature of dynamics in AdS space in five dimensions is that it is dual to Hamiltonian theory in physical space-time, quantized at fixed light-front time τ = t+z/c. This light-front holographic principle provides a precise relation between the bound-state amplitudes in AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The fifth dimension coordinate z is dual to the light front variable ζ describing the invariant separation of the quark constituents. The resulting valence Fock-state wavefuncti…
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