Mohammad Ahmady, Chandan Mondal, Ruben Sandapen, James P. Vary, Xingbo Zhao
We study the Wigner distributions of the pion using a holographic light-front pion wavefunction with dynamical spin effects to reveal its multidimensional structure.
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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…
We study the quark Wigner distributions of the pion meson which are the phase-space distributions containing the most general one-parton information.Using the pion wavefunctions deduced from a light-cone quark model, we calculate the Wigner distributions of the unpolarized, longitudinally polarized and transversely polarized quarks inside the pion meson via the Fock-state overlap representation, respectively.We present the numerical results of the transverse Wigner distributions in which the longitudinal momentum fraction is integrated out. The mixed Wigner distributions as functions of $b_y$ …
The holographic QCD prediction for the pion distribution amplitude (DA) $ϕ_{hol}(u)$ is used to compute the pion spacelike electromagnetic form factor $F_π(Q^2)$ within the QCD light-cone sum rule method. In calculations the pion's renormalon-based model twist-4 DA, as well as the asymptotic twist-4 DA are employed. Obtained theoretical predictions are compared with experimental data and with results of the holographic QCD.
We analyse the perturbative contributions from the higher helicity ($λ_{1}+λ_{1}=\pm 1$) components, which should be naturally contained in the light-cone wave function for the pion as a consequence of the Wigner rotation, in the QCD calculation of the pion form factor. It is pointed out that the contributions may provide the other fraction needed to fit the pion form factor data besides the perturbative contributions from the ordinary helicity components evaluated using the factorization formula with the asymptotic form of the distribution amplitude. We suggest a way to test the higher helici…
We report that the inclusion of dynamical spin effects in the pion holographic light-front wavefunction leads to a remarkable improvement in describing pion observables (pion mean charge radius, decay constant, spacelike electromagnetic form factor) without the need to invoke higher Fock state contributions and/or a special AdS/QCD mass scale for the pion.
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.
Wigner and Husimi partonic distributions of the pion in a chiral quark model
该研究在手征夸克模型的单圈层级计算π介子夸克的GTMDs、Wigner与Husimi分布，给出GTMDs解析式并数值分析后两种分布，表明粗粒化可显著减弱负值并改善概率解释。
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.
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 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.
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…
Pion Condensation and Pion Star from Holographic QCD
本文利用全息AdS/QCD模型研究有限同位旋密度下的QCD物质，确认π介子凝聚与超流相，推导物态方程并分析π介子星性质，结果显示模型与格点QCD及手征微扰理论高度一致。
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。
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…
Pion structure in Holographic QCD
采用修正背景的全息模型，融入线性禁闭和胶子凝聚等关键QCD特征，研究π介子的质量谱、电磁形状因子和引力形状因子，并与实验及格点QCD结果取得合理一致。
We investigate cold dense matter in the context of Sakai and Sugimoto's holographic model of QCD in the Wigner-Seitz approximation. In bulk, baryons are treated as instantons on S^3\times R^1 in each Wigner-Seitz cell. In holographic QCD, Skyrmions are instanton holonomies along the conformal direction. The high density phase is identified with a crystal of holographic Skyrmions with restored chiral symmetry at about 4 Mkk^3/pi^5. As the average density goes up, it approaches to uniform distribution while the chiral condensate approaches to p-wave over a cell. The chiral symmetry is effectivel…
In this article, we calculate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive single pion production cross section in photon-photon collisions in case of the running coupling and frozen coupling approaches within holographic QCD. We compare the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. Also, we show that in the context of frozen coupling approach a higher-twist contribution to the photon-photon collisions cross section is normalized in terms of the pion electro…
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。
We study pion in the holographic model of Hirn and Sanz which contains two Yang-Mills fields defined in the background of the sliced AdS space. The infrared boundary conditions imposed on these fields generate the spontaneous breaking of the chiral symmetry down to its vector subgroup. Within the framework of this model, we get an analytic expression for the pion form factor and a compact result for its radius. We also extend the holographic model to include Chern-Simons term which is required to reproduce the appropriate axial anomaly of QCD. As a result, we calculate the anomalous form facto…
Using a holographic dual model of QCD, we compute the pion electromagnetic form factor F_pi(Q^2) in the spacelike momentum transfer region, as well as pion couplings to vector mesons g_rho^(n) pi pi. Spontaneous and explicit chiral symmetry breaking are intrinsic features of this particular holographic model. We consider variants with both ``hard-wall'' and ``soft-wall'' infrared cutoffs, and find that the F_pi(Q^2) data tend to lie closer to the hard-wall model predictions, although both are too shallow for large Q^2. By allowing the parameters of the soft-wall model (originally fixed by obse…
A holographic analysis of the pion
本文利用光前全息方法，结合纵向动力学ansatz，研究't Hooft与Li-Vary模型的简并性及其在AdS₃中的联系，计算了π介子的低能可观测量。
We evaluate the ratio of shear viscosity to entropy density in a pion gas employing the Uehling-Uehlenbeck equation and experimental phase-shifts parameterized by means of the SU(2) Inverse Amplitude Method. We find that the ratio for this monocomponent gas stays well above the KSS 1/(4 pi) bound. We find similar results with other sets of phase shifts and conclude the bound is nowhere violated.
We study the asymmetric nuclear matter using a holographic QCD model by introducing a baryonic charge in the infrared boundary. We first show that, in the normal hadron phase, the predicted values of the symmetry energy and it's slope parameter are comparable with the empirical values. We find that the phase transition from the normal phase to the pion condensation phase is delayed compared with the pure mesonic matter: The critical chemical potential is larger than the pion mass which is obtained for the pure mesonic matter. We also show that, in the pion condensation phase, the pion contribu…
Azimuthal spin asymmetries in pion-polarized proton induced Drell-Yan process at COMPASS using holographic light-front QCD
本文利用全息光前QCD和软壁AdS/QCD模型计算介子-质子Drell-Yan过程中的领头捻度方位角自旋不对称性，引入非微扰SU(3)胶子重散射核与次对数精度演化，预测结果与COMPASS实验数据一致。
We summarize main points of our recent work where we studied the pion condensation for non-zero isospin chemical potential within a holographic QCD model. We confirmed that the second order phase transition with the mean field exponent occurs when the isospin chemical potential $μ_I$ exceed the pion mass, which is consistent with the result obtained by the chiral effective Lagrangian at $O(p^2)$. We find that a deviation for large $μ_I$ region can be understood as a higher order effects in the chiral effective Lagrangian. Our result shows that the chiral condensate defined by $\tildeσ \equiv \…
Predicting $\sin(2ϕ-ϕ_{s})$ azimuthal asymmetry in pion-proton induced Drell-Yan process using holographic light-front QCD
本研究在横动量依赖因子化框架下，结合全息光前π介子波函数与软墙AdS/QCD构建的质子TMD模型，计算Drell-Yan过程的方位角不对称性，探究非微扰SU(3)胶子再散射的作用，为研究非微扰QCD效应提供工具并指导实验。
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…
The hadron spectra and pion form factor in dynamical holographic QCD model with anomalous 5D mass of scalar field
本文在动力学全息QCD模型中引入标量场的反常五维质量修正，解决了轻味强子谱与π介子形状因子难以同时协调描述的问题，并改善了标量、赝标量和轴矢量介子谱。
Additivity of Breit-Wigner phases has been proposed to describe interfering resonances in partial waves in $ππ$ scattering. This assumption leads to an expression for partial wave amplitudes that involves products of Breit-Wigner amplitudes. We show that this expression is equivalent to a coherent sum of Breit-Wigner amplitudes with specific complex coefficients which depend on the resonance parameters of all contributing resonances. We use analyticity of $ππ$ partial wave amplitudes to show that they must have the form of a coherent sum of Breit-Wigner amplitudes with complex coefficients and…
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 extend a recent numerical calculation of the pion electromagnetic form factor F_π(Q^2) in holographic QCD to study two important issues regarding the behavior of fields in the bulk. First, we show that using a chiral symmetry-breaking field formally satisfying the boundary conditions of the ``soft-wall'' model changes numerical results very little from the earlier calculation that ignores these constraints. Second, we use a background field that interpolates between ``hard-wall'' and ``soft-wall'' models to obtain an improved model that reproduces the desirable phenomenological features of …
A holographic analysis of the pion
本文基于光前全息方法，利用't Hooft势和Li-Vary势建模纵向夸克动力学，计算了π介子质量、半径、衰变常数及形状因子，发现纵向波函数在x≈1/2处更集中，并揭示两种势的强简并性及其与AdS3四段弦动力学的联系。
By adopting the nonlinear realization of chiral symmetry, a holographic model for the baryon octet is proposed. The mass spectra of the baryon octet and their low-lying excited states are calculated, which show good consistency with experiments. The couplings of pion to nucleons are derived in two gauges and are shown to be equivalent with each other. It also shows that only derivative couplings of pion to nucleons appear in this holographic model. The coupling constant is then calculated.
We consider a holographic model of QCD, obtained by a very simple modification of the original construction, which describes at the same time the pion mass, the QCD anomalies and the baryons as topological solitons. We study in detail its phenomenological implications in both the mesonic and baryonic sectors and compare with the observations.
We try to understand the recently observed anomalous behavior of the photon-to-pion transition form factor in the holographic QCD approach. First the holographic description of the anomalous γ^*γ^*π^0 form factor is reviewed and applied to various models. It is illustrated that in describing the anomalous form factor, the holographic approach is asymptotically dual to the perturbative QCD (pQCD) framework, with the pion mode π(z)\sim z corresponding to the asymptotic pion distribution amplitude. This indicates some inconsistency in light-front holography, since π(z)\sim z would be dual to φ(x)…
Using holographic models where chiral symmetry is broken through IR b.c.'s, we determine a novel set of relations between QCD matrix elements. In particular, we find that the amplitudes of the three processes pi pi->pi pi, gamma gamma->pi pi and gamma->pi pi pi involve a single scalar function h(Q^2) given by a suitable 5D integral of the EoM Green's function. In a phenomenological analysis of gamma gamma->pi pi we find an overall agreement with the experimental cross section for a broad range of energy. Moreover, the polarizabilities at low energies show a fair agreement between the holograph…
To realize massive pions, we study variations of the holographic model of massless QCD using the D4/D8/anti-D8 brane configuration proposed by Sakai and Sugimoto. We propose deformations which break the chiral symmetry explicitly and compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. We also argue a chiral perturbation corresponding to our deformation.
We study the pion condensation at finite isospin chemical potential using a holographic QCD model. By solving the equations of motion for the pion fields together with those for the iso-singlet scalar and iso-triplet vector meson fields, we show that the phase transition from the normal phase to the pion condensation phase is second order with the mean field exponent, and that the critical value of the isospin chemical potential $μ_I$ is equal to the pion mass, consistently with the result obtained by the chiral effective Lagrangian at $O(p^2)$. For higher chemical potential, we find a deviati…
Pion Phenomenology from the Thermal Soft-Wall Model of Holographic QCD
本文基于热软墙模型研究有限温度下π介子的现象学性质，通过分析电磁形式因子、热质量等参数，验证了模型在低能强子动力学中的有效性。
We study phenomenological aspects of the holographic model of chiral symmetry breaking recently introduced by Kuperstein and Sonnenschein (KS). As a first step, we calculate the spectrum of vector and axial-vector mesons in the KS model. We numerically compute various coupling constants of the mesons and pions. Our analysis indicates that vector meson dominance is realized in this model. The pion, vector meson and axial-vector meson form factors are obtained and studied in detail. We find good agreement with QCD results. In particular, the pion form factor closely matches available experimenta…
Pion and kaon D terms from holographic QCD and coupled-channel dispersion relations
结合全息QCD与耦合道色散关系，计算π介子和K介子的D项，区分其显式质量与手征标量响应贡献，为相关格点研究提供低能参考。
High-Energy Pion Scattering in Holographic QCD: A Comparison with Experimental Data
本文研究了反德西特/纳维群QCD硬墙模型中高能介子散射，并与实验数据比较，展示了其在高能固定角度区域的定性一致性，同时预测了其他介子散射过程。
We investigate the leptonic decay constants of the pion and its excitations with a 5-d holographic model for quantum chromodynamics. We prove numerically that the leptonic decay constants of the excited states of the pion vanish in the chiral limit when chiral symmetry is dynamically broken. This nontrivial result is in agreement with a solid prediction of quantum chromodynamics and is based on a generalized Gell-Mann-Oakes-Renner relationship involving the decay constants and masses of the excited states of the pion. We also obtain an extended partially conserved axial-vector current relation…
We study one pion emission decay of the first excited state of the nucleon with negative parity $N(1535) \equiv N^*$ in the holographic model of QCD. The excited state is described as a vibrational mode along the extra $z$ direction in the five-dimensional space-time of the model. We have obtained an analytic formula for the axial coupling of $g_A^{NN^*}$. The off-diagonal axial coupling is obtained at the decaying pion momentum $|\boldsymbol{k}| = 448$ MeV as $g_A^{NN^*} \sim 0.32$, and hence a partial decay width $Γ_{N^* \to πN} \sim 30$ MeV, which is smaller than but reasonably compared to …
Elastic pion-proton and pion-pion scattering via the holographic Pomeron and Reggeon exchange
在 holographic QCD 模型中，通过 Pomeron 和 Reggeon 交换计算了弹性 π介子-质子和 π介子-π介子散射的总截面与微分截面，预测结果与实验数据一致。
Pion Gravitational Form Factors in Holographic QCD
在自上而下全息QCD框架内首次计算pion引力形状因子的动量转移依赖性，揭示胶球优势机制。
We calculate the contribution of the higher twist Feynman diagrams to the large-$p_T$ inclusive pion production cross section in proton-proton collisions in the case of the running and frozen coupling approaches within holographic QCD. The structure of infrared renormalon singularities of the higher twist subprocess cross section and it's resummed expression are found. We compare the resummed higher twist cross sections with the ones obtained in the framework of the frozen coupling approximation and leading twist cross section. We discuss the phenomenological consequences of possible higher-tw…
The total and differential cross sections of high energy pion-proton and pion-pion scattering are investigated in a holographic QCD model, focusing on the Regge regime in which the Pomeron exchange gives the dominant contribution to those cross sections. The Pomeron is described by the Reggeized spin-2 particle propagator, and the hadron-Pomeron couplings are given by gravitational form factors of the hadrons, which are obtained from the bottom-up AdS/QCD models. Since the parameters, which characterize the Pomeron trajectory, have been determined in a preceding study of the proton-proton scat…
We propose a six-dimensional light-front Wigner distribution for the complete description of partonic structures of a hadron such as pion and proton, taking advantage of the recently proposed light-front variable $\tilde{z}$ by Miller and Brodsky. Quantities derived from the Wigner distribution contain the most general information of partonic structures, including also new quantities correlating longitudinal coordinate with transverse momenta or transverse coordinates, together with spins. The new Wigner distribution can be viewed as a relativistic version of the original Wigner distribution i…
We study chiral symmetry breaking in the holographic D3-D7 system in a simple model with an arbitrary running coupling. We derive equations for the D7 embedding and show there is a light pion. In particular we present simple integral equations, involving just the running coupling and the quark self energy, for the quark condensate and the pion decay constant. We compare these to the Pagels-Stokar or constituent quark model equivalent. We discuss the implications for walking Technicolour theories. We also perform a similar analysis in the four dimensional field theory whose dual is the non-supe…
The holographic light-front QCD framework provides a unified nonperturbative description of the hadron mass spectrum, form factors and quark distributions. In this article we extend holographic QCD in order to describe the gluonic distribution in both the proton and pion from the coupling of the metric fluctuations induced by the spin-two Pomeron with the energy momentum tensor in anti--de Sitter space, together with constraints imposed by the Veneziano model{\color{blue},} without additional free parameters. The gluonic and quark distributions are shown to have significantly different effecti…
We calculate the ${α'}^4$ corrections to the non-Abelian DBI action on the D8-brane in the holographic dual of large N_c QCD proposed by Sakai and Sugimoto. These give rise to higher derivative terms, in particular, four derivative contact terms for the pion field with the coupling uniquely determined. We calculate the pion-pion scattering amplitude near threshold. The results respecting unitarity are in qualitative agreement with the experimental curves.
Gravitational form factors of pion from top-down holographic QCD
首次利用自顶向下全息QCD方法计算了介子引力形状因子，获取了D项，并发现介子通过无限胶球谱进行引力相互作用的胶球主导现象。
Holographic description of the kaon gravitational form factor
本文采用全息QCD方法计算K介子引力形式因子，并发现其在高能极限下与扰动QCD一致，同时K介子引力半径与π介子相近。
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 …
We analyze the equal-time Bethe-Salpeter quark wave functions of the pion in various models. We discuss how the quenched lattice QCD results with delocalized pion interpolators can be identified with the coarse grained wave functions, typical of low-energy effective models. Actually, we find that one-loop chiral quark models predict that pseudoscalar and tensor wave functions have the same shape, while the axial component is more extended. These facts are accurately confirmed by the lattice. We also show how the transversity information, relevant for the light-cone physics, can be straightforw…
Scalar-glueball-mediated scale-anomaly dominance of the confining pressure of the pion in holographic QCD
本研究通过拓下反引力QCD分析发现，标量胶球在传递π子限制压力中起中介作用，证实了标度异常在强子稳定性中的普遍作用。
This work studies the experiments of two-photon processes at BESIII from a theoretical viewpoint in light-cone quantum field theory. We adopt the momentum space wave function of the pion in the light-cone formalism by two forms of the Brodsky-Huang-Lepage~(BHL) prescription and the light-cone holographic QCD. We find that the wave function got by the light-cone holographic QCD can be related to the BHL wave function by a Jacobian factor. Then we calculate the transition form factor~(TFF) of the two-photon process by these two wave functions under the light-cone quark model. We compare the calc…
We study the anomalous electromagnetic pion form factor $F_{π^0γ^*γ^*}$ with a set of holographic models. By comparing with the measured value of the linear slope, some of these models can be ruled out. From the remaining models we obtain predictions for the low-energy quadratic slope parameters of $F_{π^0γ^*γ^*}$, currently out of experimental reach but testable in the near future. We find it particularly useful to encode this low-energy information in a form factor able to satisfy also QCD short-distance constraints. We choose the form factor introduced by D'Ambrosio, Isidori and Portoles in…
We quantify the importance of dynamical spin effects in the holographic light-front wavefunctions of the pion, kaon, $η$ and $η^\prime$. Using a universal AdS/QCD scale and constituent quark masses, we find that such effects are maximal in the pion where they lead to an excellent simultaneous description of a wide range of data: the decay constant, charge radius, spacelike EM and transition form factors, as well as, after QCD evolution, both the parton distribution function and the parton distribution amplitude data from Fermilab. These dynamical spin effects lead up to a $30\%$ chance of find…
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