Axial vector transition form factors in holographic QCD and their contribution to the anomalous magnetic moment of the muon
Josef Leutgeb, Anton Rebhan
备注：
23 pages, 5 figures, 4 tables; v3: more details on the MV SDC, slightly improved numerics (HW1), slightly extended summary; v4: typos corrected, summary table IV corrected by revised results of 1906.11795; v5: small corrections in appendix B
We evaluate axial vector transition form factors in holographic QCD models that have been shown to reproduce well recent experimental and theoretical results for the pion transition form factor. Comparing with L3 data on $f_1\toγγ^*$ we find remarkable agreement regarding the shape of single-virtual form factors. In the double-virtual case, the holographic results differ strongly from a simple dipole form, and this has an important impact on the corresponding estimate of the axial vector contribution to the anomalous magnetic moment of the muon $a_μ$ through hadronic light-by-light scattering. We demonstrate that hard-wall models satisfy the Melnikov-Vainshtein short-distance constraint for the latter, if and only if the infinite tower of axial vector states is included. The results for $a_μ$, however, are strongly dominated by the first few resonances. Numerically, these results turn out to be surprisingly large: (2.9 - 4.1)$\times 10^{-10}$ in the hard-wall models, 57-58% of which are due to the longitudinal contribution, which is the one responsible for the Melnikov-Vainshtein short-distance constraint. Rescaling the holographic result to obtain an optimal fit of L3 data, but then matching only 52% of the asymptotic constraint, the result is reduced to $2.2(5)\times 10^{-10}$, which is still significantly larger than most previous phenomenological estimates of the axial vector exchange contribution.
We present an analysis of the three-flavor holographic model of QCD associated to a $D4/D8$ brane configuration, with symmetry breaking induced by a worldsheet instanton associated to a closed loop connecting $D4-D8-D6-\overline{D8}$. We calculate the electromagnetic and axial couplings of all octet and decuplet baryons, as well as several negative parity excitations, with and without symmetry breaking effects, and demonstrate qualitative and quantitative agreement with many available experimental measurements, with marked improvement over the analogous two-flavor models.
Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate
利用全息术研究了弱电场作用下矢量-轴矢量味流相关器的横向部分。使用自下而上模型arxiv：1003.2377 {最近提出}计算相关器，该模型包括手性凝聚物的非线性动力学。结果表明，在低动量情况下，该结果与arXiv：1010.0718 {Son and Yamamoto}提出的由更简单的全息模型激发的关系式一致.然而，对于大的欧几里得动量，两个结果是不同的。在此过程中，还计算了矢量和轴矢量两点函数的差。在大的欧几里得动量下，发现第一非微扰贡献，如QCD所预期的那样，以$q^{-6}$的形式减少。
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…
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 …
Whereas the theoretical results for the dominant contributions to hadronic light-by-light scattering coming from pseudoscalar meson exchange have converged over the past years, the various published estimates of the contribution due to axial vector meson exchange differ wildly. Since holographic AdS/QCD models have proved to provide rather good models of singly and doubly virtual pion transition form factors, which reproduce remarkably well the known low-energy data and also the asymptotic leading-order pQCD behavior, it is of interest to consider their predictions for axial vector transition …
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 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 calculate cross sections for production of axial-vector $f_1(1285)$ mesons for double-tagged measurements of the $e^+ e^- \to e^+ e^- f_1(1285)$ reaction. Different $γ^* γ^* \to f_1(1285)$ vertices from the literature are used. Both integrated cross section as well as differential distributions are calculated. Predictions for a potential measurement at Belle II are presented. Quite different results are obtained for the different vertices proposed in the literature. Future measurements at $e^+ e^-$ colliders could test and/or constrain the $γ^* γ^* \to f_1 (a_1, f_1')$ vertices and associat…
The contribution from the axial-vector meson exchange to the potential of the muon-proton interaction in muonic hydrogen induced by anomalous axial-vector meson coupling to two photon state is calculated. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is large and important for a comparison with precise experimental data. In the light of our result, the proton radius "puzzle" is discussed.
The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model. The preliminary answer for contributions from a1 and f1 mesons to (g-2)_mu is 0.34 x 10^(-11) and does not support the Melnikov-Vainshtein estimate 2.2 x 10^(-11).
The singlet pseudoscalar sector of light mesons is investigated in the soft-wall model, a bottom-up approach to the AdS/QCD correspondence. The $η^\prime$ mass results from the mixing among the fields dual to the axial current, pseudoscalar current and the $G\tilde G$ operator. The topological susceptibility is computed for any quark mass, and the Witten-Veneziano relation is obtained in the large $N_c$ limit.
Axial-anomaly effects and chiral phase structure in holographic QCD
Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学技术大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；International Center for Theoretical Physics Asia-Pacific (ICTP-AP), UCAS（亚太理论物理中心，中国科学技术大学）；Hunan University（湖南大学）
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…
In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The coupling of mesons with the muon is via two-photon intermediate state. The parametrization of the transition form factor of two photons into PS and AV mesons, based on the experimental data on the transition form factors and QCD asymptotics, is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are …
We use light-front Holography to estimate the valence quark and the meson cloud contributions to the nucleon axial form factor. The free couplings of the holographic model are determined by the empirical data and by the information extracted from lattice QCD. The holographic model provides a good description of the empirical data when we consider a meson cloud mixture of about 30\% in the physical nucleon state. The estimate of the valence quark contribution to the nucleon axial form factor compares well with the lattice QCD data for small pion masses. Our estimate of the meson cloud contribut…
In this work we study the axial contributions to the hadronic light-by-light piece of the muon anomalous magnetic moment using the framework of resonance chiral theory. As a result, we obtain $a_μ^{\textrm{HLbL};A} = \left(0.8^{+3.5}_{-0.1}\right)\cdot 10^{-11}$, that might suggest a smaller value than most recent calculations, underlining the need of future work along this direction. In particular, we find that our results depend critically on the asymptotic behavior of the form factors, and as such, emphasizes the relevance of future experiments for large photon virtualities. In addition, we…
Status of the hadronic light-by-light contribution to the muon $g-2$ and holographic QCD predictions
Dipartimento di Fisica, Università di Napoli “Federico II（那不勒斯费德里科二世大学物理系）；INFN-Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Institut für Theoretische Physik, Technische Universität Wien（维也纳工业大学理论物理研究所）
We employ the comparatively minimal extension of hard-wall AdS/QCD due to Katz and Schwartz which takes into account the U(1)$_A$ anomaly for computing hadronic light-by-light scattering contributions of pseudoscalar and axial vector mesons to the anomalous magnetic moment of the muon $a_μ$. By including a gluon condensate as one extra tunable parameter besides those fixed by $f_π$ and the pion, kaon, and rho masses, we obtain remarkably accurate fits for $η$ and $η'$ masses and their decay rates to photons, leading to $a_μ$ contributions in complete agreement with the Standard Model result by…
The axial-vector form factor of the nucleons is considered in the framework of hard-wall model of holographic QCD. A new interaction term between the bulk gauge and matter fields was included into the interaction Lagrangian. We obtain the axial-vector form factor of nucleons in the boundary QCD from the bulk action using AdS/CFT correspondence. The momentum square dependence of the axial-vector form factor is analysed numerically.
We study the H-dibaryon (uuddss) in holographic QCD for the first time. Holographic QCD is derived from a QCD-equivalent D-brane system ($S^1$-compactified D4/D8/$\overline{\rm D8}$) in the superstring theory via the gauge/gravity correspondence. In holographic QCD, all baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons. In this framework, the H-dibaryon can be described as an SO(3)-type hedgehog state. We present the formalism of the H-dibaryon in holographic QCD, and perform the calculation to investigate its properties in the chiral limit.
Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that …
Based on a holographic far-from-equilibrium calculation of the chiral magnetic effect~(CME) in an expanding quark gluon plasma, we study collisions at various energies. We compute the time evolution of the CME current in the presence of a time-dependent axial charge density and subject to a time-dependent magnetic field. The plasma expansion leads to a dilution of the CME current. We study distinct combinations of how the initial magnetic field and initial axial charge behave with changing initial energy as proposed in previous literature. Most scenarios we consider lead to an increasing time-…
Pseudo scalar contributions to light-by-light correction of muon g-2 in AdS/QCD
利用规范/引力对偶性，我们对强子对μ子反常磁矩的贡献进行了全息计算。研究了具有硬壁截止的五维AdS背景中的全息QCD模型。考虑了5维SU（2）和U（3）味规范对称性对中性π、η和η对强子修正的贡献。我们发现赝标量对μ子反常磁矩的总贡献为a_mu=10.7 x 10^（-10），这与以前基于其他方法的估计一致。
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 …
We revisit well-known short-distance constraints relating the hadronic light-by light Green's function to the $\langle VVA \rangle$ one, that have been a subject of debate over the past years in the context of the muon $(g-2)$. Specifically, we identify a relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly that, by contrast, has not received attention in the past. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors, but further applications are disc…
V-QCD is a class of effective holographic models for QCD which fully includes the backreaction of quarks to gluon dynamics. The physics of the theta-angle and the axial anomaly can be consistently included in these models. We analyze their phase diagrams over ranges of values of the quark mass, N_f/N_c, and theta, computing observables such as the topological susceptibility and the meson masses. At small quark mass, where effective chiral Lagrangians are reliable, they agree with the predictions of V-QCD.
The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is reanalyzed in the unitary gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the 't Hooft-Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_μ^2/m_Z^2$. The…
