Generalized distribution amplitudes and gravitational form factors for pion
Qin-Tao Song
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6 pages, 5 figures, Proceedings of the XXVI International Workshop on Deep-Inelastic Scattering and Related Subjects, April 16-20, 2018, Kobe University, Japan
Generalized parton distributions (GPDs) have been investigated in the deeply virtual Compton scattering (DVCS) to solve the proton spin puzzle. On the other hand, the generalized distribution amplitudes (GDAs) can be studied in the two-photon process $γ^* γ\rightarrow h \bar{h}$ which is accessible at KEKB. Namely, the GDAs are the $s$-$t$ crossed quantities of the GPDs. In 2016, the differential cross section of the process $γ^* γ\rightarrow π^0 π^0$ was measured by the Belle collaboration in the $e^+e^-$collision , so that the pion GDAs can be obtained by analyzing the Belle data. Expressing the GDAs with a few parameters, we determined the GDAs by a $χ^2$ analysis . The form factors of the quark energy-momentum tensor are obtained from the determined GDAs. Then, we calculated the mass radius as 0.56-0.69 fm for the pion by using the form factor. This is the first study on gravitational form factors and radius of hadrons from actual experimental measurements . The Belle II will start taking data in 2018 by the upgraded SuperKEKB. Therefore, much accurate data are expected for the pion, and other hadron-pair productions will be measured in the near future. The GDA studies are valuable for understanding not only the 3D structure but also gravitational properties of hadrons.
Considering, as a limit case, an approximately flat pion distribution amplitude, which is determined from the hardest, in momentum space, solution of the Bethe-Salpeter equation for the pion wave function, we compute the pion transition form factor $F_{πγγ^{*}}(Q^{2})$ and the pion form factor $F_π(Q^2)$, taking into account the LO as well as NLO form of the hard coefficient function entering the leading-twist factorization formula. We also compute the exclusive photoproduction of pions pairs at high energies, $γγ\to π^{+}π^{-}$, where perturbative QCD can be used to compute the hard scatterin…
We present a lattice QCD determination of the distribution amplitude (DA) of the pion and the first few Mellin moments from an analysis of the quasi-DA matrix element within the leading-twist framework. We perform our study on a HISQ ensemble with $a=0.076$ fm lattice spacing with the Wilson-Clover valence quark mass tuned to the physical point. We analyze the ratios of pion quasi-DA matrix elements at short distances using the leading-twist Mellin operator product expansion (OPE) at the next-to-leading order and the conformal OPE at the leading-logarithmic order. We find a robust result for t…
We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass $M\approx 200\;$MeV in Ref. [1]. Using the relativistic three-particle quantization condition, we find $\sim 2 σ$ evidence for a nonzero value for the contact part of the three-$π^+$ ($I=3$) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold, and some tension in the energy dependent part of the three-$π^+$scattering amplitude. We also find that the two-$π^+$ ($I=2$) spectrum is fit well by …
We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those…
The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. This article describes the progress in the lattice QCD calculation of the fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion (HOPE).
Hadron tomography can be investigated by three-dimensional structure functions such as generalized parton distributions (GPDs), transverse-momentum-dependent parton distributions, and generalized distribution amplitudes (GDAs). Here, we extract the GDAs, which are $s$-$t$ crossed quantities of the GPDs, from cross-section measurements of hadron-pair production process $γ^* γ\rightarrow π^0 π^0$ at KEKB. This work is the first attempt to obtain the GDAs from the actual experimental data. The GDAs are expressed by a number of parameters and they are determined from the data of $γ^* γ\rightarrow …
Within the framework of the massive O($N$) nonlinear sigma model extended to the next-to-leading order in the chiral counting (for $N=3$ corresponding to the two(-quark)-flavor Chiral Perturbation Theory), we calculate the relativistic six-pion scattering amplitude at low energy up to and including terms $\mathcal{O}(p^4)$. Results for the pion mass, decay constant and the four-pion amplitude in the case of $N$ (meson) flavors at $\mathcal{O}(p^4)$ are also presented.
The elastic $I=1$ $p$-wave $ππ$ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with $N_{\rm f}=2+1$ dynamical quark flavors. Wilson clover ensembles generated by the Coordinated Lattice Simulations (CLS) initiative are employed at four lattice spacings down to $a = 0.05\,\mathrm{fm}$, several pion masses down to $m_π = 200\,\mathrm{MeV}$, and spatial volumes of extent $L = 3.1-5.5\,\mathrm{fm}$. The set of measurements on these ensembles, which is publicly available, enables an investigation of systematic errors due to the finite latt…
The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for high-energy exclusive processes in quantum chromodynamics. In this article, the second Mellin moment of the pion LCDA is determined as a proof-of-concept calculation for the first numerical implementation of the heavy-quark operator product expansion (HOPE) method. The resulting value for the second Mellin moment, determined in quenched QCD at a pion mass of $m_π=550$ MeV at a factorization scale of 2 GeV is $ \langle ξ^2 \rangle = 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}$. This…
We present a lattice-QCD calculation of the pion, kaon and $η_s$ distribution amplitudes using large-momentum effective theory (LaMET). Our calculation is carried out using three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC collaboration, at 310 MeV pion mass with 0.06, 0.09 and 0.12 fm lattice spacings. We use clover fermion action for the valence quarks and tune the quark mass to match the lightest light and strange masses in the sea. The resulting lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-s…
In this contribution I present a brief summary of recent progress in selected Lattice QCD techniques and subsequently illustrate them using the example of the current calculations of moments of meson distribution amplitude as well as of a direct evaluation of meson distribution amplitude.
Accessing proton generalized parton distributions and pion distribution amplitudes with the exclusive pion-induced Drell-Yan process at J-PARC
广义部分子分布（GPD）编码的强子部分子结构的多维信息出现在硬排斥反应的因式分解描述的积木。核子GPD是通过轻子束的深虚康普顿散射和深虚介子产生来实现的。与强子束互补的探测是π介子诱导的Drell-Yan过程。在本文中，我们讨论了最近的理论进展，描述这一过程的核子GPD和π分布振幅。此外，我们解决的可行性测量专有π介子诱导的Drell-Yan过程$π^- p \to μ^+μ^- n$通过光谱仪在高动量光束线正在建设中的日本J-PARC。在J-PARC实现这样的测量将提供一个新的测试微扰QCD描述的一类新的硬排斥反应。它还将提供在大型类时虚拟环境中实验性地访问核子GPD的可能性。
We provide a novel approach to calculate the gravitational form factor of pion under the ladder approximation of the Bethe-Salpeter equation, with contact interactions. Central to this approach is a symmetry-preserving treatment of the dressed $ππ$ amplitude, which shows explicitly the contributions from intrinsic quarks and bound states, the latter being necessary to produce the $D$-term of pion in the soft-pion limit. The approach we provide in this work can be applied to many processes of physical significance.
We present the state-of-the-art lattice QCD calculation of the pion and kaon light-cone distribution amplitudes (DAs) using large-momentum effective theory. The calculation is done at three lattice spacings $a\approx\{0.06,0.09,0.12\}$ fm and physical pion and kaon masses, with the meson momenta $P_z = \{1.29,1.72,2.15\}$ GeV. The result is non-perturbatively renormalized in a recently proposed hybrid scheme with self renormalization, and extrapolated to the continuum as well as the infinite momentum limit. We find a significant deviation of the pion and kaon DAs from the asymptotic form, and …
A consistent model for πN transition distribution amplitudes and backward pion electroproduction
推广广义部分子分布的概念，引入了重子-介子跃迁分布振幅（TDAs），即核子-介子态间非定域三夸克算符的非对角矩阵元。我们提出了一个通用的框架，模拟核子到π介子（$πN$）TDAs。我们的主要工具是π N TDAs的四重分布的谱表示。我们提出了一个因式分解的四重分布与输入的软π介子定理的π N TDAs。光谱表示的补充与D-项一样的贡献，从核子交换中的交叉通道。然后，我们研究了后向π介子电产生的QCD共线因式分解方法，其中振幅的非微扰部分涉及π N TDAs。在我们的π N TDAs的两个组件模型中，我们更新了以前的非极化截面的领先扭转估计。最后，我们计算了横向目标单自旋不对称性作为偏斜度的函数。我们发现它是相当大的价区域和敏感的唯象输入我们的π N TDA模型。
We discuss the pion and kaon distribution amplitudes up to twist-3 in the context of the random instanton vacuum (RIV). We construct explicitly the pertinent quasi-pion and quasi-kaon distributions in the RIV, and analyze them in leading order in the diluteness factor, at a resolution fixed by the inverse instanton size. The distribution amplitudes (DA) follow from the large momentum limit. The results at higher resolution are discussed using QCD evolution, and compared to their asymptotic limits and some lattice results.
