We calculate the one-photon loop radiative corrections to charged pion Compton scattering, $π^- γ\to π^- γ$. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Analytical expressions for the ${\cal O}(α)$ corrections to the invariant Compton scattering amplitudes, $A(s,u)$ and $B(s,u)$, are presented for 11 classes of contributing one-loop diagrams. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy threshold $λ$, and its relation to the experimental detection threshold is discussed. We find that the radiative corrections are maximal in backward directions, reaching e.g. -2.4% for a center-of-mass energy of $\sqrt{s}=4m_π$ and $λ=5 $MeV. Furthermore, we extend our calculation of the radiative corrections by including the leading pion structure effect (at low energies) in form of its electric and magnetic polarizability difference, $α_π- β_π\simeq 6\cdot 10^{-4} $fm$^3$. We find that this structure effect does not change the relative size and angular dependence of the radiative corrections to pion Compton scattering. Our results are particularly relevant for analyzing the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.
The electric ($α_π$) and magnetic ($β_π$) Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the $γπ\toγπ$ Compton scattering angular distribution at back scattering angles and $γγ\toππ$ absolute cross sections. Theory derivations are given of the $γπ\toγπ$ Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical …
We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalised polarisabilitie…
We evaluate the leading-order QED radiative corrections to the timelike Compton scattering (TCS) process $γp \to l^- l^+ p$. We study these corrections in two energy regimes using different models for the TCS amplitude. In the low-energy regime we calculate the contribution due to the proton and its lowest-energy excitation, the $Δ(1232)$ resonance. In the high-energy near-forward kinematical regime we calculate the TCS amplitude in a handbag approach in terms of Generalized Parton Distributions (GPDs). On the level of cross sections we find the QED radiative corrections to be in the $5 -10\%$…
We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $Δ$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $ γp\toγpπ^0 $ and extract the value of the $Δ^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with…
Low-energy Compton scattering off the proton is used for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The most recent determinations are based on either the fixed-$t$ dispersion relations (DR) or chiral perturbation theory in the single-baryon sector ($χ$PT). The two approaches obtain rather different results for proton polarizabilities, most notably for $β_{M1}$ (magnetic dipole polarizability). We attempt to resolve this discrepancy by…
Describing hadronic structure is one of the most intriguing problems in physics. In this respect, generalized parton distributions (GPDs) constitute an outstanding tool, allowing to draw "three dimensional pictures" of hadron's inside. Starting from contemporary models for pion's GPDs fulfilling all constraints imposed by QCD, we compute Compton form factors (CFFs) of pions subjected to deeply virtual Compton scattering. We show the behaviour of CFFs to be gluon-dominated at EIC's kinematics. Finally we evaluate lepton-beam-spin asymmetries in the Sullivan process, demonstrating the existence …
We compute the electromagnetic corrections to neutron beta decay using a low-energy hadronic effective field theory. We identify and compute new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the $β$-$ν$ angular correlations and the $β$-asymmetry. We comment on implications of our results for the comparison of the experimentally…
We investigate the vector and axial-vector form factors for the pion radiative weak decays $π^+\to e^+ν_e γ$ and $π^+\to e^+ν_e e^+ e^-$, based on the gauged effective chiral action from the instanton vacuum in the large $N_c$ limit. The nonlocal contributions, which arise from the gauging of the action, enhance the vector form factor by about $20\,\%$, whereas the axial-vector form factor is reduced by almost $30\,\%$. Both the results for the vector and axial-vector form factors at the zero momentum transfer are in good agreement with the experimental data. The dependence of the form factors…
在重子手征微扰理论（HBChPT）中计算了$π^- p \to γn$和$π^+ n \to γp$的微分截面，直到$O(p^3)$. $O(p)$和$O(p^2)$中的表达式没有自由参数。在$O(p^3)$处有三个未知参数，即HBChPT拉格朗日量的低能常数，这是通过拟合实验数据确定的。两个可接受的拟合，这可以通过与早期的色散关系计算的逆过程进行比较来分离。表达式的多极子，重点是p波多极子，获得和评估阈值。一般来说，从最好的两个拟合得到的结果是在良好的色散关系的预测。
A Continuum Schwinger Method to Study the Pion's Generalized Parton Distribution
Universidad de Valencia（瓦伦西亚大学）；IFIC-CSIC（伊菲克-西班牙高等科学研究委员会）；Universidad Pablo de Olavide（巴勃罗·德·奥拉维德大学）；Universidad de Huelva（韦尔瓦大学）；Irfu, CEA, Université Paris-Saclay（IRFU，法国原子能和替代能源委员会，巴黎萨克雷大学）
Non-perturbative model for the half-off-shell γN N vertex
用无限阶的π介子环修饰核子-光子顶点，计算了核子-光子顶点的形状因子。在模型中实现了切割规则和离散关系。利用最小替换的规定，我们构造了一个γπ N-N顶点，并证明了它必须包含在模型中，才能使γ N-N顶点的Ward-Takahashi恒等式成立.顶点是应用在耦合通道K-矩阵形式主义的康普顿散射，π介子光生和π介子散射。形状因子在π介子阈值处显示出明显的尖点结构。作为一个例子，我们计算了康普顿散射的截面。为了提供康普顿散射的规范不变性，利用极小代换构造了一个四点γγ N N接触项.
Compton scattering off the proton in the third resonance region is analyzed for the first time, owing to the full combined analysis of pion- and photo-induced reactions in a coupled-channel effective Lagrangian model with K-matrix approximation. Two isospin $I=3/2$ resonances $D_{33}(1700)$ and $F_{35}(1930)$ are found to be essential in the range of 1.6 - 1.8 GeV. The recent beam asymmetry data of Compton scattering from the GRAAL facility are used to determine the helicity couplings of these resonances, and strong constraints are coming also from $πN$ and $KΣ$ photoproduction data. The possi…
To describe low-energy (anti)neutrino fluxes in modern coherent elastic neutrino-nucleus scattering experiments as well as high-energy fluxes in precision-frontier projects such as the Enhanced NeUtrino BEams from kaon Tagging (ENUBET) and the Neutrinos from STORed Muons (nuSTORM), we evaluate (anti)neutrino energy spectra from radiative muon ($μ^- \to e^- \barν_e ν_μ(γ),~μ^+ \to e^+ ν_e \barν_μ(γ)$), pion $π_{\ell 2}$ ($π^- \to μ^- \barν_μ(γ),~π^+ \to μ^+ ν_μ(γ)$), and kaon $K_{\ell 2}$ ($K^- \to μ^- \barν_μ(γ),~K^+ \to μ^+ ν_μ(γ)$) decays. We compare detailed $\mathrm{O} \left( α\right)$ dis…
We perform a fit of the real Compton scattering (RCS) data below pion-production threshold to extract the electric ($α_{E1}$) and magnetic ($β_{M1}$) static scalar dipole polarizabilities of the proton, using fixed-$t$ subtracted dispersion relations and a bootstrap-based fitting technique. The bootstrap method provides a convenient tool to include the effects of the systematic errors on the best values of $α_{E1}$ and $β_{M1}$ and to propagate the statistical errors of the model parameters fixed by other measurements. We also implement various statistical tests to investigate the consistency …
We present the first attempt to extract the scalar dipole dynamical polarizabilities from proton real Compton scattering data below pion-production threshold. The theoretical framework combines dispersion relations technique, low-energy expansion and multipole decomposition of the scattering amplitudes. The results are obtained with statistical tools that have never been applied so far to Compton scattering data and are crucial to overcome problems inherent to the analysis of the available data set.
