L. V. Fil'kov, V. L. Kashevarov
Data on pion polarizabilities obtained in different experiments are reviewed. The values of the dipole and quadrupole polarizabilities of the pi^0 and pi^{+-} mesons found are compared with predictions of dispersion sum rules (DSRs) and two-loop calculations in the framework of chiral perturbation theory (ChPT). Possible reasons of a difference between the predictions of DSRs and ChPT are discussed.
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An analysis of different dispersion sum rules (DSRs) for the dipole and quadrupole pion polarizabilities is carried out. We prove the absence of additional spurious singularities in these approaches. The results of the calculations of the polarizabilities in the framework of DSRs are compared with ChPT predictions and with data obtained in different experiments.
We discuss main experimental works, where dipole polarizabilities of charged pions have been determined. Possible reasons for the differences between the experimental data are discussed. In particular, it is shown that the account of the $σ$-meson gives a significant correction to the value of the polarizability obtained in the latest experiment of the COMPASS collaboration.
We present a calculation of the virtual Compton scattering amplitude for $γ^\ast+π\to γ+π$ in the framework of chiral perturbation theory at ${\cal O}(p^4)$. We explicitly derive expressions for generalized electromagnetic polarizabilities and discuss alternative definitions of these quantities.
A fit of the experimental data to the total cross section of the process γγ->π^0π^0 in the energy region from 270 to 2250 MeV has been carried out using dispersion relations for the invariant amplitudes where the quadrupole polarizabilities are free parameters. As a result the sum and difference of the electric and magnetic quadrupole polarizabilities of the π^0 meson have been found for the first time: (\alpha2+\beta2)_π^0=(-0.181+-0.004)*10^{-4}fm^5, (\alpha2-\beta2)_pi^0=(39.70+-0.02)*10^{-4}fm^5. In addition, dispersion sum rules have been constructed for this sum and difference, respectiv…
The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my recent work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.
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 present a calculation of the cross section and the event generator of the reaction $πe\to πe γ$. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric $α_L(q^2)$, the transverse electric $α_T(q^2)$, and the magnetic $β(q^2)$ which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilities $\barα$ and $\barβ$, respectively. The calculation of the cross section is done in the framework of chiral perturbation theory at ${\cal O}(p^4)$. A pion VCS event generator has been written which is ready for implementat…
Recent experimental pion polarizability data are reviewed and analyzed. Data on the radiative π^+ meson photoproduction on the proton at MAMI has been used to determine the difference of the electric and magnetic dipole polarizabilities of the charged pion. Fits of the experimental data to the total cross sections of the processes γγ->π^0π^0 and γγ->π^\pmπ^\pm in the energy region from threshold to 2250 MeV and 2500 MeV, respectively, have been carried out using dispersion relations with subtractions for the invariant helicity amplitudes, where the dipole and the quadrupole polarizabilities of…
I discuss recent results regarding the influence of pion-nucleon and and nucleon-resonance physics on the (spin-) polarizabilities of the nucleon as measured in (polarized) Compton scattering.
Using the fact that the contribution of the states with isospin I=0 in the difference of the amplitudes of the processes γγ->π^+π^- and γγ->π^0π^0 is very small, we have analyzed the dispersion sum rules for the difference between the dipole polarizabilities of the charged and neutral pions as a function of the σ-meson parameters. Then taken into account the current perturbation value of (α-β)_π^0=-1.9, we have found (α-β)_π^(+-)=9.4--8.2 for values of the σ-meson parameter within the region: M_s=400--550 MeV, Γ_s=400--600 MeV, Γ_{\s->γγ}= 0--3 keV. It has been shown that the value of the deca…
Virtual Compton scattering off nucleons and pions at low energies is discussed. Predictions for the generalized polarizabilities of the nucleon are presented within the framework of heavy-baryon chiral perturbation theory and the linear sigma model. First results for the generalized polarizabilities of the charged pion in chiral perturbation theory at ${\cal O}(p^4)$ are shown.
The Compton scattering on a charged pion is studied using the dispersion relations. Unknown mass, full width and decay width into γγof the sigma meson are found from a fit to the experimental data for the process γ+γ\to π^0+π^0. These parameters are used for the calculation of the cross section of the Compton scattering on the charged pion. The analysis of the obtained results shows that the data on the elastic γ\pion scattering in the energy region up to \sqrt{s}=1 GeV (together with the data on process γγ\to π^0π^0) could be used both for a determination of the pion polarizability values wit…
A fit of the experimental data to the total cross section of the process $γγ->π^+π^-$ in the energy region from threshold to 2500 MeV has been carried out using dispersion relations with subtractions for the invariant amplitudes, where the dipole and the quadrupole polarizabilities of the charged pion are free parameters. As a result, the sum and the difference of the electric and magnetic dipole and quadrupole polarizabilities of the charged pion have been found: $(alpha_1+β_1)=(0.18+0.11-0.02)10^(-4)fm^3$, $(alpha_1-β_1)=(13.0+3.6-1.9)10^(-4)fm^3$, $(alpha_2+β_2)=(0.133+- 0.015)10^(-4)fm^5$,…
We discuss the virtual Compton scattering amplitude $γ^\ast+π\to γ+π$ which enters the reaction $π^-+e^-\toπ^-+e^-+γ$. The low-energy scattering amplitude is divided into a model-independent part, involving only the electromagnetic form factor, and a residual part which contains structure information related specifically to (virtual) Compton scattering. In the limit of vanishing final-photon energy, the residual amplitude can be expressed in terms of three generalized dipole polarizabilities which are functions of the squared virtual-photon four-momentum. We study the VCS amplitude in the fram…
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected to non-analytic structures
We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched QCD, and quenched QCD simulations. On a torus, volume dependence of electromagnetic observables is complicated by SO(4) breaking, as well as photon zero-mode interactions. We determine finite volume corrections to the Compton scattering tensor of pions. We argue, however, that such results cannot be used to ascertain volume corrections to polarizabilities determined in lattice QCD with background field methods. Con…
Pion and Sigma Polarizabilities and Radiative Transitions
费米实验室E781计划使用600 GeV的σ和π介子束和虚拟光子靶测量γ-σ和$γ$ -π介子相互作用。本实验将测量π介子的极化率和辐射跃迁。前者可以检验手征对称性的精确预测，后者对于a_1（1260）-> pi + gamma对于理解极化率是重要的。该实验还测量了Sigma超子的极化率和辐射跃迁。极化率可以检验重子手征微扰理论的预言。到Sigma*（1385）的辐射跃迁提供了对s夸克的磁矩的测量。给出了γ-π和γ-Σ相互作用的实验和理论结果。描述了E781实验。
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.
Neutral pion polarizabilities from four-point functions in lattice QCD
本研究采用四点函数法开展中性π介子极化率的晶格QCD原理验证模拟，发现电极化率与现有方法结果一致，磁极化率存在显著差异，提出夸克分解方法以探究非连通图的作用。
We calculate the spin-polarizabilities of the nucleon by means of dispersion relation, where the pion photoproduction amplitude predicted by chiral soliton model is utilized. We consider the $Nπ$ and $Δπ$ channels in the pion-photoproduction amplitude, and also evaluate the contribution of the anomalous term of the $π^0γγ$ process. In a narrow decay-width limit of the $Δ$ particle the result coincides with that in heavy baryon chiral perturbation theory (HBChPT) except for the interference part of the electric and magnetic amplitudes. A comparison with the multipole analysis is given.
Polarizabilities from kaon Compton scattering
本研究针对K介子康普顿散射极化率测量受$K^*(892)$共振影响的问题，提出利用色散理论从$Kπ$中间态模型无关地重构共振贡献以扩展可用能区的方法，并分析了电、磁偶极极化率的层级特性及角覆盖度对区分二者的灵敏度。
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…
Starting from hyperbolic dispersion relations, we present a system of Roy--Steiner equations for pion Compton scattering that respects analyticity and unitarity requirements, gauge invariance, as well as crossing symmetry, and thus all symmetries of the underlying quantum field theory. To suppress the dependence on the high-energy region, we also consider once- and twice-subtracted versions of the equations, where the subtraction constants are identified with dipole and quadrupole pion polarizabilities. We consider the resolution of the $γγ\toππ$ partial waves by a Muskhelishvili-Omnès represe…
Starting from hyperbolic dispersion relations, we derive a system of Roy--Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on high-energy input, we also consider once- and twice-subtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equatio…
Deuteron Compton scattering below pion photoproduction threshold is considered in the framework of the nonrelativistic diagrammatic approach with the Bonn OBE potential. A complete gauge-invariant set of diagrams is taken into account which includes resonance diagrams without and with NN-rescattering and diagrams with one- and two-body seagulls. The seagull operators are analyzed in detail, and their relations with free- and bound-nucleon polarizabilities is discussed. It is found that both dipole and higher-order polarizabilities of the nucleon are needed for a quantitative description of rec…
We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process gamma* h -> gamma h. We introduce a new method of obtaining a tensor basis with appropriate Lorentz-invariant amplitudes which are free from kinematical singularities and constraints. We then motivate a gauge-invariant separation into a generalized Born term containing ground-state properties only, and a residual contribution describing the model-dependent internal structure. The generalized dipole polarizabilities are defined in terms of …
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 …
The main experimental works, where dipole polarizabilities of charged pions have been determined, are considered. Possible reasons for the differences between the experimental data are discussed. In particular, it is shown that the account of the $σ$-meson gives a significant correction to the value of the polarizability obtained in the latest experiment of the COMPASS collaboration. We present also new fit results for the $(γγ\toππ)$ reaction.
A calculation of deuteron Compton scattering using non-relativistic perturbation theory is presented,with the primary motivation of investigating the feasibility of determining the neutron polarizabilities from this type of experiment. This calculation is expected to be valid for energies below 100 MeV. Pion-exchange, relativistic, and recoil corrections are also included. The low-energy theorem for gauge invariance is shown to be satisfied. The relative effects of the different terms and their effects on the determinations of the polarizabilities are discussed at energies of 49, 69, and 95 Me…
Charged and neutral, pion and kaon electric polarizabilities are extracted from lattice QCD using an ensemble of anisotropic gauge configurations with dynamical clover fermions. We utilize classical background fields to access the polarizabilities from two-point correlation functions. Uniform background fields are achieved by quantizing the electric field strength with the proper treatment of boundary flux. These external fields, however, are implemented only in the valence quark sector. A novel method to extract charge particle polarizabilities is successfully demonstrated for the first time.
An experiment on the radiative pi^+ meson photoproduction from the proton (gamma p->gamma pi^+ n) was carried out at the Mainz Microtron MAMI in the kinematic region 537 MeV <E_{gamma}<817 MeV, 140^o<theta_{gamma-gamma'}^cm<180^o. The pi^+ meson polarizabilities have been determined from a comparison of the data with the predictions of two different theoretical models, the first one being based on an effective pole model with pseudoscalar coupling while the second one is based on diagrams describing both resonant and nonresonant contributions. The validity of the models has been verified by co…
The novel measurements of the $γ^\ast N \to Δ(1232)$ Coulomb quadrupole form factor in the range $Q^2=0.04$--0.13 GeV$^2$ changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in remarkable agreement with estimates of the pion cloud contributions to the quadrupole form factors at low $Q^2$. The pion cloud contributions to the electric and Coulomb form factors can be parametrized by the relations $G_E \propto G_{En}/ \left(1 + \frac{Q^2}{2M_Δ(M_Δ-M)}\right)$ and $G_C \propto G_{En}$, where $G_{En}$ is the neutron electric form factor, and $M$, …
Models of baryon structure predict a small quadrupole deformation of the nucleon due to residual tensor forces between quarks or distortions from the pion cloud. Sensitivity to quark versus pion degrees of freedom occurs through the $Q^2$ dependence of the magnetic ($M_{1+}$), electric ($E_{1+}$), and scalar ($S_{1+}$) multipoles in the $γ^* p \to Δ^+ \to p π^0$ transition. We report new experimental values for the ratios $E_{1+}/M_{1+}$ and $S_{1+}/M_{1+}$ over the range $Q^2$= 0.4-1.8 GeV$^2$, extracted from precision $p(e,e 'p)π^{\circ}$ data using a truncated multipole expansion. Results a…
The Chiral Perturbation Theory (CHPT) has been very successful in describing low-energy hadronic properties in the non-perturbative regime of Quantum Chromodynamics. The results of ChPT, many of which are currently under active experimental investigation, provide stringent predictions of many fundamental properties of hadrons, including quantities such as electromagnetic polarizabilities. Yet, even for the simplest hadronic system, a pion, we still have a broad spectrum of polarizability measurements (MARK II, VENUS, ALEPH, TPC/2g, CELLO, Belle, Crystal Ball). The meson polarizability can be a…
Chiral dynamics makes definitive predictions for the electromagnetic polarizabilities of hadrons near the chiral limit; but, agreement with experiment is tenuous in some cases. We provide an overview of lattice QCD methods to compute the electric and magnetic polarizabilities of hadrons. Central to these methods is the lattice simulation of quarks in uniform, classical electromagnetic fields. A long-term goal is the determination of polarizabilities directly from lattice computations, however, in the near term, one may need to rely on partially quenched chiral perturbation theory. Nonetheless …
Within a multi-phase transport (AMPT) model with the string melting mechanism and imported initial electric quadrupole moment, the difference between the elliptic flow of positive and negative pions is calculated. The slope parameter $r$ of the linear dependence of $Δv_{2}=v_{2}(π^{-})-v_{2}(π^{+})$ on $A_{ch}=(N^{+}-N^{-})/(N^{+}+N^{-})$ is yielded owing to the parton cascade, which converts the initial electric quadrupole distribution into the final charge-dependent elliptic flow. The slope parameter $r$ is found to be increased by the hadronization given by the coalescence, and decreased by…
Models based on $SU(6)$ symmetry breaking and large $N_c$ limit provide relations between the pion cloud contributions to the $γ^\ast N \to Δ(1232)$ quadrupole form factors, electric ($G_E$) and Coulomb ($G_C$), and the neutron electric form factor $G_{En}$, suggesting that those form factors are dominated by the same physical processes. Those relations are improved in order to satisfy a fundamental constraint between the electric and Coulomb quadrupole form factors in the long wavelength limit, when the photon three-momentum vanishes (Siegert's theorem). Inspired by those relations, we study …
We present the spatial distributions of electromagnetic fields ($\bf E$ and $\bf B$) and electromagnetic anomaly $ \bf E \cdot B$ in Au+Au collisions at the RHIC energy $\sqrt{s}$=200 GeV based on a multi-phase transport model. A dipolar distribution of $\bf E \cdot B$ is observed in non-central collisions. We find that the coupling of the $\bf E \cdot B$ dipole and magnetic field $\bf B$ can induce an electric quadrupole moment which can further lead to the difference in elliptic flows between positive charged particles and negative charged particles through final interactions. The centrality…
Below pion threshold virtual Compton scattering off the nucleon gives access to the generalized electromagnetic polarizabilities. Different theoretical results for the generalized polarizabilities have been compared. In particular, the influence of the generalized polarizabilities on the unpolarized cross section and on double polarization observables has been investigated. Predictions for these observables have been obtained in the linear sigma model and chiral perturbation theory.
Chiral perturbation theory makes definitive predictions for the extrinsic behavior of hadrons in external electric and magnetic fields. Near the chiral limit, the electric and magnetic polarizabilities of pions, kaons, and nucleons are determined in terms of a few well-known parameters. In this limit, hadrons become quantum mechanically diffuse as polarizabilities scale with the inverse square-root of the quark mass. In some cases, however, such predictions from chiral perturbation theory have not compared well with experimental data. Ultimately we must turn to first principles numerical simul…
Starting with a spectator quark model developed for the nucleon (N) and the Delta in the physical pion mass region, we extend the predictions of the reaction gamma N -> Delta to the lattice QCD regime. The quark model includes S and D waves in the quark-diquark wavefunctions. Within this framework it is the D-wave part in the Delta wavefunction that generates nonzero valence contributions for the quadrupole form factors of the transition. Those contributions are however insufficient to explain the physical data, since the pion cloud contributions dominate. To separate the two effects we apply …
We present an extraction of the E2/M1 ratio of the $Δ$(1232) from experimental data applying an effective Lagrangian model. We compare the result obtained with different nucleonic models and we reconcile the experimental results with the Lattice QCD calculations.
The large $N_c$ limit provides relations that can be used to calculate the $γ^\ast N \to Δ(1232)$ quadrupole form factors at low and intermediate $Q^2$ under the assumption of the pion cloud dominance. There are two limitations in those parametrizations. First, the parametrization of the Coulomb quadrupole form factor underestimate the low $Q^2$ data. Second, when extrapolated for the timelike region, the form factors violate Siegert's theorem by terms of the order $1/N_c^2$. We propose here corrections to the parametrization of the electric quadrupole form factor, which violate Siegert's theo…
Recent data allow a new parametrization of the neutron charge form factor G_En. A parameter-free quark model relation between G_En and the N->Delta quadrupole form factor is used to predict the latter from the G_En data. In particular, the neutron charge radius is related to N->Delta quadrupole moment, while the fourth moment of G_En connects to the N->Delta quadrupole transition radius. From the latter we derive an experimental value for the charge radius of the light constituent quarks. Finally, the C2/M1 ratio in pion electroproduction is predicted from the elastic neutron form factor data.
Charged pion electric polarizability from four-point functions in lattice QCD
本研究针对带电强子极化能量分离困难的问题，提出基于格点QCD四点函数的替代方法，通过淬火Wilson作用量模拟带电π介子，揭示了其电极化率源于弹性与非弹性贡献的抵消。
Utilizing the methods of chiral effective field theory we present an analysis of the electromagnetic $NΔ$-transition current in the framework of the non-relativistic "small scale expansion" (SSE) to leading-one-loop order. We discuss the momentum dependence of the magnetic dipole, electric quadrupole and coulomb quadrupole transition form factors up to a momentum transfer of $Q^2<0.3$ GeV$^2$. Particular emphasis is put on the identification of the role of chiral dynamics in this transition. Our analysis indicates that there is indeed non-trivial momentum dependence in the two quadrupole form …
We examine elastic Compton scattering off the deuteron for photon energies between 50 MeV and 100 MeV in the framework of chiral effective field theories to next-to-leading order. We compare one theoretical scheme with only pions and nucleons as explicit degrees of freedom to another in which the Delta(1232) resonance is treated as an explicit degree of freedom. Whereas pion degrees of freedom suffice to describe the experimental data measured at about 70 MeV, the explicit Delta(1232) gives important contributions that help to reproduce the angular dependence at higher energies. The static iso…
A quark model relation between the neutron charge form factor and the N->Delta charge quadrupole form factor is used to predict the C2/M1 ratio in the N->Delta transition from the elastic neutron form factor data. Excellent agreement with the electro-pionproduction data is found, indicating the validity of the suggested relation. The implication of the negative C2/M1 ratio for the intrinsic deformation of the nucleon is discussed.
The Compton scattering on a charged pion and the process γγ\to π^0π^0 are studied using the dispersion relations. Unknown parameters of the S-wave ππinteraction, represented as a board Breit-Wignar resonance, and a sum and a difference of the π^0 meson polarizabilities are found from a fit to the experimental data for the process γ+γ\to π^0+π^0. This fit gives α+β=0.98\pm 0.03 and α-β=-1.6\pm 2.2. The found parameters of the S-wave ππinteraction are used for the calculation of the cross section of the Compton scattering on π^{\pm} meson. The analysis of the obtained results shows that the expe…
Motivated by developments at HIGS at TUNL that include increased photon flux and the ability to circularly polarize photons, we calculate several beam-polarization/target-spin dependent observables for elastic Compton scattering on the deuteron. This is done at energies of the order of the pion mass within the framework of Heavy Baryon Chiral Perturbation Theory. Our calculation is complete to O(Q^3) and at this order there are no free parameters. Consequently, the results reported here are predictions of the theory. We discuss paths that may lead to the extraction of neutron polarizabilities.…
Investigating Roles of Triple Excitations for High-precision Determination of Clock Properties of Alkaline Earth Metal Singly Charged Ions
本文利用RCC理论研究三激发对高精度确定碱土金属单电荷离子钟态电偶极极化率和四极矩的作用，发现其结果与文献值存在显著差异。
The E2/M1 ratio (EMR) of the $Δ$(1232) is extracted from the world data in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the $Δ$(1232) resonance. The \textit{bare} s-channel $Δ$(1232) contribution is well isolated and Final State Interactions (FSI) are effectively taken into account fulfilling Watson's theorem. The obtained EMR value, EMR$=(-1.30\pm0.52)$%, is in good agreement with the latest lattice Q…
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