The two-photon-exchange (TPE) effect plays a key role to extract the form factors (FFs) of the proton. In this work, we present some exact properties on the TPE effect in the elastic $ep$ scattering based on four types of typical and general interactions. The possible kinematical singularities, the asymptotic behaviors and the branch cuts of the TPE amplitudes are analyzed. The analytic expressions clearly indicate some exact relations between the dispersion relation (DR) method and the hadronic model (HM) method. It suggests that the two methods should be modified to general forms, respectively. After the modifications the new forms give the same results. Furthermore, they automatically and correctly include the contributions due to the seagull interaction, the meson-exchange effect, the contact interactions and the off-shell effect. To analyze the elastic $e^{\pm}p$ scattering data sets, the new forms should be used.
In this work, the two-photon-exchange (TPE) effect in $ep\rightarrow enπ^+$ at small $-t$ is discussed. In the previous work, the TPE contribution with one $π$ intermediate state is estimated numerically within a hadronic model under the pion-dominance approximation. Here we extend the discussion to include one $ρ$ intermediate state. The TPE contribution can be described by one scalar function in the limit $m_e\rightarrow 0$, the dispersion relation (DR) satisfied by this scalar function is analysed. The analytic expressions for the imaginary parts of the TPE contributions from one $π$ or one…
We apply a subtracted dispersion relation formalism with the aim to improve predictions for the two-photon exchange corrections to elastic electron-proton scattering observables at finite momentum transfers. We study the formalism on the elastic contribution, and make a detailed comparison with existing data for unpolarized cross sections as well as polarization transfer observables.
Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics
South China Normal University（华南师范大学）；New Mexico State University（新墨西哥州立大学）；RIKEN-BNL Research Center, Brookhaven National Laboratory（布鲁克海文国家实验室理研-布鲁克海文研究中心）；Brookhaven National Laboratory（布鲁克海文国家实验室）；University of Kentucky（肯塔基大学）；University of Dhaka（达卡大学）
In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to $(g-2)_μ$. We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coe…
Theoretical predictions for elastic neutrino-electron scattering have no hadronic or nuclear uncertainties at leading order making this process an important tool for normalizing neutrino flux. However, the process is subject to large radiative corrections that differ according to experimental conditions. In this paper, we collect new and existing results for total and differential cross sections accompanied by radiation of one photon, $νe \to νe (γ)$. We perform calculations within the Fermi effective theory and provide analytic expressions for the electron energy spectrum and for the total el…
Parity violation in elastic electron-nucleon scattering is studied with the basic goal of improving the understanding of electroweak hadronic structure with special emphasis on the strangeness content in the nucleon. Models for the parity-violating (PV) asymmetry are provided and compared with the world data measured at very different kinematics. The effects introduced in the PV asymmetry due to alternative descriptions of the hadronic structure are analyzed in detail. In particular, a wide selection of prescriptions for dealing with the electromagnetic and neutral current weak interaction nuc…
The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon $(g-2)_μ$ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for $(g-2)_μ$ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space- and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the corr…
Two-photon exchange (TPE) contributions to elastic electron-proton scattering in the forward regime and in leading log $\sim t\ln|t|$ approximation in the momentum transfer $|t|$ are considered. The imaginary part of TPE amplitude in these kinematics is related to the total photo absorption cross section. The real part of the TPE amplitude is obtained from the imaginary part by means of a fixed-$t$ dispersion relation. The dispersion integrals for the relevant elastic $ep$-scattering amplitude converge and do not need subtraction. This allows us to make clean a prediction for the real part of …
We analyze the dispersion correction to elastic parity violating electron-proton scattering due to $γZ$ exchange. In particular, we explore the theoretical uncertainties associated with modeling contributions of hadronic intermediate states. Taking into account constraints from low- and high-energy, parity-conserving electroproduction measurements, choosing different models for contributions from the non-resonant processes, and performing the corresponding flavor rotations to obtain the electroweak amplitude, we arrive at an estimate of the uncertainty in the total contribution to the parity-v…
We consider the electromagnetic and transition pion form factors. Using dispersion relations we simultaneously describe both the hadronic, time-like region and the asymptotic region of large energy-momentum transfer. For the latter we propose a novel mechanism of Regge fermion exchange. We find that hadronic contributions dominate form factors at all currently available energies.
We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller and Meissner [Ann. Phys. (NY) 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum L>=2 is solved in the presence of L-…
All contemporary phenomenological models of elastic hadronic scattering have been based in principle on the assumption of optical theorem validity that has been overtaken from optics. It will be shown that the given theorem which has not been actually proved in particle physics cannot be applied to short-ranged strong interactions. The analysis of corresponding collision experiments is to be done under new basic assumptions. The actual progress in description of hadronic collision processes might then exist only if the initial states are specified on the basis of impact parameter values of col…
We compare and review the theoretical predictions for the $\bar{K}N$ and $ηN$ elastic amplitudes where sizable variations are found among the considered approaches, especially at subthreshold energies relevant for studies of kaonic atoms and meson-nuclear quasi-bound states. Conditions for an appearance of dynamically generated states in meson-baryon multi-channel interactions are established and discussed for the $\bar{K}N$ and $ηN$ systems.
In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_μ$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $γ^*γ^*\toππ$…
Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from pi pi intermediate states to the partial waves for the process gamma^* gamma^* --> pi pi. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.
All contemporary phenomenological models of elastic hadronic scattering have been based on the assumption of validity of optical theorem that was overtaken from optics. It has been stated that it may be proven in particle physics. However, it will be shown that its derivation in the framework of unitary S-matrix theory (which is supposed to be the most general approach in this case) has been based on several requirements that do not correspond to the actual collision characteristics of two particles. It will be shown that especially in the case of short-ranged interaction (for which the theore…
The s-channel unitarity condition for the imaginary part of the hadronic elastic scattering amplitude outside the diffraction peak is studied within different assumptions about the behavior of its real part. The integral equation for the imaginary part is derived with the asymptotical expression for the real part inserted in the unitarity condition. The conclusions about the asymptotical approach to the black disk limit and possible zeros of the imaginary part of the amplitude are obtained. Their relation to the present day experiments is discussed.
Estimates of QED and dispersion effects on the cross section for elastic electron scattering from a 12C nucleus are provided for collision energies in the range of 120-450 MeV. While in general such corrections are smoothly varying with energy or scattering angle, they show structures in the vicinity of diffraction minima which are very sensitive to details of the theoretical models. This casts doubt on the assertion that the discrepancy between QED background-corrected experimental data and theory in these minima originates solely from dispersion.
Factorization of elastic, single, and double diffractive $pp$ scattering
MIT Center For Theoretical Physics – A Leinweber Institute（麻省理工学院理论物理中心——莱因韦伯研究所）；High Energy Physics Division, Argonne National Laboratory（阿贡国家实验室高能物理部）；Physics and Theoretical Divisions, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室物理与理论部）
We report calculations of hadronic light-by-light scattering amplitudes via lattice QCD evaluation of Euclidean four-point functions of vector currents. These initial results include only the fully quark-connected contribution. Particular attention is given to the case of forward scattering, which can be related via dispersion relations to the $γ^* γ^* \to$ hadrons cross section, and thus allows lattice data to be compared with phenomenology. We also present a strategy for computing the hadronic light-by-light contribution to the muon anomalous magnetic moment.
