E. A. Kuraev, E. Tomasi-Gustafsson
In this note we give arguments in favor of the statement that the contribution of the box diagram calculated for electron muon elastic scattering can be considered an upper limit to electron proton scattering. As an exact QED calculation can be performed, this statement is useful for constraining model calculations involving the proton structure.
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We consider the role of the two-photon corrections to the small angle $μp$ and $ep$ elastic scattering and the expected $σ(μ^- p)/σ(μ^+ p)$ ratio.
We studied the high energy quark anti-quark elastic scattering with an exchange of a mesonic state in the $t$ channel with $-t/Λ_{QCD}^{2} \gg 1$. Two methods are proposed to eliminate the strong background from bare pomeron, reggized gluon and odderon exchange. The feasibility of measuring mesonic reggeon exchange is discussed.
Using the available cross section and polarization data for elastic electron-proton scattering, we provide an extraction of the two-photon exchange amplitudes at a common value of four-momentum transfer, around Q^2 = 2.5 GeV^2. This analysis also predicts the e^+ p / e^- p elastic scattering cross section ratio, which will be measured by forthcoming experiments.
We calculate two-photon exchange amplitude for the elastic electron-pion scattering in the dispersion-relation inspired approach, including both elastic and inelastic contributions. The latter was modelled as a sum of ρand b_1(1235) meson contributions. We find that at Q^2 < 2 GeV^2 the elastic contribution is dominant, similarly to electron-proton scattering case. At higher Q^2 the inelastic contribution is not negligible, but still smaller than the elastic one. We also explain observed rapid amplitude growth at backward angles.
Recent theoretical developments in the studies of two-photon exchange effects in elastic electron-proton scattering are reviewed. Two-photon exchange mechanism is considered a likely source of discrepancy between polarized and unpolarized experimental measurements of the proton electric form factor at momentum transfers of several GeV$^2$. This mechanism predicts measurable effects that are currently studied experimentally.
We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer $Q^2$. It is shown that the leading two-photon exchange amplitude behaves as $1/Q^4$ relative to the one-photon amplitude, and can be expressed in a model independent way in terms of the leading twist nucleon distribution amplitudes. Using several models for the nucleon distribution amplitudes, we provide estimates for existing data and for ongoing experiments.
We studies the high energy elastic scattering of quark anti-quark with an exchange of a mesonic state in the $t$ channel with $-t/Λ^{2} \gg 1$. Both the normalization factor and the Regge trajectory can be calculated in PQCD in cases of fixed (non-running) and running coupling constant. The dependence of the Regge trajectory on the coupling constant is highly non-linear and the trajectory is of order of $0.2$ in the interesting physical range.
We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer through the scattering off a parton in the proton. We relate the process on the nucleon to the generalized parton distributions which also enter in other wide angle scattering processes. We find that when taking the polarization transfer determinations of the form factors as input, adding in the 2 photon correction, does reproduce the Rosenbluth data.
Two boson exchange (TBE) correction to the cross section for the quasi-elastic charged current $νn$ and $\barν p$ scattering is evaluated. The TBE is given by $Wγ$ box diagrams. The calculations are performed for 1 GeV neutrinos. The averaged TBE correction is of the order of $2\div4 %$ (with respect to Born contribution) in the case of $ν_e$ and $\barν_e$ and $1\div2 %$ in the case of $ν_μ$ and $\barν_μ$. The impact of the TBE effect on the systematic discrepancy between the $ν_e$ and $ν_μ$ cross sections is discussed.
Odderon Exchange in Elastic Proton-Proton and Proton-Antiproton Scattering at TeV Energies
本论文详述了通过分析LHC和Tevatron在TeV尺度下的弹性散射测量数据，最终在强相互作用的非微扰域中发现了48年来悬而未决的Odderon交换。
We asses a role of the double helicity-flip amplitudes in small-angle elastic pp-scattering and obtain a new unitary bound for the double helicity-flip amplitude F_2 in elastic pp-scattering at small values of t on the basis of the U-matrix method of the s-channel unitarization.
Scenario for restoration of the real part of the elastic scattering amplitude has been proposed for the unitarity saturation case. Dependence of the real part of the elastic scattering amplitude on the transferred momentum $-t$ at the asymptotical energies has been restored from the corresponding imaginary part on the basis of derivative analyticity relations (analytization procedure).
Lepton mass effects play a decisive role in description of elastic lepton-proton scattering when the beam's energy is comparable to the mass of the lepton. The future MUSE experiment, which is devised to solve the "Proton Radius Puzzle", is going to cover the corresponding kinematic region for a scattering of muons by a proton target. We anticipate that helicity-flip meson exchanges will make a difference in comparison of elastic electron-proton versus muon-proton scattering in MUSE. In this article, we estimate the $σ$ meson exchange contribution in the $t$-channel. This contribution, mediate…
The general spin structure of the matrix element, taking into account the two--photon exchange contribution, for the elastic electron (positron) --deuteron scattering has been derived using general symmetry properties of the hadron electromagnetic interaction, such as P--, C-- and T--invariances as well as lepton helicity conservation in QED at high energy. Taking into account also crossing symmetry, the amplitudes of $e^{\mp}d-$scattering can be parametrized in terms of fifteen real functions. The expressions for the differential cross section and for all polarization observables are given in…
Analytical Evaluation of Elastic Lepton-Proton Two-Photon Exchange in Chiral Perturbation Theory
本文在重子手征微扰理论框架下，以次领头阶精度解析计算了弹性轻子-质子散射中的双光子交换贡献，识别了软光子近似缺失项，并分析了缪子与电子散射的差异。
We discuss a role of the double helicity-flip amplitudes and derive new unitary bounds for these amplitudes in elastic $pp$-scattering at small values of $t$. We show that the usual assumption on the smallness of such amplidudes can be justified only in the shrinking with energy region of small $t$ values.
The $O(p^4)$ calculation on pion-nucleon elastic scattering amplitude in EOMS scheme within covariant baryon chiral perturbation theory is reviewed. Numerical fits to partial wave amplitudes up to $\sqrt{s}=1.13$ GeV and 1.20 GeV are performed and the results are compared with previous studies.
A behavior of imaginary and real parts of the high-energy elastic hadron scattering amplitude is examined in the diffraction region. It is shown that the interference between Coulomb and hadronic scattering at small momentum transfers and especially in the region of diffractive minimum can bring some information about the structure of the hadron spin-non-flip amplitude.
Several methods of extracting the magnitude of the real parts of the elastic hadron scattering amplitude - from the experimental data are presented. These methods allows us to obtain the real parts at one definite point of the transfer momentum and with a high accuracy without knowledge of the precise values of the normalization coefficient and with minimum theoretical assumptions.
The elastic scattering amplitude (ESA) is obtained in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) for planar charged fermions in an external constant magnetic field. We obtain the elastic scattering amplitude in the corresponding massive theory and then discuss and calculate the massless limit of ESA. The imaginary part of ESA are related to the total probability of photons emission by charged fermions in the considered magnetic field. Simple analytical formulas are obtained when planar charged fermions in initial states occupy high excited Landau le…
We study the large-$t$ small angle behavior of quark-quark elastic scattering. We employ a factorization procedure previously developed for fixed angle scattering, which depends on the color structure of the factorized hard subprocess. We find an evolution in $t$ that (in leading logarithmic approximation) becomes diagonal in a singlet-octet basis in the $t$-channel as $s\rightarrow \infty$. Octet exhange in the hard scattering is associated with the familiar `reggeized', $s^{α_g(t)}$ behavior, which arises from $s$-dependence in Sudakov suppression. In contrast, Sudakov suppression for $t$-ch…
The model-independent solution of the s-channel unitarity condition for the imaginary part of the hadronic elastic scattering amplitude outside the diffraction peak allows to make conclusions about its real part at nonzero transferred momenta. The asymptotical properties of the ratio of the real to imaginary part of the amplitude are discussed. In particular, it is explicitly shown that the ratio changes its sign at a defnite value of the transferred momentum. Some comments concerning the present day experimental results about the behavior of the differential cross-section of elastic scatterin…
Existing data for large-$t$ $pp$ elastic-scattering differential cross-sections are energy-independent and behave as $t^{-8}$. This has been explained in terms of triple-gluon exchange, or alternatively through triple-singlet exchange. A discussion is given of the problems raised by each of these explanations, and of the possibility that at RHIC or LHC energies the exchange of three BFKL pomerons might result in a rapid rise with energy.
The parity-conserving single-spin beam asymmetry of elastic electron-proton scattering is induced by an absorptive part of the two-photon exchange amplitude. We demonstrate that this asymmetry has logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons. An optical theorem is used to evaluate the asymmetry in terms of the total photoproduction cross section on the proton, predicting its magnitude at a few parts per million for high electon beam energies and small scattering angles. At fixed 4-momentum transfers, the asymmetry is rising logarithmi…
Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all high energy region, the behavior of observables in the LHC collisions in the range $\sqrt{s}$ = 2.76 - 14 TeV is discussed. Similarly to the case of 7 TeV data, the proposed amplitudes give excellent description of the preliminary 8 TeV data. We discuss the expected energy dependence of the observable quantities, and present predictions for the experiments at 2.76, 13 and 14 TeV.
With relation to the RHIC spin program we research the polarization effects in elastic proton-proton scattering at small momentum transfer and in the diffraction dip region. The calculations take into account the Coulomb-hadron interference effects including the additional Coulomb-hadron phase. In particular we show the impact of the form of the hadron potential at large distances on the behavior of the hadron spin-flip amplitude at small angles. The $t$-dependence of the spin-flip amplitude of high energy hadron elastic scattering is analyzed under different assumptions on the hadron interact…
The explicit procedures are described for reconstruction of the full set of helicity amplitudes in proton-proton and proton-antiproton elastic scattering. The procedures are based on the derivative relations for the helicity amplitudes in s-channel, on the explicit parametrization of the leading spin non flip amplitudes and crossing - symmetry relations. Asymptotic theorems are used for definition of free parameters in derivative relations. We also study the Odderon influence on the helicity amplitude reconstruction. Reconstruction procedures are valid at extremely wide energy domain and broad…
Oscillations in the elastic high energy amplitude
本文讨论了在 $\sqrt{s}=13$~TeV 的 TOTEM 数据中，弹性 $pp$ 微分截面在通常平滑行为之上出现的振荡现象。
A precise analysis of the pp elastic scattering data at 7 TeV in terms of its amplitudes is performed as an extension of previous studies for lower energies. Slopes $B_{R}$ and $B_{I}$ of the real and imaginary amplitudes are independent quantities, and a proper expression for the Coulomb phase is used. The real and imaginary amplitudes are fully disentangled, consistently with forward dispersion relations for amplitudes and for slopes. We present analytic expressions for the amplitudes that cover all $t$ range completely, while values of total cross section $σ$, ratio $ρ$, $B_{I}$ and $B_{R}$…
A new method for the determination of the real part of the elastic scattering amplitude is examined for high energy proton-proton elastic scattering at small momentum transfer. This method allows us to decrease the number of model assumptions, to obtain the real part in a narrow region of momentum transfer and to test different models. The real part is computed at a given point t_min near t=0 from the known Coulomb amplitude. Hence one obtains an important constraint on the real part of the forward scattering amplitude and therefore on the rho-parameter (measuring the ratio of the real to imag…
We calculate $γZ$ exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a parton model using the formalism of generalized parton distributions(GPDs). We also examine the validity of the zero-momentum-transfer approximation adopted in the literatures and find that it overestimates the $γZ$ exchange effect significantly at the forward scattering angles.
Using the relativistic Eikonal approximation, we study the one and two photon exchange amplitudes in elastic electron-nucleon scattering for the case of transversely polarized nucleons with unpolarized electrons beam. In our approach, we utilize the convolution theory of Fourier transforms and the transverse charge density in transverse momentum space to evaluate the one and two photon exchange Eikonal amplitudes. The results obtained for the $2γ$ amplitude in impact parameter space are compared to the corresponding 4D case. We show that while the one and two photon cross sections are azimutha…
The TOTEM 2.76, 7, 8, and 13 TeV pp elastic differential cross sections are extrapolated using a data-driven approach to obtain the 1.96 TeV pp elastic cross section. A difference with a 3.4$σ$ significance is observed between the extrapolated pp elastic cross section and the D0 p$\bar{\rm p}$ elastic cross section at 1.96 TeV in the region of the diffractive minimum and the second maximum of the pp cross section, providing evidence for colourless C-odd gluonic exchanges, also denoted as odderon. These results are combined with a TOTEM analysis of the same $t$-channel C-odd exchanges based on …
We analyse the recent LHC data at 7 and 8 TeV for pp elastic scattering with special attention for the structure of the real part, which is shown to be crucial to describe the differential cross section in the forward region. We determine accurately the position of the zero of the real amplitude, which corresponds to the zero of a theorem by A. Martin.
We evaluate the possible deviation (from the conventional Cahn's result) of the phase between the one-photon-exchange and the `nuclear' high energy $pp$ scattering amplitudes in a small $t\to 0$ region caused by a more complicated (not just $exp(Bt)$) behaviour of the nuclear amplitude. Furthermore we look at the possible role of the $t$-dependence of the $ρ(t) \equiv$ Real/Imaginary amplitude ratio. It turns out that both effects are rather small - much smaller than to have any influence on the experimental accuracy of $ρ(t=0)$ extracted from the elastic proton-proton scattering data.
In the present review we discuss different aspects of the two-photon exchange (TPE) physics in elastic $ep$ scattering, at high $Q^2$ as well as at low $Q^2$. The imaginary part of the TPE amplitude gives rise to beam and target single-spin asymmetries. Different theoretical approaches to calculation of these observables are considered. The real part of the TPE amplitude influence unpolarized cross section and double-spin observables and is, most likely, responsible for discrepancy between two methods of proton form factors measurements. We review different methods of calculations of the TPE a…
Dependence of the structure of the elastic scattering amplitude on Mandelstam variables at high energies
本文利用HEGS模型分析LHC、SPS和Tevatron对撞机数据，确定了高能强子弹性散射振幅各组成部分对曼德尔斯塔姆变量s和t的依赖关系。
In the present paper the equations for the spin evolution of a particle in a storage ring are analyzed considering contributions from the tensor electric and magnetic polarizabilities of the particle. Study of spin rotation and birefringence effect for a particle in a high energy storage ring provides for measurement as the real part of the coherent elastic zero-angle scattering amplitude as well as tensor electric and magnetic polarizabilities. We proposed the method for measurement the real part of the elastic coherent zero-angle scattering amplitude of particles and nuclei in a storage ring…
We present a simple parameterization of the two-photon exchange amplitude in elastic electron-proton scattering, suitable for fast numerical evaluation.
Recent measurements of the differential cross sections in the forward region of pp elastic scattering at 7 and 8 TeV show precise form of the $t$ dependence. We propose a detailed analysis of these measurements including the structures of the real and imaginary parts of the scattering amplitude. A good description is achieved, confirming in all experiments the existence of a zero in the real part in the forward region close to the origin, in agreement with the prediction of a theorem by A. Martin, with important role in the observed form of $dσ/dt$. Universal value for the position of this zer…
The dips observed in the differential cross sections of elastic pp and p$\bar{\rm p}$ scattering are studied in terms of the locations of the zeros of the real and imaginary parts of the amplitude and of the sign of real part at large $|t|$. It is confirmed that the differences in shapes of the dips in the pp and p$\bar{\rm p}$ systems are determined by a change of sign of the real tail, which seems to be determined by perturbative QCD contributions.
We construct a nonlocal gauge invariant Lagrangian to model the electromagnetic interaction of proton. The Lagrangian includes all allowed operators with dimension up to five. We compute the two photon exchange contribution to elastic electron-proton scattering using this effective nonlocal Lagrangian. The one loop calculation in this model includes the standard box and cross box diagram with the standard on-shell form of the hadron electromagnetic vertices. Besides this we find an extra contribution which depends on an unknown constant. We use experimentally extracted form factors for our cal…
We analyse the 13 TeV TOTEM data on elastic proton-proton scattering through a thorough statistical analysis, and obtain that $ρ=0.096\pm 0.006$ and $σ_{tot}=(107.5\pm 1.5)$ mb. Theoretical errors could lower the cross section by about 2 mb and increase $ρ$ by about 0.002. We also show that these results do not imply the existence of an odderon at $t=0$.
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.
We obtain the solution of the unitarity equation for the elastic processes in terms of the expansion coefficients of the amplitude as a function on the SO_mu(2.1) group. This approach is a generalization of the eikonal representation to the case of small impact parameters and large transverse momenta. We show how the unitarity relation is modified when the contributions of the backward scattering are taken into account. We discuss the simplest models of the profile functions in the following cases: full reflection, full absorption and the combination of these two cases.
The data on p$\mathrm{\bar p}$ elastic scattering at 1.8 and 1.96 TeV are analysed in terms of real and imaginary amplitudes, in a treatment with high accuracy, covering the whole t-range and satisfying the expectation of dispersion relation for amplitudes and for slopes. A method is introduced for determination of the total cross section and the other forward scattering parameters and to check compatibility of E-710, CDF and the recent D0 data. Slopes $B_R$ and $ B_I$ of the real and imaginary amplitudes, treated as independent quantities, influence the amplitudes in the whole t-range and are…
$γZ$-exchange contribution in elastic $ep$ scattering by perturbative QCD
本文通过微扰QCD计算了大动量转移下弹性$ep$散射中$γZ$交换贡献，推导了幅值表达式，并估计了高动量转移下幅值和物理量$A_{\text{PV}}$的渐进行为，指出通常用于轴矢部分的散射关系不适用于高$Q^2$，需修改为一次减去的形式。
We describe the discovery of the colorless $C$-odd gluonic compound, the odderon, by the D0 and TOTEM Collaborations by comparing elastic differential cross sections measured in $pp$ and $p \bar{p}$ interactions at high energies
The differential cross-sections are calculated for proton-proton and proton-antiproton elastic scattering using the phenomenological model based on the analytic parameterizations for global scattering parameters (total cross-section and $ρ$ - parameter), crossing symmetry and derivative relations. We confront our model predictions with experimental data in wide range of energy and momentum transfer. The suggested method may be useful for PAX Program (GSI) as well as for high-energy experiments at RHIC and LHC.
Higher-order QED effects play an important role in precision measurements of nucleon elastic form factors in electron scattering. Here we introduce a two-photon exchange QED correction to the parity-violating polarization asymmetry of elastic electron-proton scattering. We calculate this correction in the parton model using the formalism of generalized parton distributions, and demonstrate that it can reach several per cent in certain kinematics, becoming comparable in size with existing experimental measurements of strange-quark effects in the proton neutral weak current.
A recent Schwinger Generating Functional based formulation, by H.M.Fried,Y.Gabellini,T.Grandou and Y-M.Sheu and P.H.Tsang provided gauge-invariant, exact, non-perturbative solutions for QCD. After choosing a renormalization scheme and assuming a simpler 2 body quark-quark scattering problem, this formalism is tested against experimental elastic proton-proton scattering at LHC energies (7, 8, 13 TeV). This formulation was previously compared with ISR energies at (23.5 - 62.5 GeV). The full scattering amplitude with infinite gluons summed, infinite loops summed and their interference terms are n…
We extract two-photon exchange amplitudes for the elastic electron-proton scattering at Q^2=2.5 GeV^2 from the unpolarized cross-section and recent polarization transfer measurements. There are three independent amplitudes, but only one of them, δG_M, can be determined with a reasonable accuracy(about 10%). The result is in good agreement with theoretical predictions. Rough estimates for two other amplitudes are obtained.
Leading electroweak corrections play an important role in precision measurements of the strange form factors. We calculate the two-photon-exchange (TPE) and $γZ$-exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a simple hadronic model including the finite size of the proton. We find both can reach a few percent and are comparable in size with the current experimental measurements of strange-quark effects in the proton neutral weak current. The effect of $γZ$-exchange is in general larger than that of TPE, especially at low momentum transfer $Q…
The compatibility of the multi--Regge form of QCD amplitudes in the quasi--multi--Regge kinematics (QMRK) and the s--channel unitarity imposes some constraints on the effective jet--production vertices. We demonstrate that these constraints known as bootstrap conditions are satisfied for the amplitudes with the Reggeized quark exchanges.
A detailed study of the rescattering series is performed within a model, using a generalized procedure of eikonalization and fitted to the $pp$ and $\bar pp$ elastic scattering data. We estimate and compare the various rescattering corrections to be added to the Born contribution in the amplitude. We find that their number is finite, whereas it increases with the energy and the transfer, like does their importance. In the domain where data exist, we find also that a correct computation must include, at least, all two- and three-Reggeon exchanges and some four- and five-Reggeon exchanges. Any a…
We extend the general formalism of two-photon exchange to elastic lepton-nucleon scattering by accounting for all lepton mass terms. We then perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the future MUSE experiment. For this purpose, we estimate the two-photon exchange corrections to muon-proton scattering observables by considering the contribution of the proton intermediate state, which is expected to dominate at very low momentum transfers. We find that the two-photon exchange effect to the unpolarized muon- proton scattering cross section in …
At high energies, elastic hadronic cross sections are believed to be dominated by vacuum exchange. In leading order of the leading $1/N_c$ expansion this exchange process has been identified as the BFKL {\em Pomeron} or its strong AdS dual the closed string graviton \cite{Brower:2006ea}. However difference of particle anti-particle cross sections are given by a so-called {\em Odderon} carrying C = -1 quantum numbers identified in weak coupling with odd numbers of exchanged gluons. Here we show that the dual description associates this with the Neveu-Schwartz ($B_{μν}$) sector of closed string …
The Regge features of elastic $K^\pm N\to K^\pm N$, and charge exchange $K^-p\to\bar{K}^0n$ and $K^+n\to K^0p$ reactions are described by using a combined analysis of all these channels at high momenta. Based on the meson exchanges in the $t$-channel with their decays to $K\bar{K}$ pair allowed, the exchanges of $ρ(775)+ω(782)$ are excluded in contrast to existing model calculations and the present work follows a new scheme for the meson exchanges $a_0(980)+ϕ(1020)+f_2(1275)+a_2(1320)$ reggeized for the forward elastic scattering amplitude together with Pomeron. The charge exchange reactions a…
With analytical representation for the pp scattering amplitudes introduced and tested at lower energies, a description of high precision is given of the $dσ/dt$ data at $\sqrt{s}$= 13 TeV for all values of the momentum transfer, with explicit identification of the real and imaginary parts. In both $t$ and $b$ coordinates the amplitudes have terms identified as of non-perturbative and perturbative nature, with distinction of their influences in forward and large $|t|$ ranges and in central and peripheral regions respectively. In the forward range, the role of the Coulomb-nuclear interference ph…
Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state
本研究利用色散关系计算弹性 μ 子-质子散射的双光子交换修正，通过在一个 MUSE 束流能量处固定减除函数来预测其余能量，并给出含轻子质量的极化可观测量。
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