Electromagnetic moments of quasi-stable particle
We deal with the problem of assigning electromagnetic moments to a quasi-stable particle (i.e., a particle with mass located at particle's decay threshold). In this case, an application of a small external electromagnetic field changes the energy in a non-analytic way, which makes it difficult to assign definitive moments. On the example of a spin-1/2 field with mass $M_{*}$ interacting with two fields of masses $M$ and $m$, we show how a conventionally defined magnetic dipole moment diverges at $M_{*}=M+m$. We then show that the conventional definition makes sense only when the values of the applied magnetic field $B$ satisfy $|eB|/2M_{*}\ll|M_{*}-M-m|$. We discuss implications of these re…
Leading order corrections to the Bethe-Heitler process in the $\gamma p\rightarrow l^+l^-p$ reaction
The ratio of di-lepton production cross sections on a proton, using the $\gamma p\rightarrow l^+ l^- p$ process, above and below di-muon production threshold allows to extract the effective lepton-proton interaction, which is required to be identical for electrons and muons if lepton universality is exact. To test for a scenario of broken universality at the percent level, of the size which could explain the different proton charge radii extracted from electron scattering and from muonic hydrogen spectroscopy, we evaluate all one-loop QED corrections to this process, including the full lepton mass dependencies. We furthermore show that two-photon exchange processes with both photons attache…
Accessing the real part of the forward $J/\psi$-p scattering amplitude from $J/\psi$ photo-production on protons around threshold
We provide an updated analysis of the forward $J/\psi$-p scattering amplitude, relating its imaginary part to $\gamma p \to J/\psi p$ and $\gamma p \to c \bar c X$ cross section data, and calculating its real part through a once-subtracted dispersion relation. From a global fit to both differential and total cross section data, we extract a value for the spin-averaged $J/\psi$-p s-wave scattering length $a_{\psi p} = 0.046 \pm 0.005$ fm, which can be translated into a $J/\psi$ binding energy in nuclear matter of $B_\psi = 2.7 \pm 0.3$ MeV. We estimate the forward-backward asymmetry to the $\gamma p \to e^- e^+ p$ process around the $J/\psi$ resonance, which results from interchanging the le…
Search for Effects Beyond the Born Approximation in Polarization Transfer Observables ine→pElastic Scattering
Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, $$G_{E}/G_{M}$$, obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two-photon-exchange (TPEX) contribution. In an effort to search for effects beyond the one-photon-exchange or Born approximation, we report measurements of polarization transfer observables in the elastic $$H(\vec{e},e'\vec{p})$$ reaction for three different beam energies at a fixed squared momentum transfer $Q^2 = 2.5$ GeV$^2$, spanning a wide range of the virtual photon p…
Real and Virtual Compton Scattering (experiments)
This paper deals with Real and Virtual Compton Scattering off the proton at threshold and the way to deduce information about the nucleon polarizabilities.
Two-photon exchange correction to2S−2Psplitting in muonicHe3ions
We calculate the two-photon exchange correction to the Lamb shift in muonic $^{3}\mathrm{He}$ ions within the dispersion relations framework. Part of the effort entailed making analytic fits to the electron-$^{3}\mathrm{He}$ quasielastic scattering data set, for purposes of doing the dispersion integrals. Our result is that the energy of the $2S$ state is shifted downwards by two-photon exchange effects by 15.14(49) meV, in good accord with the result obtained from a potential model and effective field theory calculation.
Virtual Compton scattering and the generalized polarizabilities of the proton atQ2=0.92and 1.76 GeV2
Virtual Compton Scattering (VCS) on the proton has been studied at Jefferson Lab using the exclusive photon electroproduction reaction (e p --> e p gamma). This paper gives a detailed account of the analysis which has led to the determination of the structure functions P{sub LL}-P{sub TT}/epsilon and P{sub LT}, and the electric and magnetic generalized polarizabilities (GPs) alpha{sub E}(Q{sup 2}) and beta{sub M}(Q{sup 2}) at values of the four-momentum transfer squared Q{sup 2} = 0.92 and 1.76 GeV{sup 2}. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q{sup 2}-…
Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
We merge the dispersive relation approach and the ab initio method to compute nuclear structure corrections to the Lamb shift in muonic deuterium. We calculate the deuteron response functions and corresponding uncertainties up to next-to-next-to-next-to-leading order in chiral effective field theory and compare our results to selected electromagnetic data to test the validity of the theory. We then feed response functions calculated over a wide range of kinematics to the dispersion-theory formalism and show that an improved accuracy is obtained compared to that with the use of available experimental data in the dispersive analysis. This opens up the possibility of applying this hybrid metho…
Dispersive analysis of the γγ⁎ → ππ process
Abstract We present a theoretical study of the γ γ ⁎ → π + π − , π 0 π 0 processes from the threshold through the f 2 ( 1270 ) region in the ππ invariant mass. We adopt the Omnes representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the f 0 ( 980 ) resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.
Light-front transverse charge densities
We discuss the recent interpretation of quark-distribution functions in the plane transverse to the light-cone direction. Such a mapping is model independent and allows one to build up multidimensional pictures of the hadron and to develop a semi-classical interpretation of the quark dynamics. We comment briefly the results obtained from the form factors of the nucleon. We show that a generalization to a target with arbitrary spin leads to a set of preferred values for the electromagnetic coupling characterizing structureless particles. Finally, we present the Wigner distribution for an unpolarized quark in an unpolarized proton and we propose an interpretation of the observed distortion as…
Lepton Universality Test in the Photoproduction ofe−e+Versusμ−μ+Pairs on a Proton Target
In view of the significantly different proton charge radius extracted from muonic hydrogen Lamb shift measurements as compared to electronic hydrogen spectroscopy or electron-scattering experiments, we study in this Letter the photoproduction of a lepton pair on a proton target in the limit of very small momentum transfer as a way to provide a test of the lepton universality when extracting the proton charge form factor. By detecting the recoiling proton in the γp→l^{-}l^{+}p reaction, we show that a measurement of a ratio of e^{-}e^{+}+μ^{-}μ^{+} over e^{-}e^{+} cross sections with an absolute precision of 7×10^{-4} would allow for a test to distinguish, at the 3σ level, between the two di…
Burkhardt-Cottingham sum rule and forward spin polarizabilities in Heavy Baryon Chiral Perturbation Theory
We study spin-dependent sum rules for forward virtual Compton scattering(VVCS) off the nucleon in heavy baryon chiral perturbation theory at order $O(p^4)$. We show how these sum rules can be evaluated from low energy expansions (in the virtual photon energy) of the forward VVCS amplitudes. We study in particular the Burkhardt -Cottingham sum rule in HBChPT and higher terms in the low energy expansion, which can be related to the generalized forward spin polarizabilities of the nucleon. The dependence of these observables on the photon virtuality $Q^2$ can be accessed, at small and intermediate $Q^2$ values, from existing and forthcoming data at Jefferson Lab.
Double deeply virtual Compton scattering off the nucleon.
We study the double deeply virtual Compton scattering (DDVCS) process off the nucleon, through the scattering of a spacelike virtual photon with large virtuality resulting in the production of a timelike virtual photon, decaying into an e^+ e^- pair. This process is expressed in the Bjorken regime in terms of generalized parton distributions (GPDs) and it is shown that by varying the invariant mass of the lepton pair, one can directly extract the GPDs from the observables. We give predictions for the DDVCS cross section and beam helicity asymmetry and discuss its experimental feasibility.
The first Virtual Compton Scattering experiment at MAMI
Abstract Virtual Compton scattering, i.e. the exclusive reaction γ ∗ p → γ′p′ with γ ∗ denoting a virtual photon, provides new insights on the internal structure of the proton. Below π 0 production threshold, this experiment measures the generalized polarizabilities of the proton as defined by Guichon et al [1], [2] and Drechsel et al [3]. These new electromagnetic observables, functions of Q 2 , enlarge the concept of electric (α0 and magnetic (β) polarizabilities in Real Compton Scattering ( Q 2 =0) [4]. The first VCS experiment [5] of this kind was measured at the three spectrometer facility at the Mainz Microtron MAMI for Q 2 =0.33 GeV 2 and we present in this paper the preliminary resu…
Theoretical framework to analyze searches for hidden light gauge bosons in electron scattering fixed target experiments
Motivated by anomalies in cosmic ray observations and by attempts to solve questions of the Standad Model of particle physics like the (g-2)_mu discrepancy, U(1) extensions of the Standard Model have been proposed in recent years. Such U(1) extensions allow for the interaction of Dark Matter by exchange of a photon-like massive force carrier \gamma' not included in the Standard Model. In order to search for \gamma' bosons various experimental programs have been started. One approach is the dedicated search at fixed-target experiments at modest energies as performed at MAMI or at the Jefferson Lab. In these experiments the process e(A,Z)->e(A,Z)l^+l^- is investigated and a search for a very …
Monte Carlo simulation of virtual Compton scattering below pion threshold
This paper describes the Monte Carlo simulation developed specifically for the VCS experiments below pion threshold that have been performed at MAMI and JLab. This simulation generates events according to the (Bethe-Heitler + Born) cross section behaviour and takes into account all relevant resolution-deteriorating effects. It determines the `effective' solid angle for the various experimental settings which are used for the precise determination of photon electroproduction absolute cross section.
Dilepton photoproduction on a deuteron target
We investigate the sensitivity of the cross section for lepton pair production off a deuteron target, $\gamma d \to l^+ l^- d$, to the deuteron charge radius. We show that for small momentum transfers the Bethe-Heitler process dominates, and that it is sensitive to the charge radius such that a cross section ratio measurement of about $0.1 \%$ relative accuracy could give a deuteron charge radius more accurate that the current electron scattering value and sufficiently accurate to distinguish between the electronic and muonic atomic values.
Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state
We evaluate the two-photon exchange correction to the unpolarized cross section in the elastic muon-proton scattering within dispersion relations. One of the six independent invariant amplitudes requires a subtraction. We fix the subtraction function to the model estimate of the full two-photon exchange at one of three MUSE beam energies and make a prediction for the two other energies. Additionally, we present single and double polarization observables accounting for the lepton mass.
Soft-photon radiative corrections to the e−p→e−pl−l+ process
We calculate the leading-order QED radiative corrections to the process ${e}^{\ensuremath{-}}p\ensuremath{\rightarrow}{e}^{\ensuremath{-}}p{l}^{\ensuremath{-}}{l}^{+}$ in the soft-photon approximation, in two different energy regimes which are of relevance to extract nucleon structure information. In the low-energy region, this process is studied to better constrain the hadronic corrections to precision muonic hydrogen spectroscopy. In the high-energy region, the beam-spin asymmetry for double-virtual Compton scattering allows us to directly access the generalized parton distributions. We find that the soft-photon radiative corrections have a large impact on the cross sections and are there…
Light-by-light scattering sum rule for radiative transitions of bottomonia
We generalize a forward light-by-light scattering sum rule to the case of heavy quarkonium radiative transitions. We apply such sum rule to the bottomonium states, and use available data on radiative transitions in its evaluation. For the transitions that are not known experimentally, we provide theoretical estimates within a potential model, and consider the spread between similar approaches in the literature as an estimate for the model error. For the $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ states we observe that, due to a cancellation between transitions involving $\chi_{b0}, \chi_{b1}$, and $\chi_{b2}$ states, the sum rule is satisfied within experimental and theoretical erro…
Tomographic image of the proton
We determine, based on the latest experimental Deep Virtual Compton Scattering experimental data, the dependence of the spatial size of the proton on the quark's longitudinal momentum. This results in a three-dimensional momentum-space image and tomography of the proton.
Generalized Parton Distributions in the valence region from Deeply Virtual Compton Scattering
This work reviews the recent developments in the field of Generalized Parton Distributions (GPDs) and Deeply virtual Compton scattering in the valence region, which aim at extracting the quark structure of the nucleon. We discuss the constraints which the present generation of measurements provide on GPDs, and examine several state-of-the-art parametrizations of GPDs. Future directions in this active field are discussed.
Data-driven dispersive analysis of the ππ and πK scattering
We present a data-driven analysis of the resonant $S$-wave $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K\ensuremath{\rightarrow}\ensuremath{\pi}K$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $\ensuremath{\pi}\ensuremath{\pi}$ scattering we present both a single- and a coupled-channel analysis by including additionally the $K\overline{K}$ channel. For the latter the central result is the Omn\`es m…
Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent …
Light-Front Interpretation of Proton Generalized Polarizabilities
We extend the recently developed formalism to extract light-front quark charge densities from nucleon form factor data to the deformations of these quark charge densities when applying an external electric field. We show that the resulting induced polarizations can be extracted from proton generalized polarizabilities. The available data for the generalized electric polarizabilitiy of the proton yield a pronounced structure in its induced polarization at large transverse distances, which will be pinned down by forthcoming high precision virtual Compton scattering experiments.
ϒ photoproduction on the proton at the Electron-Ion Collider
We present a dispersive analysis with the aim to extract the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ scattering length from $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}p$ experiments. In this framework, the imaginary part of the $\mathrm{\ensuremath{\Upsilon}}\text{\ensuremath{-}}p$ forward scattering amplitude is obtained from $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Upsilon}}p$ cross section measurements and is constrained at high energies from existing HERA and LHC data. Its real part is calculated through a once-subtracted dispersion relation, and the subtraction constant is proportional to the $\mathrm{\ensuremath{\…
Virtual Compton Scattering and polarizabilities
Abstract Virtual Compton Scattering (VCS) off the proton below pion threshold allows access to generalized polarizabilities of the proton. These observables measure the response of the nucleon to low energy electromagnetic field perturbations. This paper presents a comparison with Real Compton Scattering and also results for the first dedicated VCS experiment performed at the Mainz Microtron MAMI with high resolution spectrometers at Q2 = 0.33 GeV2.
First measurement of proton's charge form factor at very low $Q^2$ with initial state radiation
We report on a new experimental method based on initial-state radiation (ISR) in e-p scattering, in which the radiative tail of the elastic e-p peak contains information on the proton charge form factor ($G_E^p$) at extremely small $Q^2$. The ISR technique was validated in a dedicated experiment using the spectrometers of the A1-Collaboration at the Mainz Microtron (MAMI). This provided first measurements of $G_E^p$ for $0.001\leq Q^2\leq 0.004 (GeV/c)^2$.
Baryon resonance analysis from MAID
The unitary isobar model MAID2007 has been used to analyze the recent data of pion electroproduction. The model contains all four-star resonances in the region below W=2 GeV and both single-Q^2 and Q^2 dependent transition form factors could be obtained for the Delta, Roper, D13(1520), S11(1535), S31(1620), S11(1650), D15(1675), F15(1680) and P13(1720). From the complete world data base, including also pi- data on the neutron, also Q^2 dependent neutron form factors are obtained. For all transition form factors we also give convenient numerical parameterizations that can be used in other reactions. Furthermore, we show how the transition form factors can be used to obtain empirical transver…
Theoretical analysis of the pp¯→π0e+e− process within a Regge framework
Abstract We study the annihilation process p p ¯ → π 0 e + e − within a Regge framework, as a means to provide constraints on timelike nucleon form factors. We present results for the e + e − angular distributions and the differential cross sections in kinematics which will be accessible by PANDA@FAIR. To check the consistency of the model, we first test the approach on the process of real photon production, p ¯ p → π 0 γ , where data in the energy range of 2.911 GeV ⩽ s ⩽ 3.686 GeV exist. We find that a Regge pole model is able to well reproduce the available data. The analysis is then extended to a timelike virtual photon in the final state.
Higher Order Polarizabilities of the Proton
Compton scattering results are used to probe proton structure via measurement of higher order polarizabilities. Values for $\alpha_{E2}^p,\beta_{E2}^p,\alpha_{E\nu}^p,$ $\beta_{E\nu}^p$ determined via dispersion relations are compared to predictions based upon chiral symmetry and from the constituent quark model. Extensions to spin-polarizabilities are also discussed.
Nucleon resonance contributions to unpolarised inclusive electron scattering
The first CLAS12 experiments will provide high-precision data on inclusive electron scattering observables at a photon virtuality Q2 ranging from 0.05 to 12GeV2 and center-of-mass energies W up to 4 GeV. In view of this endeavor, we present the modeling of the resonant contributions to the inclusive electron scattering observables. As input, we use the existing CLAS electrocoupling results obtained from exclusive meson electroproduction data off protons, and evaluate for the first time the resonant contributions based on the experimental results on the nucleon resonance electroexcitation. The uncertainties are given by the data and duly propagated through a Monte Carlo approach. In this way…
Two-photon exchange corrections to elastic e− -proton scattering: Full dispersive treatment of πN states at low momentum transfers
We evaluate the pion-nucleon intermediate-state contribution to the two-photon exchange (TPE) correction in the elastic electron-nucleon scattering within a dispersive framework. We calculate the contribution from all $\ensuremath{\pi}N$ partial waves using the MAID parametrization. We provide the corresponding TPE correction to the unpolarized $ep$ scattering cross section in the region of low momentum transfer ${Q}^{2}\ensuremath{\lesssim}0.064\text{ }\text{ }{\mathrm{GeV}}^{2}$, where no analytical continuation into the unphysical region of the TPE scattering amplitudes is required. We compare our result in the forward angular region with an alternative TPE calculation, in terms of struc…
Spin-dependent sum rules connecting real and virtual Compton scattering verified
We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly-virtual Compton scattering. For example, the polarizability $\delta_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability $\gamma_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.
Soft-photon corrections to the Bethe-Heitler process in the γp→l+l−p reaction
We report on the calculation of first-order quantum electrodynamics (QED) corrections for the $\ensuremath{\gamma}p\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}{p}^{\ensuremath{'}}$ process. An upcoming experiment at MAMI (Mainz) aims to compare the cross sections of muon- and electron-pair production in this reaction to test lepton universality. Precise knowledge of the electromagnetic radiative corrections is needed for these measurements. As a first step, we present the leading QED radiative corrections in the soft-photon approximation when accounting for the finite lepton mass. For the kinematics at MAMI, we find corrections of the percent level for muons, and of order 10% for ele…
QCD radiative corrections to the soft spectator contribution in the wide angle Compton scattering
We derive the complete factorization formula for the leading power contribution in wide angle Compton scattering. It consists of the soft- and hard-spectator contributions. The hard-spectator contribution is well known and defined in the form of the convolution of a hard kernel with the nucleon distribution amplitudes. The soft-spectator contribution describes the scattering which involves the soft modes. We use the soft collinear effective theory in order to define this term in a field theoretical approach. Using the SCET framework we provide the proof of the factorization formula. We also compute the next-to-leading QCD corrections to the hard coefficient function of the soft spectator co…
QED radiative corrections to Virtual Compton Scattering
The QED radiative corrections to virtual Compton scattering (reaction $e p \to e p \gamma$) are calculated to first order in $\alpha_{em} \equiv e^2 / 4 \pi$. A detailed study is presented for the one-loop virtual corrections and for the first order soft-photon emission contributions. Furthermore, a full numerical calculation is given for the radiative tail, corresponding with photon emission processes, where the photon energy is not very small compared with the lepton momenta. We compare our results with existing works on elastic electron-proton scattering, and show for the $e p \to e p \gamma$ reaction how the observables are modified due to these first order QED radiative corrections. We…
The role of charged exotic states in e+e− → ψ(2S) π+π−
Abstract In this work, we use the dispersion theory to provide a physical description of recent BESIII data on the reaction e + e − → ψ ( 2 S ) π + π − . Taking into account explicitly the effects of charged exotic intermediate states in the t- and u-channels as well as the two-pion final state interaction, we describe the invariant mass distribution for four different e + e − center-of-mass energies. The effects of the ππ rescattering are accounted for in a single channel Omnes approach which is found to explain the ππ-invariant mass distributions at all e + e − center-of-mass energies. For q = 4.226 GeV and q = 4.258 GeV the already established charged exotic state Z c ( 3900 ) is conside…
Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung ($ep\to ep\gamma$) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (B$\chi$PT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well-known from elsewhere. Within the relatively large unc…
Two-photon exchange in elastic electron-proton scattering: a QCD factorization approach.
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.
Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering
We present a dispersive representation of the D-term form factor for hard exclusive reactions, using unsubtracted $t$-channel dispersion relations. The $t$-channel unitarity relation is saturated with the contribution of two-pion intermediate states, using the two-pion distributions amplitude for the $\gamma^*\gamma\rightarrow \pi\pi$ subprocess and reconstructing the $\pi\pi\rightarrow N\bar N$ subprocess from available information on pion-nucleon partial-wave helicity amplitudes. Results for the D-term form factor as function of $t$ as well as at $t=0$ are discussed in comparison with available model predictions and phenomenological parametrizations.
Proton spin polarizabilities from polarized Compton scattering
Polarized Compton scattering off the proton is studied within the framework of subtracted dispersion relations for photon energies up to 300 MeV. As a guideline for forthcoming experiments, we focus the attention on the role of the proton's spin polarizabilities and investigate the most favorable conditions to extract them with a minimum of model dependence. We conclude that a complete separation of the four spin polarizabilities is possible, at photon energies between threshold and the $\Delta(1232)$ region, provided one can achieve polarization measurements with an accuracy of a few percent.
Dispersion Theory in Electromagnetic Interactions
We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information on hadron structure constants by connecting information from complementary scattering processes. We consider the real and virtual Compton scattering processes off the proton, and summarize recent advances in the DR analysis of experimental data to extract the proton polarizabilities, in comparison with alternative studies based on chiral effective field theories. We discuss a multipole analysis of real Compton scattering data, along with a DR fit of the energy-dependent dynamical polarizabilities. Furthermore, we review new sum rul…
Magnetic dipole moment of theΔ+(1232)from theγp→γπ0preaction
The $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\gamma}{\ensuremath{\pi}}^{0}p$ reaction in the $\ensuremath{\Delta}(1232)$-resonance region is investigated as a method to access the ${\ensuremath{\Delta}}^{+}(1232)$ magnetic dipole moment. The calculations are performed within the context of an effective Lagrangian model containing both the $\ensuremath{\Delta}$-resonant mechanism and a background of nonresonant contributions to the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\gamma}{\ensuremath{\pi}}^{0}p$ reaction. Results are shown both for existing and forthcoming $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\…
Λ polarization in associated K+–Λ electro-production
Abstract The result of a feasibility study to measure the Λ polarization in associated K + – Λ electro-production is presented. This measurement was performed in the experimental Hall C at Jefferson Lab. The scattered electron was detected in the HMS spectrometer, and the electro-produced kaon and the proton from the Λ → pπ − decay were both detected in the SOS spectrometer. This quantity is very sensitive to the elementary p ( e , e ′ K ) Λ process and gives information on resonance production, and Regge exchange, among others. The result presented was measured at Q 2 =1.50 (GeV/c) 2 and cos θ Kγ CM =14°. The limits of the Λ polarization, with respect to the p γ × p K axis, were found to b…
Dispersion relations in real and virtual Compton scattering
A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general…
Off-forward Matrix Elements in Light-front Hamiltonian QCD
We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.
Proton photoproduction from 12C
Abstract The 12 C(γ,p) differential cross-section in the Δ-resonance region has been measured using tagged photons. Data are presented for 20 MeV wide photon energy bins at 200, 300, 400 and 500 MeV and for proton angles from 52° to 128°. The present 12 C(γ,p) measurements are compared with previous experiments carried out at Frascati, Tokyo and Bonn. Comparisons are also made with theoretical calculations developed at Gent and Valencia which provide an interpretation of the photon reaction mechanism in terms of the major contributing processes. Coincidence data with correlated neutrons, protons and pions are also presented.
Dispersion relation formalism for virtual Compton scattering and the generalized polarizabilities of the nucleon
A dispersion relation formalism for the virtual Compton scattering (VCS) reaction on the proton is presented, which for the first time allows a dispersive evaluation of 4 generalized polarizabilities at a four-momentum transfer $Q^2 \leq$ 0.5 GeV$^2$. The dispersive integrals are calculated using a state-of-the-art pion photo- and electroproduction analysis. The dispersion formalism provides a new tool to analyze VCS experiments above pion threshold, thus increasing the sensitivity to the generalized polarizabilities of the nucleon.
Generalized parton distributions and hard exclusive reactions
Abstract We discuss how generalized parton distributions (GPDs) enter in a variety of hard exclusive processes such as deeply virtual Compton scattering (DVCS) and hard meson electroproduction reactions on the nucleon. We discuss the links between GPDs and elastic nucleon form factors as well as the information contained in the second moment of GPDs. We subsequently show some key observables which are sensitive to the various hadron structure aspects of the GPDs, and discuss their experimental status.
Simultaneous description of the e+e−→J/ψππ(KK¯) processes
In this work, we provide a simultaneous and accurate description of the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}J/\ensuremath{\psi}$ invariant mass distributions of the recent BESIII data on ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, together with the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ cross sections at ${e}^{+}{e}^{\ensuremath{-}}$ center-of-mass energies $q=4.23\text{ }\text{ }\mathrm{GeV}$ and $q=4.26\text{ }\text{ }\mathrm{GeV}$. The rescattering effects between p…
Beam normal spin asymmetry for the ep→eΔ(1232) process
We calculate the single spin asymmetry for the $e p \to e \Delta(1232)$ process, for an electron beam polarized normal to the scattering plane. Such single spin asymmetries vanish in the one-photon exchange approximation, and are directly proportional to the absorptive part of a two-photon exchange amplitude. As the intermediate state in such two-photon exchange process is on its mass shell, the asymmetry allows one to access for the first time the on-shell $\Delta \to \Delta$ as well as $N^\ast \to \Delta$ electromagnetic transitions. We present the general formalism to describe the $e p \to e \Delta$ beam normal spin asymmetry, and provide a numerical estimate of its value using the nucle…
Transverse Beam Spin Asymmetries at Backward Angles in Elastic Electron-Proton and Quasielastic Electron-Deuteron Scattering
We have measured the beam-normal single-spin asymmetries in elastic scattering of transversely polarized electrons from the proton, and performed the first measurement in quasi-elastic scattering on the deuteron, at backward angles (lab scattering angle of 108 degrees) for Q2 = 0.22 GeV^2/c^2 and 0.63 GeV^2/c^2 at beam energies of 362 MeV and 687 MeV, respectively. The asymmetry arises due to the imaginary part of the interference of the two-photon exchange amplitude with that of single photon exchange. Results for the proton are consistent with a model calculation which includes inelastic intermediate hadronic (piN) states. An estimate of the beam-normal single-spin asymmetry for the scatt…
Leading order corrections to the Bethe-Heitler process in the γp→l+l−p reaction
This paper focuses on all one-loop corrections to the Bethe-Heitler process involved in the reaction $\ensuremath{\gamma}\phantom{\rule{0}{0ex}}p\ensuremath{\rightarrow}{l}^{+}\phantom{\rule{0.333em}{0ex}}{l}^{\ensuremath{-}}\phantom{\rule{0}{0ex}}p$. These corrections are of paramount interest as they serve to check the exactness of the so called $l\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n$ $u\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}i\phanto…
Reggeized model forηandη′photoproduction
A Reggeized model for $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ photoproduction on the nucleon is presented. In this model, $t$-channel vector meson exchanges are described in terms of Regge trajectories to comply with the correct high energy behavior. We compare this Reggeized model with an isobar model ($\ensuremath{\eta}$-MAID), where the $t$-channel exchanges are described by $\ensuremath{\rho}$ and $\ensuremath{\omega}$ poles. Both models contain the same resonance contributions, and describe current $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\eta}p$ data up to ${E}_{\ensuremath{\gamma}}^{\text{lab}}=2\phantom{\rule{0.3em}{0ex}}\text{GeV}$ quite well,…
Virtual Compton Scattering at MAMI γ*p→ γ1p1
The virtual Compton scattering (VCS) is the electron scattering on a proton which radiates a real photon before being detected. The new observables, called Generalized Polarizabilities (GP), extracted from this VCS at threshold can be understood as the deformation of the charge and current distributions of the proton [1]. These GP are functions of the mass of the virtual photon Q2. In real Compton scattering (Q2 = 0), some polarizabilities of the nucleon are already measured [2]. With the VCS, we will generalize these observables by measuring them at different values of Q2.
Accessing the real part of the forwardJ/ψ−pscattering amplitude fromJ/ψphotoproduction on protons around threshold
We provide an updated analysis of the forward $J/\ensuremath{\psi}$-p scattering amplitude, relating its imaginary part to $\ensuremath{\gamma}p\ensuremath{\rightarrow}J/\ensuremath{\psi}p$ and $\ensuremath{\gamma}p\ensuremath{\rightarrow}c\overline{c}X$ cross section data, and calculating its real part through a once-subtracted dispersion relation. From a global fit to both differential and total cross section data, we extract a value for the spin-averaged $J/\ensuremath{\psi}$-p s-wave scattering length ${a}_{\ensuremath{\psi}p}=0.046\ifmmode\pm\else\textpm\fi{}0.005\text{ }\text{ }\mathrm{fm}$, which can be translated into a $J/\ensuremath{\psi}$ binding energy in nuclear matter of ${B}_…
Higher-order proton structure corrections to the Lamb shift in muonic hydrogen
The recent conundrum with the proton charge radius inspires reconsideration of the corrections that enter into determinations of the proton size. We study the two-photon proton-structure corrections, with special consideration of the non-pole subtraction term in the dispersion relation, and using fits to modern data to evaluate the energy contributions. We find that individual contributions change more than the total, and present results with error estimates.
Quark transverse charge densities in the from lattice QCD
Abstract We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the Δ ( 1232 ) isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the Δ-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three…
Light-by-light scattering sum rules constraining meson transition form factors
Relating the forward light-by-light scattering to energy weighted integrals of the \gamma* \gamma -fusion cross sections, with one real photon (\gamma) and one virtual photon (\gamma*), we find two new exact super-convergence relations. They complement the known super-convergence relation based on the extension of the GDH sum rule to the light-light system. We also find a set of sum rules for the low-energy photon-photon interaction. All of the new relations are verified here exactly at leading order in scalar and spinor QED. The super-convergence relations, applied to the \gamma* \gamma -production of mesons, lead to intricate relations between the \gamma \gamma -decay widths or the \gamma…
Empirical transverse charge densities in the nucleon-to-P11(1440) transition
Abstract Using recent experimental data, we analyze the electromagnetic transition from the nucleon to the P 11 ( 1440 ) resonance. From the resulting empirical transition form factors, we map out the quark transverse charge densities which induce the N → P 11 ( 1440 ) transition. It is found that the transition from the proton to its first radially excited state is dominated by up quarks in a central region of around 0.5 fm and by down quarks in an outer band which extends up to about 1 fm.
Leading-order QED radiative corrections to timelike Compton scattering on the proton
We evaluate the leading-order QED radiative corrections to the timelike Compton scattering (TCS) process $\gamma p \to l^- l^+ p$. 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 $\Delta(1232)$ 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 $5 -10\%$ range in the low-energy regime and around $20\%$ in the high-energy regime. We show tha…
Radiative decays χcJ→Vγ within the QCD factorization framework
We present a discussion of radiative decays ${\ensuremath{\chi}}_{cJ}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rho}(\ensuremath{\omega},\ensuremath{\phi})$. The decay amplitudes are computed within the QCD factorization framework. NRQCD has been used in the heavy meson sector as well as a collinear expansion in order to describe the overlap with light mesons in the final state. The color-singlet contributions to all helicity amplitudes have been computed using the light-cone distribution amplitudes of twist-2 and twist-3. All obtained expressions are well defined at least in the leading-order approximation. The color-octet contributions have also been studied in the Coulomb li…
Nucleon andΔ(1232)form factors at low momentum transfer and small pion masses
An expansion of the electromagnetic form factors of the nucleon and $\ensuremath{\Delta}(1232)$ in small momentum transfer and pion mass is performed in a manifestly covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and $\ensuremath{\Delta}(1232)$ electromagnetic form factors, charge radii, and electromagnetic moments in the framework of $SU(2)$ baryon chiral perturbation theory, with nucleon and $\ensuremath{\Delta}$-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and electron-scattering process, we extract values for the seco…
Dispersion relation formalism for virtual Compton scattering of the proton
We present in detail a dispersion relation formalism for virtual Compton scattering (VCS) off the proton from threshold into the $\Delta(1232)$-resonance region. Such a formalism can be used as a tool to extract the generalized polarizabilities of the proton from both unpolarized and polarized VCS observables over a larger energy range. We present calculations for existing and forthcoming VCS experiments and demonstrate that the VCS observables in the energy region between pion production threshold and the $\Delta(1232)$-resonance show an enhanced sensitivity to the generalized polarizabilities.
Two-photon exchange contribution to elastic e− -proton scattering: Full dispersive treatment of πN states and comparison with data
We evaluate the two-photon exchange correction to the elastic electron-proton scattering cross section within a dispersive framework. Besides the elastic contribution, we account for all $\ensuremath{\pi}N$ intermediate state contributions using the phenomenological MAID fit as an input. We develop a novel method for the analytical continuation of the two-photon exchange amplitudes into the unphysical region and generalize our previous work to the momentum transfer region $0.064\text{ }\text{ }{\mathrm{GeV}}^{2}\ensuremath{\lesssim}{Q}^{2}\ensuremath{\lesssim}1\text{ }\text{ }{\mathrm{GeV}}^{2}$. We compare our results with recent OLYMPUS, CLAS and VEPP-3 data as well as with empirical fits…
Production of a tensor glueball in the reaction γγ → G2π0 at large momentum transfer
Abstract We study the production of a tensor glueball in the reaction γ γ → G 2 π 0 . We compute the cross section at higher momentum transfer using the collinear factorisation approach. We find that for a value of the tensor gluon coupling of f g T ∼ 100 MeV, the cross section can be measured in the near future by the Belle II experiment.
Neutron skins of atomic nuclei: per aspera ad astra
The complex nature of the nuclear forces generates a broad range and diversity of observational phenomena. Heavy nuclei, though orders of magnitude less massive than neutron stars, are governed by the same underlying physics, which is enshrined in the nuclear equation of state. Heavy nuclei are expected to develop a neutron-rich skin where many neutrons collect near the surface. Such a skin thickness is strongly sensitive to the poorly-known density dependence of the symmetry energy near saturation density. An accurate and model-independent determination of the neutron-skin thickness of heavy nuclei would provide a significant first constraint on the density dependence of the nuclear symmet…
Anomalous magnetic moment of the muon in a dispersive approach
We present a new general dispersive formalism for evaluating the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. In the suggested approach, this correction is related to the imaginary part of the muon's electromagnetic vertex function. The latter may be directly related to measurable hadronic processes by means of unitarity and analyticity. As a test we apply the introduced formalism to the case of meson pole exchanges and find agreement with the direct two-loop calculation.
How to reconcile the Rosenbluth and the polarization transfer method in the measurement of the proton form factors
The apparent discrepancy between the Rosenbluth and the polarization transfer method for the ratio of the electric to magnetic proton form factors can be explained by a two-photon exchange correction which does not destroy the linearity of the Rosenbluth plot. Though intrinsically small, of the order of a few percent of the cross section, this correction is kinematically enhanced in the Rosenbluth method while it is small for the polarization transfer method, at least in the range of (Q^2) where it has been used until now.
Leading order corrections to the Bethe-Heitler process in the γp→l+l−p reaction
The ratio of dilepton production cross sections on a proton, using the γp→l+l−p process, above and below the dimuon production threshold allows one to extract the effective lepton-proton interaction, which is required to be identical for electrons and muons if lepton universality is exact. To test for a scenario of broken universality at the percent level, of the size that could explain the different proton charge radii extracted from electron scattering and from muonic hydrogen spectroscopy, we evaluate all one-loop QED corrections to this process, including the full lepton mass dependencies. We furthermore show that two photon–exchange processes with both photons attached to the proton li…
The first dedicated Virtual Compton Scattering experiment at MAMI
We measured the absolute cross sections for photon electro-production off the proton, ep to ep gamma , with the high resolution spectrometers at MAMI at momentum transfer q=600 MeV/c and photon polarization epsilon =0.62. We covered the momentum range for the outgoing real photon q'=33/111 MeV/c. From the extracted virtual Compton scattering amplitude we deduce values for two structure functions related to the generalized polarizabilities of the proton.
Magnetic moment of the S11 (1535) resonance
Abstract The γ p a γη p reaction in the S 11 (1535) resonance region is investigated as a method to access the S 11 (1535) magnetic dipole moment. To study the feasibility, we perform calculations of the γ p → γη p process within an effective Lagrangian approach containing both the S 11 resonant mecanism and a background of non-resonant contributions. Predictions are made for the forthcoming experiments. In particular, we focus on the sensitivity of cross sections and photon asymmetries to the S 11 (1535) magnetic dipole moment.
Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer
We evaluate the two-photon exchange (TPE) correction to the unpolarized elastic electron-proton scattering at small momentum transfer $ Q^2 $. We account for the inelastic intermediate states approximating the double virtual Compton scattering by the unpolarized forward virtual Compton scattering. The unpolarized proton structure functions are used as input for the numerical evaluation of the inelastic contribution. Our calculation reproduces the leading terms in the $ Q^2 $ expansion of the TPE correction and goes beyond this approximation by keeping the full $ Q^2 $ dependence of the proton structure functions. In the range of small momentum transfer, our result is in good agreement with …
Dispersive analysis of the γ*γ*→ππ process
We present a dispersive analysis of the double-virtual photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this process is very sensitive to hadronic final-state interaction. For the $s$-wave, we use a coupled-channel $\ensuremath{\pi}\ensuremath{\pi}$, $K\overline{K}$ analysis which allows for a simultaneous description of both ${f}_{0}(500)$ and ${f}_{0}(980)$ resonances. For higher energies, ${f}_{2}(1270)$ shows up as a dominant structure which we approximate by a single-channel $\ensuremath{\pi}\ensuremath{\pi}$ rescattering in the $d$-wave. In the dispersive approach, the latter requires taking into account $t$- and $u$-channel vector-meson exchange left-hand cuts …
Description of the spacelike and timelike proton form factors at large momentum transfer in the QCD factorization approach
Abstract We propose QCD factorization approach for description of the soft spectator scattering contribution. It is expected that such contribution is very important for description of the many exclusive processes at moderate values of Q 2 . Assuming the dominance of this mechanism we provide qualitative consideration of the proton form factors in the spacelike and timelike regions. Using the same approach we also provide estimates of the cross sections for the processes γ γ → p p and p p → γ γ at large energy and momentum transfer.
Virtual compton scattering under π0 threshold at Q2=0.33 GeV2. Preliminary results
We have measured the absolute unpolarized cross sections for photon electro-production off the proton ep → epγ with the Three-Spectrometer-Setup at MAMI at a momentum transfer q=600 MeV/c and a virtual photon polarization ɛ=0.62. The momentum q ′ of the outgoing real photon range from 33 to 111 MeV/c. We extracted two combinations of the recently introduced generalized polarizabilities [1,2].
Light-by-light scattering sum rules in light of new data
We evaluate the light-quark meson contributions to three exact light-by-light scattering sum rules in light of new data by the Belle Collaboration, which recently has extracted the transition form factors of the tensor meson $f_2(1270)$ as well as of the scalar meson $f_0(980)$. We confirm a previous finding that the $\eta, \eta^\prime$ and helicity-2 $f_2(1270)$ contributions saturate one of these sum rules up to photon virtualities around 1 GeV$^2$. At larger virtualities, our sum rule analysis shows an important contribution of the $f_2(1565)$ meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0…
Deeply virtual electroproduction of photons and mesons on the nucleon : leading order amplitudes and power corrections
We estimate the leading order amplitudes for exclusive photon and meson electroproduction reactions at large Q^2 in the valence region in terms of skewed quark distributions. As experimental investigations can currently only be envisaged at moderate values of Q^2, we estimate power corrections due to the intrinsic transverse momentum of the partons in the meson wavefunction and in the nucleon. To this aim the skewed parton distribution formalism is generalized so as to include the parton intrinsic transverse momentum dependence. Furthermore, for the meson electroproduction reactions, we calculate the soft overlap type contributions and compare with the leading order amplitudes. We give firs…
Low-energy doubly virtual Compton scattering from dilepton electroproduction on a nucleon
We propose a new way to experimentally determine the subleading low-energy structure constant of doubly virtual Compton scattering on a proton. Such empirical determination will reduce the theoretical model error in estimates of the hadronic correction to the muonic hydrogen Lamb shift. We demonstrate that the dilepton forward-backward asymmetry in the e−p→e−pe−e+ process, which can be accessed at electron scattering facilities, yields a large sensitivity to this so far unknown low-energy constant.
Long Range Structure of the Nucleon
The long range structure of the nucleon is discussed starting from the old model of a quark bag with a pion cloud (``cloudy bag'') carrying on to the more recent ideas of the parton model of the nucleon. On the basis of the most recent measurements of the form factors at MAMI, JLab and MIT quantitative results for nucleon charge densities are presented within both non-relativistic and relativistic frameworks.
Quark model predictions for the SU(6)-breaking ratio of the proton momentum distributions
The ratio between the anomalous magnetic moments of proton and neutron has been recently parametrized by the ratio of proton momentum fractions $M_{2}^{q_{val}}$. This ratio is evaluated using different constituent quark models, starting from the CQM density distributions and calculating the next-to leading order distributions. We show that this momentum fractions $M_{2}^{q_{val}}$ ratio is a sensitive test for SU(6)-breaking effects and therefore it is useful to distinguish among different CQMs. We investigate also the possibility of getting constraints on the formulation of quark structure models.
Lepton universality test in the photoproduction of $e^- e^+$ versus $\mu^- \mu^+$ pairs on a proton target
In view of the significantly different proton charge radius extracted from muonic hydrogen Lamb shift measurements as compared to electronic hydrogen spectroscopy or electron scattering experiments, we study in this work the photoproduction of a lepton pair on a proton target in the limit of very small momentum transfer as a way to provide a test of the lepton universality when extracting the proton charge form factor. By detecting the recoiling proton in the $\gamma p \to l^- l^+ p$ reaction, we show that a measurement of a ratio of $e^-e^+ + \mu^-\mu^+$ over $e^-e^+$ cross sections with a relative precision of around 2%, would allow for a test to distinguish between the two different prot…
Sum rules for light-by-light scattering
We derive a set of sum rules for the light-by-light scattering and fusion: $\gamma\gamma \to all$, and verify them in lowest order QED calculations. A prominent implication of these sum rules is the superconvergence of the helicity-difference total cross-section for photon fusion, which in the hadron sector reveals an intricate cancellation between the pseudoscalar and tensor mesons. An experimental verification of superconvergence of the polarized photon fusion into hadrons is called for, but will only be possible at $e^+ e^-$ and $\gamma\gamma$ colliders with both beams polarized. We also show how the sum rules can be used to measure various contributions to the low-energy light-by-light …
The anomalous magnetic moment of the muon in the Standard Model
We are very grateful to the Fermilab Directorate and the Fermilab Theoretical Physics Department for their financial and logistical support of the first workshop of the Muon g -2 Theory Initiative (held near Fermilab in June 2017) [123], which was crucial for its success, and indeed for the successful start of the Initiative. Financial support for this workshop was also provided by the Fermilab Distinguished Scholars program, the Universities Research Association through a URA Visiting Scholar award, the Riken Brookhaven Research Center, and the Japan Society for the Promotion of Science under Grant No. KAKEHNHI-17H02906. We thank Shoji Hashimoto, Toru Iijima, Takashi Kaneko, and Shohei Nis…
Exclusive electroproduction of vector mesons, pseudoscalar mesons and photons in the Bjorken regime
Deeply virtual Compton scattering (DVCS) and the exclusive electroproduction of vector mesons (ϱ 0 , ϱ ± , ω, ) and pseudoscalar mesons (π 0 , π ± , …) in the Bjorken regime are sensitive to the recently introduced off-forward parton distributions. We calculate the leading order amplitudes for DVCS and hard meson electroproduction reactions in the valence region and use a model ansatz for the OFPD's to give estimates of observables relevant for experiments at COMPASS, HERMES and JLAB.
Nuclear structure contribution to the Lamb shift in muonic deuterium
We consider the two-photon exchange contribution to the $2P-2S$ Lamb shift in muonic deuterium in the framework of forward dispersion relations. The dispersion integrals are evaluated using experimental data on elastic deuteron form factors and inelastic electron-deuteron scattering, both in the quasielastic and hadronic range. The subtraction constant that is required to ensure convergence of the dispersion relation for the forward Compton amplitude $T_1(\nu,Q^2)$ is related to the deuteron magnetic polarizability $\beta(Q^2)$. Based on phenomenological information, we obtain for the Lamb shift $\Delta E_{2P-2S}=2.01\pm0.74$ meV. The main source of the uncertainty of the dispersion analysi…
Unitary model for theγp→γπ0preaction and the magnetic dipole moment of theΔ+(1232)
Radiative pion photoproduction in the $\ensuremath{\Delta}(1232)$-resonance region is studied with the aim of accessing the ${\ensuremath{\Delta}}^{+}(1232)$ magnetic dipole moment. We present a unitary model of the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}N$ ($\ensuremath{\pi}N={\ensuremath{\pi}}^{0}p,\phantom{\rule{0.6em}{0ex}}{\ensuremath{\pi}}^{+}n$) reactions, where the $\ensuremath{\pi}N$ rescattering is included in an onshell approximation. In this model, the low-energy theorem which couples the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}N$ process in the limit of a soft final photon to the $\ensuremath{\gamm…
Theoretical analysis of the γγ→π0η process
We present a theoretical study of the $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\eta}$ process from the threshold up to 1.4 GeV in the $\ensuremath{\pi}\ensuremath{\eta}$ invariant mass. For the s-wave ${a}_{0}(980)$ resonance state we adopt a dispersive formalism using a coupled-channel Omn\`es representation, while the d-wave ${a}_{2}(1320)$ state is described as a Breit-Wigner resonance. An analytic continuation to the ${a}_{0}(980)$ pole position allows us to extract its two-photon decay width as ${\mathrm{\ensuremath{\Gamma}}}_{{a}_{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}}=0.27(4)\text{ }\text{ }\mathrm{keV}$.
Light-by-light forward scattering sum rules for charmonium states
We apply three forward light-by-light scattering sum rules to charmonium states. We show that these sum rules imply a cancellation between charmonium bound state contributions, which are mostly known from the $\gamma \gamma$ decay widths of these states, and continuum contributions above $D \bar D$ threshold, for which we provide a duality estimate. We also show that two of these sum rules allow to predict the yet unmeasured $\gamma^\ast \gamma$ coupling of the $\chi_{c1}(1P)$ state, which can be tested at present high-luminosity $e^+ e^-$ colliders.
Analytic structure ofϕ4theory using light-by-light sum rules
Abstract We apply a sum rule for the forward light-by-light scattering process within the context of the ϕ 4 quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a K-matrix pole. For another domain …
The hadronic light-by-light contribution to the muon's anomalous magnetic moment
In view of the current 3 - 4 $\sigma$ deviation between theoretical and experimental values for the muon's anomalous magnetic moment, we review the ongoing efforts in constraining the hadronic light-by-light contribution to $a_\mu$ by using dispersive techniques combined with a dedicated experimental program to obtain the required hadronic input.
A dispersion relation for the pion-mass dependence of hadron properties
We present a dispersion relation in the pion-mass squared, which static quantities (nucleon mass, magnetic moment, etc.) obey under the assumption of analyticity in the entire complex $m_\pi^2$ plane modulo a cut at negative $m_\pi^2$ associated with pion production. The relation is verified here in a number of examples of nucleon and $\Delta$-isobar properties computed in chiral perturbation theory up to order $p^3$. We outline a method to obtain relations for other mass-dependencies, and illustrate it on a two-loop example.
Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon
We present a systematic study of generalized transverse-momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. We present such simultaneous modeling by considering a light-cone wave function overlap representation of the GTMDs. We construct the different quark-quark correlation functions from the 3-quark Fock components within both the light-front constituent quark model as well as within the chiral quark-soliton model. We provide a comparison with available data and make prediction…