Mikhail Gorchtein

Model dependence of the γ Z dispersion correction to the parity-violating asymmetry in elastic ep scattering

We analyze the dispersion correction to elastic parity violating electron-proton scattering due to γZ exchange. In particular, we explore the theoretical uncertainties associated with modeling contributions of hadronic intermediate states. Taking into account constraints from low- and high-energy, parity-conserving electroproduction measurements, choosing different models for contributions from the nonresonant processes, and performing the corresponding flavor rotations to obtain the electroweak amplitude, we arrive at an estimate of the uncertainty in the total contribution to the parity-violating asymmetry. At the kinematics of the Q-Weak experiment, we obtain a correction to the asymmetry equivalent to a shift in the proton weak charge of (0.0054±0.0020). This should be compared to the value of the proton’s weak charge of QW^p=0.0713±0.0008 that includes Standard Model contributions at tree level and one-loop radiative corrections. Therefore, we obtain a new Standard Model prediction for the parity-violating asymmetry in the kinematics of the Q-Weak experiment of (0.0767±0.0008±0.0020_(γZ)). The latter error leads to a relative uncertainty of 2.8% in the determination of the proton’s weak charge and is dominated by the uncertainty in the isospin structure of the inclusive cross section. We argue that future parity-violating inelastic ep asymmetry measurements at low to moderate Q^2 and W^2 could be exploited to reduce the uncertainty associated with the dispersion correction. Because the corresponding shift and error bar decrease monotonically with decreasing beam energy, a determination of the proton’s weak charge with a lower-energy experiment or measurements of “isotope ratios” in atomic parity violation could provide a useful cross-check on any implications for physics beyond the Standard Model derived from the Q-Weak measurement.

Model Independent Bounds on Magnetic Moments of Majorana Neutrinos

Abstract We analyze the implications of neutrino masses for the magnitude of neutrino magnetic moments. By considering electroweak radiative corrections to the neutrino mass, we derive model-independent naturalness upper bounds on neutrino magnetic moments, μ ν , generated by physics above the electroweak scale. For Dirac neutrinos, the bound is several orders of magnitude more stringent than present experimental limits. However, for Majorana neutrinos the magnetic moment contribution to the mass is Yukawa suppressed. The bounds we derive for magnetic moments of Majorana neutrinos are weaker than present experimental limits if μ ν is generated by new physics at ∼ 1 TeV , and surpass current experimental sensitivity only for new physics scales > 10 – 100 TeV . The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles.

Dispersive contributions to e+ p/e- p cross section ratio in forward regime

Abstract Two-photon exchange (TPE) contributions to elastic electron–proton scattering in the forward regime are considered. The imaginary part of TPE amplitude in these kinematics is related to the DIS nucleon structure functions. The real part of the TPE amplitude is obtained from the imaginary part by means of dispersion relations. We demonstrate that the dispersion integrals for the relevant elastic ep -scattering amplitude converge and do not need subtraction. This allows us to make clean prediction for the real part of the TPE amplitude at forward angles. We furthermore compare e + p and e − p cross sections which depends on the real part of TPE amplitude, and predict the positron cross section to exceed the electron one by a few per cent, with the difference ranging from 1.4% to 2.8% for electron lab energies in the range from 3 to 45 GeV. We furthermore predict that the absolute value of this asymmetry grows with energy, which makes it promising for experimental tests.

Form factors of pseudoscalar mesons

Photons interact with quarks, the charged constituents of hadrons and the resulting electromagnetic form factors probe the quark energy-momentum distribution in hadrons. In this letter we examine the charged pion electromagnetic form factor F2π(s), which is defined by the matrix element 〈π(p)π(p)|Jμ|0〉 = e(p′ − p)μF2π(s), and the transition from factor between the neutral pion and a real photon, Fπγ(s) determined by 〈π0(p′)γ(λ, p)|Jμ|0〉 = ie/4πfπ μναβ (λ)ppFπγ(s). Above, Jμ is the electromagnetic current, s = (p′+p)2 is the four-momentum transfer squared and fπ = 92.4 MeV is the pion decay constant. Current conservation implies F2π(0) = 1 and, in the chiral limit, axial anomaly determination of the π → 2γ decay leads to the expectation Fπγ(0) ≈ 1. Because at short distances quark/gluon interactions are asymptotically free, it has been postulated that at high energy or momentum transfer, |s| μ, both form factors measure hard scattering of the photon with a small number of the QCD constituents [1–3]. One would then expect μ ∼ O(1 GeV), which is the typical hadronic scale, however, given the current status of the data it seems that μ could be as large as O(10−100GeV) [4, 5]. This implies that an alternative description of the underlying dynamics might be in order and the subject of applicability of pQCD to exclusive reactions has in fact a long history [6]. Perturbative QCD (pQCD) analysis of the form factor asymptotics assumes specific properties of certain non-perturbative quantities, i.e. the parton momentum distribution amplitudes in the lowmomentum,”wee” region. If these had different behavior from what is assumed in the pQCD analysis the arguments leading to dominance of leading twist perturbative scattering would break down [7]. Such pion distribution amplitudes were considered recently in [8, 9], however, the authors used perturbative evolution to soften the wee region and use pQCD formulae. The available data on the pion electromagnetic form factor ranges up to |s| ∼ < 10 GeV [10] and is approximately a factor of three above the asymptotic prediction [11]. Even more spectacular discrepancy is observed in the transition form factor recently measured by BaBar [12]. For momentum transfers as large as −s ≈ 40GeV the measurement disagrees with the asymptotic prediction not only in normalization but also in the overall s-dependence. While pQCD predicts sFπγ(s) → 2fπ as |s| → ∞ [3], the data suggest that the magnitude of −sFπγ(s) grows with |s|. Crossing symmetry implies that form factors in the space-like (s < 0) and time-like (s > 0) region are boundary values of an analytical function defined in the complex-s plane with a unitarity cut running over the positive s-axis and starting at the two pion production threshold branch point sth = 4m 2 π. In the time-like region the electromagnetic (transition) form factor describes the amplitude for production of a spin-1, π+π− pair (πγ) in the external electromagnetic field of the virtual photon. In the space-like region the form factors are usually interpreted in terms of parton three-momentum distribution in a hadron (and/or photon). Analyticity demands these apparently distinct physical pictures to be smoothly connected. The dominant feature of the spin1, π+π− state is the isovector ρ(770) resonance, which also dominates the electromagnetic form factor. There is no time-like data available for the transition form factor, however, also in this case one expects to see the ρ, and the isoscalar, ω(782) resonance. The analytical continuation to the space-region implies that for −s ∼ < 1GeV , i.e. in the hadronic range, the quark wave function is dual to the vector-meson exchange in the crossed channel. In the following, we relate the space-like and time-like regions through dispersion relations, and focus on the dynamics in the asymptotic region, s→ +∞. In view of the BaBar ”anomaly” and the apparent failure of the pQCD description, we propose a novel description for the dominant mechanism that drives the asymptotic behavior of the form factors. The discontinuity of Fπγ(s) across the unitary cut is given by

Forward sum rule for the

xedt dispersion relation. This allows for a clean prediction for the real part of the TPE amplitude at forward angles with the leading term t lnjtj. Numerical estimates are comparable with or exceed the experimental precision in extracting the charge radius from the experimental data. PACS numbers: 11.55.Hx, 13.40.Gp, 13.60.Fz, 13.60.Hb Nucleon structure has been studied with elastic electron scattering since the 1950’s. By means of the Rosenbluth separation the measurement of the unpolarized cross section allows to extract the electromagnetic form factors of the nucleon. The interest in measuring the elastic cross section at low (negative) t is, e.g., the extraction of the slope of the electric Sachs form factor GE that is related to the charge radius RE as GE(t! 0) = 1 +R 2t=6 +O(t 2 ) (1)

2\gamma

We analyze the implications of neutrino masses for the magnitude of neutrino magnetic moments. By considering electroweak radiative corrections to the neutrino mass, we derive model‐independent naturalness upper bounds on neutrino magnetic moments, generated by physics above the electroweak scale. For Majorana neutrinos, these bounds are weaker than present experimental limits if μν if generated by new physics at ∼ 1 TeV, and surpass current experimental sensitivity only for new physics scales > 10 – 100 TeV. The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles.

-exchange correction to the charge-radius extraction from elastic electron scattering

Background: Parity-violating elastic electron-nucleon scattering at low momentum transfer allows one to access the nucleons weak charge, the vector coupling of the Z-boson to the nucleon. In the Standard Model and at tree level, the weak charge of the proton is related to the weak mixing angle and accidentally suppressed, QWp,tree=1−4sin2θW≈0.07. Modern experiments aim at extracting QWp at ∼1% accuracy. Similarly, parity nonconservation in atoms allows to access the weak charge of atomic nuclei. Purpose: We consider a novel class of radiative corrections due to the exchange of two photons, with parity violation in the hadronic/nuclear system. These corrections are prone to long-range interactions and may affect the extraction of sin2θW from the experimental data at the relevant level of precision. Methods: The two-photon exchange contribution to the parity-violating electron-proton scattering amplitude is studied in the framework of forward dispersion relations. We address the general properties of the parity-violating forward Compton scattering amplitude and use relativistic chiral perturbation theory to provide the first field-theoretical proof that it obeys a superconvergence relation. Results: We show that the significance of this new correction increases with the beam energy in parity-violating electron scattering, but the superconvergence relation protects the formal definition of the weak charge as a limit at zero-momentum transfer and zero energy. We evaluate the new correction in a hadronic model with pion loops and the Δ(1232) resonance, supplemented with a high-energy contribution. For the kinematic conditions of existing and upcoming experiments we show that two-photon exchange corrections with hadronic or nuclear parity violation do not pose a problem for the interpretation of the data in terms of the weak mixing angle at the present level of accuracy. Conclusions: Two-photon exchange in presence of hadronic or nuclear parity violation gives rise to long-range parity-violating interactions. Depending on the kinematic conditions and precision goal, this novel correction may affect the extraction of weak charges from experiments with atoms and electron scattering.

Model Independent Naturalness Bounds on Magnetic Moments of Majorana Neutrinos

We consider deeply virtual Compton scattering and deep inelastic scattering in presence of Regge exchanges. Recently, we have proposed a model in which the diffractive phenomena that are expected to govern the low-xB DIS are incorporated at the parton nucleon level [1, 2]. Such effective parton-nucleon amplitude gives the correct description of low-x structure functions. Surprisingly, however, we have found that in the case of DVCS it breaks collinear factorization, i.e. Bjorken scaling, while it naturally leads to the Regge-type scaling, as it was in fact predicted by Bjorken and Kogut in [3]. In particular, we discuss the contribution of the Pomeron exchange to DVCS in HERA kinematics. A new fit of the DVCS total cross section data from H1 and ZEUS is proposed.