We consider elastic scattering of electrons off a proton target. The parity violating (PV) asymmetry arises at leading order in $α$ due to interference of $γ$ and $Z$ exchange. The radiative corrections to this leading mechanism were calculated in the literature and included in experimental analyses, except for $γZ$ box and cross-box contributions. We present here a dispersion calculation of these corrections in forward kinematics. We demonstrate that at the GeV energies of current PV experiments, such corrections are not suppressed by the small vector weak charge of the electron, as occurs in the atomic PV. Our results suggest that the current theoretical uncertainty in the analysis of the QWEAK experiment might be substantially underestimated, and more accurate account of the dispersion corrections are needed in order to interprete the PV data.
We present the fully up-to-date calculation of the $γZ$-box correction which needs to be taken into account to determine the weak mixing angle at low energies from parity-violating electron proton scattering. We make use of neutrino and antineutrino inclusive scattering data to predict the parity-violating structure function $F_3^{γZ}$ by isospin symmetry. Our new analysis confirms previous results for the axial contribution to the $γZ$-box graph, and reduces the uncertainty by a factor of~2. In addition, we note that the presence of parity-violating photon-hadron interactions induces an addit…
We perform a fit of the real Compton scattering (RCS) data below pion-production threshold to extract the electric ($α_{E1}$) and magnetic ($β_{M1}$) static scalar dipole polarizabilities of the proton, using fixed-$t$ subtracted dispersion relations and a bootstrap-based fitting technique. The bootstrap method provides a convenient tool to include the effects of the systematic errors on the best values of $α_{E1}$ and $β_{M1}$ and to propagate the statistical errors of the model parameters fixed by other measurements. We also implement various statistical tests to investigate the consistency …
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 w…
Recently, the first ever lattice computation of the $γW$-box radiative correction to the rate of the semileptonic pion decay allowed for a reduction of the theory uncertainty of that rate by a factor of $\sim3$. A recent dispersion evaluation of the $γW$-box correction on the neutron also led to a significant reduction of the theory uncertainty, but shifted the value of $V_{ud}$ extracted from the neutron and superallowed nuclear $β$ decay, resulting in a deficit of the CKM unitarity in the top row. A direct lattice computation of the $γW$-box correction for the neutron decay would provide an …
Dispersion theory of nucleon (nucleus) Compton scattering spin polarizabilities and quasi-optical $γ$-ray polarization plane rotation and birefringence effect in a matter with polarized protons (nuclei)
I summarize the dispersion-theoretical analysis of the nucleon electromagnetic form factors. Special emphasis is given on the extraction of the proton charge radius and its relatives, the proton magnetic radius as well as the neutron magnetic radius. Some recent work on the hyperfine splitting in leptonic hydrogen and on radiative corrections to muon-proton scattering is also discussed. Some views on future studies are given.
Subtracted Dispersion Relations for Virtual Compton Scattering off the Proton
Johannes Gutenberg-Universität, Mainz（美因茨约翰内斯·古腾堡大学）；Università degli Studi di Pavia（帕维亚大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Pavia（意大利国家核物理研究所帕维亚分部）
Grup de Física Teòrica, Departament de Física, Universitat Autònoma de Barcelona（巴塞罗那自治大学物理系理论物理组）；Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology (BIST)（高等能量物理研究所（IFAE），巴塞罗那科学技术研究院（BIST））
We present the dispersion relation approach based on unitarity and analyticity to evaluate the two-photon exchange contribution to elastic electron-proton scattering. The leading elastic and first inelastic $πN$ intermediate state contributions are accounted for in the region of small momentum transfer $Q^2 < 1~\mathrm{GeV}^2$ based on the available data input. The novel methods of analytical continuation allow us to exploit the MAMI form factor data and the MAID parameterization for the pion electroproduction amplitudes as input in the calculation. The results are compared to the recent CLAS,…
We revisit the role of the chiral "triangle" anomaly in deeply inelastic scattering (DIS) of electrons off polarized protons employing a powerful worldline formalism. We demonstrate how the triangle anomaly appears at high energies in the DIS box diagram for the polarized proton structure function $g_1(x_B,Q^2)$ in both the Bjorken limit of large $Q^2$ and in the Regge limit of small $x_B$. We show that the operator product expansion is not required to extract the anomaly in either asymptotics though it is sufficient in the Bjorken limit. Likewise, the infrared pole in the anomaly arises in bo…
Using dispersion theory with an improved description of the two-pion continuum based on the precise Roy-Steiner analysis of pion-nucleon scattering, we analyze recent data from electron-proton scattering. This allows for a high-precision determination of the electric and magnetic radius of the proton, $r_E = (0.838^{+0.005}_{-0.004}{}^{+0.004}_{-0.003})\,$fm and $r_M = (0.847\pm{0.004}\pm{0.004})\,$fm, where the first error refers to the fitting procedure using bootstrap and the data while the second one refers to the systematic uncertainty related to the underlying spectral functions.
We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant $g_A$ in the neutron $β$-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function $g_1$, we determine the contribution from the $γW$-box diagram to a precision better than $10^{-4}$. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron $β$-decay are almost identical, i.e. the ratio $λ=g_A/g_V$ is almost unrenormalized. With this result, we predict…
We extract the proton magnetic radius from the high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-$Q^2$ form factors. It allows us to use data up to $Q^2\sim$ 0.5 GeV$^2$ for constraining the radii and overcomes the difficulties of empirical fits and $Q^2 \rightarrow 0$ extrapolation. We obtain a magnetic radius $r_M^p$ = 0.850 $\pm$0.001 (fit 68%) $\pm$0.010 (theory full range) fm, significantly different from earlier results ob…
In this paper, one presents some results concerning the behavior of the total cross section and $ρ$-parameter at asymptotic energies in proton-proton ($pp$) and antiproton-proton ($\bar{p}p$) collisions. For this intent, we consider three of the main theoretical results in high energy physics: the crossing property, the derivative dispersion relation, and the optical theorem. The use of such machinery allows the analytic formulas for wide set of the measured global scattering parameters and some important relations between them. The suggested parameterizations approximate simultaneously the en…
We present a dispersion theoretical analysis of recent date from electron-proton scattering. This allows for a high-precision extraction of the electric and magnetic radius of the proton, $r_E = (0.839\pm 0.002{}^{+0.002}_{-0.003})$~fm and $r_M = (0.846\pm 0.001{}^{+0.001}_{-0.005})$~fm, where the first error refers to the statistical type estimated from the bootstrap method, and the second one refers to the systematic uncertainty related to the underlying spectral functions.
We present a comprehensive analysis of the $γW$ interference radiative correction to the neutron $β$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $γW$ box amplitude $\Box^{γW}_{A}$ in terms of the isoscalar part of the $F_3^{γW}$ interference structure function. Using the latest available phenomenology for $F_3^{γW}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be $\Box^{γW}_A = 3.90(9) \times 10^{-3}$. This improved correction gives a theoretical estimate of the C…
We present a dispersion theoretical analysis of the experimental data on the electromagnetic form factors of the nucleon covering both the space- and time-like regions. The nucleon form factors over the full range of momentum transfers and the nucleon radius are extracted with high precision. The statistical uncertainties of the extracted form factors and radius are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. For the proton charge radius, we find $r_E^p = 0.840^{+0.003}_{-0.002}{}^{+0.002}_{-0.002}$~fm, in line with pr…
We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 = 0$. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to u…
We present a dispersive analysis with the aim to extract the $Υ$-p scattering length from $γp \to Υp$ experiments. In this framework, the imaginary part of the $Υ$-p forward scattering amplitude is obtained from $γp \to Υp$ 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 $Υ$-p scattering length. We perform a feasibility study for $Υ$ photo-production experiments at an Electron-Ion Collider and discuss the sensitivity and…
The next-to-leading order of the differential cross section of the subprocess of annihilation of quark-antiquark pair of prompt photon production in proton-proton collisions at NICA energies
Baku State University（巴库国立大学）；Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）
