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Register a new userLepton mass effects in the Bethe-Heitler process
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We develop the full finite lepton mass formalism for the production of real photons via the Bethe-Heitler reaction of unpolarized leptons off unpolarized nucleons. Genuine lepton mass effects are described, in particular their dependence upon the lepton mass and the initial beam energy, as well as their sensitivity to the nucleon isospin. In the minimum momentum transfer region, these effects dominate the muon induced proton cross section and become significant for electron scattering at small $x_B$.
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The ratio of di-lepton production cross sections on a proton, using the $gamma prightarrow l^+ l^- p$ 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 attached to the proton line vanish after averaging over di-lepton angles, and estimate the relatively small radiation off the proton. We compare the full one-loop calculation with a soft-photon approximation of the same order, and present estimates for a planned experiment.
In this work, we discuss exclusive semileptonic $B_c$-meson decays: $B_cto eta_c(J/psi)l u$ and $B_cto D(D^*)l u$ in the framework of the relativistic independent quark(RIQ) model based on an average flavor independent confining potential in equally mixed scalar-vector harmonic form. We calculate the invariant form factors representing decay amplitudes from the overlapping integrals of meson wave functions derivable in the RIQ model. To evaluate the lepton mass effects in the semileptonic decays, we first study the $q^2$-dependence of the form factors in the accessible kinematic range of $q^2$ involved in the decay process in its $e^-$ and $tau^-$ mode separately. Similar studies on helicity amplitudes, $q^2-$spectra for different helicity contributions, and total $q^2$-spectra for each decay process are carried out separately in their $e^-$ and $tau^-$ modes. We predict the decay rates/ branching fractions, forward-backward asymmetry, and the asymmetry parameter in reasonable agreement with other model predictions, which can hopefully be tested in future experiments at the Tevatron and LHC. We also predict the observable $R$ which corresponds to the ratio of branching fractions for the decay process in its $e^-$ mode to its corresponding value in the $tau^-$ mode. Our results are comparable to another standard model(SM) predictions which highlight the failure of the lepton flavor universality hinting at new physics beyond SM for the explanation of the observed deviation of observable $R$ value from the corresponding SM predictions.
We note that off the quark mass shell the operators $(p_i+p_f)_mugamma_5$ and $isigma_{mu u}(p_i -p_f)^ ugamma_5$, both of which reduce to $-vec{sigma}cdotvec{E}$ in the non-relativistic limit, are no longer identical. In this paper we explore the effects of this difference in the contribution of these quark electric moments to hadronic electric moments.
Using our solutions of the Bethe-Salpeter equation with OBE kernel in Minkowski space both for the bound and scattering states, we calculate the transition form factors for electrodisintegration of the bound system which determine the electromagnetic current J of this process. Special emphasis is put on verifying the gauge invariance which should manifest itself in the current conservation. We find that for any value of the momentum transfer q the contributions of the plane wave and the final state interaction to the quantity J.q cancel each other thus providing J.q=0. However, this cancellation is obtained only if the initial Bethe-Salpeter amplitude (bound state), the final one (scattering state) and the current operator are strictly consistent with each other. A reliable result for the transition form factor can be found only in this case.
The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.
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