The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV is evaluated up to NLO in Standard Model couplings. The results apply in the so-called relativistic regime, referring parametrically to a mass M ~ πT, generalizing thereby previous NLO results which only apply in the non-relativistic regime M ≫ πT. The non-relativistic expansion is observed to converge for M ≳ 15T, but the smallness of any loop corrections allows it to be used in practice already for M ≳ 4T. In the latter regime any non-covariant dependence of the differential rate on the spatial momentum is shown to be mild. The loop expansion breaks down in the ultrarelativistic regime M ≪ πT, but after a simple mass resummation it nevertheless extrapolates reasonably well towards a result obtained previously through complete LPM resummation, apparently confirming a strong enhancement of the rate at high temperatures (which facilitates chemical equilibration). When combined with other ingredients the results may help to improve upon the accuracy of leptogenesis computations operating above the electroweak scale.

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Thermal right-handed neutrino production rate in the non-relativistic regime

We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion electrodynamics in manifestly covariant and consistent manner.

Generalized Octonion Electrodynamics

The production rate of heavy Majorana neutrinos is relevant for models of thermal leptogenesis in the early Universe. In the high temperature limit the production can proceed via the 1 2 (inverse) decays which are allowed by the thermal masses. We consider new production mechanisms which are obtained by including additional soft gauge interactions with the plasma. We show that an arbitrary number of such interactions gives leading order contributions, and we sum all of them. The rate turns out to be smooth in the region where the 1 2 processes are kinematically forbidden. At higher temperature it is enhanced by a factor 3 compared to the 1 2 rate.

Thermal production of relativistic Majorana neutrinos: Strong enhancement by multiple soft scattering

We compute the next-to-leading order O(g) correction to the thermal photon production rate in a QCD plasma. The NLO contributions can be expressed in terms of gauge invariant condensates on the light cone, which are amenable to novel sum rules and Euclidean techniques. We expect these technologies to be generalizable to other NLO calculations. For the phenomenologically interesting value of alpha_s=0.3, the NLO correction represents a 20% increase and has a functional form similar to the LO result.

Next-to-leading order thermal photon production in a weakly coupled quark-gluon plasma

We present an extension to next-to-leading order in the strong coupling constant $g$ of the AMY effective kinetic approach to the energy loss of high momentum particles in the quark-gluon plasma. At leading order, the transport of jet-like particles is determined by elastic scattering with the thermal constituents, and by inelastic collinear splittings induced by the medium. We reorganize this description into collinear splittings, high-momentum-transfer scatterings, drag and diffusion, and particle conversions (momentum-preserving identity-changing processes). We show that this reorganized description remains valid to NLO in $g$, and compute the appropriate modifications of the drag, diffusion, particle conversion, and inelastic splitting coefficients. In addition, a new kinematic regime opens at NLO for wider-angle collinear bremsstrahlung. These semi-collinear emissions smoothly interpolate between the leading order high-momentum-transfer scatterings and collinear splittings. To organize the calculation, we introduce a set of Wilson line operators on the light-cone which determine the diffusion and identity changing coefficients, and we show how to evaluate these operators at NLO.

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Jet-Medium Interactions at NLO in a Weakly-Coupled Quark-Gluon Plasma

The quaternionic formulation of generalized field equations of the field associated with dyons has been developed and it has been shown that the quaternionic generalized field equations are unique and consistent ones which reproduce the usual electrodynamics in the absence of magnetic charge on dyons.

Quaternionic formulation for generalized field equations in the presence of dyons

Starting with a brief description of dyons and gravito-dyons, combined field equations and the equation of motion for generalized electromagnetic and generalized gravito-Heavisidian fields are derived in a manifestly covariant way. A non-Abelian gauge theory of dyons and gravito-dyons is described in terms of a generalized Yang-Mills potential, field strengths, and generalized field equations each carrying electric and magnetic constituents. A null tetrad formulation of a generalized Yang-Mills potential and field strength of dyons is discussed in detail in terms of symmetric spinors and spin coefficients. Generalized Yang-Mills field equations of dyons are rewritten in terms of null tetrad notation, and dyon solutions of source-free Dirac equations are obtained.

Null tetrad formulation of non-Abelian dyons

Quark Confinement through Dyonic Condensation

By considering the generalized charge, the generalized four-current density and the generalized four-potential associated with dyons, the field equation and the equation of motion of the dyons have been derived by choosing a suitable Lagrangian density for generalized electromagnetic fields.

Generalized fields associated with dyons

The study of gauge invariant and rotationally symmetric angular-momentum operators of dyons has been undertaken and the corresponding properties of their eigenvalues have been analysed. It has been shown that the presence of magnetic charge on dyons gives rise to a residual angular momentum and chirality-dependent multiplicity in the eigenvalues of the third component of the angular-momentum operator.

B. S. Rajput

Papers

Quaternionic formulation for generalized field equations in the presence of dyons

Null tetrad formulation of non-Abelian dyons

Quark Confinement through Dyonic Condensation

Generalized fields associated with dyons

Angular-momentum operators for dyons