QCD Corrections to the Radiative Decay B -> X_s gamma

In this short review, the calculation of the next-to-next-to-leading order QCD corrections to the inclusive radiative decay B -> X_s gamma is described. I summarize the salient features of the calculational framework adopted, discuss the results obtained in the last few years, and indicate the technical tools that made the NNLO calculations possible. I conclude by comparing the current NNLO theoretical estimate for the branching ratio with the experimental measurement and by briefly discussing the size and origin of the residual theoretical uncertainty.Comment: 18 pages, 7 figures. Invited review for Modern Physics Letters

Two-Loop Heavy-Flavor Contribution to Bhabha Scattering

We evaluate the two-loop QED corrections to the Bhabha scattering cross section which involve the vacuum polarization by heavy fermions of arbitrary mass m_f >> m_e. The results are valid for generic values of the Mandelstam invariants s,t,u >> m_e^2.Comment: 13 pages, 6 figures. Equations in the appendix generalized to the heavy-quark cas

Master integrals for the two-loop light fermion contributions to gg→Hgg \to H and H→γγH \to \gamma\gamma

We give the analytic expressions of the eight master integrals entering our previous computation of two-loop light fermion contributions to $gg \to H$ and $H \to \gamma\gamma$. The results are expressed in terms of generalized harmonic polylogarithms with maximum weight four included.Comment: 9 pages, 6 figure

Two-Loop Self-Energy Corrections to the Fine-Structure

We investigate two-loop higher-order binding corrections to the fine structure, which contribute to the spin-dependent part of the Lamb shift. Our calculation focuses on the so-called ``two-loop self-energy'' involving two virtual closed photon loops. For bound states, this correction has proven to be notoriously difficult to evaluate. The calculation of the binding corrections to the bound-state two-loop self-energy is simplified by a separate treatment of hard and soft virtual photons. The two photon-energy scales are matched at the end of the calculation. We explain the significance of the mathematical methods employed in the calculation in a more general context, and present results for the fine-structure difference of the two-loop self-energy through the order of $\alpha^8$.Comment: 19 pages, LaTeX, 2 figures; J. Phys. A (in press); added analytic results for two-loop form-factor slopes (by P. Mastrolia and E. Remiddi

Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering

In this paper we present the master integrals necessary for the analytic calculation of the box diagrams with one electron loop (N_{F}=1) entering in the 2-loop (\alpha^3) QED virtual corrections to the Bhabha scattering amplitude of the electron. We consider on-shell electrons and positrons of finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both UV and soft IR divergences are regulated within the continuous D-dimensional regularization scheme. After a brief overview of the method employed in the calculation, we give the results, for s and t in the Euclidean region, in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The corresponding results in the physical region can be recovered by analytical continuation. For completeness, we also provide the analytic expression of the 1-loop scalar box diagram including the first order in (D-4).Comment: Misprints in Eqs. (36), (38), (39), and (B.9) have been corrected. The results are now available at http://pheno.physik.uni-freiburg.de/~bhabha, as FORM input file

An efficient modeling framework for wall heat flux prediction in rocket combustion chambers using non adiabatic flamelets and wall-functions

In this work an efficient numerical framework for the prediction of wall heat loads in Liquid Rocket Engine combustion chambers is presented. The proposed framework is based on a new version of the non-adiabatic flamelet model and on wall functions for turbulent boundary layer modeling. Different wall function models are applied to 2D and 3D wall heat flux simulations of an experimental single-element gaseous oxygen-gaseous methane combustor in an Unsteady Reynolds Averaged Navier Stokes context. A systematic analysis and a comprehensive comparison of the selected wall models is carried out. The role of the constant or variable properties assumption on the near-wall turbulent quantities affecting the wall heat flux is assessed and the resulting friction velocity scaling investigated. When the skin friction velocity based on the local turbulent kinetic energy is defined by considering constant properties across the boundary layer, the equilibrium boundary layer assumption is not fulfilled and a significant overestimation of the wall heat flux is observed. Results obtained with the corrected near-wall turbulence modeling, on the other hand, showed a substantial improvement in terms of wall heat flux when compared with both experimental data and higher fidelity simulations results

Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations

The differential equation in the external invariant p^2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p^2=0 is obtained analytically. The system composed by this differential equation with those of the master integrals related to the general massive 2-loop sunrise diagram is numerically solved by the Runge-Kutta method in the complex p^2 plane. A numerical method to obtain results for values of p^2 at and close to thresholds and pseudo-thresholds is discussed in details.Comment: Latex, 20 pages, 7 figure

Two-Loop N_F=1 QED Bhabha Scattering Differential Cross Section

We calculate the two-loop virtual, UV renormalized corrections at order \alpha^4 (N_F=1) in QED to the Bhabha scattering differential cross section, for arbitrary values of the squared c.m. energy s and momentum transfer t, and on-shell electrons and positrons of finite mass m. The calculation is carried out within the dimensional regularization scheme; the remaining IR divergences appear as polar singularities in (D-4). The result is presented in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3.Comment: 61 pages, 4 figures. Overall sign mistakes in some formulas in appendix corrected, references adde

Two-Loop N_F =1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross-section

Recently, we evaluated the virtual cross-section for Bhabha scattering in pure QED, up to corrections of order alpha^4 (N_F =1). This calculation is valid for arbitrary values of the squared center of mass energy s and momentum transfer t; the electron and positron mass m was considered a finite, non vanishing quantity. In the present work, we supplement the previous calculation by considering the contribution of the soft photon emission diagrams to the differential cross-section, up to and including terms of order alpha^4 (N_F=1). Adding the contribution of the real corrections to the renormalized virtual ones, we obtain an UV and IR finite differential cross-section; we evaluate this quantity numerically for a significant set of values of the squared center of mass energy s.Comment: 24 pages, 15 figures. Formulas in Appendix B corrected, changes in Section 3, references adde