Steps towards full two-loop calculations for 2 fermion to 2 fermion processes: running versus pole masses schemes

Recent progress in the calculation of the two-loop on-shell mass counterterms within the electroweak Standard Model (SM) for the massive particles are discussed. We are in progress of developing a package for full two-loop SM calculations of 2 -> 2 fermion processes, with emphasis on the analytical approach where feasible. The complete two-loop on-shell renormalization is implemented. Substantial progress has been made in calculating the master integrals. We are able to compute in an efficient and stable manner up to a few thousands of diagrams of very complex mass structure.Comment: 4 pages, 1 style file. To appear in the proceedings of 9th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 03), Tsukuba, Japan, 1-5 Dec 200

New Aspects of B -> pi pi, pi K and their Implications for Rare Decays

We analyse the B -> pi pi, pi K modes in the light of the most recent B-factory data, and obtain the following new results: (i) the B0 -> pi+ pi-, pi- K+ modes prefer gamma=(74+-6)deg, which - together with |V_ub/V_cb| - allows us to determine the ``true'' unitarity triangle and to search for CP-violating new-physics contributions to B0_d-\bar B0_d mixing; (ii) the B -> pi K puzzle reflected in particular by the low experimental value of the ratio R_n of the neutral B -> pi K rates persists and still favours new physics in the electroweak penguin sector with a new CP-violating phase phi ~ -90deg, although now also phi ~ +90deg can bring us rather close to the data; (iii) the mixing-induced B0 -> pi0 K_S CP asymmetry is a sensitive probe of the sign of this phase, and would currently favour phi ~ +90deg, as well as the direct CP asymmetry of B+- -> pi0 K+-, which suffers, however, from large hadronic uncertainties; (iv) we investigate the sensitivity of our B -> pi K analysis to large non-factorizable SU(3)-breaking effects and find that their impact is surprisingly small so that it is indeed exciting to speculate on new physics; (v) assuming that new physics enters through Z0 penguins, we study the interplay between B -> pi K and rare B, K decays and point out that the most recent B-factory constraints for the latter have interesting implications, bringing us to a few scenarios for the future evolution of the data, where also the mixing-induced CP violation in B0 -> pi0 K_S plays a prominent role.Comment: Two references added, to appear in the European Physical Journal

The B -> pi K Puzzle and its Relation to Rare B and K Decays

The Standard-Model interpretation of the ratios of charged and neutral B-> pi K rates, R_c and R_n, respectively, points towards a puzzling picture. Since these observables are affected significantly by colour-allowed electroweak (EW) penguins, this ``B -> pi K puzzle'' could be a manifestation of new physics in the EW penguin sector. Performing the analysis in the R_n-R_c plane, which is very suitable for monitoring various effects, we demonstrate that we may, in fact, move straightforwardly to the experimental region in this plane through an enhancement of the relevant EW penguin parameter q. We derive analytical bounds for q in terms of a quantity L, that measures the violation of the Lipkin sum rule, and point out that strong phases around 90 deg are favoured by the data, in contrast to QCD factorisation. The B -> pi K modes imply a correlation between q and the angle gamma that in the limit of negligible rescattering effects and colour suppressed EW penguins depends only on the value of L. Concentrating on a minimal flavour-violating new-physics scenario with enhanced Z^0 penguins, we find that the current experimental values on B -> X_s mu^+ mu^- require roughly L pi K data give L = 5.7 +- 2.4, L has either to move to smaller values once the B -> pi K data improve or new sources of flavour and CP violation are needed. In turn, the enhanced values of L seen in the B -> pi K data could be accompanied by enhanced branching ratios for rare decays. Most interesting turns out to be the correlation between the B -> pi K modes and BR(K^+ -> pi^+ nu nu), with the latter depending approximately on a single ``scaling'' variable \bar L= L (|V_{ub}/V_{cb}|/0.086)^2.3.Comment: 19 pages, 7 figures, a few typos corrected and two references adde

The influence of negative-energy states on proton-proton bremsstrahlung

We investigate the effect of negative-energy states on proton-proton bremsstrahlung using a manifestly covariant amplitude based on a T-matrix constructed in a spectator model. We show that there is a large cancellation among the zeroth-order, single- and double-scattering diagrams involving negative-energy nucleonic currents. We thus conclude that it is essential to include all these diagrams when studying effects of negative-energy states.Comment: 12 pages revtex and 3 figure

MS vs. Pole Masses of Gauge Bosons: Electroweak Bosonic Two-Loop Corrections

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represents a gauge invariant subclass of diagrams. All calculations were performed in the linear $R_\xi$ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters $\sin^2\theta_W$ and mass ratio $m_Z^2/m_H^2$. As a byproduct we obtain the bosonic two-loop contributions to the renormalization of the weak mixing parameter $\sin^2\theta_W$ and of the Fermi constant. The running of Fermi constant will become important at high energy colliders.Comment: LaTeX, 36 p., 10 fig.; in v3 more technical details about renormalization procedure are adde

Two-loop QCD corrections of the massive fermion propagator

The off-shell two-loop correction to the massive quark propagator in an arbitrary covariant gauge is calculated and results for the bare and renormalized propagator are presented. The calculations were performed by means of a set of new generalized recurrence relations proposed recently by one of the authors. From the position of the pole of the renormalized propagator we obtain the relationship between the pole mass and the \bar{MS} mass. This relation confirms the known result by Gray et al.. The bare amplitudes are given for an arbitrary gauge group and for arbitrary space-time dimensions.Comment: 18 pages LaTeX, misprints in formula (12) are correcte

O(\alpha \alpha_s) correction to the pole mass of the t-quark within the Standard Model

We have calculated the O(\alpha \alpha_s) contributions to the relationship between the MS-mass and the pole of the t-quark propagator in the Standard Model in the limit of a diagonal CKM matrix and for a massless b-quark. Analytical results for the so far unknown master-integrals appearing in the calculation are also given.Comment: 23 pages, LaTeX, 5-eps figures; In v.2 the typos in Eqs.(4.41), (5.54), (5.56), (5.57) and Fifure 4 corrected. New references are adde

Long-range two-body final-state interactions and direct CP asymmetry in {B}^{+}\to{\pi}^{+} {K}^{0} decay

We present a calculation of the direct CP asymmetry, $A_{CP}^{dir}$, for the process $B^+ \to \pi^+ K^0$ including the effects of long-range inelastic final-state interactions (FSI). We admit three channels in our calculation: $B^+ \to (\pi^+ K^0), (\eta K^+)$, and $(D_s^+ \bar{D}^0)$. The strong scattering is described in terms of Pomeron and Regge exchanges. We find that the direct CP asymmetry is enhanced by a factor of $\sim 3$ as a result of FSI, but remains well short of the claims of (10 - 20)% in recent literature. A critical assessment of papers claiming large CP asymmetries is also presented.Comment: 21 pages, latex, no figures. Added the charge-exchange channel {B}^{+}\to {\pi}^{0} {K}^{+}. Expanded the discussion section. To be published in Phys. Rev.

In Pursuit of New Physics with B_s Decays

The presence of a sizeable CP-violating phase in B_s^0-B_s^0-bar mixing would be an unambiguous signal of physics beyond the Standard Model. We analyse various possibilities to detect such a new phase considering both tagged and untagged decays. The effects of a sizeable width difference Delta Gamma between the B_s mass eigenstates, on which the untagged analyses rely, are included in all formulae. A novel method to find this phase from simple measurements of lifetimes and branching ratios in untagged decays is proposed. This method does not involve two-exponential fits, which require much larger statistics. For the tagged decays, an outstanding role is played by the observables of the time-dependent angular distribution of the B_s -> J/psi [-> l^+ l^-] \phi [-> K^+K^-] decay products. We list the formulae needed for the angular analysis in the presence of both a new CP-violating phase and a sizeable Delta Gamma, and propose methods to remove a remaining discrete ambiguity in the new phase. This phase can therefore be determined in an unambiguous way.Comment: minor changes, lattice prediction of Delta Gamma updated, appears in PR

FIRCLA, one-loop correction to e+ e- to nu anti-nu H and basis of Feynman integrals in higher dimensions

An approach for an effective computer evaluation of one-loop multi-leg diagrams is proposed. It's main feature is the combined use of several systems - DIANA, FORM and MAPLE. As an application we consider the one-loop correction to Higgs production in e+ e- to nu anti-nu H, which is important for future e+ e- colliders. To improve the stability of numerical evaluations a non-standard basis of integrals is introduced by transforming integrals to higher dimensions.Comment: 6 pages 1 figure, reference to G. Belanger et al. adde