Renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking

The renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking is presented using spurion fields for introducing the breaking terms. It is proven that renormalization of the fields and parameters in the classical action yields precisely the correct counterterms to cancel all divergences. In the course of the construction of higher orders additional independent parameters appear, but they can be shown to be irrelevant in physics respects. Thus, the only parameters with influence on physical amplitudes are the supersymmetric and the well-known soft breaking parameters.Comment: 29 pages, published in The European Physical Journal

One-loop MSSM Contribution to the Weak Magnetic Dipole Moments of Heavy Fermions

The MSSM predictions at the one-loop level for the weak-magnetic dipole moments of the $\tau$ lepton and the $b$ quark are analysed. The entire supersymmetric parameter space is scannedwith the usual GUT constraint and common squark and slepton mass parameters. The real part of $a^W_\tau$ is dominated by the chargino contribution, being the same order as the SM one or even larger in the high $\tan\beta$ region whereas the imaginary part, due to Higgs boson diagrams, is negligible comparedto the SM value. The real part of$a^W_b$ is controlled mainly by charginos andalso by gluinos, when the mixing in the bottom squark sector is large, to yield, for high $\tan\beta$, a contribution one order of magnitude largerthan the pure electroweak SM value but a factor five smaller than the standard QCD contribution. The imaginary part of $a^W_b$ is the same order as in the SM.Comment: 14 pages, Latex, 4 eps and 1 ps figure, needs epsfig.sty. Minor changes, new references added. To be published in Phys. Lett.

Computation of H→ggH\to gg in FDH and DRED: renormalization, operator mixing, and explicit two-loop results

The $H\to gg$ amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (FDH) and in dimensional reduction (DRED) at the two-loop level. The required renormalization is developed and described in detail, including the treatment of evanescent $\epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $\epsilon$-scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED

SCET approach to regularization-scheme dependence of QCD amplitudes

We investigate the regularization-scheme dependence of scattering amplitudes in massless QCD and find that the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED) are consistent at least up to NNLO in the perturbative expansion if renormalization is done appropriately. Scheme dependence is shown to be deeply linked to the structure of UV and IR singularities. We use jet and soft functions defined in soft-collinear effective theory (SCET) to efficiently extract the relevant anomalous dimensions in the different schemes. This result allows us to construct transition rules for scattering amplitudes between different schemes (CDR, HV, FDH, DRED) up to NNLO in massless QCD. We also show by explicit calculation that the hard, soft and jet functions in SCET are regularization-scheme independent.Comment: 46 pages, 6 figure

Factorization and regularization by dimensional reduction

Since an old observation by Beenakker et al., the evaluation of QCD processes in dimensional reduction has repeatedly led to terms that seem to violate the QCD factorization theorem. We reconsider the example of the process and show that the factorization problem can be completely resolved. A natural interpretation of the seemingly non-factorizing terms is found, and they are rewritten in a systematic and factorized form. The key to the solution is that the D- and (4−D)-dimensional parts of the 4-dimensional gluon have to be regarded as independent partons

Photonic SUSY Two-Loop Corrections to the Muon Magnetic Moment

Photonic SUSY two-loop corrections to the muon magnetic moment are contributions from diagrams where an additional photon loop is attached to a SUSY one-loop diagram. These photonic corrections are evaluated exactly, extending a leading-log calculation by Degrassi and Giudice. Compact analytical expressions are provided and the numerical behaviour is discussed. The photonic corrections reduce the SUSY one-loop result by 7...9%. The new terms are typically around ten times smaller than the leading logarithms, but they can be larger and have either sign in cases with large SUSY mass splittings. We also provide details on renormalization and regularization and on how to incorporate the photonic corrections into a full SUSY two-loop calculation.Comment: 25 page

Status of the Fermilab Muon (g-2) Experiment

The New Muon $(g-2)$ Collaboration at Fermilab has proposed to measure the anomalous magnetic moment of the muon, $a_\mu$, a factor of four better than was done in E821 at the Brookhaven AGS, which obtained $a_\mu = [116 592 089 (63)] \times 10^{-11}$ $\pm 0.54$ ppm. The last digit of $a_{\mu}$ is changed from the published value owing to a new value of the ratio of the muon-to-proton magnetic moment that has become available. At present there appears to be a difference between the Standard-Model value and the measured value, at the $\simeq 3$ standard deviation level when electron-positron annihilation data are used to determine the lowest-order hadronic piece of the Standard Model contribution. The improved experiment, along with further advances in the determination of the hadronic contribution, should clarify this difference. Because of its ability to constrain the interpretation of discoveries made at the LHC, the improved measurement will be of significant value, whatever discoveries may come from the LHC.Comment: Proceedings of the PhiPsi09, Oct. 13-16, 2009, Beijing, China, 4 pages 2 figures. Version 2 includes Fermilab report number, minor corrections and one additional referenc

Precision Observables in the MSSM: W mass and the muon magnetic moment

The precision observables M_W and g-2 of the muon are discussed in the framework of the MSSM. Recent progress in the evaluation of the theoretical predictions is described, and the MSSM predictions are compared with the SM predictions and the experimental values.Comment: 4 pages, 2 figures. To appear in Proceedings of SUSY06, the 14th International Conference on Supersymmetry and the Unification of Fundamental Interactions, UC Irvine, California, 12-17 June 200