Recent theoretical and experimental improvements in the determination of charm- and bottom-quark masses are discussed. The final results, m_c(3 GeV)=986(13) MeV and m_b(m_b)=4163(16) MeV represent the presently most precise determinations of these two fundamental Standard Model parameters.

We compute the three-loop corrections to the potential of two heavy quarks. In particular we consider in this Letter the purely gluonic contribution which provides in combination with the fermion corrections of Ref. \cite{Smirnov:2008pn} the complete answer at three loops.

We present next-to-next-to-leading order corrections to the inclusive production of the Higgs bosons at the CERN Large Hadron Collider (LHC) including finite top quark mass effects. Expanding our analytic results for the partonic cross section around the soft limit we find agreement with a very recent publication by Harlander and Ozeren \cite{Harlander:2009mq}.

We compute the O(alpha_s) corrections to the Wilson coefficients of the dimension five operators emerging from the Operator Product Expansion of inclusive radiative B decays. We discuss the impact of the resulting O(alpha_s Lambda_QCD^2/m_b^2) corrections on the extraction of m_b and mu_pi^2 from the moments of the photon spectrum.

We consider the currents formed by a heavy and a light quark within Quantum Chromodynamics and compute the matching to Heavy Quark Effective Theory to three-loop accuracy. As an application we obtain the third-order perturbative corrections to ratios of $B$-meson decay constants.

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.

The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin-Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators and Speer sectors as a strategy, the possibility to evaluate more general parametric integrals.

We derive new constraints on the quantities delta_{XY}^{ij, X,Y=L,R, which parametrise the flavour-off-diagonal terms of the charged slepton mass matrix in the MSSM. Considering mass and anomalous magnetic moment of the electron we obtain the bound delta^{13}_{LL}*delta^{13}_{RR} < 0.1, which involves the poorly constrained element delta^{13}_{RR}. We improve the predictions for the decays tau → mu gamma, tau → e gamma and mu → e gamma by including two-loop corrections which are enhanced if tan beta is large. The finite renormalisation of the PMNS matrix from soft SUSY-breaking terms is derived and applied to the charged-Higgs-lepton vertex. We find that the experimental bound on BR(tau → e gamma) severely limits the size of the MSSM loop correction to the PMNS element U_{e3}, which is important for the proper interpretation of a future U_{e3} measurement. Subsequently we confront our new values for delta^{ij}_{LL} with a GUT analysis. As a novel feature we consider dimension-5 Yukawa terms, which are needed to fix the Yukawa unification of the first two generations. If universal supersymmetry breaking occurs above the GUT scale, we find the flavour structure of the dimension-5 Yukawa couplings tightly constrained by mu → e gamma.

We probe the unification of down quarks and leptons in a supersymmetric $\text{SO}(10)$ GUT. The large atmospheric neutrino mixing angle induces $b_R-s_R$ transitions, which can account for the sizeable $CP$ phase $\phi_s$ measured in $B_s-\ovl{B}_s$ mixing. Corrections to down-quark-lepton unification from higher-dimensional Yukawa terms translate neutrino mixing also into $s_R-d_R$ and $b_R-d_R$ currents. We find the flavour structure of Yukawa corrections to be strongly constrained by $\epsilon_K$.

For large values of tan(beta) interesting effects arise in the MSSM due to the enhancement of down-quark self-energies. These effects are well-studied within the decoupling limit, i.e. in the limit of supersymmetric masses far above the electroweak scale. In this article I discuss those issues which emerge from a treatment of these effects that goes beyond the decoupling limit.

The discrepancies found in the B-&gt;pi K decays between theory and experiment suggest the presence of new physics in the electroweak penguin sector of the theory. We show that this hypothesis can be tested more efficiently including in the analysis the non-leptonic decays B_s-&gt;phi pi, B_s-&gt;phi rho.

We present an update of the determination of charm- and

       bottom-quark masses from the low-energy expansion of the vacuum
       polarization function in combination with experimental data for
       R(s). This analysis leads to the most precise determination of
       the masses of the charm and bottom quarks:
       m_c(3GeV) = 986(13)MeV, m_b(m_b) =
       4163(16)MeV.

Predictions for energy levels, production and decay rate of gluinonia, non-relativistic boundstates of gluinos, are presented. The potential between color-octet constituents is derived in next-to-next-to leading order and one-loop QCD corrections are derived for the production cross section and the decay rate into gluon jets. In addition we evaluate the decay rate into top quarks and into two photons. The signal-to-background ratio is estimated for the dominant decay mode and found to be around 0.5%. For relatively light gluinos the bound states thus might be detectable.

We present results of our study of tan(beta)-enhanced loop corrections in the Minimal Supersymmetric Standard Model (MSSM) with Minimal Flavour Violation (MFV). We demonstrate that these corrections induce flavour changing neutral current (FCNC) gluino couplings which have a large impact on the Wilson coefficient C_8 of the chromomagnetic operator. To illustrate the phenomenological consequences of this gluino-squark contribution to C_8, we briefly discuss its effect on the mixing-induced CP asymmetry in the decay B_d -&gt; phi K_S.

One of the main challenges of the Tevatron at Fermilab and the Large Hadron Collider (LHC) at CERN is the determination of Standard Model (SM) parameters at the TeV scale. In this context various processes will be investigated which involve bottom-quark jets in the final state, for example decays of top-quarks or gauge bosons of the weak interaction. Hence the theoretical understanding of processes with bottom-quark jets is necessary. In this paper analytic results will be presented for the weak corrections to bottom-quark jet production – neglecting purely photonic corrections. The results will be used to study differential distributions, where sizeable effects are observed.

The two-loop relations between the running gluino-quark-squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. Furthermore, we verify with the help of these relations that the three-loop beta-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. This result confirms the equivalence of the two schemes through three-loops, if applied to SUSY-QCD.

Chirally enhanced supersymmetric QCD corrections to FCNC processes are investigated in the framework of the MSSM with generic sources of flavor violation. These corrections arise from flavor-changing self-energy diagrams and can be absorbed into a finite renormalization of the squark-quark-gluino vertex. In this way enhanced two-loop and even three-loop diagrams can be efficiently included into a leading-order (LO) calculation. Our corrections substantially change the values of the parameters delta^{d,LL}_{23}, delta^{d,LR}_{23}, delta^{d,RL}_{23}, and delta^{d,RR}_{23} extracted from Br[B-&gt;X_s gamma] if tan(beta) is large. We find stronger (weaker) constraints compared to the LO result for negative (positive) values of mu. The constraints on delta^{d,LR,RL}_{13} and delta^{d,LR,RL}_{23} from B_d mixing and B_s mixing change drastically if the third-generation squark masses differ from those of the first two generations. K mixing is more strongly affected by the chirally enhanced loop diagrams and even sub-percent deviations from degenerate down and strange squark masses lead to profoundly stronger constraints on delta^{d,LR,RL}_{12}.

X+ nu nu bar decays in the Standard Model > The tree-level contributions to the rare decays B+ –> pi+ nu anti-nu, B+ –> K+ nu anti-nu, and B+ –> K*+ nu anti-nu are analyzed and compared to those occurring in K+ –> pi+ nu anti-nu, D+ –> pi+ nu anti-nu, and Ds+ –> pi+ nu anti-nu. It is shown that these purely long-distance contributions, arising from the exchange of a charged lepton, can be significant in B+ decays for an intermediate tau, potentially blurring the distinction between the modes used to extract B –> tau nu and those used to probe the genuine short-distance b –> (s,d) nu anti-nu FCNC transitions. Numerically, the tree-level contributions are found to account for 97%, 12% and 14% of the total B+ –> pi+ nu anti-nu, B+ –> K+ nu anti-nu, and B+ –> K*+ nu anti-nu rates, respectively.

We study the Minimal Supersymmetric Standard Model with Minimal

 Flavour Violation for the case of a large parameter tan beta and
 arbitrary values of the supersymmetric mass parameters. We derive
 several resummation formulae for tan-beta-enhanced loop
 corrections, which were previously only known in the limit of
 supersymmetric masses far above the electroweak scale. Studying first
 the renormalisation-scheme dependence of the resummation formula for
 the bottom Yukawa coupling, we clarify the use of the sbottom mixing
 angle in the supersymmetric loop factor Delta_b. As a new feature,
 we find tan-beta-enhanced loop-induced flavour-changing neutral
 current (FCNC) couplings of gluinos and neutralinos which in turn give
 rise to new effects in the renormalisation of the
 Cabibbo-Kobayashi-Maskawa matrix and in FCNC processes of B mesons.
 For the chromomagnetic Wilson coefficient C8, these gluino-squark
 loops can be of the same size as the known chargino-squark
 contribution. We discuss the phenomenological consequences for the
 mixing-induced CP asymmetry in B_d -> phi K_S. We further quote
 formulae for B_s -> mu mu and B <-> anti-B mixing valid beyond the
 decoupling limit and find a new contribution affecting the phase of
 the B <-> anti-B mixing amplitude. Our resummed tan-beta-enhanced effects are
 cast into Feynman rules permitting an easy implementation in automatic
 calculations.

We report on the status of the perturbative calculation in the QCD factorization framework to charmless hadronic $B$ meson decays and present a compilation of available NNLO results.

We study the effect of a right-handed coupling of quarks to the

 W-boson on the measurements of |V_{ub}| and |V_{cb }|. It is shown that
 such a coupling can remove the discrepancies between the
 determinations of |V_{ub}| from B\to \pi \ell \nu, B^+\to \tau^+
 \nu and B\to X_u \ell \nu.  Further the measurements of |V_{cb}|
 from B\to D^* \ell \nu, B\to D \ell \nu and inclusive B\to X_c
 \ell\nu decays can be brought into better agreement.  We demonstrate
 that a right-handed coupling can be generated within the MSSM by a
 finite gluino-squark loop. The effect involves the parameters
 \delta^{u RL}_{23} and \delta^{u RL}_{13} of the squark mass
 matrices, which are poorly constrained from other processes. On the
 other hand, all gluino-squark corrections to the regular left-handed
 coupling of the W-boson are found to be too small to be relevant.

In this letter we present the three-loop virtual corrections to the Higgs boson production in the gluon fusion channel where finite top quark mass effects are taken into account. We perform an asymptotic expansion and manage to evaluate five terms in the expansion parameter $M_H^2/M_t^2$. A good convergence is observed almost until $M_H\approx 2M_t$.

pi- pi0 / rho- rho0 to NNLO in QCD factorization > The approximate tree decays B- → pi- pi0/rho- rho0 may serve as benchmark channels for testing the various theoretical descriptions of the strong interaction dynamics in hadronic B meson decays. The ratios of hadronic and differential semileptonic B → pi l nu/rho l nu decay rates at maximum recoil provide particularly clean probes of the QCD dynamics. We confront the recent NNLO calculation in the QCD factorization framework with experimental data and find support for the factorization assumption. A detailed analysis of all tree-dominated B → pi pi/pi rho/rho rho decay modes seems to favour somewhat enhanced colour-suppressed amplitudes, which may be accommodated in QCD factorization by a small value of the first inverse moment of the B meson light-cone distribution amplitude, lambda_B ~ 250 MeV. Precise measurements of the B → rho l nu spectrum could help to clarify this point.

This is the first part of lectures about effective field theories. Decoupling of heavy-particle loops is considered (heavy leptons in QED, heavy quarks in QCD).

In this paper we investigate supersymmetric effects to the threshold production cross section of top quark pairs in electron positron annihilation. In particular, we consider the complete one-loop corrections from the strong and weak sector of the Minimal Supersymmetric Standard Model.

We report on some technical aspects of our calculation of alpha_s^4 corrections to R(s) and the semi-leptonic tau decay width [1-3]. We discuss the inner structure of the result as well as the issue of its correctness. We demonstrate recently appeared independent evidence positively testing one of two components of the full result.

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charm- and bottom-quark mass from experimental data for &sigma;(e⁺ e^- &rarr; hadrons).

s</sub>³) > We construct approximate formulas for the O(&alpha;_s³) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Pad&eacute; approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.

Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and bottom-quark masses through sum rules has been performed. The previous result for the charm-quark mass, $m_c(3 {\rm GeV})= 0.986(13) {\rm GeV}$, based on the lowest moment, is supported by the new results from higher moments which lead to consistent values with comparable errors. The new value for the bottom quark, $m_b(10 {\rm GeV})= 3.610(16) {\rm GeV}$, corresponding to $m_b(m_b)= 4.163(16) {\rm GeV}$, makes use both of the new data and the new perturbative results and is consistent with the earlier determination.

We present the three-loop QCD corrections to the quark chromomagnetic moment including two different nonzero masses. This is a necessary ingredient to obtain the corresponding corrections to the chromomagnetic coefficient in the Heavy Quark Effective Theory (HQET) Lagrangian.

I present results for the finite renormalization of the Cabibbo-Kobayashi-Maskawa ( CKM)

matrix induced by gluino--squark diagrams in the MSSM with non-minimal
 sources of flavour violation. Subsequently I derive bounds on the
 flavour--off--diagonal elements of the squark mass matrices by requiring that the

radiative corrections to

 the CKM elements do not exceed the experimental values. The constraints on
 the associated dimensionless quantities $\delta^{d\,LR}_{ij}$, $j>i$, are
 stronger than the bounds from flavour-changing neutral current (FCNC)
 processes if gluino and squarks are heavier than 500$\,\gev$. The
 results imply that it is still possible to generate all observed flavour
 violation from the soft supersymmetry-breaking terms without conflicting
 with present-day data on FCNC processes. Therefore we reappraise the idea that onl

y $Y^q_{33}$

 is different from zero at tree-level and all other Yukawa couplings are generated

radiatively. This model solves the SUSY flavour as well as the SUSY CP problem. The presented results are published in \cite{Crivellin:2008mq}.

A number of $\drbar$ renormalization constants in softly broken \susy{}-\qcd{} are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts, and \epscalar{}s, and the renormalization constants for the quark and

 gluino mass as well as for all cubic vertices. The latter allow us to

derive the corresponding $\beta$ functions through three loops, all of which we find to be identical to the expression for the gauge $\beta$ function obtained by Jack, Jones, and North~\cite{Jack:1996vg} (see also Ref.\,\cite{Pickering:2001aq}). This explicitely demonstrates the consistency of \dred{} with \susy{} and gauge invariance, an important pre-requisite for precision calculations in supersymmetric theories.

An improved description of four-pion production in electron-positron annihilation and in tau lepton decays is presented. The model amplitude is fitted to recent data from BaBar which cover a wide energy range and which were obtained exploiting the radiative return. Predicting tau decay distributions from e+e- data and comparing these predictions with ALEPH and CLEO results, the validity of isospin symmetry is confirmed within the present experimental errors. A good description of two- and three-pion sub-distributions is obtained. Special emphasis is put on the predictions for omega pi (→ pi+pi-pi0) in e+e- annihilation and in tau decay. The model amplitude is implemented in the Monte Carlo generator PHOKHARA.

A combined analysis of the electromagnetic pion and kaon form factors in the neighborhood of J/psi and psi(2S) and of the strong decay amplitude of these resonances into kaons is presented. In the presence of a large relative phase between strong and electromagnetic resonance amplitudes the branching ratio, as measured in electron-positron annihilation, receives an additional contribution from the interference between resonance and continuum amplitude neglected in earlier papers. Our study is model independent and does not rely on the SU(3) symmetry assumptions used in earlier papers. We note that the large relative phase between strong and electromagnetic amplitudes observed in earlier analyses is model dependent and relies critically on the specific assumptions on SU(3) symmetry and breaking.

We consider corrections to the unification of down-quark and charged-lepton Yukawa couplings in supersymmetric GUTs, which links the large nu_tau-nu_mu mixing angle to b → s transitions. These corrections generically occur in simple grand-unified models with small Higgs representations and affect s → d and b → d transitions via the mixing of the corresponding right-handed superpartners. On the basis of a specific SUSY-SO(10) model, we analyze the constraints from K-Kbar and B-Bbar mixing on the additional \tilde{d}_R-\tilde{s}_R rotation angle theta. We find that epsilon_K already sets a stringent bound on theta, theta^{max}=O(1 degree), indicating a very specific flavor structure of the correction operators. The impact of the large neutrino mixings on the unitarity triangle analysis is also briefly discussed, as well as their ability to account for the sizeable CP-violating phase observed recently in B_s → psi phi decays.

We evaluate the corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order containing a closed heavy-fermion loop. The result constitutes a building block both for the bottom- and top-quark system at threshold. Strong emphasis is put on our completely automated approach of the calculation including the generation of the Feynman diagrams, the identification of the topologies, the reduction to master integrals and the automated numerical computation of the latter.

All three-loop on-shell QCD Feynman integrals with two masses can be reduced to 27 master integrals. Here we calculate these master integrals, expanded in epsilon, both exactly in the mass ratio and as series in limiting cases.

I give an introduction to the theory of meson-antimeson mixing, aiming at students who plan to work at a flavour physics experiment or intend to do associated theoretical studies. I derive the formulae for the time evolution of a neutral meson system and show how the mass and width differences among the neutral meson eigenstates and the CP phase in mixing are calculated in the Standard Model. Special emphasis is laid on CP violation, which is covered in detail for \kkm, \bbmd\ and \bbms. I explain the constraints on the apex $(\ov \rho,\ov \eta)$ of the unitarity triangle implied by $\e_K$, $\dm_{B_d}$, $\dm_{B_d}/\dm_{B_s}$ and various mixing-induced CP asymmetries such as $a_{\rm CP} (\ov B_d \to J/\psi K_{\rm

 short})(t)$.

The impact of a future measurement of CP violation in flavour-specific $B_d$ decays is also shown.

We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in epsilon. Using Riemann zeta functions of up to weight six, we give fully analytic results for one integral; for a second, analytic results for all but the finite term; for the third, analytic results for all but the last two coefficients in the Laurent expansion. The remaining coefficients are given numerically to sufficiently high accuracy for phenomenological applications.

We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons to three-loop order within massless perturbative Quantum Chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.

The CP-violating phenomenology of the MSSM with Minimal Flavor Violation (MFV) in the lepton sector is revisited. To this end, the most general parametrizations of the slepton soft-breaking terms are constructed assuming a seesaw mechanism of type I. After a critical reassessment of how the CP-symmetry is broken within the MFV framework, all possible CP-violating phases are introduced. From the strong hierarchy of their contributions to the Electric Dipole Moments (EDMs), these phases are split into three classes: flavor-blind, flavor-diagonal and flavor off-diagonal. In particular, the phases from the neutrino sector belong to the last class; they start to contribute only at the second order in the mass-insertion approximation and have thus a negligible effect. It is then shown that to each class of phases corresponds a unique largely dominant term in the MFV expansion. Numerically, for a realistic range of MSSM and neutrino parameters, such that B(mu –> e gamma) does not exceed its experimental bound, the three types of phases are found to be allowed by the current bound on the electron EDM, though the next generation of experiments should constrain tightly the flavor-blind phase. Finally, we relax the MFV hypothesis and show how in the general MSSM, the MFV operator basis can be used to judge of the naturality of the slepton soft-breaking terms.

We report on the status of the current development in parallelization of the symbolic manipulation system FORM. There are two parallel versions available, one is based on POSIX threads and is optimal for modern multicore computers while another one uses MPI and can be used to parallelize FORM on clusters and Massive Parallel Processing systems. Most of existing FORM programs will be able to take advantage of the parallel execution, without the need for modifications. In some cases some minor additions may be needed.

We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization. Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators. The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced at NNLO. We in particular do not find an enhancement of the phenomenologically important ratio |C/T| from the perturbative calculation.

We match the Higgs sector of the most general flavour breaking and CP violating minimal supersymmetric standard model (MSSM) onto a generic two-Higgs-doublet model, paying special attention to the definition of $\tan\beta$ in the effective theory. In particular no $\tan\beta$-enhanced loop corrections appear in the relation to $\tan\beta$ defined in the $\overline{\textrm{DR}}$ scheme in the MSSM. The corrections to the Higgs-mediated flavour-changing amplitudes which result from this matching are especially relevant for the $B_d$ and $B_s$ mass differences $\dm_{d,s}$ for minimal flavour violation, where the superficially leading contribution vanishes. We give a symmetry argument to explain this cancellation and perform a systematic study of all Higgs-mediated effects, including Higgs loops. The corrections to $\dm_s$ are at most 7\% for $\mu&gt;0$ and $M_A &lt; 600\gev$ if constraints from other observables are taken into account. For $\mu&lt;0$ they can be larger, but are always less than about 20\%. Contrary to recent claims we do not find numerically large contributions here, nor do we find any $\tan\beta$-enhanced contributions from loop corrections to the Higgs potential in $B^+ \to \tau^+ \nu$ or $B \to X_s \gamma$. We further update supersymmetric loop corrections to the Yukawa couplings, where we include all possible CP-violating phases and correct errors in the literature. The possible presence of CP-violating phases generated by Higgs exchange diagrams is briefly discussed as well. Finally we provide improved values for the bag factors $P^{\rm VLL}_1$, $P^{\rm

 LR}_2$, and $P^{\rm SLL}_1$ at the electroweak scale.