The next-to-leading order analysis for the cross section for hadroproduction of top quark pairs close to threshold is presented. Within the framework of non-relativistic QCD a significant enhancement compared to fixed order perturbation theory is observed which originates from the characteristic remnant of the 1S peak below production threshold of top quark pairs. The analysis includes all color singlet and color octet configurations of top quark pairs in S-wave states and, for the dominant configurations, it employs all-order soft gluon resummation for the hard parton cross section. Numerical results for the Large Hadron Collider at $\sqrt{s} = 14 $TeV and $\sqrt{s} = 10 $TeV and also for the Tevatron are presented. The possibility of a top quark mass measurement from the invariant mass distribution of top quark pairs is discussed.

In this paper we compute the three-loop corrections to the $\beta$ function in a momentum subtraction (MOM) scheme with a massive quark. The calculation is performed in the background field formalism applying asymptotic expansions for small and large momenta. Special emphasis is devoted to the relation between the coupling constant in the MOM and $\overline{\rm{MS}}$ schemes as well as their ability to describe the phenomenon of decoupling. It is demonstrated by an explicit comparison that the $\overline{\rm{MS}}$ scheme can be consistently used to relate the values of the MOM-scheme strong-coupling constant in the energy regions higher and lower than the massive-quark production threshold. This procedure obviates the necessity to know the full mass dependence of the MOM $\beta$ function and clearly demonstrates the equivalence of both schemes for the description of physics outside the threshold region.

We compute 2-loop QCD corrections to the hard coefficient functions which arise in the factorization formula for B → X_u l nu decays in the shape-function region. Our calculation provides the last missing piece required for a NNLO analysis of inclusive semileptonic B decays, which may significantly reduce the theoretical uncertainty in the extraction of the CKM matrix element |V_ub|. Among the technical aspects, we find that the 2-loop hard coefficient functions are free of infrared singularities as predicted by the factorization framework. We perform a brief numerical analysis of the NNLO corrections and include a discussion on charm mass effects.

(D) tau nu decays > We update and compare the capabilities of the purely leptonic mode B –> tau nu and the semileptonic mode B –> D tau nu in the search for a charged Higgs boson.

We present a brief review of current methods for the calculation of multi-loop amplitudes including recent developments. As an example we present the calculation of the second moment of the heavy quark current correlator and the extraction of the values of the charm and bottom quark masses using the results of this calculation.

Nufact08 is the tenth in a series of workshops started in 1999, whose main goal is to understand options for future neutrino-oscillation experiments to attack the problems of the neutrino mass hierarchy and CP violation in the leptonic sector. I present a very brief review of what we know and what we would like to know about neutrino mass, mixing, and flavor change. I consider the interplay between neutrino physics and forthcoming information from the Large Hadron Collider. I comment on a decade's progress and offer some context for work that lies ahead.

I offer a brief summary, with commentary, of theoretical contributions to Moriond QCD 2008.

We report on the calculation of the next-to-leading order QCD corrections to the production of top–antitop-quark pairs in association with a hard jet at the Tevatron and at the LHC. Results for integrated and differential cross sections are presented. We find a significant reduction of the scale dependence. In most cases the corrections are below 20% indicating that the perturbative expansion is well under control. Moreover, the forward–backward charge asymmetry of the top-quark, which is analyzed at the Tevatron, is studied at next-to-leading order. We find large corrections suggesting that the definition of the observable has to be refined.

We compute the last missing piece of the two-loop ${\cal O}(\alpha \alpha_s)$ corrections to $\gamma t \bar{t}$ vertex at the $t \bar{t}$ threshold due to the exchange of a $W$ boson and a gluon. This contribution constitutes a building block of the top quark threshold production cross section at electron positron colliders.

A large set of techniques needed to compute decay rates at the two-loop level are derived an d systematized. The main emphasis of the paper is on the two Standard Model decays H → gamm a gamma and H → g g. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple

recipes for handling internal unstable particles in two-loop processes; they illustrate sim

ple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Fu rthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electr oweak contributions to different physical (pseudo-)observables, showing how they can be tran sformed in a way that allows for a stable numerical integration. Numerical results for the t wo-loop percentage corrections to H → gamma gamma, g g are presented and discussed. When ap plied to the process pp → gg + X → H + X, the results show that the electroweak scaling fa ctor for the cross section is between -4 % and + 6 % in the range 100 GeV < Mh < 500 GeV, wi thout incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections u nder control.

We compute the finite renormalisation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix induced by gluino-squark diagrams in the MSSM with non-minimal sources of flavour violation. Subsequently we 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. Our 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. Our bound on |delta^{u LR}_{12}| is stronger than the FCNC bound from D-D-bar mixing for superpartner masses above 900 GeV. We further find a useful bound on |delta_{13}^{u LR}|, for which no FCNC constraint is known. Our 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. We suggest that a flavour symmetry renders the Yukawa sector flavour-diagonal and the trilinear supersymmetry-breaking terms are the spurion fields breaking this flavour symmetry. We further derive the dominant supersymmetric radiative corrections to the couplings of charged Higgs bosons and charginos to quarks and squarks.

The impact of recent multi-loop calculations on precise determinations of charm- and bottom-quark masses and the strong coupling constant is discussed.

The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10 % level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.

Results for the complete NLO electroweak corrections to Standard Model Higgs production via gluon fusion are included in the total cross section for hadronic collisions. Artificially large threshold effects are avoided working in the complex-mass scheme. The numerical impact at LHC (Tevatron) energies is explored for Higgs mass values up to 500 GeV (200 GeV). Assuming a complete factorization of the electroweak corrections, one finds a +5 % shift with respect to the NNLO QCD cross section for a Higgs mass of 120 GeV both at the LHC and the Tevatron. Adopting two different factorization schemes for the electroweak effects, an estimate of the corresponding total theoretical uncertainty is computed.

In this contribution two recent analyses for the extraction of the charm quark mass are discussed. Although they rely on completely different experimental and theoretical input the two methods provide the same final results for the charm quark mass and have an uncertainty of about 1\%.

The necessity of the FORM project is discussed. Then the evolutionary needs in particle physics are considered, looking at the trends over the years. A guess is made at what will be needed in the (near) future. The whole is concluded with some critical remarks concerning the publication of results and programs.

We report on a two-loop supersymmetric contribution to the magnetic moment (g-2)_mu of the muon which is enhanced by two powers of tan(beta). This contribution arises from a shift in the relation between the muon mass and Yukawa coupling and can increase the supersymmetric contribution to (g-2)_mu sizably. As a result, if the currently observed 3 sigma deviation between the experimental and SM theory value of (g-2)_mu is analyzed within the Minimal Supersymmetric Standard Model (MSSM), the derived constraints on the parameter space are modified significantly: If (g-2)_mu is used to determine tan(beta) as a function of the other MSSM parameters, our corrections decrease tan(beta) by roughly 10% for tan(beta)=50.

We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Gr\“obner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system.

B physics is sensitive to the effects of Higgs bosons in the

 Minimal Supersymmetric Standard Model, if
 the parameter $\tan\beta$ is large. I briefly summarise the role
 of $B\to \mu^+\mu^-$ and $\BTNp$ in the hunt for new Higgs effects
 and present new results on the decay $\BDTN$:
 Using the analyticity properties of form factors one can predict the
 ratio $R\equiv\mathcal{B}(\BDTN)/\mathcal{B}(\BDLN)$, $\ell=e,\mu$,
 with small hadronic uncertainties. In the Standard Model one
 finds $R= 0.31 \pm 0.02$, ${\cal B} (B^- \to D^0 \tau^-
 \bar{\nu}_{\tau}) = (0.71\pm 0.09)\% $ and ${\cal B} (\bar{B}^0 \to
 D^+ \tau^- \bar{\nu}_{\tau})= (0.66\pm 0.08)\% $, if the vector form
 factor of the Heavy Flavor Averaging Group is used. $\BDTN$ is
 competitive with $\BTNp$ in the search for effects of charged Higgs
 bosons. Especially sensitive to the latter is the differential
 distribution in the decay chain $\bar{B}\to
 D\bar{\nu}_{\tau}\tau^-[\to\pi^-\nu_{\tau}]$.

Up to the moment there are two known algorithms of sector decomposition: an original private algorithm of Binoth and Heinrich and an algorithm made public lastyear by Bogner and Weinzierl. We present a new program performing the sector decomposition and integrating the expression afterwards. The program takes a set of propagators and a set of indices as input and returns the epsilon-expansion of the corresponding integral.

We report on automating the Catani-Seymour dipole subtraction which is a general procedure to treat infrared divergences in real emission processes at next-to-leading order in QCD. The automatization rests on three essential steps: the creation of the dipole terms, the calculation of the color linked squared Born matrix elements, and the evaluation of different helicity amplitudes. The routines have been tested for a number of complex processes, such as the real emission process gg –> t anti-t ggg.

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.

We report on automating the Catani-Seymour dipole subtraction which is a general procedure to treat infrared divergences in real emission processes at next-to-leading order in QCD. The automatization rests on three essential steps: the creation of the dipole terms, the calculation of the color linked squared Born matrix elements, and the evaluation of different helicity amplitudes. The routines have been tested for a number of complex processes, such as the real emission process gg –> t anti-t ggg.

Recent results for the cross section of electron-positron annihilation into hadrons and for the decay rates of the $Z$ boson and the $\tau$ lepton into hadrons including corrections of order $\alpha_s^4$ are reviewed. The consistency between two values of $\alpha_s$ measured at vastly different energies constitutes a striking test of asymptotic freedom and requires the proper matching conditions at charm and bottom thresholds. Combining the results from $Z$ and $\tau$ decays leads to $\alpha_s(M_Z)=0.1198 \pm 0.0015$ as one of the most precise and presently only NNNLO result for the strong coupling constant. We report a recent determination of $\alpha_s$ which is based on a lattice evaluation of the pseudoscalar correlator for the charm quarks combined with continuum perturbation theory.

We report on two recent multiloop results in QED: (i) the four-loop corrections to the conversion relations between the QED charge renormalized in the on-shell and MS-bar schemes; (ii) analytical evaluation of a class of asymptotic contributions to the muon anomaly at five-loops.

heoretical predictions for Bhabha scattering at the two-loop level require the inclusion of hadronic vacuum polarization in the photon propagator. We present predictions for the contri butions from reducible amplitudes which are proportional to the vacuum polarization $\pi(q^2 )$ and from irreducible ones where the vacuum polarization appears in a loop representing ve rtex or box diagrams. The second case can be treated by using dispersion relations with a we ight function proportional to the $R$-ratio as measured in electron-positron annihilation in to hadrons and kernels that can be calculated perturbatively. We present simple analytical f orms for the kernels and, using two convenient parametrizations for the function $R(s)$, num erical results for the quantities of interest. As a cross check we evaluate the correspondin g corrections resulting from light and heavy lepton loops and we find perfect agreement with

previous calculations. For the hadronic correction our result are in good agreement with a

previous evaluation.

We compute the exact two-loop matching coefficients for the strong coupling constant alpha_s and the bottom-quark mass m_b within the Minimal Supersymmetric Standard Model (MSSM), taking into account O(alpha_s^2) contributions from Supersymmetric Quantum Chromodynamics (SQCD). We find that the explicit mass pattern of the supersymmetric particles has a significant impact on the predictions of alpha_s and m_b at high energies. Further on, the three-loop corrections exceed the uncertainty due to the current experimental accuracy. In case of the the running bottom-quark mass, they can reach in the large tan(beta) regime up to 30% from the tree-level value.

This is a status report of the evaluation of the three-loop corrections to the static QCD potential of a heavy quark and an antiquark. The families of Feynman integrals that appear in the evaluation are described. To reduce any integral of the families to master integrals we solve integration-by-parts relations by the algorithm called FIRE. To evaluate the corresponding master integrals we apply the Mellin-Barnes technique. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.

The impact of multi-loop calculations on precise determinations of charm- and bottom-quark masses and the strong coupling constant is discussed. Recent $N^3LO$ calculations, combined with new precision data, lead to a significant reduction of the errors. The results of these analyses, $m_c(3~\mbox{GeV}) = 0.986(13)~\mbox{GeV}$, $m_b(10~\mbox{GeV}) = 3.609(19)~\mbox{GeV}$ and $\alpha_s(M_Z)=0.1198(15)$ constitute the most precise and presently only $N^3LO$ determinations of these fundamental quantities.

Recent results for the cross section of electron-positron annihilation into hadrons and for the decay rates of the $Z$-boson and the $\tau$-lepton into hadrons including corrections of order $\alpha_s^4$ are reviewed. The consistency between two values of $\alpha_s$ measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from $Z$ and $\tau$ decays we find $\alpha_s(M_Z)=0.1198 \pm 0.0015$ as one of the most precise and presently only NNNLO result for the strong coupling constant.

Using the asymptotic-expansion technique, we compute the dominant two-loop electroweak corrections, of O(G_F m_t2), to production and decay via a pair of photons or gluons of the CP-odd Higgs boson A0 in a two-Higgs-doublet model with low- to intermediate values of the Higgs-boson masses and ratio tan(beta)=v_2/v_1 of the vacuum expectation values. We also study the influence of a sequential heavy-fermion generation. The appearance of three gamma_5 matrices in closed fermion loops requires special care in the dimensional regularisation of ultraviolet divergences. The finite renormalisation constant for the pseudoscalar current effectively restoring the anticommutativity of the gamma_5 matrix, familiar from perturbative quantum chromodynamics, is found not to receive a correction in this order. We also revisit the dominant two-loop electroweak correction to the H → gamma gamma decay width in the standard model with a fourth fermion generation.

The second moment of the heavy quark vector correlator at ${\cal O}(\alpha_s^3)$ is presented. The implications of this result on recent determinations of the charm and bottom quark mass are discussed.

We use lattice QCD simulations, with MILC configurations and HISQ $c$-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the $\msb$ mass of the charm quark. We find $m_c(3 \mathrm{GeV})=0.984 (16)$ GeV, or, equivalently, $m_c(m_c)=1.266 (14)$ GeV. This agrees well with results from continuum analyses of the vector correlator using experimental data for $e^+e^-$ annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. We also obtain a new result for the QCD coupling: $\alpha_\msb^{(n_f=4)}(3 \mathrm{GeV}) = 0.230 (18)$, or, equivalently, $\alpha_\msb^{(n_f=5)}(M_Z) = 0.113 (4)$.

Recent results and methods of three-loop calculations in HQET are reviewed.

We discuss the production of top–anti-top quark pairs in association with a hard jet at the Tevatron and at the LHC and we report on the calculation of the next-to-leading order QCD corrections to this process. Numerical results for the top–anti-top+jet cross section and the forward–backward charge asymmetry are presented. The corrections stabilize the leading-order prediction for the cross section. In contrast, the charge asymmetry receives large corrections. The dependence of the cross section as well as the asymmetry on the minimum transverse momenta used to define the additional jet is studied in detail for the Tevatron.

We evaluate the last missing piece of the two-loop QED corrections to the high-energy electron-positron scattering cross section originated from the vacuum polarization by heavy fermions. The calculation is performed within a new approach applicable to a wide class of perturbative problems with mass hierarchy. The result is crucial for the high-precision physics program at existing and future $e^+e^-$ colliders.

We present an update of the theoretical predictions for the cross section of top-quark pair production at Tevatron and LHC. In particular we employ improvements due to soft gluon resummation at next-to-next-to-leading logarithmic accuracy. We expand the resummed results and derive analytical finite-order cross sections through next-to-next-to-leading order which are exact in all logarithmically enhanced terms near threshold. These results are the best present estimates for the top-quark pair production cross section. We investigate the scale dependence as well as the sensitivity on the parton luminosities.

After a brief recollection of joint scientific work with Staszek Jadach, recent results on electroweak radiative corrections for scattering processes in the TeV region are presented. The status of the four-fermion scattering amplitudes is discussed, with emphasis on logarithmically enhanced contributions in two-loop approximation. Predictions for the production of $\gamma$, $Z$ and $W$ with large transverse momenta together with a jet are presented. For $p_T$ above 1TeV the electroweak corrections may well reach several tens of percent. A similar situation is observed for top-antitop quark producition at large invariant mass of the $t\bar{t}$ system.

In this lecture, the early history of asymptotic freedom is discussed. The first completely correct derivation of \beta_0 in non-abelian gauge theory (Khriplovich, 1969) was done in the Coulomb gauge; this derivation is reproduced (in modernized terms) in Sect. 2. A qualitative physical explanation of asymptotic freedom via chromomagnetic properties of vacuum (Nielsen, 1981) is discussed in Sect. 3.

We compute the third-order correction to the heavy-quark current correlation function due to th e emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QC D sum rules.

In a previous paper [Phys. Rev. D 68, 034017 (2003)], we investigated the inclus ive production of prompt J/psi mesons in polarized hadron-hadron, photon-hadron,

and photon-photon collisions in the factorization formalism of nonrelativistic

quantum chromodynamics providing compact analytic results for the double longitu dinal-spin asymmetry A_{LL}. For convenience, we adopted a simplified expression

for the tensor product of the gluon polarization four-vector with its charge co

njugate, at the expense of allowing for ghost and anti-ghosts to appear as exter nal particles. While such ghost contributions cancel in the cross section asymme try A_{LL} and thus were not listed in our previous paper, they do contribute to

the absolute cross sections. For completeness and the reader's convenience, the

y are provided in this addendum.

We compute the leading-log QED, the next-to-leading-log QED-QCD, and the electroweak corrections to the charm quark contribution relevant for the rare decay K+ → pi+ nu nu-bar. The corresponding parameter P_c(X) is increased by up to 2% with respect to the pure QCD estimate to P_c(X) = 0.372 +- 0.015 for m_c(m_c)= (1.286 +- 0.013) GeV, alphas(M_Z) = 0.1176 +- 0.0020 and |V_us| = 0.2255. For the branching ratio we find B(K+ → pi+ nu nu-bar) = (8.5 +- 0.7)*10^{-11}, where the quoted uncertainty is dominated by the CKM elements.

Within the minimal supersymmetric extension of the Standard Model, the mass of the light CP-even Higgs boson is computed to three-loop accuracy, taking into account the next-to-next-to-leading order effects from supersymmetric Quantum Chromodynamics. We consider two different scenarios for the mass hierarchies of the supersymmetric spectrum. Our numerical results amount to corrections of about 500 MeV which is of the same order as the experimental accuracy expected at the CERN Large Hadron Collider (LHC).

We calculate light-cone distribution amplitudes for non-relativistic bound states, including radiative corrections from relativistic gluon exchange to first order in the strong coupling constant. We distinguish between bound states of quarks with equal (or similar) mass, m_1 ~ m_2, and between bound states where the quark masses are hierarchical, m_1 » m_2. For both cases we calculate the distribution amplitudes at the non-relativistic scale and discuss the renormalization-group evolution for the leading-twist and 2-particle distributions. Our results apply to hard exclusive reactions with non-relativistic bound states in the QCD factorization approach like, for instance, (B_c → eta_c l nu) or (e^+ e^- → J/psi eta_c). They also serve as a toy model for light-cone distribution amplitudes of light mesons or heavy B and D mesons, for which certain model-independent properties can be derived. In particular, we calculate the anomalous dimension for the B meson distribution amplitude phi_B^-(w) in the Wandzura-Wilczek approximation and derive the according solution of the evolution equation at leading logarithmic accuracy.

D tau nu differential decay distribution > We present a detailed analysis of charged-Higgs effects in the decay B → D tau nu. Updating the relevant formfactors, we find this decay mode competitive with and complementary to B → tau nu. The differential distribution in the decay chain B → D nu tau[→ pi nu] excellently discriminates between Standard-Model and charged-Higgs contributions. By measuring the D and pi energies and the angle between the D and pi tracks one can determine the magnitude and phase of the effective charged-Higgs coupling g_S.

We present the dominant two-loop electroweak corrections to the partial decay widths to gluon jets and prompt photons of the neutral CP-odd Higgs boson $A^0$, with mass $M_{A^0}<2M_W$, in the two-Higgs-doublet model for low to intermediate values of the ratio $\tan\beta=v_2/v_1$ of the vacuum expectation values. They apply as they stand to the production cross sections in hadronic and two-photon collisions, at the Tevatron, the LHC, and a future photon collider. The appearance of three $\gamma_5$ matrices in closed fermion loops requires special care in the dimensional regularization of ultraviolet divergences. The corrections are negative and amount to several percent, so that they fully compensate or partly screen the enhancement due to QCD corrections.

We present new results on the NNNLO top-antitop production cross section near threshold from potential and ultrasoft gluon corrections. The new non-logarithmic third-order terms are in the 10% range and lead to a significant reduction in the theoretical error.

We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order $\alpha_s^4$ to the absorptive part of the polarization function in QCD with $n_f=3$;(ii) the five-loop contribution to the $\beta$ function of quenched QED.

The Mellin-Barnes technique to evaluate master integrals and the algorithm called FIRE to solve IBP relations with the help of Groebner bases are briefly reviewed. In FIRE, an extension of the classical Buchberger algorithm to construct Groebner bases is combined with the well-known Laporta algorithm. It is explained how both techniques are used when evaluating the three-loop correction to the static QCD quark potential. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values of alpha_s measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only NNNLO result for the strong coupling constant.