We present the analytical calculation of the contribution of order m_q^2 \alpha_s^4 n_f^2 to the absorptive part of the vacuum polarization function of vector currents. This term constitutes an important gauge-invariant part of the full O(m_q^2 alpha_s^4) correction to the total cross-section of e^+ e^- annihilation into hadrons. The results are compared to predictions following from various optimization schemes.

We give a short presentation of the first genuine QCD five-loop calculations, viz. analytical contributions of order \alpha_s^4 n_f^2 and m_q^2 \alpha_s^4 n_f^2 to the vacuum polarization function of vector currents. These corrections form an important gauge-invariant subset of the full O(\alpha_s^4) correction to the total cross-section of e^+ e^- annihilation into hadrons.

The radiative return offers the unique possibility for a measurement of the cross section of electron–positron annihilation into hadrons over a wide range of energies. The large luminosity of present phi- and B-factories easily compensates for the additional factor of alpha due to the emission of a hard photon. Final states with photons at large angles can be easily identified. The rate for events with collinear photons, however, is enhanced by a large logarithm and allows, in particular at lower energies, for a complementary measurement.

The Monte Carlo generator PHOKHARA, which includes next to leading order

corrections from virtual and real photon emission, has been extended from large photon angles into the collinear region, using recent results for the virtual corrections. In addition, the present version includes final state radiation for muon and pion pair production and final states with four pions. Implications for the experimental analysis at three typical energies, 1.02, 4 and 10.6 GeV, are presented: the magnitude of these new corrections is studied, possibilities for the separation of initial and final state radiation are proposed, and the differences with respect to the previous treatment based on structure functions are investigated.

We study the cancellations among Feynman diagrams that implement the Ward and Slavnov-Taylor identities corresponding to the conserved supersymmetry current in supersymmetric quantum field theories. In particular, we show that the Faddeev-Popov ghosts of gauge- and supersymmetries never decouple from the physical fields, even for abelian gauge groups. The supersymmetric Slavnov-Taylor identities provide efficient consistency checks for automatized calculations and can verify the supersymmetry of Feynman rules and the numerical stability of phenomenological predictions simultaneously.

Recently computed terms of orders O(\alpha_s^4 n_f^2) in the perturbative series for the tau decay rate, and similar (new) strange quark mass corrections, are used to discuss the validity of various optimization schemes. The results are then employed to arrive at improved predictions for the complete terms order O(\alpha_s^4) and O(\alpha_s^5) in the massless limit as well as for terms due to the strange quark mass. Phenomenological implications are presented.

The anomalous magnetic moments of both fermions are included in the fully relativistic eight-component bound state equation. When these moments are of order unity or larger, a discrepancy with the standard sixteen-component formalism appears in the hyperfine mixing of P and D states for unequal masses at the leading order Z^4\alpha^4.

We consider the scalar integral associated to the 3-loop sunrise graph with a massless line, two massive lines of equal mass $M$, a fourth line of mass equal to $Mx$, and the external invariant timelike and equal to the square of the fourth mass. We write the differential equation in $x$ satisfied by the integral, expand it in the continuous dimension $d$ around $d=4$ and solve the system of the resulting chained differential equations in closed analytic form, expressing the solutions in terms of Harmonic Polylogarithms. As a byproduct, we give the limiting values of the coefficients of the $(d-4)$ expansion at $x=1$ and $x=0$.

The two-loop electroweak bosonic correction to the muon lifetime is computed using methods of asymptotic expansion. Combined with previous calculations this completes the full two-loop correction to $\Delta r$ in the Standard Model.

We summarize the current view on Parton-Hadron duality as it applies to $B$ meson decays. It is emphasized that an OPE treatment is essential for properly formulating duality and its limitations. Duality violations are unlikely to become the limiting factor in describing semileptonic $B$ width vis-a-vie higher order corrections. The consistent extraction of the $b$ quark mass from $B$ production and decays provides a striking example of the theoretical control achieved.

We discuss two-loop leading and angular-dependent next-to-leading logarithmic electroweak virtual corrections to arbitrary processes at energies above the electroweak scale. The relevant Feynman diagrams involving soft-collinear gauge bosons gamma, Z, W, have been evaluated in eikonal approximation. We present results obtained from the analytic evaluation of massive loop integrals. To isolate mass singularities we used the Sudakov method and alternatively the sector decomposition method in the Feynman-parameter representation.

The energy dependence of the electron - positron hadronic cross section can be measured not only by a straightforward energy scan, but also by means of the radiative return method. To provide extensive comparisons between theory and experiment a Monte Carlo event generator is an indispensable tool. We have developed such a generator called PHOKHARA, which simulates e+e- → mesons + photon(s) processes. In this paper we present its latest tests and upgrades.

3 jets: the fermionic contribution > We review a new technique for the calculation of two-loop amplitudes and discuss as an example the fermionic contributions to e+ e- –> q qbar g.

We present results for two-loop MSSM corrections to the relation between pole and running masses of heavy quarks up to the order ${\cal O}(\alpha_s^2)$. The running masses are defined in \DR scheme, usually used in multiloop calculations in supersymmetric theories. An analysis of the value of these corrections in different regions of the parameter space is provided.

Recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit are discussed including next-to-leading logarithmic (NLL) and NNLL corrections. These are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in $e^+e^-$ annihilation at high energy. The importance of angular dependent as well as subleading terms is emphasized.

The details of the recent calculation of the two-loop bosonic corrections to the muon lifetime in the Standard Model are presented. The matching on the Fermi theory is discussed. Renormalisation in the on-shell and in the \MSb scheme is studied and transition between the schemes is shown to lead to identical results. High precision numerical methods are compared with mass difference and large mass expansions.

3 jets at next-to-next-to-leading order QCD > We present the calculation of the fermionic contribution to the QCD two-loop amplitude for e^+e^- –> q qbar g.

In this paper we investigate the subleading twist corrections to the photon energy spectrum in the decay Lambda_b → X_s \gamma and to the lepton energy spectrum in Lambda_b → X_u l \bar{\nu}. As a first step we rederive the matching coefficients of the subleading twist using a much simpler method. Parametrizing the matrix elements for Lambda_b and using reparametrization invariance, we show that the energy spectra close to the endpoints are given in terms of only a single universal function.

The endpoint region of the inclusive lepton energy spectrum in $B \to X_u \ell \bar\nu$ can be used for a determination of $V_{ub}$ by comparing it to the endpoint region of the inclusive photon spectrum of $B \to X_s \gamma$. We consider the subleading twist contributions to this $V_{ub}$ determination.

Recent experimental data for the total cross section $\sigma(e^+e^-\to\mbox{hadrons})$ are compared with the up-to-date theoretical prediction of perturbative QCD for those energies where perturbation theory is reliable. This allows for a determination of the strong coupling $\alpha_s^{(4)}(5~\mbox{GeV})=0.235\pm0.047$. The precise data from the charm threshold region, when combined with the recent evaluation of moments with three loop accuracy, lead to a direct determination of the short distance $\overline{\rm MS}$ charm quark mass $m_c(m_c)=1.304(27)$. Applying the same approach to the bottom quark we obtain $m_b(m_b)=4.191(51)$~GeV.

We discuss the impact of precision measurements of $\sigma(e^+e^-\to \mbox{hadrons})$ in the center-of-mass range between 3 and 12~GeV, including improvements in the electronic widths of the narrow charmonium and bottonium resonances, on the determination of parameters of the Standard Model. In particular we discuss the impact of potential improvements on the extraction of the strong coupling constant $\alpha_s$, on the evaluation of the hadronic contributions to the electromagnetic coupling $\alpha(M_Z)$, and the determination of the charm and bottom quark masses.

Electron–positron annihilation into hadrons plus an energetic photon from initial-state radiation allows the hadronic cross-section to be measured over a wide range of energies at high luminosity meson factories. Weighted integrals over this cross-section are a decisive input for electroweak precision tests. A Monte Carlo event generator called PHOKHARA has been developed, which simulates e^+ e^- \to hadrons + photon(s) at the NLO accuracy. The latest tests and upgrades are presented in this paper.

Top quark pair production and decay at hadron colliders: Predictions at NLO QCD including spin correlations

QCD sum rules are overviewed with an emphasize on the practical applications of this method to the physics of light and heavy hadrons.

We compute the fermionic (n_f) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic deep-inelastic scattering at third order of massless

      perturbative QCD. Complete results are presented for the

corresponding nf-parts of the three-loop anomalous dimension and the three-loop coefficient functions for the structure

      functions F_2 and F_L. Our results agree with all partial and

approximate results available in the literature. The present calculation also facilitates a complete determination of the

      threshold-resummation parameters B_2 and D_2^DIS of which only the

sum was known so far, thus completing the information required for the next-to-next-to-leading logarithmic

      resummation. We find that D_2^DIS vanishes in the MSbar scheme.

The two-loop electroweak bosonic correction to the muon lifetime and the M_W-M_Z interdependece is computed using analytical methods of asymptotic expansion. Combined with previous calculations this copmletes the full two-loop correction to $\Delta r$ in the Standard Model. The shift to the prediction of W-boson mass due to two-loop bosonic corrections does not exceed 1 MeV for the range of the Higgs mass from 100 to 1000 GeV.

We describe calculations of $b \overline b$ production to next-to-next-to-leading order (NNLO) and next-to-next-to-leading logarithm (NNLL) near threshold in $pp$ interactions. Our calculations are in good agreement with the $b \overline b$ total cross section measured by HERA-B.

We report on the status of the calculation of deep-inelastic structure functions at three loops in perturbative QCD. The method employed allows to calculate the Mellin moments of structure functions analytically as a general function of N. As an illustration, we present the leading fermionic contributions to the non-singlet anomalous dimension of F_2 at three loops and, as a new result, to the non-singlet coefficient function of F_2 at three loops.

Three topics of relevance for $\tau$-decays will be presented: i) the possibility to search for CP violation in the Cabbibo suppressed channels $\tau \to \nu K \pi \mbox{and} \nu K \pi \pi$, ii) recent partial results on the semileptonic decay rate in $\as^4$ accuracy, and iii) the possibility to determine the strange quark mass in inclusive Cabbibo suppressed decays.

This Report documents the results obtained by the Working Group on Quantum ChromoDynamics and the Standard Model for the Workshop ``Physics at TeV Colliders'', Les Houches, France, 21 May - 1 June 2001. The

      account of uncertainties in Parton Distribution Functions is

reviewed. Progresses in the description of multiparton final states at Next-to-Leading Order and the extension of calculations for precision QCD observables

      beyond this order are summarized. Various issues concerning the

relevance of resummation for observables at TeV colliders is examined. Improvements to algorithms of jet reconstruction are discussed and predictions for

      diphoton and photon pi-zero production at the LHC are made for

kinematic variables of interest regarding searches for a Higgs boson decaying into two photons. Finally, several improvements implemented in Monte-Carlo

      event generators are documented. 

The $B\to \pi\pi$ hadronic matrix element of the chromomagnetic dipole operator $O_{8g}$ (gluonic penguin) is calculated using the QCD light-cone sum rule approach. The resulting sum rule for $\langle \pi\pi |O_{8g}|B\rangle $ contains, in addition to the $O(\alpha_s)$ part induced by hard gluon exchanges, a contribution due to soft gluons. We find that in the limit $m_b\to \infty$ the soft-gluon contribution is suppressed as a second power of $1/m_b$ with respect to the leading-order factorizable $B\to \pi\pi$ amplitude, whereas the hard-gluon contribution has only an $\alpha_s$ suppression. Nevertheless, at finite $m_b$, soft and hard effects of the gluonic penguin in $B\to \pi\pi$ are of the same order. Our result indicates that soft contributions are indispensable for an accurate counting of nonfactorizable effects in charmless $B$ decays. On the phenomenological side we predict that the impact of gluonic penguins on $\bar{B}^0_d\to \pi^+\pi^-$ is very small, but is noticeable for $\bar{B}^0_d\to \pi^0\pi^0$.

We consider two loop sunset diagrams with two mass scales m and M at the threshold and pseudotreshold that cannot be treated by earlier published formula. The complete reduction to master integrals is given. The master integrals are evaluated as series in ratio m/M and in epsilon with the help of differential equation method. The rules of asymptotic expansion in the case when q^2 is at the (pseudo)threshold are given.

I summarize the current status of the QCD light-cone sum rule predictions for the $B\to \pi$ form factor $f^+_{B\pi}$ that is needed to extract $|V_{ub}|$ from experimental data on $B\to \pi l\nu$ decays.

q qbar g > We present the calculation of the $\nf$-contributions to the two-loop amplitude for $e^+e^-\to q \qb g$ and give results for the full one-loop amplitude to order $\eps^2$ in the dimensional regularization parameter. Our results agree with those recently obtained by Garland et al.. The calculation makes extensive use of an efficient method based on nested sums to calculate two-loop integrals with arbitrary powers of the propagators. The use of nested sums leads in a natural way to multiple polylogarithms with simple arguments, which allow a straightforward analytic continuation.

We present a model of neutrino masses combining the seesaw mechanism and strong Dirac mass hierarchy and at the same time exhibiting a significantly reduced hierarchy at the level of active neutrino masses. The heavy Majorana masses are assumed to be degenerate. The suppression of the hierarchy is due to a symmetric and unitary operator R whose role is discussed. The model gives realistic mixing and mass spectrum. The mixing of atmospheric neutrinos is attributed to the charged lepton sector whereas the mixing of solar neutrinos is due to the neutrino sector. Small U_e3 is a consequence of the model. The masses of the active neutrinos are given by $\mu_3\approx\sqrt{\Delta m_{@}^2}$ and $\mu_1/\mu_2\approx \tan^2\theta_\odot$.

We investigate the structure of the leading IR renormalon singularity in the QCD/HQET matching coefficients for heavy-light quark currents beyond the large-\beta_0 limit. From this result, we derive the large-order behaviour of the perturbative series for these coefficients, and for ratios of meson matrix elements, such as f_{B^*}/f_B.

This paper is a written version of a talk presented at the FPCP conference, 16-18 May 2002, Philadelphia, PA.

We analyze the higher-twist effects and the $SU(3)$-flavour symmetry breaking in the correlation functions used to calculate form factors of pseudoscalar mesons in the QCD light-cone sum rule approach. It is shown that the Ward identities for these correlation functions yield relations between twist-4 two- and three-particle distribution amplitudes. In addition to the relations already obtained from the QCD equations of motions, we have found a new one. With the help of these relations, the twist-4 contribution to the light-cone sum rule for the pion electromagnetic form factor is reduced to a very simple form. Simultaneously, we correct a sign error in the earlier calculation. The updated light-cone sum rule prediction for the pion form factor at intermediate momentum transfers is compared with the recent Jefferson Lab data. Furthermore, from the correlation functions with strange-quark currents the kaon electromagnetic form factor and the $K\to \pi$ weak transition form factors are predicted with $O(m_s)\sim O(m_K^2)$ accuracy.

We calculate the subleading twist contributions to the endpoint of the inclusive lepton energy spectrum in $B \to X_u \ell \bar\nu$. We show that the same two subleading twist functions that appear in the decay $B \to X_s \gamma$ govern the subleading effects in this decay. Using these results we find large ${O}(\lqcd/m_B)$ corrections to the determination of $|V_{ub}|$ from the endpoint of the charged lepton spectrum. Using a simple model for the relevant subleading shape functions, we estimate the uncertainty in $|V_{ub}|$ from $\lqcd/m_b$ corrections to be at the $\sim 15\%$ level for a lower lepton energy cut of 2.2 GeV.

Electron–positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies at high luminosity meson factories. A Monte Carlo generator called PHOKHARA has been constructed, which simulates this process at the next-to-leading order accuracy.

We present results for the differential distributions of jets from non-leptonic decays of polarized top quarks within the Standard Model, including QCD radiative corrections. Our work extends existing results which are only available for semileptonic top quark decays at the parton level. For $t(\uparrow)\to b$-jet $+2$ light jets we compute in particular the QCD-corrected top-spin analysing power of the $b$-quark jet and the least energetic light jet. The dependence of the results on the choice of the jet recombination scheme is found to be small. In addition we compute the spin analysing power of the thrust axis. Our results constitute a so far missing ingredient to analyse top quark production and subsequent non-leptonic decay at next-to-leading order in $\alpha_s$, keeping the full information on the top quark polarization.

Virtual corrections for electron–positron annihilation into one real and one off-shell photon of invariant mass $Q^2$ are evaluated. Special attention is paid to those configurations where the real photon is collinear with the beam direction. This calculation is an important ingredient of a Monte Carlo program, which simulates events with tagged photons from initial-state radiation, including NLO corrections.

We discuss the calculation of the

   $n_f$-contributions to the two-loop
   amplitude for $ e^+ e^- \rightarrow q g \bar{q}$.
   The calculation uses an efficient method based on nested sums.
   The result is presented in terms of multiple polylogarithms
   with simple arguments, which allow for analytic continuation 
   in a straightforward manner.

We consider the two-loop self-mass sunrise amplitude with two equal masses $M$ and the external invariant equal to the square of the third mass $m$ in the usual $d$-continuous dimensional regularization. We write a second order differential equation for the amplitude in $x=m/M$ and show as solve it in close analytic form. As a result, all the coefficients of the Laurent expansion in $(d-4)$ of the amplitude are expressed in terms of harmonic polylogarithms of argument $x$ and increasing weight. As a by product, we give the explicit analytic expressions of the value of the amplitude at $x=1$, corresponding to the on-mass-shell sunrise amplitude in the equal mass case, up to the $(d-4)^5$ term included.