arXiv subjects

M. Steinhauser

Publications and source records attributed to M. Steinhauser.

At least 73 records · Page 4Linked to original sources

arXiv2002

Evidence for Colour-Octet Mechanism from CERN LEP2 gamma gamma -> J/psi + X Data

We present theoretical predictions for the transverse-momentum distribution of J/psi mesons promptly produced in gamma gamma collisions within the factorization formalism of nonrelativistic quantum chromodynamics, including the contributions from both direct and resolved photons, and we perform a conservative error analysis. The fraction of J/psi mesons from decays of bottom-flavoured hadrons is estimated to be negligibly small. New data taken by the DELPHI Collaboration at LEP2 nicely confirm these predictions, while they disfavour those obtained within the traditional colour-singlet model.

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arXiv2002

Results and Techniques of Multi-Loop Calculations

In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order $α_s^4$ and $α_s^3$, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In a further application four-loop diagrams are considered which contribute to the order $α^2$ QED corrections to the $μ$ decay. Finally the calculation of the three-loop relation between the $\bar{\rm MS}$ and on-shell quark mass definitions is presented. To complete the presentation, some technical details are presented in the Appendix, where also explicit analytical results are listed.

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arXiv2002

Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order

The next-to-next-to-next-to-leading order (N^3LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative bound-state calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavy-quarkonium spectrum is obtained at N^3LO for the case of vanishing QCD beta function. Our results set the stage for a full N^3LO analysis of the heavy-quarkonium system.

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arXiv2001

Heavy-Light Meson Decay Constant from QCD Sum Rules in Three-Loop Approximation

In this paper we compute the decay constant of the pseudo-scalar heavy-light mesons in the heavy quark effective theory framework of QCD sum rules. In our analysis we include the recently evaluated three-loop result of order $α_s^2$ for the heavy-light current correlator. The value of the bottom quark mass, which essentially limits the accuracy of the sum rules for $B$ meson, is extracted from the nonrelativistic sum rules for $Υ$ resonances in the next-to-next-to-leading approximation. We find stability of our result with respect to all types of corrections and the specific form of the sum rule which reduces the uncertainty. Our results $f_B=206\pm 20$ MeV and $f_D=195\pm 20$ MeV for the $B$ and $D$ meson decay constants are in impressive agreement with recent lattice calculations.

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arXiv2001

Heavy-light current correlators at order $α_s^2$ in QCD and HQET

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass $M$. We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the non-logarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order $α_s^2$. As applications of the vector and scalar correlator we consider the single-top-quark production via the process $q\bar{q}\to t\bar{b}$ and the decay rate of a charged Higgs boson into hadrons, respectively. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones. On the contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic decay rate of a heavy-light meson proves to be comparable to the leading one.

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arXiv2001

J/psi plus dijet associated production in two-photon collisions

We study the production of a J/psi meson in association with one or two jets in gamma gamma collisions concentrating on the direct-photon contribution, which is expected to be dominant for large J/psi-meson transverse momentum and/or large dijet invariant mass. We work at leading order in the factorization formalism of nonrelativistic QCD and include all relevant colour-octet processes. We present distributions in J/psi-meson transverse momentum and rapidity appropriate for CERN LEP2, a future e^+e^- linear collider, and a possible gamma gamma collider mode of the latter. In the case of the e^+e^- linear collider, we assume the beamstrahlung spectrum appropriate for DESY TESLA.

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arXiv2001

The Algebraic Method

Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within non-invariant regularization schemes is drastically simplified. The present technique is suitable for gauge models and, here, is applied to the Standard Model. The use of the BFM allows a powerful organization of the counterterms and avoids complicated Slavnov-Taylor identities. Furthermore, the Becchi-Rouet-Stora-Tyutin (BRST) variation of background fields plays a special role in disentangling Ward-Takahashi identities (WTI) and Slavnov-Taylor identities (STI). Finally, the strategy to be applied to physical processes is exemplified for the process $b\to sγ$.

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arXiv2000

Three-loop non-diagonal current correlators in QCD and NLO corrections to single-top-quark production

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries the mass $M$. As applications we consider the single-top-quark production via the process $q\bar{q}\to t\bar{b}$ and the decay rate of a charged Higgs into hadrons. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones.

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arXiv2000

Non-invariant two-loop counterterms for the three-gauge-boson vertices

Some practical applications of algebraic renormalization are discussed. In particular we consider the two-loop QCD corrections to the three-gauge-boson vertices involving photons, Z and W bosons. For this purpose also the corresponding two-point functions have to be discussed. A recently developed procedure is used to analyze the breaking terms of the functional identities and explicit formulae for the universal counterterms are provided. Special attention is devoted to the treatment of infra-red divergences.

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arXiv2000

Practical Algebraic Renormalization

A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process $B \to X_s γ$.

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arXiv2000

MATAD: a program package for the computation of MAssive TADpoles

In the recent years there has been an enormous development in the evaluation of higher order quantum corrections. An essential ingredient in the practical calculations is provided by vacuum diagrams, i.e. integrals without external momenta. In this paper a program package is described which can deal with one-, two- and three-loop vacuum integrals with one non-zero mass parameter. The principle structure is introduced and the main parts of the package are described in detail. Explicit examples demonstrate the fields of application.

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arXiv2000

Gauge-Independent W-Boson Partial Decay Widths

We calculate the partial decay widths of the W boson at one loop in the standard model using the on-shell renormalization scheme endowed with a gauge-independent definition of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix. We work in $R_ξ$ gauge and explicitly verify that the final expressions are independent of the gauge parameters. Furthermore, we establish the relationship between the on-shell and $\bar{\mathrm{MS}}$ definitions of the CKM matrix, both in its generic form and in the Wolfenstein parameterization. As a by-product of our analysis, we recover the beta function of the CKM matrix.

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arXiv2000

The relation between the $\bar{\rm MS}$ and the on-shell quark mass at order $α_s^3$

The relation between the on-shell and $\bar{\rm MS}$ mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Padé improvement in order to construct a numerical approximation for the relation [1]. The errors of our final result are conservatively estimated to be below 3%. The numerical implications of the results are discussed in particular in view of top and bottom quark production near threshold. We show that the knowledge of new ${\cal O}(α_s^3)$ correction leads to a significant reduction of the theoretical uncertainty in the determination of the quark masses.

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arXiv2000

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses

In this paper the formulae are collected which are needed for the computation of the strong coupling constant and quark masses at different energy scales and for different number of active flavours. All equations contain the state-of-the-art QCD corrections up to three- and sometimes even four-loop order. For the practical implementation {\tt Mathematica} is used and a package containing useful procedures is provided.

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arXiv1999

Second Order QCD Corrections to the Top Decay Rate

We report on a recent calculation of the top decay rate up to order α_s^2. It is based on asymptotic expansions of the off-shell top propagator, followed by a Padé approximation in order to reach the physically relevant point q^2=Mt^2.

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arXiv1999

Second Order Corrections to the Muon Lifetime and the Semileptonic B Decay

In this article two-loop QED corrections to the muon decay and corrections of order $α_s^2$ to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Padé approximation. Via this method we confirm the existing results by an independent calculation.

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arXiv1999

Second Order QCD Corrections to $Γ(t \to Wb)$

Corrections of $O(α_s^2)$ to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum, q, as compared to the top quark mass, M_t. The physical point q^2 = M_t^2 is reached through Padé approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate $b \to u l \barν$ and the two-loop QED corrections to $μ$-decay are performed.

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arXiv1999

Short Distance Mass of a Heavy Quark at Order α_s^3

The relation between the on-shell quark mass and the mass defined in the modified minimal subtraction scheme is computed up to order α_s^3. Implications for the numerical values of the top and bottom quark masses are discussed. We show that the new three-loop correction significantly reduces the theoretical uncertainty in the determination of the quark masses.

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