arXiv subjects
Publications and source records attributed to M. Steinhauser.
Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $β$ function and the anomalous dimension of the quark masses are derived to three-loop order. Special emphasis is put on the proper treatment of the so-called $ε$-scalars and the additional couplings which have to be considered.
In this paper we consider the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) to three-loop order in perturbation theory. We evaluate the fermionic corrections containing a closed massless fermion loop. The results are building blocks both for the bottom and top quark system at threshold. We explain in detail the methods used for the evaluation of the Feynman diagrams, classify the occurring master integrals and provide results for the latter. The numerical effects are significant. They have the tendency to improve the behaviour of the perturbative series -- both for the bottom and top quark system.
In this paper we consider the production of top quark pairs close to threshold and compute the dependence on the Higgs boson mass to order $αα_s$. This requires the evaluation of the matching coefficient of the vector current to two-loop level and the inclusion of Higgs mass dependent operators in the non-relativistic effective theory. For Higgs boson masses below 200 GeV moderate contributions to the top quark mass and the peak cross section are observed. We also provide additional information to the on-shell wave function renormalization which is relevant for the matching coefficient.
In this paper we consider the matching coefficients up to two loops between Quantum Chromodynamics (QCD) and Non-Relativistic QCD (NRQCD) for the vector, axial-vector, scalar and pseudo-scalar currents. The structure of the effective theory is discussed and analytical results are presented. Particular emphasis is put on the singlet diagrams.
In this paper we consider mixed two-loop electroweak corrections to the top quark propagator in the Standard Model. In particular, we compute the on-shell renormalization constant for the mass and wave function, which constitute building blocks for many physical processes. The results are expressed in terms of master integrals. For the latter practical approximations are derived. In the case of the mass renormalization constant we find agreement with the results in the literature.
We compute the matching relation for the strong coupling constant within the framework of QCD up to four-loop order. This allows a consistent five-loop running (once the $β$ function is available to this order) taking into account threshold effects. As a side product we obtain the effective coupling of a Higgs boson to gluons with five-loop accuracy.
We compute the four-loop contribution to the electroweak $ρ$ parameter induced by the singlet diagrams of the $Z$-boson self-energy. The numerical impact on the weak mixing angle and the $W$-boson mass is small.
When relating the strong coupling $α_s$, measured at the scale of the $Z$ boson mass, to its numerical value at some higher energy, for example the scale of Grand Unification, it is important to include higher order corrections both in the running of $α_s$ and the decoupling of the heavy particles. We compute the two-loop matching coefficients for $α_s$ within the Minimal Supersymmetric Standard Model (MSSM) which are necessary for a consistent three-loop evolution of the strong coupling constant. Different scenarios for the hierarchy of the supersymmetric scales are considered and the numerical effects are discussed. We find that the three-loop effects can be as large as and sometimes even larger than the uncertainty induced by the current experimental accuracy of $α_s(M_Z)$.
We compute the third-order corrections to the heavy quarkonium spectrum and production/annihilation rates due to the leading renormalization group running of the static potential. The previously known complete ${\cal O}(m_qα_s^5)$ result for the heavy quarkonium ground state energy is extended to the exited states. After including the ${\cal O}(α_s^3)$ corrections the perturbative results are in surprisingly good agreement with the experimental data on the masses of the excited $Υ$ resonances and the leptonic width of the $Υ(1S)$ meson. The impact of the corrections on the $Υ$ sum rules and top quark-antiquark threshold production cross section is also discussed.
In this letter, we extend the known results for the QCD potential between a static quark and its antiquark by computing the two-loop corrections to the colour-octet state.
We calculate the cross section of J/psi plus prompt-photon inclusive production in gamma gamma collisions at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) focusing on direct photoproduction. Apart from direct J/psi production, we also include the feed-down from directly-produced chi_{cJ} and psi' mesons. We discuss the analytical calculation, in particular the treatment of the various types of singularities and the NRQCD operator renormalization, in some detail. We present theoretical predictions for the future e^+e^- linear collider TESLA, taking into account both brems- and beamstrahlung.
We calculate the cross section of J/psi plus jet inclusive production in gamma gamma collisions at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) focusing on direct photoproduction. Apart from direct J/psi production, we also include the feed-down from directly-produced chi_{cJ} and psi' mesons. We discuss the analytical calculation, in particular the treatment of the various types of singularities and the NRQCD operator renormalization, in some detail. We present theoretical predictions for the future e^+e^- linear collider TESLA, taking into account both brems- and beamstrahlung.
We investigate the inclusive production of prompt J/psi mesons in polarized hadron-hadron, photon-hadron, and photon-photon collisions in the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD) providing all contributing partonic cross sections in analytic form. In the case of photoproduction, we also include the resolved-photon contributions. We present numerical results appropriate for BNL RHIC-Spin, the approved SLAC fixed-target experiment E161, and the e^+e^- and gamma gamma modes of TESLA. Specifically, we assess the feasibility to access the spin-dependent parton distributions in the polarized proton and photon. We also point out that preliminary data on J/psi inclusive production taken by the PHENIX Collaboration in unpolarized proton-proton collisions at RHIC tends to favor the NRQCD factorization hypothesis, while it significantly overshoots the theoretical prediction of the color-singlet model at large values of transverse momentum.
We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by Baikov can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential.
The precise data for the total cross section $σ(e^+e^-\to{hadrons})$ from the charm threshold region, when combined with the evaluation of moments with three loop accuracy, lead to a direct determination of the short distance $\bar{\rm MS}$ 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. A complementary method for the determination of $m_b$ is based of the analysis of the $Υ(1S)$ system which is confronted with a next-to-next-to-next-to-leading order calculation of the corresponding energy level. This leads to $m_b(m_b)=4.346(70)$ GeV.
We discuss the impact of precision measurements of $σ(e^+e^-\to {hadrons})$ 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 $α_s$, on the evaluation of the hadronic contributions to the electromagnetic coupling $α(M_Z)$, and the determination of the charm and bottom quark masses.
In this paper we compare recent experimental data for the total cross section $σ(e^+e^-\to{hadrons})$ with the up-to-date theoretical prediction of perturbative QCD for those energies where perturbation theory is reliable. The excellent agreement suggests the determination of the strong coupling $α_s$ from the measurements in the continuum. The precise data from the charm threshold region, when combined with the recent evaluation of moments with three loop accurracy, lead to a direct determination of the short distance $\bar{\rm MS}$ charm quark mass. Our result for the strong coupling constant $α_s^{(4)}(5 {GeV})=0.235^{+0.047}_{-0.047}$ corresponds to $α_s^{(5)}(M_Z)=0.124^{+0.011}_{-0.014}$, for the charmed quark mass we find $m_c(m_c)=1.304(27)$. Applying the same approach to the bottom quark we obtain $m_b(m_b)=4.191(51)$ GeV. Whereas our result for $α_s(M_Z)$ serves as a useful cross check for other more precise determinations, our values for the charm and bottom quark masses are more accurate than other recent analyses.
We present the next-to-next-to-next-to-leading ${\cal O}(α_s^5m_q)$ result for the ground state energy of a heavy quarkonium system. On the basis of this result we determine the bottom quark mass from $Υ(1S)$ resonance and provide an explicit formula relating the top quark mass to the resonance energy in $t\bar t$ threshold production.