arXiv subjects

K. G. Chetyrkin

Publications and source records attributed to K. G. Chetyrkin.

120 records · Page 7Linked to original sources

arXiv1995

Second Order QCD Corrections to Scalar and Pseudoscalar Higgs Decays into Massive Bottom Quarks

Quark mass effects in ${\cal O}(α_s^2)$ QCD corrections to the decay rates of intermediate Higgs bosons are studied. The total hadronic rate and the partial decay rate into bottom quarks are analyzed for the Standard (scalar) Higgs boson as well as for pseudoscalar Higgs bosons. The calculations of three different contributions are presented. First, the flavour singlet diagrams containing two closed fermion loops are calculated for a nonvanishing bottom mass in the heavy top limit. Their leading contribution, which is of the same order as the quasi-massless nonsinglet corrections, and the subleading terms are found. Large logarithms arise due to the separation of the pure gluon final state from the bottom final states. Second, quadratic bottom mass corrections originating from nonsinglet diagrams are presented.Third, nonsinglet corrections induced by virtual heavy top quarks are calculated in leading and subleading orders. It is demonstrated that, in order $α_s^2$, the first contribution numerically dominates over the second and the third ones.

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arXiv1995

QCD Corrections from Top Quark to Relations between Electroweak Parameters to Order $α_s^2$

The vacuum polarization functions $Π(q^2)$ of charged and neutral gauge bosons which arise from top and bottom quark loops lead to important shifts in relations between electroweak parameters which can be measured with ever-increasing precision. The large mass of the top quark allows approximation of these functions through the first two terms of an expansion in $M_Z^2/M_t^2$. The first three terms of the Taylor series of $Π(q^2)$ are evaluated analytically up to order $\as^2$. The first two are required to derive the approximation, the third can be used to demonstrate the smallness of the neglected terms. The paper improves earlier results based on the leading term $\propto G_F M_t^2 \as^2$. Results for the subleading contributions to $\dr$ and the effective mixing angle $\sineff$ are presented.

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arXiv1995

Five-loop renormalization group functions of ${O}(n)$-symmetric $ϕ^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $β$-function and the anomalous dimensions of the ${O}(n)$-symmetric $ϕ^4$-theory in $D=4-\ep$ dimensions we present the results of a full analytic reevaluation of all diagrams. The divergences are removed by minimal subtraction and $\ep$-expansions are given for the critical exponents $η$, $ν$, and $ω$ up to order $ε^5$.

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arXiv1995

QCD Corrections to the $e^+e^-$ Cross Section and the $Z$ Boson Decay Rate

QCD corrections to the electron positron annihilation cross-section into hadrons and to the hadronic $Z$ boson decay rate are reviewed. Formal developments are introduced in a form particularly suited for practical applications. These include the operator product expansion, the heavy mass expansion, the decoupling of heavy quarks and matching conditions. Exact results for the quark mass depen- dence are presented whenever available, and formulae valid in the limit of small bottom mass ($m_{b}^2\ll s$) or of large top mass ($m_{t}^2\gg s$) are presen- ted. The differences between vector and axial vector induced rates as well the classification of singlet and nonsinglet rates are discussed. Handy formulae for all contributions are collected and their numerical relevance is investi- gated. Prescriptions for the separation of the total rate into partial rates are formulated. The applicability of the results in the low energy region, relevant for measurements around 10 GeV and below, is investigated and numerical predictions are collected for this energy region.

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arXiv1995

Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $ρ$ parameter

The three-loop QCD corrections to the $ρ$ parameter from top and bottom quark loops are calculated. The result differs from the one recently calculated by Avdeev et al. As function of the pole mass the numerical value is given by $\drho=\frac{3G_F M_t^2}{8\sqrt{2}π^2}(1- 2.8599 \api - 14.594 (\api)^2 )$.

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arXiv1994

$R_{had}$ at the $B$-factory

A systematic theoretical evaluation of the cross section for hadron production in electron-positron collisions in the energy range just below the $B$ meson threshold is presented which includes charm and bottom mass effects and is accurate to order $\as^3$. The corresponding measurement in the energy region several $GeV$ above the threshold is also discussed.

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arXiv1994

Mass singularities in light quark correlators: the strange quark case

The correlators of light-quark currents contain mass-singularities of the form log(m^2/Q^2). It has been known for quite some time that these mass- logarithms can be absorbed into the vacuum expectation values of other operators of appropriate dimension, provided that schemes without normal- ordering are used. We discuss in detail this procedure for the case of the mass logarithms m^4 log(m^2/Q^2), including also the mixing with the other dimension-4 operators to two-loop order. As an application we present an improved QCD sum rule determination of the strange-quark mass. We obtain m_s(1 GeV)=171 \pm 15 MeV.

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arXiv1994

Perturbative QCD Corrections to the $Z$ Boson Width and the Higgs Decay Rate

Radiative QCD corrections significantly influence the theoretical predictions for the decay rates of the $Z$ and the Higgs boson. The status of the QCD calculations to the hadronic $Z$ width is reviewed. The role of mass corrections from bottom quark final states is emphasized. An estimate of the theoretical uncertainties is given. New results for quartic mass terms of order ${\cal O}(α_s^2)$ are presented. The impact of secondary radiation of bottom quarks on the determination of $Γ(Z\rightarrow b\bar{b})$ is discussed. Second order QCD corrections to the partial decay rate $Γ(H\rightarrow b\bar{b})$ are also presented in this talk. A recent result for the flavour singlet contribution to this quantity is presented. It includes quark mass effects and completes the otherwise massless calculations of order $\ordas^2)$.

hep-ph↗

arXiv1994

Quartic Mass Corrections to $R_{had}$

The influence of nonvanishing quark masses on the total cross section in electron positron collisions and on the $Z$ decay rate is calculated. The corrections are expanded in $m^2/s$ and $\as$. Methods similar to those applied for the quadratic mass terms allow to derive the corrections of order $\as m^4/s^2$ and $\as^2m^4/s^2$. Coefficients which depend logarithmically on $m^2/s$ and which cannot be absorbed in a running quark mass arise in order $\as^2$. The implications of these results on electron positron annihilation cross sections at LEP and at lower energies in particular between the charm and the bottom threshold and for energies several GeV above the $b\bar b$ threshold are discussed.

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arXiv1994

Renormalization of 4-Quark Operators and QCD-Sum Rules

We compute the renormalization mismatch displayed in 1--loop approximation by classically equivalent 4-quark operators and coming from different possible definitions of the $γ_5$ matrix in dimensional regularization. The result is then employed to study the effect of the various treatments of $γ_5$ upon the size of radiative corrections to 4-quark condensates in the QCD sum rules for $ρ$ and $A_1$ mesons. We find that a fully anticommuting $γ_5$ which automatically respects non-anomalous chiral Ward-Slavnov identities leads to considerably smaller corrections and reduces theoretical uncertainty in the QCD prediction for the $τ$ hadronic decay rate.

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arXiv1993

The $α_s^3$ Corrections to the Effective Neutral Current and to the Z Decay Rate in the Heavy Top Quark Limit

We find the effective neutral current in the heavy top quark limit up to and including the terms of order $α_s^3$. The result is then employed to compute the correction of the same order to the axial part of the Z decay rate into hadrons ($\G^h_Z$) induced by the top-bottom quark mass splitting. The calculations confirm the prediction made in a previous work of K.G.Ch. and J.H.Kühn (Phys. Lett. B 308 (1993) 127), namely, the effect of the singlet corrections of order $α^3_s$ to the axial part of the $\G^h_Z$ should not exceed 25\% - 30\% (depending on the values chosen for $α_s(M_Z)$ and $m_t$) of the magnitude of the leading (singlet) $α_s^2$ term.

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arXiv1993

Flavour Singlet ${\cal O}(α_s^2 m_b^2/m_t^2)$ Corrections to the Partial Decay Rate $Γ(Z\rightarrow b\bar{b})$

We analytically compute the flavour singlet ${\cal O}(α_s^2 m_b^2/m_t^2)$ radiative corrections to the partial decay rate $Γ(Z\rightarrow b\bar{b})$. These corrections arise from anomalous ``double traingle'' diagrams containing a single $γ_5$ matrix inside each of two closed fermion loops. They represent the next-to-leading term of the asymptotic expansion in the inverse large top mass. As a byproduct of the calculcation we confirm the results of B.Kniehl and J.H.Kühn for the flavour singlet massless corrections \cite{KniKue90} as well as our previous ${\cal O}(α_s^2 m_b^2/M_Z^2)$ result \cite{CheKwi93}.

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