arXiv subjects

K. G. Chetyrkin

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

At least 91 records · Page 5Linked to original sources

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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arXiv2000

Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops

We derive explicit transformation formulae relating the renormalized quark mass and field as defined in the MS-bar scheme with the corresponding quantities defined in any other scheme. By analytically computing the three-loop quark propagator in the high-energy limit (that is keeping only massless terms and terms of first order in the quark mass) we find the NNNLO conversion factors transforming the MS-bar quark mass and the renormalized quark field to those defined in a ``Regularization Invariant'' (RI) scheme which is more suitable for lattice QCD calculations. The NNNLO contribution in the mass conversion factor turns out to be large and comparable to the previous NNLO contribution at a scale of 2 GeV --- the typical normalization scale employed in lattice simulations. Thus, in order to get a precise prediction for the MS-bar masses of the light quarks from lattice calculations the latter should use a somewhat higher scale of around, say, 3 GeV where the (apparent) convergence of the perturbative series for the mass conversion factor is better. We also compute two more terms in the high-energy expansion of the MS-bar renormalized quark propagator. The result is then used to discuss the uncertainty caused by the use of the high energy limit in determining the MS-bar mass of the charmed quark. As a by-product of our calculations we determine the four-loop anomalous dimensions of the quark mass and field in the Regularization Invariant scheme. Finally, we discuss some physical reasons lying behind the striking absence of zeta(4) in these computed anomalous dimensions.

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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

Quark mass effects to σ(e^+e^- -> hadrons) at O(α_s^3)

The calculation of the quartic mass terms at order α_s^3 to the hadronic R ratio is described. It is based on the operator product expansion for the quark current correlator, combined with an application of the renormalization group equation.

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arXiv1999

alpha_s^3 conversion relation betweeen MS-bar and Euclidean quark masses

We report on the analytical calculation of NNNLO (of order alpha_s^3) conversion factor between the MS-bar quark mass and the one defined in the so-called Regularization Invariant scheme. The NNNLO contribution in the conversion factor turns out to be relatively large and comparable to the known NNLO term.

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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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arXiv1999

Short-distance tachyonic gluon mass and 1/Q^2 corrections

We consider the assumption that a tachyonic gluon mass imitates short-distance nonperturbative physics of QCD. The phenomenological implications include modifications of the QCD sum rules for correlators of currents with various quantum numbers. The new 1/Q^2 terms allow to resolve in a natural way old puzzles in the pion and scalar-gluonium channels. They lead to a slight reduction of the values of the running light quark masses from the (pseudo)scalar sum rules and of alpha_s(M_τ) from tau decay data. Further tests can be provided by precision measurements of the correlators on the lattice and by the e^+e^- --> hadrons data.

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arXiv1999

Non-Singlet Corrections of O(α_s^2 G_F M_t^2) to Γ(Z\to b\bar{b})

The partial decay rate of the $Z$ boson into bottom quarks constitutes an important decay channel. This is mainly due to the virtual presence of the top quark in the loop diagrams giving rise to correction factors which are quadratic in the top quark mass. At one- and two-loop order it turned out that the leading term in the heavy-top expansion leads to very good approximations to the exact result. In this work the non-singlet diagrams at O(α_s^2 G_F M_t^2) are considered.

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arXiv1998

Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops

In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.

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arXiv1998

Determining the Strange Quark Mass in Cabibbo Suppressed Tau Lepton Decays

In this work radiative corrections in the total hadronic decay rate of the tau-lepton and some moments of its differential distributions are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections in the strange mass to the decay rate ratio R_tau to the order O(α_s^3 m^2) and find that they contribute appreciably to the Cabibbo suppressed decay modes of the tau-lepton. Using the results of a recent experimental analysis, we obtain m_s(1 GeV) = 200 \pm 40_exp \pm 30_th MeV.

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arXiv1998

Mass Corrections to the Tau Decay Rate

In this note radiative corrections to the total hadronic decay rate of the $τ$-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate ration $R_τ$ to the order ${\cal O}(α_s^2 m^2)$ and find that they contribute appreciably to the Cabbibo supressed decay modes of the $τ$-lepton. We also discuss corrections of mass dimension D=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.

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arXiv1998

Singlet Polarization Functions at O(α_s^2)

We consider the three-loop singlet diagrams induced by axial-vector, scalar and pseudo-scalar currents. Expansions for small and large external momentum $q$ are presented. They are used in combination with conformal mapping and Padé approximations in order to arrive at results for the polarization functions valid for all $q^2$. Results are presented for the imaginary parts which are directly related to physical quantities like the production of top quarks or the decay of scalar or pseudo-scalar Higgs bosons.

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arXiv1997

Massive Quark Production in Electron Positron Annihilation to Order $α_s^2$

Recent analytical and numerical results for the three-loop polarization function allow to present a phenomenological analysis of the cross section for massive quark production in electron positron annihilation to order $α_s^2$. Numerical predictions based on fixed order perturbation theory are presented for charm and bottom production above 5 and 11.5 GeV, respectively. The contribution from these energy regions to $α(M_Z^2)$, the running QED coupling constant at scale M_Z, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $β$, are presented.

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arXiv1997

Decoupling Relations to O(alpha_s^3) and their Connection to Low-Energy Theorems

If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant alpha_s and the quark masses m_q exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, zeta_g and zeta_m, respectively. Adopting the modified MS (MS-bar) scheme, we derive simple formulae which reduce the calculation of zeta_g and zeta_m to the solution of vacuum integrals. This allows us to evaluate zeta_g and zeta_m through three loops. We also establish low-energy theorems, valid to all orders, which relate the effective couplings of the Higgs boson to gluons and light quarks, due to the virtual presence of a heavy quark h, to the logarithmic derivatives w.r.t. m_h of zeta_g and zeta_m, respectively. Fully exploiting present knowledge of the anomalous dimensions of alpha_s and m_q, we thus calculate these effective couplings through four loops. Finally, we perform a similar analysis for the coupling of the Higgs boson to photons.

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arXiv1997

Complete QCD Corrections of Order O(α_s^3) to the Hadronic Higgs Decay

We consider the decay of an intermediate mass Higgs boson into hadrons up to order O(α_s^3). The results from the diagrams containing only light degrees of freedom were recently computed in a previous work by K.G. Ch. (Phys. Lett. B 390 (1997) 309). In this letter the remaining contributions involving the top quark are evaluated analytically using an effective field theory approach. Coupled with the previous result the present calculation determines the complete next-next-to-leading order correction to the hadronic decay rate of an intermediate mass Higgs boson.

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arXiv1997

Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme

We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.

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arXiv1997

Extracting alpha_s from Electron-Positron Annihilation around 10 GeV

The total cross section for electron-positron annihilation into hadrons is calculated in the region just below the B meson threshold. QCD corrections up to third order, quark mass effects, initial state radiation, the running of alpha_QED and the tails of the Upsilon resonances are included in the prediction. For given alpha_s the prediction is accurate to 0.5 percent. An experimental measurement with the corresponding precision would allow to determine alpha_s with high accuracy at intermediate energies.

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