Heavy Quark Pole Mass Research Articles

Relation Between Pole and Running Masses of Heavy Quarks Using the Principle of Maximum Conformality

Abstract The relation of the pole and running heavy quark masses of the order of $\mathcal {O}\left(\alpha _s^4\right)$ in perturbative quantum chromodynamics (pQCD) can be obtained using the principle of maximum conformality (PMC), a formalism that provides a rigorous method for eliminating renormalization scale and scheme ambiguities for observables in pQCD. Using PMC, optimal renormalization scale for the heavy quark mass ratio is determined, independent of the renormalization scale and scheme up to order $\alpha _s^4$. Precise values are then obtained for the PMC pole masses of the heavy quarks $M_b^{\text{PMC}}=4.86^{+0.03}_{-0.02}$ GeV, $M_t^{\text{PMC}}=172.3\pm 0.6$ GeV, and the running mass $\overline{m}_t^{\text{PMC}}=162.6\pm 0.7$ GeV at the PMC scale.

Hyperasymptotic approximation to the top, bottom, and charm pole mass

We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV) prescription. We apply such hyperasymptotic expansions to the $B/D$ meson masses, and $\bar \Lambda $ computed in the lattice. The issue of the uncertainty of the (top) pole mass is critically reexamined. The present theoretical uncertainty in the relation between ${\bar m}_t$, the $\bar{\rm MS}$ top mass, and $m_{t, \rm PV}$, the top pole mass regulated using the PV prescription, is numerically assessed to be $\delta m_{t,\rm PV}= 28\;{\rm MeV}$ for ${\bar m}_t =163$ GeV.

Dependence of Five- and Six-Loop Estimated QCD Corrections to the Relation between Pole and Running Masses of Heavy Quarks on the Number of Light Flavors

In this paper various theoretical approaches are used to define the dependence of the estimated $\mathcal{O}(\alpha^5_s)$ and $\mathcal{O}(\alpha^6_s)$-corrections to the QCD relation between pole and $\rm{\overline{MS}}$ running masses of heavy quarks on the number of light flavours. It is found that recently studied asymptotic formula for the coefficients of this relation, based on the infared-renormalon method, does not reproduce sign-alternating structure in the flavour-dependence of the five and six-loop corrections, which holds in three other used by us approaches.

Flavor dependence of normalization constant for an infrared renormalon

An ansatz is proposed for the flavor dependence of the normalization constant for the first IR renormalon in heavy quark pole mass.

Borel resummation with low order perturbations in QCD

The bilocal expansion of Borel transform provides an efficient way of Borel resummation with low order perturbations in QCD. Its applications to the heavy quark pole mass, static potential, and lattice calculation are reviewed.

Constraining renormalon effects in lattice determination of heavy quark mass

The Borel summation technique of infrared renormalons is applied to the lattice determination of heavy quark mass. With Borel summation a physical heavy quark pole mass and binding energy of a heavy-light meson can be defined in a rigorous and calculable manner. A notable feature of the Borel summation, compared to the usual perturbative cancellation of IR renormalons, is an automatic scale separation. The two approaches of handling renormalon divergence are compared in the B-meson as well as in an (imaginary) heavy-light meson with a mass much larger than the inverse of the lattice spacing.

Heavy quark mass determination from the quarkonium ground state energy: a pole mass approach

The heavy quark pole mass in perturbation theory suffers from a renormalon caused, inherent uncertainty of $O(\Lambda_{\rm QCD})$. This fundamental difficulty of determining the pole mass to an accuracy better than the inherent uncertainty can be overcome by direct resummation of the first infrared renormalon. We show how a properly defined pole mass as well as the $\bar {\rm MS}$ mass for the top and bottom quarks can be determined accurately from the $O(m\alpha_s^5)$ quarkonium ground state energy.

Two-loop $\cal O$ $(\alpha_{s}^2)$ MSSM corrections to the pole masses of heavy quarks

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

Renormalon cancellation and Borel summability of the Gross-Neveu model mass gap

The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally similar to the QCD heavy quark pole mass renormalons, potentially leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the precise vanishing mechanism of such infrared renormalons, which avoids this (only apparent)contradiction, and operates without need of (Borel) summation contour prescription, usually preventing unambiguous separation of perturbative contributions. As a consequence we stress the direct Borel summability of the (1/N) perturbative expansion of the mass gap. We briefly speculate on a possible similar behaviour of analogous non-perturbative QCD quantities.

A quark mass definition adequate for threshold problems

Recent calculations of heavy quark cross sections near threshold at next-to-next-to-leading order have found second-order corrections as large as first-order ones. We analyse long-distance contributions to the heavy quark potential in momentum and coordinate space and demonstrate that long-distance contributions in momentum space are suppressed as Λ QCD 2/ q 2 . We then show that the long-distance sensitivity of order Λ QCD r introduced by the Fourier transform to coordinate space cancels to all orders in perturbation theory with long-distance contributions to the heavy quark pole mass. This leads us to define a subtraction scheme – the `potential subtraction scheme' – in which large corrections to the heavy quark potential and the `potential-subtracted' quark mass are absent. We compute the two-loop relation of the potential-subtracted quark mass to the MS quark mass. We anticipate that threshold calculations expressed in terms of the scheme introduced here exhibit improved convergence properties.

Annihilation of S-wave quarkonia and the measurement of αs

We analyze the relativistic corrections to annihilation rates of S-wave quarkonia within the framework of NRQCD. We show that order v^2 corrections can be expressed in terms of the heavy quark pole mass and the quarkonium mass. The ratio of hadronic to radiative annihilation rates for eta_b and eta_c can therefore be predicted accurately. The contributions of color-octet operators to the hadronic decay rates of spin-triplet quarkonia are shown to be significant, even though they arise at order v^4 in the velocity expansion. We provide a rough estimate of the color-octet contributions and extract the value of alpha_s from the experimental data on Upsilon decays.

Renormalized sum rules for structure functions of heavy meson decays.

We consider properties of the structure functions of inclusive heavy meson decays $B\to X_c$ and treat the $c$ quark mass as a free parameter. We show that in two extreme cases of heavy and light $c$ quark the structure functions of heavy--heavy and heavy--light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a time--like and a light--like segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of heavy--heavy transition is renormalized multiplicatively while that of heavy-light transition obeys the GLAP--type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the ``third'' sum rules) with a soft exponential factorization cut--off, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at $u=\frac12$ are exactly cancelled by the similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at $u=1$ are parameterized by the matrix element $\mu_\pi^2$ which is proportional to the heavy quark kinetic energy.

Resummation of ( ß0αs) n corrections in QCD: techniques and applications to the τ hadronic width and the heavy quark pole mass

We propose to resum exactly any number of one-loop vacuum polarization insertions into the scale of the coupling of lowest order radiative corrections. This makes maximal use of the information contained in one-loop perturbative corrections combined with the one-loop running of the effective coupling and provides a natural extension of the familiar BLM scale-fixing prescription to all orders in the perturbation theory. It is suggested that the remaining radiative corrections should be reduced after resummation. In this paper we implement this resummation by a dispersion technique and indicate a possible generalization to incorporate two-loop evolution. We investigate in some detail higher-order perturbative corrections to the τ-decay width and the pole mass of a heavy quark. We find that these corrections tend to reduce α s ( m τ ) determined from τ-decays by approximately 10% and increase the difference between the bottom pole and MS -renormalized mass by 30%.

Perturbative strong interaction corrections to the heavy quark semileptonic decay rate

We calculate the part of the order α s 2 correction to the semileptonic heavy quark decay rate proportional to the number of light quark flavors, and use our result to set the scale for evaluating the strong coupling in the order α s term according to the scheme of Brodsky, Lepage and Mackenzie. Expressing the decay rate in terms of the heavy quark pole mass m Q , we find the scale for the MS strong coupling to be 0.07 m Q . If the decay rate is expressed in terms of the MS heavy quark mass m Q ( m Q ) then the scale is 0.12 m Q . We use these results along with the existing calculations for hadronic τ decay to calculate the BLM scale for the nonleptonic decay width and the semileptonic branching ratio. The implications for the value of | V bc | extracted from the inclusive semileptonic B meson decay rate are discussed.