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M. Beneke

Publications and source records attributed to M. Beneke.

142 records · Page 8Linked to original sources
arXiv1996

Resummation of threshold corrections in QCD to power accuracy: the Drell-Yan cross section as a case study

Resummation of large infrared logarithms in perturbation theory can, in certain circumstances, enhance the sensitivity to small gluon momenta and introduce spurious nonperturbative contributions. In particular, different procedures -- equivalent in perturbation theory -- to organize this resummation can differ by $1/Q$ power corrections. The question arises whether one can formulate resummation procedures that are explicitly consistent with the infrared behaviour of finite-order Feynman diagrams. We explain how this problem can be treated and resolved in Drell-Yan (lepton pair) production and briefly discuss more complicated cases, such as top quark production and event shape variables in the $e^+e^-$ annihilation.

hep-ph↗
arXiv1996

Width Difference in the $B_s-\bar{B_s}$ System

We use the heavy quark expansion to investigate the width difference $ΔΓ_{B_s}$ between the $B_s$ mass eigenstates. The corrections of ${\cal O}(Λ_{QCD}/m_b)$ and ${\cal O}(m_s/m_b)$ to the leading order expression in the operator product expansion are derived and estimated to yield a sizable reduction of the leading result for $ΔΓ_{B_s}$ by typically $30\%$. For completeness we also quantify small effects due to penguin operators and CKM suppressed contributions. Based on our results we discuss the prediction for $(ΔΓ/Γ)_{B_s}$ with particular emphasis on theoretical uncertainties. We find $(ΔΓ/Γ)_{B_s}=0.16^{+0.11}_{-0.09}$, where the large error is dominated by the uncertainty in hadronic matrix elements. An accuracy of about $10\%$ in $(ΔΓ/Γ)_{B_s}$ should be within reach, assuming continuing progress in lattice calculations. In addition we address phenomenological issues and implications of a $ΔΓ_{B_s}$ measurement for constraints on $ΔM_{B_s}$ and CKM parameters. We further consider in some detail the lifetime ratio $τ(B_s)/τ(B_d)$ and estimate that, most likely, $|τ(B_s)/τ(B_d)-1|<1\%$.

hep-ph↗
arXiv1996

Hadro-production of Quarkonia in Fixed Target Experiments

We analyze charmonium and bottomonium production at fixed target experiments. We find that inclusion of color octet production channels removes large discrepancies between experiment and the predictions of the color singlet model for the total production cross section. Furthermore, including octet contributions accounts for the observed direct to total $J/ψ$ production ratio. As found earlier for photo-production of quarkonia, a fit to fixed target data requires smaller color octet matrix elements than those extracted from high-$p_t$ production at the Tevatron. We argue that this difference can be explained by systematic differences in the velocity expansion for collider and fixed-target predictions. While the color octet mechanism thus appears to be an essential part of a satisfactory description of fixed target data, important discrepancies remain for the $χ_{c1}/χ_{c2}$ production ratio and $J/ψ$ ($ψ'$) polarization. These discrepancies, as well as, the differences between pion and proton induced collisions emphasize the need for including higher twist effects in addition to the color octet mechanism.

hep-ph↗
arXiv1996

The $B_c$ Meson Lifetime

We investigate the total inclusive decay rate of the (ground state) $B_c$ meson within the framework of an operator product expansion in inverse powers of the heavy quark masses and subsequent matching onto nonrelativistic QCD. The expansion is organized as a series in the strong coupling and in powers of the heavy quark velocities in the $B_c$, reflecting the nonrelativistic nature of a heavy-heavy bound state. In this aspect the character of the expansion differs from the more familiar case of heavy-light mesons. The framework incorporates systematically corrections to the leading $b$- and $c$-quark decays due to binding effects, as well as contributions from weak annihilation and Pauli interference. Based on this approach we find for the $B_c$ meson lifetime $τ_{B_c}=(0.4 - 0.7)\,$ps, the dominant mechanism being the decay of the charm constituent.

hep-ph↗
arXiv1995

Ultraviolet renormalons in abelian gauge theories

We analyze the large-order behaviour in perturbation theory of classes of diagrams with an arbitrary number of chains (i.e. photon lines, dressed by vacuum polarization insertions). We derive explicit formulae for the leading and subleading divergence as $n\to\infty$, and a complete result for the vacuum polarization at the next-to-leading order in $1/N_f$. In general, diagrams with more chains yield stronger divergence. We define an analogue of the familiar diagrammatic $R$-operation, which extracts ultraviolet renormalon counterterms as insertions of higher-dimension operators. We then use renormalization group equations to sum the leading $(\ln n/N_f)^k$-corrections to all orders in $1/N_f$ and find the asymptotic behaviour in $n$ up to a constant that must be calculated explicitly order by order in $1/N_f$.

hep-ph↗
arXiv1995

$ψ'$ Polarization as a test of colour octet quarkonium production

We calculate the $α_s$ corrections to the transverse polarization fraction of $ψ^\prime$'s produced at the Tevatron. If the `$ψ^\prime$-anomaly' is explained by gluon fragmentation into a colour octet Fock component of the $ψ^\prime$, the $ψ^\prime$'s should be $100\%$ transversely polarized at leading order in $α_s$, up to spin symmetry breaking long-distance corrections. We find that the short-distance correction to the transverse polarization fraction is a few percent, so that a polarization measurement would provide a reliable test of the colour octet mechanism.

hep-ph↗
arXiv1995

Resummation of Running Coupling Effects in Semileptonic B Meson Decays and Extraction of $|V_{cb}|$

We present a determination of $|V_{cb}|$ from semileptonic B decays that includes resummation of supposedly large perturbative corrections, originating from the running of the strong coupling. We argue that the low value of the BLM scale found previously for inclusive decays is a manifestation of the renormalon divergence of the perturbative series starting already in third order. A reliable determination of $|V_{cb}|$ from inclusive decays is possible if one either uses a short-distance b quark mass or eliminates all unphysical mass parameters in terms of measured observables, such that all infra-red contributions of order $1/m_b$ cancel explicitly. We find that using the $\overline{\rm MS}$ running mass significantly reduces the perturbative coefficients already in low orders. For a semileptonic branching ratio of $10.9\%$ we obtain $|V_{cb}|(τ_B/1.50\,{\rm ps})^{1/2}= 0.041\pm 0.002$ from inclusive decays, in good agreement with the value extracted from exclusive decays.

hep-ph↗
arXiv1995

Power corrections and renormalons in Drell-Yan production

The resummed Drell-Yan cross section in the double-logarithmic approximation suffers from infrared renormalons. Their presence was interpreted as an indication for non-perturbative corrections of order $\lqcd/(Q(1-z))$. We find that, once soft gluon emission is accurately taken into account, the leading renormalon divergence in the resummed cross section is cancelled by higher-order perturbative contributions in the exponent of the resummed cross section. From this evidence, `higher twist' corrections to the hard cross section in Drell-Yan production should therefore intervene only at order $\lqcd^2/((Q^2 (1-z)^2)$ in the entire perturbative domain $Q (1-z) > \lqcd$. We compare this result with hadronic event shape variables, comment on the potential universality of non-perturbative corrections to resummed cross sections, and on possible implications for phenomenology.

hep-ph↗
arXiv1995

Resummation of $(β_0 α_s)^n$ 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\%.

hep-ph↗
arXiv1994

Naive nonabelianization and resummation of fermion bubble chains

We propose to extend the Brodsky-Lepage-Mackenzie scale-fixing prescription by resumming exactly any number of one-loop vacuum polarization insertions into one-loop diagrams. In this way, one makes maximal use of the information contained in one-loop perturbative corrections combined with the one-loop running of the effective coupling. The scale ambiguity at leading order is converted into an intrinsic uncertainty of perturbative approximations induced by IR renormalons. Practical implementation of this resummation requires only knowledge of one-loop radiative corrections with non-vanishing gluon mass. We find that higher order corrections to the pole mass and the top quark decay width are dominated by renormalons already in low orders and demonstrate the impact of eliminating the pole mass on the convergence of the perturbative series.

hep-ph↗
arXiv1994

More on ambiguities in the pole mass

The relation between the pole quark mass and the $\overline{MS}$-renormalized mass is governed by an infrared renormalon singularity, which leads to an ambiguity of order $Λ_{QCD}$ in the definition of the pole mass. We use the renormalization group and heavy quark effective theory to determine the exact nature of this singularity up to an overall normalization. In the abelian gauge theory, the normalization is computed partially to next-to-leading order in the flavour expansion.

hep-ph↗
arXiv1994

Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term

We study the asymptotic behaviour of the perturbative series in the heavy quark effective theory (HQET) using the $1/N_f$ expansion. We find that this theory suffers from an {\it ultraviolet} renormalon problem, corresponding to a non-Borel-summable behaviour of perturbation series in large orders, and leading to a principal nonperturbative ambiguity in its definition. This ambiguity is related to an {\it infrared} renormalon in the pole mass and can be understood as the necessity to include the residual mass term $δm$ in the definition of HQET, which must be considered as ambiguous (and possibly complex), and is required to cancel the ultraviolet renormalon singularity generated by the perturbative expansion. The formal status of $δm$ is thus identical to that of condensates in the conventional short-distance expansion of correlation functions in QCD. The status of the pole mass of a heavy quark, the operator product expansion for inclusive decays, and QCD sum rules in the HQET are discussed in this context.

hep-ph↗
arXiv1994

Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays

We investigate the one-loop radiative corrections to the semileptonic decay of a charged particle at finite gauge boson mass. Extending the Bloch-Nordsieck cancellation of infrared logarithms, the subsequent non-analytic terms are also found to vanish after eliminating the pole mass in favor of a mass defined at short distances. This observation justifies the operator product expansion for inclusive decays of heavy mesons and implies that infrared effects associated with the summation of the radiative corrections are suppressed by at least three powers of the mass of the heavy decaying particle.

hep-ph↗
arXiv1993

Instanton contributions to the $τ$ decay widths

Contrary to some previous claims, we find a sizable instanton contribution to the finite energy sum rule used to extract the value of the strong coupling from the measured $τ$ decay widths. It is of the same order of magnitude as standard nonperturbative corrections induced by vacuum quark and gluon condensates. Our result indicates that there might be no hierarchy of power corrections in finite energy sum rules at the scale of $τ$ mass. Therefore, the standard nonperturbative corrections do not necessarily improve the accuracy of the theoretical predicition, but can rather be used to estimate an intrinsic accuracy of the pure perturbative calculation, which turns out to be rather high on this evidence, of order one percent.

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