arXiv subjects

Matthias Neubert

Publications and source records attributed to Matthias Neubert.

214 records · Page 12Linked to original sources

arXiv1994

Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory

Recently, it has been shown that the concept of the pole mass of a heavy quark becomes ambiguous beyond perturbation theory, because of the presence of infrared renormalons. We argue that the predictions of heavy quark effective theory, whose construction is based on the pole mass, are free of such ambiguities. In the $1/m_Q$ expansion of physical quantities, infrared and ultraviolet renormalons compensate each other between coefficient functions and matrix elements. We trace the appearance of these compensations for current-induced exclusive heavy-to-heavy and heavy-to-light transitions, and for inclusive decays of heavy hadrons. In particular, we show that the structure of the heavy quark expansion is not obscured by renormalons, and none of the predictions of heavy quark effective theory are invalidated.

hep-ph↗

arXiv1994

Resummation of Nonperturbative Corrections to the Lepton Spectrum in Inclusive $B\to X\,\ell\,\barν$ Decays

We apply the operator product expansion to resum the leading nonperturbative corrections to the endpoint region of the lepton spectrum in inclusive semileptonic $B\to X_q\,\ell\,\barν$ decays, taking into account a finite quark mass $m_q$ in the final state. We show that both for $b\to c$ and $b\to u$ transitions, it is consistent to describe these effects by a convolution of the parton model spectrum with a fundamental light-cone structure function. The moments of this function are proportional to forward matrix elements of higher-dimension operators. The prospects for an extraction of the structure function from a measurement of the lepton spectrum are discussed.

hep-ph↗

arXiv1994

Analysis of the Photon Spectrum in Inclusive $B\to X_s\,γ$ Decays

Using a combination of the operator product and heavy quark expansions, we resum the leading nonperturbative contributions to the inclusive photon spectrum in $B\to X_s\,γ$ decays. The shape of the spectrum is determined by a universal structure function, which describes the distribution of the light-cone momentum of the $b$-quark inside the $B$-meson. The moments of this function are proportional to forward matrix elements of higher-dimension operators. As a by-product, we obtain the bound $λ_1<0$ for one of the parameters of the heavy quark effective theory. The integral over the $B\to X_s\,γ$ structure function is related to the shape function that governs the fall-off of the lepton spectrum close to the endpoint in $B\to X_u\,\ell\,\barν$ decays. A measurement of the photon spectrum in rare $B$-decays can therefore help to obtain a model-independent determination of $V_{ub}$.

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arXiv1994

Heavy Quark Expansion for the Inclusive Decay $\bar B\toτ\,\barν\,X$

We calculate the differential decay rate for inclusive $\bar B\toτ\,\barν\,X$ transitions to order $1/m_b^2$ in the heavy quark expansion, for both polarized and unpolarized tau leptons. We show that using a systematic $1/m_b$ expansion significantly reduces the theoretical uncertainties in the calculation. We obtain for the total branching ratio ${\rm BR}(\bar B\toτ\,\barν\,X)=2.30\pm 0.25\%$, and for the tau polarization $A_{\rm pol}=-0.706\pm0.006$. {}From the experimental measurement of the branching ratio at LEP, we derive the upper bound $\lo\leq 0.8\gev^2$ for one of the parameters of the heavy quark effective theory.

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arXiv1993

QCD-Based Interpretation of the Lepton Spectrum in Inclusive $\bar B\to X_u\,\ell\,\barν$ Decays

We present a QCD-based approach to the endpoint region of the lepton spectrum in $\bar B\to X_u\,\ell\,\barν$ decays. We introduce a genuinely nonperturbative form factor, the shape function, which describes the fall-off of the spectrum close to the endpoint. The moments of this function are related to forward scattering matrix elements of local, higher-dimension operators. We find that nonperturbative effects are dominant over a finite region in the lepton energy spectrum, the width of which is related to the kinetic energy of the $b$-quark inside the $B$ meson. Applications of our method to the extraction of fundamental standard model parameters, among them $V_{ub}$, are discussed in detail.

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arXiv1993

A Virial Theorem for the Kinetic Energy of a Heavy Quark inside Hadrons

The formalism of the heavy quark effective theory is used to derive the field-theory analog of the virial theorem, which relates the matrix element of the kinetic energy of a heavy quark inside a hadron to a matrix element of the gluon field strength tensor. The existing QCD sum rule calculations of the kinetic energy are not consistent with this theorem.

hep-ph↗

arXiv1993

The Decay $B\toπ\ellν$ in Heavy Quark Effective Theory

We present a systematic analysis of the $B^{(*)}\toπ\,\ell\,ν$ weak decay form factors to order $1/m_b$ in the heavy quark effective theory, including a discussion of renormalization group effects. These processes are described by a set of ten universal functions (two at leading order, and eight at order $1/m_b$), which are defined in terms of matrix elements of operators in the effective theory. In the soft pion limit, the effective theory yields normalization conditions for these functions, which generalize the well-known current algebra relations derived from the combination of heavy quark and chiral symmetries to next-to-leading order in $1/m_b$. In particular, the effects of the nearby $B^*$-pole are correctly contained in the form factors of the effective theory. We discuss the prospects for a model independent determination of $|V_{ub}|$ and the $B B^*π$ coupling constant from these processes.

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arXiv1993

Short-Distance Expansion of Heavy-Light Currents at Order 1/m

The short-distance expansion of the heavy-light currents $\bar q\,γ^μQ$ and $\bar q\,γ^μγ_5\,Q$ is constructed to order $1/m_Q$, and to next-to-leading order in renormalization-group improved perturbation theory. It is shown that the $10\times 10$ anomalous dimension matrix, which describes the scale dependence of the dimension-four effective current operators in the heavy quark effective theory, is to a large extent determined by the equations of motion, heavy quark symmetry, and reparameterization invariance. The next-to-leading order expressions for the Wilson coefficients at order $1/m_Q$ depend on only five unknown two-loop anomalous dimensions, among them that of the chromo-magnetic operator.

hep-ph↗

arXiv1993

Heavy Hadron Weak Decay Form Factors to Next-to-Leading Order in 1/m

Based on the short-distance expansion of currents in the heavy quark effective theory, we derive the exact expressions for the heavy-to-heavy meson and baryon weak decay form factors to order $1/m_Q$ in the heavy quark expansion, and to all orders in perturbation theory. We emphasize that the Wilson coefficients in this expansion depend on a kinematic variable $\bar w$ that is different from the velocity transfer $w=v\cdot v'$ of the hadrons. Our results generalize existing ones obtained in the leading-logarithmic approximation. Some phenomenological applications are briefly discussed.

hep-ph↗

arXiv1993

Heavy Quark Symmetry

We review the current status of heavy quark symmetry and its applications to weak decays of hadrons containing a single heavy quark. After an introduction to the underlying physical ideas, we discuss in detail the formalism of the heavy quark effective theory, including a comprehensive treatment of symmetry breaking corrections. We then illustrate some nonperturbative approaches, which aim at a dynamical, QCD-based calculation of the universal form factors of the effective theory. The main focus is on results obtained using QCD sum rules. Finally, we perform an essentially model-independent analysis of semileptonic $B$ meson decays in the context of the heavy quark effective theory.

hep-ph↗

arXiv1993

Reparametrization invariance and the expansion of currents in the heavy quark effective theory

The coefficients appearing at leading and subleading order in the $1/m$ expansion of bilinear heavy quark currents are related to each other by imposing reparametrization invariance on both the effective current operators and the short-distance coefficient functions in the heavy quark effective theory. When combined with present knowledge about the leading order coefficients, the results allow to calculate all coefficients appearing at order $1/m$ to next-to-leading order in renormalization-group improved perturbation theory. They also provide a meaningful definition of the velocity transfer variable $v\cdot v'$ to order $1/m$.

hep-ph↗

arXiv1992

Two-loop corrections to the Isgur-Wise function in QCD sum rules

We complete the QCD sum rule analysis of the Isgur Wise form factor $ξ(v\cdot v')$ at next-to-leading order in renormalization-group improved perturbation theory. To this end, the exact result for the two-loop corrections to the perturbative contribution is derived using the heavy quark effective theory. Several techniques for the evaluation of two-loop integrals involving two different types of heavy quark propagators are discussed in detail, among them the methods of integration by parts and differential equations. The order-$α_s$ corrections to the Isgur-Wise function turn out to be small and well under control. At large recoil, they tend to decrease the form factor by $5-10\%$.

hep-ph↗

arXiv1992

Second Order Power Corrections in the Heavy Quark Effective Theory I. Formalism and Meson Form Factors

In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, this expansion is constructed at order $1/m_Q^2$. A minimal set of universal form factors is defined in terms of matrix elements of higher dimension operators in the effective theory. The zero recoil normalization conditions following from vector current conservation are derived. Several phenomenological applications of the general results are discussed in detail. It is argued that at zero recoil the semileptonic decay rates for $B\to D\,\ell\,ν$ and $B\to D^*\ell\,ν$ receive only small second order corrections, which are unlikely to exceed the level of a few percent. This supports the usefulness of the heavy quark expansion for a reliable determination of $V_{cb}$.

hep-ph↗

arXiv1992

Second Order Power Corrections in the Heavy Quark Effective Theory II. Baryon Form Factors

The analysis of $1/m_Q^2$ corrections of the previous paper is extended to the semileptonic decays of heavy baryons. We focus on the simplest case, the ground state $Λ_Q$ baryons, in which the light degrees of freedom are in a state of zero total angular momentum. The formalism, while identical in spirit, is considerably less cumbersome than for heavy mesons. The general results are applied to the semileptonic decay $Λ_b\toΛ_c\,\ell\,ν$. An estimate of the leading power corrections to the decay rate at zero recoil, which are of order $1/m_Q^2$, is presented. It is pointed out that a measurement of certain asymmetry parameters would provide a direct measurement of $1/m_Q^2$ corrections. Finally, it is shown how the analysis could be extended to include excited heavy baryons such as the $Σ_Q$ and the $Σ_Q^*$.

hep-ph↗

arXiv1992

Recent Developments in the Theory of Heavy-Quark Decays

I report on recent developments in the heavy-quark effective theory and its application to $B$ meson decays. The parameters of the effective theory, the spin-flavor symmetry limit, and the leading symmetry-breaking corrections to it are discussed. The results of a QCD sum rule analysis of the universal Isgur-Wise functions that appear at leading and subleading order in the $1/m_Q$ expansion are presented. I illustrate the phenomenological applications of this formalism by focusing on two specific examples: the determination of $V_{cb}$ from the endpoint spectrum in semileptonic decays, and the study of spin-symmetry violating effects in ratios of form factors. I also briefly comment on nonleptonic decays.

hep-ph↗

arXiv1992

The Residual Mass Term in the Heavy Quark Effective Theory

We reformulate the heavy quark effective theory in the presence of a residual mass term, which has been taken to vanish in previous analyses. While such a convention is permitted, the inclusion of a residual mass allows us to resolve a potential ambiguity in the choice of the expansion parameter which defines the effective theory. We show to subleading order in the mass expansion that physical quantities computed in the effective theory do not depend on the expansion parameter.

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