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Matthias Neubert

Publications and source records attributed to Matthias Neubert.

At least 199 records · Page 11Linked to original sources
arXiv1997

Hybrid Renormalization of Penguins and Dimension-5 Heavy--Light Operators

We discuss the renormalization of local, scalar and pseudoscalar dimension-5 operators containing a heavy and a light quark field at scales below the heavy-quark mass, using the formalism of the heavy-quark effective theory (HQET). We calculate the anomalous dimensions of these operators and their mixing to one-loop order. We also perform the one-loop matching of gluon and photon penguin operators onto operators of the HQET. We discuss applications of our results to the mixing of gluon and photon penguin operators at low renormalization scales, and to the calculation of $1/m_Q^2$ corrections to meson decays constants.

hep-ph↗
arXiv1996

Exploring the Invisible Renormalon: Renormalization of the Heavy-Quark Kinetic Energy

Using the virial theorem of the heavy-quark effective theory, we show that the mixing of the operator for the heavy-quark kinetic energy with the identity operator is forbidden at the one-loop order by Lorentz invariance. This explains why such a mixing was not observed in several one-loop calculations using regularization schemes with a Lorentz-invariant UV regulator, and why no UV renormalon singularity was found in the matrix elements of the kinetic operator in the bubble approximation (the ``invisible renormalon''). On the other hand, we show that the mixing is not protected in general by any symmetry, and it indeed occurs at the two-loop order. This implies that the parameter $λ_1^H$ of the heavy-quark effective theory is not directly a physical quantity, but requires a non-perturbative subtraction.

hep-ph↗
arXiv1996

Heavy-Quark Effective Theory

We give an introduction to the heavy-quark effective theory and the $1/m_Q$ expansion, which provide the modern framework for a systematic, model-independent description of the properties and decays of hadrons containing a heavy quark. We discuss the applications of these concepts to spectroscopy and to the weak decays of $B$ mesons.

hep-ph↗
arXiv1996

Heavy-Quark Effective Theory

We give an introduction to the heavy-quark effective theory and the $1/m_Q$ expansion, which provide the modern framework for a systematic, model-independent description of the properties and decays of hadrons containing a heavy quark. We discuss the applications of these concepts to spectroscopy and to the weak decays of $B$ mesons.

hep-ph↗
arXiv1996

QCD Sum-Rule Calculation of the Kinetic Energy and Chromo-Interaction of Heavy Quarks Inside Mesons

We present a QCD sum-rule determination of the heavy-quark kinetic energy inside a heavy meson, $-λ_1/2 m_Q$, which is consistent with the field-theory analog of the virial theorem. We obtain $-λ_1\approx (0.10\pm 0.05)~\mbox{GeV}^2$, significantly smaller than a previous sum-rule result, but in good agreement with recent determinations from the analysis of inclusive decays. We also present a new determination of the chromo-magnetic interaction, yielding $λ_2(m_b)=(0.15\pm 0.03)~\mbox{GeV}^2$. This implies $m_{B^*}^2-m_B^2=(0.60\pm 0.12)~\mbox{GeV}^2$, in good agreement with experiment. As a by-product of our analysis, we derive the QCD sum rules for the three form factors describing the meson matrix element of a velocity-changing current operator containing the gluon field-strength tensor.

hep-ph↗
arXiv1996

Asymptotics of Heavy-Meson Form Factors

Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\ll |v\cdot v'|\ll m_Q/Λ$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\cdot v'|\gg m_Q/Λ$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\cdot v'|\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\cdot v'\sim m_b/Λ$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\cdot v'\sim -m_b/Λ$). We obtain the evolution equations and sum rules for the wave functions of leading and subleading twist as well as for their moments. We briefly discuss applications to heavy-meson pair production in $e^+ e^-$ collisions.

hep-ph↗
arXiv1996

Measuring $α_s(Q^2)$ in $τ$ Decays

The decay rate of the $τ$ lepton into hadrons of invariant mass smaller than $Q\ggΛ_{\rm QCD}$ can be calculated in QCD using the OPE. Using experimental data on the hadronic mass distribution, the running coupling constant $α_s(Q^2)$ is extracted in the range $0.85~\mbox{GeV}<Q<m_τ$, where its value changes by about a factor~2. At $Q=m_τ$, the result is $α_s(m_τ^2)=0.33\pm 0.03$, corresponding to $α_s(m_Z^2)=0.119\pm 0.004$. The running of the coupling constant is in excellent agreement with the QCD prediction based on the three-loop $β$-function.

hep-ph↗
arXiv1996

B Decays and CP Violation

We review the status of the theory and phenomenology of heavy-quark symmetry, exclusive weak decays of $B$ mesons, inclusive decay rates and lifetimes of $b$ hadrons, and CP violation in $B$-meson decays.

hep-ph↗
arXiv1996

Test of the Running of $α_s$ in $τ$ Decays

The $τ$ decay rate into hadrons of invariant mass smaller than $\sqrt{s_0}\ggΛ_{\rm QCD}$ can be calculated in QCD assuming global quark--hadron duality. It is shown that this assumption holds for $s_0>0.7$~GeV$^2$. From measurements of the hadronic mass distribution, the running coupling constant $α_s(s_0)$ is extracted in the range 0.7~GeV$^2<s_0<m_τ^2$. At $s_0=m_τ^2$, the result is $α_s(m_τ^2)=0.329\pm 0.030$. The running of $α_s$ is in good agreement with the QCD prediction.

hep-ph↗
arXiv1996

Improved Bounds for the Slope and Curvature of $\bar B\to D^{(*)}\ell\barν$ Form Factors

We derive a theoretically allowed domain for the slope $\widehat\varrho^2$ and curvature $\widehat c$ of the physical form factor appearing in the decay $\bar B\to D^*\ell\barν$. Using heavy-quark symmetry, we relate this function to a particular $\bar B \to D$ form factor free of ground-state $B_c$ poles below the threshold for $B D$ production, for which almost model-independent constraints are derived from QCD using unitarity and analyticity. Our results are of interest for the extraction of $|V_{cb}|$ from the recoil spectrum in exclusive semileptonic $B$ decays. Making conservative estimates of the theoretical uncertainties, we find (up to $1/m_Q$ corrections) $\widehat\varrho^2<1.11$ and $\widehat c\simeq 0.66\widehat\varrho^2-0.11$. We also derive the corresponding bounds for the form factor in the decay $\bar B\to D\ell\barν$.

hep-ph↗
arXiv1995

Heavy Flavour Physics

The current status of the theory and phenomenology of weak decays of hadrons containing a heavy quark is reviewed. Exclusive semileptonic and rare decays of $B$ mesons are discussed, as well as inclusive decay rates, the semileptonic branching ratio of the $B$ meson, and the lifetimes of $b$-flavoured hadrons. Determinations of $α_s$ from $Υ$ spectroscopy are briefly presented.

hep-ph↗
arXiv1995

QCD Analysis of Hadronic $τ$ Decays Revisited

The calculation of perturbative corrections to the spectral moments observable in hadronic $τ$ decays is reconsidered. The exact order-$α_s^3$ results and the resummation procedure of Le~Diberder and Pich are compared with a partial resummation of the perturbative series based on the analysis of so-called renormalon chains. The perturbative analysis is complemented by a model-independent description of power corrections. For the contributions of dimension four and six in the OPE, it is demonstrated how infrared renormalon ambiguities in the definition of perturbation theory can be absorbed by a redefinition of nonperturbative parameters. We find that previous determinations of QCD parameters from a measurement of spectral moments in $τ$ decays have underestimated the theoretical uncertainties. Given the present understanding of the asymptotic behaviour of perturbation theory, the running coupling constant can be measured at best with a theoretical uncertainty $δα_s(m_τ^2)\simeq 0.05$, and the gluon condensate with an uncertainty of order its magnitude. Two weighted integrals of the hadronic spectral function are constructed, which can be used to test the absence of dimension-two operators and to measure directly the gluon condensate.

hep-ph↗
arXiv1995

Uncertainties in the Determination of $|V_{cb}|$

I discuss the theoretical uncertainties in the extraction of $|\,V_{cb}|$ from semilep\-to\-nic decays of $B$ mesons, taking into account the most recent theoretical developments. The main sources of uncertainty are identified both for the exclusive decay mode $B\to D^*\ell\,\barν$ and for the inclusive channel $B\to X\,\ell\,\barν$. From an analysis of the available experimental data, I obtain $|\,V_{cb}|_{\rm excl} = 0.041\pm 0.003_{\rm exp}\pm 0.002_{\rm th}$ from the exclusive mode, and $|\,V_{cb}|_{\rm incl} = 0.040\pm 0.001_{\rm exp}\pm 0.005_{\rm th}$ from the inclusive mode. I also give a prediction for the slope of the form factor ${\cal{F}}(w)$ at zero recoil, which is $\widehat\varrho^2=0.8\pm 0.3$.

hep-ph↗
arXiv1995

Resummation of Renormalon Chains for Cross Sections and Inclusive Decay Rates

Recently, we have developed a formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. This corresponds to an all-order resummation of certain terms (the so-called renormalon chains) in a perturbative series and provides a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie. In its original form, the method is applicable to Green functions without external gluons and to euclidean correlation functions. Here we generalize the approach to the case of cross sections and inclusive decay rates, which receive both virtual and real gluon corrections. We encounter nonperturbative ambiguities in the resummation of the perturbative series, which may hinder the construction of the operator product expansion in the physical region. The origin of these ambiguities and their relation to renormalon singularities in the Borel plane is investigated by introducing an explicit infrared cutoff. The ratios $R_{e^+ e^-}$ and $R_τ$ are discussed in detail.

hep-ph↗
arXiv1994

Scale Setting in QCD and the Momentum Flow in Feynman Diagrams

We present a formalism to evaluate QCD diagrams with a single virtual gluon using a running coupling constant at the vertices. This method, which corresponds to an all-order resummation of certain terms in a perturbative series, provides a description of the momentum flow through the gluon propagator. It can be viewed as a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie to all orders in perturbation theory. In particular, the approach can be used to investigate why in some cases the ``typical'' momenta in a loop diagram are different from the ``natural'' scale of the process. It offers an intuitive understanding of the appearance of infrared renormalons in perturbation theory and their connection to the rate of convergence of a perturbative series. Moreover, it allows one to separate short- and long-distance contributions by introducing a hard factorization scale. Several applications to one- and two-scale problems are discussed in detail.

hep-ph↗
arXiv1994

Higher-Order Perturbative Corrections to $b\to c$ Transitions at Zero Recoil

We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents $\bar c\,γ^μb$ and $\bar c\,γ^μγ_5\,b$ by calculating the terms of order $n_f\,α_s^2$ and substituting the dependence on the number of flavours by the first coefficient of the $β$-function. Both for vector and axial vector currents, we find moderate two-loop corrections below 1\% in magnitude. Using the Brodsky--Lepage--Mackenzie prescription to set the scale in the order-$α_s$ corrections in the $\overline{\rm MS}$ scheme, we obtain $μ_V\simeq 0.92\sqrt{m_b m_c}$ and $μ_A\simeq 0.51\sqrt{m_b m_c}$ in the two cases. These scales are sufficiently large for perturbation theory to be well-behaved. The implications of our results to the extraction of $|\,V_{cb}|$ are briefly discussed.

hep-ph↗
arXiv1994

Theoretical Uncertainties in the Extraction of $|V_{cb}|$ from $\bar B\to D^*\ell\,\barν$ Decays near Zero Recoil

I discuss the theoretical uncertainties in the extraction of $|\,V_{cb}|$ from a measurement of the $\bar B\to D^*\ell\,\barν$ decay rate close to zero recoil. In particular, I combine previous estimates of the $1/m_Q^2$ corrections to the normalization of the hadronic form factor at zero recoil with sum rules derived by Shifman {\it et al}.\ to obtain a new prediction with less uncertainty. I also give a prediction for the slope of the form factor $\widehatξ(w)$ at zero recoil: $\widehat\varrho^2=0.7\pm 0.2$. Using the most recent experimental results, I obtain the model-independent value $|\,V_{cb}|=0.0395\pm 0.0030$.

hep-ph↗