Effective Field Theory and Heavy Quark Physics

These notes are based on five lectures presented at the 2004 Theoretical Advanced Study Institute (TASI) on ``Physics in D>=4''. After a brief motivation of flavor physics, they provide a pedagogical introduction to effective field theory, the effective weak Lagrangian, and the technology of renormalization-group improved perturbation theory. These general methods are then applied in the context of heavy-quarks physics, introducing the concepts of heavy-quark and soft-collinear effective theory.Comment: Lectures presented at TASI 2004 (39 pages

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 $R_\tau$ are discussed in detail.Comment: 37 pages LaTeX, uses epsf, 8 figures. Largely revised version with an extended discussion and several new result

Uncertainties in the Determination of ∣Vcb∣|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 $B\to D^*\ell\,\bar\nu$ and for the inclusive channel $B\to X\,\ell\,\bar\nu$. 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 $\widehat\varrho^2=0.8\pm 0.3$.Comment: Proceedings of 1995 Moriond Conference on Electroweak Interactions and Unified Theories, 11 pages, 3 figures available as uu-encoded postscript file

Soft-Collinear Factorization and the Calculation of the B->Xs+gamma Rate

Using results on soft-collinear factorization for inclusive B-meson decay distributions, a systematic study of the partial B->Xs+gamma decay rate with a cut E_gamma<E_0 on photon energy is performed. For values E_0<1.9 GeV the rate can be calculated without reference to shape functions. The result depends on three large scales: m_b, \sqrt{m_b Delta}, and Delta=m_b-2E_0. The sensitivity to the scale Delta=1.1 GeV (for E_0=1.8 GeV) introduces significant uncertainties, which have been ignored in the past. Our new prediction for the B->Xs+gamma branching ratio with E_gamma<1.8 GeV is Br(B->Xs+gamma)=(3.44+-0.53+-0.35)*10^{-4}, where the errors refer to perturbative and parameter uncertainties, respectively. The implications of larger theory uncertainties for New Physics searches are explored with the example of the type-II two-Higgs-doublet model.Comment: Invited talk presented at the 39th Rencontres de Moriond: Electroweak Interactions and Unified Theories (La Thuile, Italy, 21-28 March 2004), and at Continuous Advances in QCD 2004 (Minneapolis, Minnesota, 13--16 May 2004). 11 pages, 1 figur

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

We estimate the two-loop perturbative corrections to zero-recoil matrix elements of the flavour-changing currents $\bar c\,\gamma^\mu b$ and $\bar c\,\gamma^\mu\gamma_5\,b$ by calculating the terms of order $n_f\,\alpha_s^2$ and substituting the dependence on the number of flavours by the first coefficient of the $\beta$-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-$\alpha_s$ corrections in the $\overline{\rm MS}$ scheme, we obtain $\mu_V\simeq 0.92\sqrt{m_b m_c}$ and $\mu_A\simeq 0.51\sqrt{m_b m_c}$ 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.Comment: 9 pages LaTeX, CERN-TH.7454/9

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, $-\lambda_1/2 m_Q$, which is consistent with the field-theory analog of the virial theorem. We obtain -\lambda_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 \lambda_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.Comment: 13 pages LaTeX (A4), 3 figure