1,233 research outputs found

### 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 $|V_{cb}|$

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 $b\to c$ 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

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