2,656 research outputs found
Precision Studies of Duality in the 't Hooft Model
We address numerical aspects of local quark-hadron duality using the example
of the exactly solvable 't Hooft model, two-dimensional QCD with N_c -->
infinity. The primary focus of these studies is total semileptonic decay widths
relevant for extracting |V_{cb}| and |V_{ub}|. We compare the exact
channel-by-channel sum of exclusive modes to the corresponding rates obtained
in the standard 1/m_Q expansion arising from the Operator Product Expansion. An
impressive agreement sets in unexpectedly early, immediately after the
threshold for the first hadronic excitation in the final state. Yet even at
higher energy release it is possible to discern the seeds of duality-violating
oscillations. We find the ``Small Velocity'' sum rules to be exceptionally well
saturated already by the first excited state. We also obtain a convincing
degree of duality in the differential distributions and in an analogue of
R_{e^+e^-}(s). Finally, we discuss possible lessons for semileptonic decays of
actual heavy quarks in QCD.Comment: 45 pages, 16 eps figures include
A Vademecum on Quark-Hadron Duality
We present an elementary introduction to the problem of quark-hadron duality
and its practical limitations, in particular as it concerns local duality
violation in inclusive B meson decays. We show that the accurate definition of
duality violation elaborated over the recent years allows one to derive
informative constraints on violations of local duality. The magnitude of
duality violation is particularly restricted in the total semileptonic widths.
This explains its strong suppression in concrete dynamical estimates. We
analyze the origin of the suppression factors in a model-independent setting,
including a fresh perspective on the Small Velocity expansion. A new
potentially significant mechanism for violation of local duality in
\Gamma_sl(B) is analyzed. Yet we conclude that the amount of duality violation
in \Gamma_sl(B) must be safely below the half percent level, with realistic
estimates being actually much smaller. Violation of local duality in
\Gamma_sl(B) is thus far below the level relevant to phenomenology. We also
present a cautionary note on the B->D^* decay amplitude at zero recoil and show
that it is much more vulnerable to violations of quark-hadron duality than
\Gamma_sl(B). A critical review of some recent literature is given. We point
out that the presently limiting factor in genuinely model-independent
extraction of V_cb is the precise value of the short-distance charm quark mass.
We suggest a direct and precise experimental check of local quark-hadron
duality in semileptonic B->X_c l\nu decays.Comment: 48 pages, 4 figures; LaTe
Final state phases in B -> D\pi, \bar{D}\pi decays and CP-asymmetry
Final state phases \delta_f and \delta_f' in B-> D pi, barD pi decays are
shown to be equal i.e. \delta =\delta_f-\delta_f' = 0. Thus CP-violating
asymmetry A(t) is independent of final state phases. The estimate for the
phases \delta_f and \delta_f' is also given.Comment: 6 pages, no figur
Transverse Momentum Distribution in b-> s Gamma
We present the complete calculation of the transverse momentum distribution
for the decay b->s Gamma. The contributions of the leading operator O_7 are
computed: infrared logarithms are resummed with next-to-leading accuracy,
according to usual techniques of resummation. Non logarithmic terms are
evaluated to O(alpha_S) by calculating one loop diagrams.Comment: Talk given 10th International QCD Conference (QCD 03), Montpellier,
France, 2-9 Jul 2003. 4 page
Analytical Heavy Quark Expansion in the 't Hooft Model
We present a number of exact relations for the heavy quark limit and develop
an analytical 1/m_Q expansion for heavy mesons in the 't Hooft model. Among the
new results are relation 3\mu_\pi^2=\bar\Lambda^2 - m_{sp}^2+\beta^2, 1/m_Q
corrections to the decay constants, to the kinetic expectation values and
1/m_Q^2 nonperturbative corrections to the B->D amplitude at zero recoil. The
properties of the IW functions are addressed and the small velocity sum rules
are verified.Comment: 22 pages, plain LaTeX (no figures
Hadron Spectra for Semileptonic Heavy Quark Decay
We calculate the leading perturbative and power corrections to the hadronic
invariant mass and energy spectra in semileptonic heavy hadron decays. We apply
our results to the system. Moments of the invariant mass spectrum, which
vanish in the parton model, probe gluon bremsstrahlung and nonperturbative
effects. Combining our results with recent data on meson branching ratios,
we obtain a lower bound and an upper bound
GeV. The Brodsky-Lepage-Mackenzie scale setting
procedure suggests that higher order perturbative corrections are small for
bottom decay, and even tractable for charm decay.Comment: 24 pages, uses REVTeX, 5 EPS figures embedded with epsf.sty, slightly
modified version to appear in Phys. Rev.
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