38 research outputs found
Semileptonic decays in Lattice QCD : a feasibility study and first results
We compute the decays and with finite
masses for the and quarks. We first discuss the spectral properties of
both the meson as a function of its momentum and of the and
at rest. We compute the theoretical formulae leading to the decay
amplitudes from the three-point and two-point correlators. We then compute the
amplitudes at zero recoil of which turns out not to be
vanishing contrary to what happens in the heavy quark limit. This opens a
possibility to get a better agreement with experiment. To improve the continuum
limit we have added a set of data with smaller lattice spacing. The vanishes at zero recoil and we show a convincing signal but only
slightly more than 1 sigma from 0. In order to reach quantitatively significant
results, we plan to fully exploit smaller lattice spacings as well as another
lattice regularization.Comment: 31 pages with 15 figures ; sections 5 and 6 revised and update
Uraltsev Sum Rule in Bakamjian-Thomas Quark Models
We show that the sum rule recently proved by Uraltsev in the heavy quark
limit of QCD holds in relativistic quark models \`a la Bakamjian and Thomas,
that were already shown to satisfy Isgur-Wise scaling and Bjorken sum rule.
This new sum rule provides a {\it rationale} for the lower bound of the slope
of the elastic IW function obtained within the BT
formalism some years ago. Uraltsev sum rule suggests an inequality
. This difference is interpreted in the BT
formalism as due to the Wigner rotation of the light quark spin, independently
of a possible LS force. In BT models, the sum rule convergence is very fast,
the state giving the essential contribution in most of the
phenomenological potential models. We underline that there is a serious
problem, in the heavy quark limit of QCD, between theory and experiment for the
decays , independently of any model
calculation.Comment: 16 pages, Late
One Interesting New Sum Rule Extending Bjorken's to order {1/m_Q}
We explicitly check quark-hadron duality to order
for decays in the limit including ground state
and orbitally excited hadrons. Duality occurs thanks to a new sum rule which
expresses the subleading HQET form factor or, in other notations,
in terms of the infinite mass limit form factors and some level
splittings. We also demonstrate the sum rule, which is not restricted to the
condition , applying OPE to the longitudinal axial component
of the hadronic tensor without neglecting the subleading contributions
to the form factors. We argue that this method should produce a new class of
sum rules, depending on the current, beyond Bjorken, Voloshin and the known
tower of higher moments. Applying OPE to the vector currents we find another
derivation of the Voloshin sum rule. From independent results on we
derive a sum rule which involves only the and
form factors and the corresponding level splittings. The
latter strongly supports a theoretical evidence that the semileptonic decay
into narrow orbitally-excited resonances dominates over the decay into the
broad ones, in apparent contradiction with some recent experiments. We discuss
this issue.Comment: 9 page
Duality in the non-relativistic harmonic oscillator quark model in the Shifman-Voloshin limit : a pedagogical example
The detailed way in which duality between sum of exclusive states and the
free quark model description operates in semileptonic total decay widths, is
analysed. It is made very explicit by the use of the non relativistic harmonic
oscillator quark model in the SV limit, and a simple interaction current with
the lepton pair. In particular, the Voloshin sum rule is found to eliminate the
mismatches of order .Comment: 11 pages, Latex2e, AMS-LaTe
On P-wave meson decay constants in the heavy quark limit of QCD
In previous work it has been shown that, either from a sum rule for the
subleading Isgur-Wise function or from a combination of Uraltsev and
Bjorken SR, one infers for -wave states . This implies, in the heavy quark limit of QCD, a hierarchy
for the {\it production} rates of -states that seems at
present to be contradicted by experiment. It was also shown that the decay
constants of -states vanish in the heavy quark limit of
QCD, . Assuming the {\it model} of factorization in the
decays , one expects the opposite hierarchy for
the {\it emission} rates , since
-states are coupled to vacuum. Moreover, using Bjorken SR and previously
discovered SR involving heavy-light meson decay constants and IW functions, one
can prove that the sums ,
(where and
are the decay constants of -states and
-states) are divergent. This situation seems to be realized in the
relativistic quark models \`a la Bakamjian and Thomas, that satisfy HQET and
predict decays constants and that do not decrease
with the radial quantum number .Comment: 7 pages, Late
Decay constants in the heavy quark limit in models \`a la Bakamjian and Thomas
In quark models \`a la Bakamjian and Thomas, that yield covariance and
Isgur-Wise scaling of form factors in the heavy quark limit, we compute the
decay constants and of S-wave and P-wave mesons
composed of heavy and light quarks. Heavy quark limit scaling is obtained, and it is shown that this class of models satisfies the sum
rules involving decay constants and Isgur-Wise functions recently formulated by
us in the heavy quark limit of QCD. Moreover, the model also satisfies the
selection rules of the type that must hold in this limit.
We discuss different Ans\"atze for the dynamics of the mass operator at rest.
For non-relativistic kinetic energies the decay constants are
finite even if the potential has a Coulomb part. For the relativistic
form , the S-wave decay constants diverge if there is a
Coulomb singularity. Using phenomenological models of the spectrum with
relativistic kinetic energy and regularized short distance part (Godfrey-Isgur
model or Richardson potential of Colangelo et al.), that yield for the elastic Isgur-Wise function, we compute the decay constants in the
heavy quark limit, and obtain 300 MeV, of the same order although
slightly smaller than in the static limit of lattice QCD. We find the decay
constants of with of the same order of magnitude. The
convergence of the heavy quark limit sum rules is also studied.Comment: 21 pages, 2 figures, LaTeX2e, amsbsy (from the AMS-LaTeX package),
eps
semileptonic decay in covariant quark models \`a la Bakamjian Thomas
Once chosen the dynamics in one frame, for example the rest frame, the
Bakamjian and Thomas method allows to define relativistic quark models in any
frame. These models have been shown to provide, in the heavy quark limit, fully
covariant current form factors as matrix elements of the quark current
operator. They also verify the Isgur-Wise scaling and give a slope parameter
for all the possible choices of the dynamics. In this paper we
study the excited states and derive the general formula, valid for any
dynamics, for the scaling invariant form factors and
. We also check the Bjorken-Isgur-Wise sum rule already
demonstrated elsewhere in this class of models.Comment: 14 pages, Latex2e, AMS-LaTe
Slope of the Isgur-Wise function in the heavy mass limit of quark models \`a la Bakamjian-Thomas
The slope of the Isgur-Wise function for ground state mesons is evaluated for
the heavy mass limit of quark models \`a la Bakamjian-Thomas, which has been
previously discussed by us in general terms. A full calculation in various
spectroscopic models with relativistic kinetic energy gives a rather stable
result , much lower than previous estimates. Attention is
paid to a careful comparison of this result with the ones of QCD fundamental
methods (lattice QCD, QCD sum rules) and with experimental data.Comment: 15 pages, Latex, AMS-LaTe