Simply modeling meson heavy-quark effective theory

Holdom, Bob; Sutherland, Mark

doi:10.1103/physrevd.47.5067

Cited by 23 publications

(50 citation statements)

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“…A model for baryon transition amplitudes may then be constructed by joining external baryons to a quark-diquark loop with specified vertices and propagators. (Similar models have been defined for mesons in [6] and for Λ Q baryons in [7].) One of the main advantages of such a model is that recoil effects are incorporated in a completely relativistic way in the loop graphs.…”

Section: ( * )mentioning

confidence: 99%

“…It is possible to make rough estimates of m and Λ, and hence α. In [6] and [7], reasonable values of m q = 250 and 2m q = 500 MeV were found for the nonstrange light quark and scalar diquark masses, respectively. The light quark hyperfine interaction causes Σ c to be heavier than Λ c by 170 MeV.…”

Section: ( * )mentioning

confidence: 99%

“…The same holds for the semileptonic decay form factors; they all have imaginary parts for the same reason as the mass functions do, and only the real parts are retained in the model. It was demonstrated in [6] and [7] that this procedure is consistent with the form of the heavy-quark expansion dictated by QCD in the case of mesons and Λ Q baryons, respectively, that it preserves the Ward identities, and that it leads to sensible physical predictions. Heavy-quark symmetries relate properties of Ω baryons to those of Ω * .…”

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confidence: 97%

“…3, and are expanded using (4), (5) and (6). At zeroth order, consistency with the form shown in Tables 1 and 2 is almost trivial, a consequence of the equality of the vertex factors in the heavy-quark limit and of some standard gamma-matrix algebra.…”

Section: ( * )mentioning

confidence: 99%

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1/m c expansion of Ω b () →Ω c () semileptonic decay form factors

Sutherland

1994

Z. Phys. C - Particles and Fields

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A simple model of Ω Q and Ω * Q baryons containing one heavy quark Q is constructed. Amplitudes are represented by loop graphs with one line for the heavy quark and another for the light degrees of freedom. The latter are modelled as a freely-propagating vector particle interacting nonlocally with the heavy baryon and a free heavy quark. It is argued that the physics of confinement plays an inessential role in determining semileptonic decay form factors. The model has a well-defined heavy-quark expansion which has a form consistent (through order 1/m Q ) with that determined by QCD through the heavy-quark effective theory. The slope of the Isgur-Wise function is consistent with the Bjorken sum rule bound. The effect of the Ω * Q − Ω Q mass splitting on the first-order form factors is examined.There is presently a large amount of theoretical interest in properties of baryons with one heavy quark Q. This is because the spin-flavor symmetries of QCD in the limit m Q → ∞ give rise to relations between certain weak decay form factors and to model-independent absolute normalizations for others at zero recoil [1,2]. More generally, the heavy-quark effective theory (HQET) may be used to derive relations among the many a priori independent corrections to the form factors at any order in the expansion in inverse powers of heavy quark masses. (For a review, see [3].) This information serves to organize and classify the unknown quantities of QCD, but to be of real use it remains necessary to have a model with which to perform computations. Of course, the QCD relations must be checked in any particular model for consistency. One case in which such considerations place constraints on model parameters is described in [4]. The purpose of this paper is to define a model for Ω Q and Ω ( * )Q baryons and to show that it is consistent with the form of the heavy-quark expansion in QCD at order 1/m Q as derived in [5], with no extra constraints on its parameters.In the heavy-quark limit, the Ω Q and Ω ( * ) Q are the s = 1/2 and s = 3/2 combinations, respectively, of a heavy quark Q and light degrees of freedom with ss quantum numbers and unit spin. The latter may be regarded as a vector particle, hereafter referred to as a diquark. A model for baryon transition amplitudes may then be constructed by joining external baryons to a quark-diquark loop with specified vertices and propagators. (Similar models have been defined for mesons in [6] and for Λ Q baryons in [7].) One of the main advantages of such a model is that recoil effects are incorporated in a completely relativistic way in the loop graphs. An essential physical effect of soft gluons is to damp out the loop momentum integrals, and this may be accomplished by including damping factors at the baryon-quark-diquark vertices. The model vertices are chosen to be those shown in Fig. 1. The Lorentz structure is determined by heavy-quark symmetry [2]. Standard propagators with constant masses m Q and m are used for heavy quark and diquark, respectively; the propagator for th...

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Section: ( * )mentioning

confidence: 99%

Section: ( * )mentioning

confidence: 99%

mentioning

confidence: 97%

Section: ( * )mentioning

confidence: 99%

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1/m c expansion of Ω b () →Ω c () semileptonic decay form factors

Sutherland

1994

Z. Phys. C - Particles and Fields

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“…Models related to the one discussed here, with different regularization prescriptions and different approaches are [4,5]. The cut-off prescription used here is implemented via a proper time regularization.…”

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A quark loop model for heavy mesons

Deandrea¹

2001

AIP Conference Proceedings

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Abstract. I consider a model based on a quark-meson interaction Lagrangian. The transition amplitudes are evaluated by computing diagrams in which heavy and light mesons are attached to quark loops. The light chiral symmetry relations and the heavy quark spin-flavour symmetry dictated by the heavy quark effective theory are implemented. The model allows to compute the decay form factors and therefore can give predictions for the decay rates, the invariant mass spectra and the asymmetries.

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Anomalous thresholds and the Isgur-Wise function

Holdom

Sutherland

1995

Z. Phys. C - Particles and Fields

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The original de Rafael-Taron bound on the slope of the Isgur-Wise function at zero recoil is known to be violated in QCD by singularities appearing in an unphysical region. To be consistent, quark models must have corresponding singularity structures. In an existing relativistic quark-loop model, the mesonquark-antiquark vertex is such that the required singularity is an anomalous threshold. We also discuss the implications of another anomalous threshold, whose location is determined by quark masses alone. a holdom@utcc.utoronto.ca b marks@medb.physics.utoronto.caThe properties of QCD as the quark masses m b , m c → ∞ [1] imply that the spectrum of the semileptonic decay B → D * ℓν at the zero-recoil point ω ≡ v B ·v D * = 1 is absolutely normalized at leading order and receives no corrections at order 1/m Q [2]. This gives rise to the possibility of a precise measurement of V cb [3], provided a) the corrections beginning at order 1/m 2 Q are proven to be negligible, and b) a way can be found to extrapolate from the data at nonzero recoil ω > 1 back to the zero-recoil point, where the rate vanishes kinematically. The latter requires knowledge of the shape of the Isgur-Wise function ξ(ω) which determines the spectrum at leading order and satisfies ξ(1) = 1. [In practice, it also requires knowledge of the magnitude and shape of the higher-order corrections, which are nonvanishing away from zero recoil even at order 1/m Q .]In this letter we wish to look at the leading-order problem, namely the shape of the Isgur-Wise function. Some time ago, de Rafael and Taron derived a lower bound on its slope at zero recoil [4], the value of which is ξ ′ (1) ≥ −0.89 [5]. This bound has since been shown to depend on assumptions which are not true in QCD. The bound also seems to be at odds with the data which favors a slope somewhat more negative than −1. We view any significant violation of the bound as providing an interesting clue to the underlying physics.In particular it was pointed out by several groups [6] that the original derivation assumed that the b-number form factor F (q 2 ) defined byis analytic in the region below the BB threshold at q 2 = 4M 2 B . The singularities corresponding to the three Υ's which lie just below threshold were ignored. These singularities can cause ∂F/∂q 2 to become more positive at q 2 = 0. A quantitative estimate of the contribution of these singularities to the slope requires knowledge of the couplings of the Υ's to the vacuum and the BB pair, and involves large uncertainties [5,6].In the heavy-quark limit m b → ∞, the Isgur-Wise function is related to F byso the effect of the singularities is to allow ξ ′ (ω) to become more negative at ω = 1. In the following, we will use ω as the variable. The BB threshold occurs at ω = −1, and the original derivation of the bound assumed that ξ(ω) is analytic for all ω > −1.The authors of the first three papers of Ref.[6] also pointed out that it is possible to construct an example of a meson for which the slope would be large and negative even w...

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Simply modeling meson heavy-quark effective theory

Cited by 23 publications

References 24 publications

1/m c expansion of Ω b () →Ω c () semileptonic decay form factors

1/m c expansion of Ω b () →Ω c () semileptonic decay form factors

A quark loop model for heavy mesons

Anomalous thresholds and the Isgur-Wise function

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Simply modeling meson heavy-quark effective theory

Cited by 23 publications

References 24 publications

1/m c expansion of Ω b (*) →Ω c (*) semileptonic decay form factors

1/m c expansion of Ω b (*) →Ω c (*) semileptonic decay form factors

A quark loop model for heavy mesons

Anomalous thresholds and the Isgur-Wise function

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Resources

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1/m c expansion of Ω b () →Ω c () semileptonic decay form factors

1/m c expansion of Ω b () →Ω c () semileptonic decay form factors