No abstract

We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parameterizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic estimates of truncation errors associated with the parameterizations. We include higher resonances in the hadronic sum that, * boyd@fermi.phys.cmu.edu † bgrinstein@ucsd.edu ‡ rlebed@ucsd.edu 1 together with heavy quark symmetry relations near zero recoil, further tighten the sum rule bounds. Utilizing all these improvements, we show that each of the six form factors inB → Dℓν andB → D * ℓν can be described with 3% or smaller precision using only the overall normalization and one unknown parameter. A similar one-coefficient parameterization of one of the Λ b → Λ c ℓν form factors, together with heavy quark symmetry relations valid to order 1/m 2 , describes the differential baryon decay rate in terms of one unknown parameter and the phenomenologically interesting quantityΛWe discuss the validity of slope-curvature relations derived by Caprini and Neubert, and present weaker, corrected relations. Finally, we present sample fits of current experimentalB → D * ℓν andB → Dℓν data to the improved one-parameter expansion.

We use rigorous QCD dispersion relations to derive model-independent bounds on the B → πlν, D → πlν and D → K lν form factors. These bounds are particularly restrictive when the value of the observable form factor at one or more kinematic points is assumed.With reasonable assumptions we find f B ≤ 195 MeV and that the shape of the form factor becomes severely constrained. These constraints are useful both for model discrimination and for model-insensitive extraction of CKM mixing parameters.

We consider in detail the mass operator analysis for the nonstrange lϭ1 excited baryons in large N c QCD. We present a straightforward procedure for constructing the large N c baryon wave functions, and provide complete analytic expressions for the matrix elements of all the independent isosinglet mass operators. We discuss the relationship between the old-fashioned operator analyses based on nonrelativistic SU͑6͒ symmetry and the modern large N c approach, which has a firmer theoretical foundation. We then suggest a possible dynamical interpretation for the subset of operators preferred strongly by the data. ͓S0556-2821͑99͒07809-1͔

UCSD/PTH 95-01 hep-ph/9502227The I = 0, 1, 2, 3 mass splittings of the spin-1/2 octet and spin-3/2 decuplet baryons are analyzed in the 1/Nc expansion combined with perturbative flavor breaking. We show there is considerable experimental evidence that the baryon masses satisfy the hierarchy predicted by this expansion. Since flavor symmetry-breaking suppression factors alone are not sufficient to describe the observed hierarchy, we conclude that there is firm evidence for the 1/Nc expansion in the baryon masses. Our analysis differs from non-relativistic SU (6).

Starting with the dynamical picture of the exotic cc-containing states XYZ as the confinementinduced hadronization of a rapidly separating pair of a compact diquark and antidiquark, we describe the pentaquark candidates P + c (4380) and P + c (4450) in terms of a confined but rapidly separating color-antitriplet diquark cu and color-triplet "triquark"c(ud). This separation explains the relatively small P + c widths, despite these 5-quark systems lying far above both the J/ψ p and ΛcD ( * )0 thresholds. The P + c states are predicted to form isospin doublets with neutral partners P 0 c .

We present the first phenomenological study of the masses of orbitally excited baryons in large N c QCD. Restricting here to the nonstrange sector of the ℓ = 1 baryons, the 1/N c expansion is used to order and select a basis of effective operators that spans the nine observables (seven masses and two mixing angles). Fits are performed using subsets of the complete set of nine operators, including corrections up to O(1/N c ) where leading order is N 1 c .This study shows that the 1/N c expansion provides an excellent framework for analyzing the mass spectrum, and uncovers a new hierarchy of operator contributions.

We present a new dynamical picture that identifies the formation of the exoticcc-containing states XYZ with the confinement-induced hadronization of a rapidly separating pair of a compact diquark and antidiquark. This picture combines the advantages of diquark-based models, which can accommodate much of the known XYZ spectrum, with the experimental fact that such states are both relatively narrow and are produced promptly. It also naturally explains the preference of some of the exotic states to decay to ψ(2S), rather than J/ψ, in terms of a simple wave-function overlap effect. [3]. These states do not fit into the standard nonrelativistic quark model of a singlecc pair with separation r interacting via a potential V (r), which had been successful in accommodating all of the previously known charmonium states [4-6]; instead they are believed to be tetraquark (ccqq ′ ) states currently named X, Y , or Z 1 . Notable evidence supporting this identification includes the facts that X(3872) is an extremely narrow (Γ < 1.2 MeV) J P C = 1 ++ state but is tens of MeV lighter than the nearest quark-model candidate χ c1 (2P ) [6], and the recent confirmation at LHCb [7] of the charged J P = 1 + state Z(4430) as a resonance decaying into π − ψ(2S). This first verification of the existence of exotic hadrons, which possess neither meson (qq) nor baryon (qqq) valence structure, is an exciting advance for QCD; a key challenge is to uncover the dynamical structure of these states.One can imagine the binding of a (q 1 q 2q3 q 4 ) state to occur in a variety of ways. First, the four valence quarks can all interact democratically, which one may * Electronic address: sjbth@slac.stanford.edu † Electronic address: dshwang@sejong.ac.kr ‡ Electronic address: richard.lebed@asu.edu 1 In the current nomenclature, the neutral(charged) states observed in B decays are labeled X(Z), whereas the Y are the neutral, J P C = 1 −− states observed in initial-state radiation e + e − processes.call a "true" tetraquark. However, simple SU(3) color group theory shows that the combination of two quarks (each a color 3) and two antiquarks (each a color3) can form an overall color singlet in only two independent ways-matching the color structure of factorized two-meson states (q 1 q 2 )(q 3 q 4 ) and (q 1 q 4 )(q 3 q 2 ). In large N c QCD, this fact has long been used to argue that narrow tetraquark states do not occur, since the four-quark source operators needed to create them are saturated by two-meson states. Weinberg has recently showed [8] that this argument contains a loophole; however, his scenario requires modifications that go beyond the usual large N c counting rules and structures [9][10][11].The color factorization property of the tetraquark naively suggests a two-meson molecule structure for the observed states. Indeed, many of the XYZ states lie close to such thresholds (e.g., m X(3872) ≈ m D + m D * ≈ m J/ψ + m ω ), suggesting a molecule with a small binding energy E b via a van der Waals-type attraction [12]. However, the typical scatteri...