J.-C. Raynal

Strong decays of ψdblac; (4.028) as a radial excitation of charmonium

Abstract The decay rates of ψdblac; (4.028)→ D D, D D ∗ + D D ∗ , D ∗ , D ∗ D ∗ can be fairly well understood with the assignment this state as a second radial excitation of charmonium. The nodes of the wave function and the different Q -value in each of these decays allow to understand the failure of the simple quark spin counting prediction.

Why is ψ(4.414) so narrow

Abstract The width of ψ(4.414) is surprisingly small for a c c state far above the charm threshold, Γexp ≈ 33 MeV. This fact can be qualitatively understood if one makes the conservative assignment 4 3S1. The nodes of the wave function reflect as zeros of the decay amplitude in the momentum of the decay products, and are responsible for the suppression of the couplings to the ground state charmed mesons, Γ(ψ(4.414)→D D + D D ∗ + D D∗ + D∗ D ∗ + F F + F F ∗ + F F∗ + F∗ F ∗) ≈ 15 MeV. All the modes are suppressed by factors of the order of 103 with respect to the k3 spin counting prediction. The dominant modes are predicted to be D∗ D ∗, F F ∗ + F F∗ and D D . Moreover, we show that the contributions from P-wave charmed mesons are reasonably expected to be suppressed either by phase space or by the nodes if their masses lie within certain range. We emphasize however that the smallness of the photon coupling remains to be understood.

Non-leptonic hyperon decays and the baryon spectrum

Abstract We propose a parallel treatment of S- and P-waves in non-leptonic hyperon decays through the commutator term plus pole contributions from the lowest levels of the baryon spectrum as described by the quark model: the positive parity ( 56 ,0 + ) for P-waves, and the negative parity ( 70 ,1 − ) for S-waves, connected to the ground state, respectively, by the parity conserving and the parity violating parts of Hw. All these contributions satisfy the ΔI = 1 2 rule. The new piece we introduce, which comes from the ( 70 , 1 − ) intermediate states, provides a natural large correction to the soft pion limit for S-waves, of order δ m/ω ⋍ 0.5 relative to the commutator (δm, SU(3) breaking parameter = pion energy; ω, mean baryon level spacing). We obtain a simple expression for this new term in the absence of spin-dependent perturbations, and we fix its magnitude from the properties of the baryon spectrum. We get a significant improvement of the relative magnitude of S- and P-waves, correcting the discrepancy of a relative factor of 2 which appears when considering only the commutator and 1 2 + poles. The new piece also leads to a correct D/F ratio for S-waves.

Estimation of ΔΓ for the Bs−Bs system. Exclusive decays and the parton model☆

Abstract We estimate ΔΓ for the B s − B s system by making a sum over exclusive decay modes into ground state mesons, and compare our result to the parton model prediction. For the modes D s D s , D s D ∗ s + D ∗ s D s and D ∗ s D ∗ s (class I) which give the largest contribution to ΔΓ, we find duality between the exclusive calculation and the parton model in the heavy quark limit with 2 m c → m b and with the standard factorization assumption, which amounts to exact duality in the N c → ∞ limit. In this limit, for the dominant spectator contribution, we find the selection rule Γ[B 2 (CP=−)→D s D ∗ s ]=0 , so that the modes D s D ∗ s + D ∗ s D s contribute constructively to ΔΓ, with the same sign as D s D s (S wave) and D ∗ s D ∗ s ((S + D)-waves). Most of the modes of the modes of class II (ψη, η c ϕ, ψϕ, …) contribute also constructively to ΔΓ but are suppressed by the effective color factor. On the other hand, from a purely theoretical point of view, we find a rather subtle and interesting difficulty as regards duality in the standard factorization assumption when considering together classes I and II. This unwanted violation of duality could correspond to the well known necessity of correcting this standard factorization assumption. On the basis of both the exclusive and the parton model calculations, we conclude that the sign of ΔΓ is well-defined and its magnitude is stable against theoretical uncertainties. Our estimate gives ΔΓ Γ of the order of 0.15, a value that could be measured at LEP.

Bilinear terms in the penguin contribution to K → 2π

Abstract We show that the chiral constraints on the penguin K- π matrix element are satisfied by a cancellation between the well known vacuum insertion estimate of Shifman, Vainshtein and Zakharov and currently omitted matrix elements of bilinear operators. We also show how the usual factorization prescription for K → 2 π does satisfy the chiral constraints.

Absolute magnitude of non-leptonic hyperon decays and electromagnetic hyperfine splittings

Abstract In the quark model with current-current interaction, non-leptonic hyperon decays are controlled by the baryon wave function at small distances. An independent estimate of this quantify is provided by a related phenomenon: the baryon electromagnetic hyperfine splittings, given by the Fermi contact interaction. A good estimate is obtained with the standard Cabibbo-suppressed interaction. Important remaining problems for S -waves are emphasized.

Parity violating radiative weak decays and the quark model

We propose a model for radiative weak decays of hyperons with baryons exchanges in the s- and u-channels as described by the quark model: the 12+ (56, 0+) for parity conserving, and the first excited 12− (70, 1−) for parity violating amplitudes. Special attention is drawn on the problem of gauge invariance. We get a large ∑+ → pγ asymmetry of the right sign. The parity violating amplitude although SU(3)-suppressed, is of the order δm/ω (δm, SU (3)-breaking parameter; ω, baryon level spacing), which is not small. In the quark model the parity conserving amplitude is also SU(3)-suppressed contrarily to the usual belief.

Uncertainties on the CP phase α due to Penguin diagrams

Abstract A major problem in the determination of the the CP angle α, that should be measured through modes of the type B d , B d → ππ, … , is the uncertainty coming from Penguin diagrams. We consider the different ground state modes ππ, πϱ, ϱϱ, and, assuming the FSI phases to be negligible, we investigate the amount of uncertainty coming from Penguins that can be parametrized by a dilution factor D and an angle shift Δα. The parameter D is either 1 or very close to 1 in all these modes, and it can be measured independently, up to a sign ambiguity, by the t dependence. Assuming factorization, we show that Δα is much smaller for the modes ϱπ and ϱϱ than for ππ, and we plot their allowed region as a function of α itself. Moreover, we show that most of the modes contribute to the asymmetry with the same sign, and define for their sum an effective Deff and an effective Δαeff, an average of Δα for the different modes. It turns out that Deff is of the order of 0.9, Δαeff is between 5% and 10% and, relative to ππ, the statistical gain for the sum is of about a factor 10. Finally, we compute the ratios Kπ ππ , … that test the strength of the Penguins and depend on the CP angles, as emphasized by Silva and Wolfenstein and by Deandrea et al.

Bd0(t)→DPP time-dependent Dalitz plots, CP-violating angles 2β, 2β+γ, and discrete ambiguities

We study CP-violation in resonant three-body B -> DPP decays, where PP stands for either Dpi, DK_S, pipi or piK_S. Analogously to the B -> 3pi channel and the extraction of 2alpha, the first three channels are shown to measure cos(2beta) in addition to sin(2beta), thus allowing to resolve the beta -> pi/2 -beta ambiguity, while the DpiK_S final state leads to a measurement of 2beta+gamma. The B0(t) -> D+D-pi0 channel via the interference between D** orbitally excited resonances is taken as an example, although this Cabibbo-suppressed decay suffers from irreducible penguin uncertainties. Then two penguin-free and Cabibbo-dominant modes are proposed: B0(t) -> D+D-K_S with the D_s** resonances, and B0(t) -> D0_CP pi+pi- with the D** plus the rho. Finally, the B0(t) -> D+-pi-+K_S channel with the D_s** and K* resonances provides a new clean method to measure the unusual angle 2beta+gamma. We present in all cases a crude estimate of the number of cos(2beta) (respectively 2beta+gamma) sensitive events. We show that this number is an increasing function of the resonance mass, a favorable situation compared to the more extensively studied three-pion Dalitz plot. However, the poor detection efficiency of the D mesons could pose a problem. As an annex and speculative application of these Dalitz plot based methods, the penguin-dominated B0(t) -> K_SK_SK_L decay also measures 2beta.

New heavy quark limit sum rules involving Isgur-Wise functions and decay constants

Abstract We consider the dominant c c contribution to ΔΓ for the B s 0 − B s 0 system in the heavy quark limit for both b and c quarks. In analogy with the Bjorken-Isgur-Wise sum rule in semileptonic heavy hadron decay, we impose duality between the parton model calculation of ΔΓ and its estimation by a sum over heavy mesons. Varying the mass ratio m c m b and assuming factorization and saturation by narrow resonances (Nc → ∞), we obtain new sum rules that involve the Isgur-Wise functions ξ(n)(w) and τ 1 2 (n) (w) and the decay constants f(n), f 1 2 (n) (n stands for any radial excitation). Alternatively, we deduce the sum rules with another method free of the factorization hypothesis, from the saturation of the expectation value of a product of two currents by heavy hadrons and by the corresponding free quarks. The sum rules read ∑ n f (n) f (0) ξ (n) (w)= 2 ∑ n f (n) 1 2 f (0) τ (n) 1 2 (w)=1; valid for all w. Moreover, we obtain, in the heavy quark limit, f 3 2 (n) = 0 . As a consequence, unlike the BIW sum rule, the slope of the elastic function ξ(w) is related to radial excitations alone. These are generalizations, rigorous for QCD in the heavy quark limit, of results that have an easy understanding in the non-relativistic quark model.