Weak decays of charm and quark masses

We calculate the effects of finite quark masses for the semileptonic and nonleptonic decays of charmed particles. The total lifetimes of charmed particles are not sensitive to the masses of the quarks in the final state. However the semileptonic branching ratios changes considerably. Using conventional constituent quark masses, one expect e.g. B_e(D⁺)≈ 21%. The brancing ratios and lifetimes of the charmed particles are estimated, taking into account the annihilation hypothesis.     

The surprising nonleptonic decays

Recent experiments onD-meson decays necessitate a revision of the standard theoretical model for weak decays. In this paper we argue that the presence of gluons in hadrons as required by local color gauge-invariance of Quantum Chromodynamics vitiates, in particular, two assumptions previously made:

1. color suppression factors in amplitudes for weak decays like \(D^0 \to \bar K^0 \pi ^0 \) ,
2. helicity suppression of two-quark interactions in weak decays.

A formula for estimating inclusive rates of mesons decaying via two-quark interactions is derived. Estimates for decay rates and branching ratios of several interesting decays of charmed hadrons are given. In particular, we obtain lifetime estimates forD ⁰,D ⁺, andF ⁺, and we predict the branching ratio for Cabibbo-suppressed decays ofD ⁺ to be of order 0.3 rather than of order tan²Θ _c as expected within the conventional model for weak decays.B-meson decays, which would provide an additional test of our scheme, are briefly discussed. Furthermore we point out that our approach sheds new light on the old problem of strongly enhanced |ΔI|=1/2 amplitudes in nonleptonic decays of strange particles.     

Exclusive non-leptonic decays ofD-,D s - andB-mesons

Recent experimental results onD-,D _s - andB-decays are interpreted on the basis of the valence quark model. For nonleptonic decays generally good results are obtained using factorization with little direct annihilation. Final state interaction causes corrections, however: small bare amplitudes can be fed by stronger amplitudes through channel mixing. This effect can simulate or enhance weak annihilation processes in particular if high lying resonances contribute. A comparison of \(D^0 \to \bar K^0 \phi \) withD _s →?π decays will clarify this issue. The effective QCD coefficients obtained in the analysis are discussed and used to estimate the contribution of two-body decays to the total widths. The result reflects already the lifetime differences betweenD ⁰ andD ⁺ mesons. Predictions for numerousB-decay branching rations allow for further tests and for a determination of so far unknown decay constants. A first bound on |V _ub | from nonleptonic decays is found from the experimental limit on \(\bar B^0 \to \pi ^ + \pi ^ - \) .     

Non-leptonic weak charmed baryon decays in theSU(4) semidynamical scheme

We study here the Cabibbo enhanced charmed baryon decays in theSU(4) semidynamical model. The weak Hamiltonian 20″ + 15 + 45 + 45* can have the parity violating amplitude for charmed baryon decays. Decay width and α for some modes are also calculated.     

The second EMC effect,semileptonic baryon decays and the chiral bag

TheU(1) anomaly gives a massiveη ₀ in the chiralSU(3) limit. We show in this limit how a chiral bag model givesboth theF andD amplitudes consistent with all baryon semileptonic decays,and the integral over the spin structure function measured by the EMC collaboration.     

Some comments on selection rules for nonleptonic decays of charmed particles

We show that even if only the decays of charmed mesons into two body final states are concerned, the Δn _t=0 rule is stillnot equivalent to sextet dominance. We also isolate the significant contribution of each quark diagram to non-leptonic decays of charmed particles. Thereby pointing out that the recent SLAC observation of Λ _c ⁺ →K ^?Δ⁺⁺ has already given evidence that theW-exchange diagram may be important in charmed baryon decays.     

Non-leptonic decays of charmed and beautiful particles

By fitting simultaneously the values of ζ-1/N _c and α _s (m _c ² ) on the inclusive rates of the Cabibbo allowed decaysD, F→PP andD→PV, which are independent of the final state interactions, we find ζ=0 and α _s (m _c ² )=0.44. This value for ζ is the same found by other authors [1, 4]. In order to explain the rescattering of the final states produced in the non-leptonic decays of charmedD-particles and to make theoretical predictions for all the exclusive channels, we propose a rescattering model based on the production of resonances inSU(3)-symmetry. In thePP sector we predict a new multiplet of meson resonances 0⁺ which allows us, with few free parameters, to obtain a satisfactory agreement between theoretical predictions and experimental data. Unfortunately, such an agreement cannot be obtained in thePV sector, for which the presence of other rescattering effects is needed to balance the exotic channelD ⁺→PV. In thePV sector we do not use any free parameter. Finally, we also make predictions for the Cabibbo allowed decay channelsB→PP, PV, without considering in this case the final state interactions, because of the high energy of the decay products.     

CP violation in decay rates of charged bottom mesons

In the standard theory we discuss a mechanism of interference between two different tree-level charged current amplitudes to induce CP violation. The asymmetry between conjugate Cabibbo disfavoured modes of charged bottom meson decays is considered. Estimates for two-body decays ofB _u andB _c are presented. We find thatB _u ^? →D ^?+D ₀ ^* , for instance, can give a big CP asymmetry with values ≈1–50%, depending on the angle and phase parameters.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.     

Electromagnetic properties of theZ boson

Direct (nonresonant) 3-body decays of charmed mesons are calculated in chiral perturbation theory. The magnitudes of the 20 and 84 representations of the effective chiralSU(4)×SU(4) Lagrangian are determined from the measured 2-bodyD→Kπ rate. For decay modes which do not contain nonspectator contributions, the agreement of theoretical predictions with the data is satisfactory. Nevertheless, the large discrepancy between theory and experiment for decays which can proceed through theW-exchange orW-annihilation might imply the importance of nonperturbative corrections to the nonspectator diagram and the existence of final-state interactions.     

Penguins,trees and final state interactions in B decays in broken SU3

The availability of data on B_s decays to strange quasi-two-body final states, either with or without charmonium opens new possibilities for understanding different contributions of weak diagrams and in particular the relative contributions of tree and penguin diagrams. Corresponding B_d and B_s decays to charge conjugate final states are equal in the SU(3) symmetry limit and the dominant SU(3) breaking mechanism is given by ratios of CKM matrix elements. Final State Interactions effects should be small, because strong interactions conserve C and should tend to cancel in ratios between charge conjugate states. Particularly interesting implications of decays into final states containing η and η′ are discussed.     

D meson production and decay in e+e− annihilation at 4.03 and 4 GeV c.m. energy

Decay modes of the charmed mesons, D⁰ and D⁺, are studied in e⁺e^? annihilation data at 4.03 and 4.41 GeV c.m. energy. The products of cross section times branching ratio are measured for the K^?π⁺, K^?π⁺π⁺π^?, K_Sπ⁺π^? and K^?π⁺π⁺ final states. Upper limits are established for the Cabibbo forbidden decays via π⁺π^?, K⁺K^?, K⁺K^? π⁺, K⁺π⁺π^? and π⁺π^?π⁺. The K^?π⁺π⁺π^? final state is shown to be dominated by K^?π⁺ρ⁰.     

Charm changing weak decays 1/2+ → 3/2+ + 0−/γ in SU(4) and SU(8) w

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8) _w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ* ₃ ⁺⁺ and Θ⁻ are also discussed. SU(8) _w symmetry predictsα , which is consistent with the experimental value.     

The magnitude of annihilation and penguin contributions to charm-meson decays

A consistent treatment of color singlet and octet contributions in the spectator constituent gluon model for pseudoscalar meson decays is attempted. The result comes out one order of magnitude too small to explain the observed life-time difference of D⁰ and D⁺. Furthermore, it is found that ‘penguin’ interactions in the annihilation channel may give contributions to the asymmetry of the (D⁰ → K⁺K^?)/(D⁰ → π⁺π^?) ratio of the order of the phase-space difference or larger. Finally, it is argued that annihilation cannot explain the $\text{ΔI =}\text{1}\text{2}$ rule for kaon decays; dynamical effects including the penguin interactions seem still to be needed.     

中间玻色子理论Ⅰ.基本假设和对称性

本文提出了一个中间玻色子理论,把弱作用中宇称、同位旋和奇异数的不守恒都归之于中间玻色子的特殊性质(破缺性质)。这个理论统一描述了轻子型和非轻子型蜕变过程。当应用于轻子型蜕变,可以得到Cabibbo理论,并且给他的“单位长度”假设以自然的解释(几率归一条件)。当应用于非轻子型蜕变,可以得到|△I|=1/2等规律。     

The chiral-bag model andK→2π decays

Nonleptonic kaon decays (K→2π) have been analyzed using the chrial-bag model. This continues the research of nonleptonic decays by the authors (Ref. [7] below). The results obtained are in qualitative agreement with those based on QCD-duality. the decay amplitudeA(K ⁺→π⁺π⁰) (ΔI=3/2) can be explained while the ΔI=1/2 decay amplitudes are 4 to 5 times smaller then the observed values. The ratio ofK ⁰ decay amplitudes ξ=|A(K ⁰→π⁺π^?)/A(K ⁰→π⁰π⁰| is larger than one, as it is experimentally. This is an improvement in comparison with MIT-bag model, where ζ was always smaller than one, even if ΔI=1/2 pieces in the theoretical expressions were enhanced.     

Dispersion approach to quark-binding effects in weak decays of heavy mesons

The dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed:Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at q² > 0 are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full q² range of the weak decay in terms of the wave functions of the participating mesons.The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by QCD for these limits is demonstrated.Predictions for form factors for B_(s) and D_(s) decays to light mesons are given.The B → γℓν decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B⁰ mixing are calculated.Inclusive weak B decays are analysed and the differential distributions are obtained in terms of the B meson wave function.     

ψ″ Decays to charmless final states

The importance of measuring the decays of the ψ″ = ψ (3770) resonance is discussed. These decays can shed light on a possible discrepancy between the total and cross-sections at the ψ″, and on a proposed mechanism for enhancement of penguin amplitudes in B meson decays through charm-anticharm annihilation. Measurements (including the ψ″ line shape) in states of definite G-parity and in inclusive charmless final states such as η′ + X are found to be particularly important.     

Factorization and polarization in two charmed-meson B decays

We provide a comprehensive test of factorization in the heavy–heavy B decays motivated by the recent experimental data from the BELLE and BABAR collaborations. The penguin effects are not negligible in the B decays with two pseudoscalar mesons. The direct CP asymmetries are found to be a few percent. We give estimates on the weak annihilation contributions by analogy to the observed annihilation-dominated processes. The N_c insensitivity of branching ratios indicates that the soft final state interactions are not dominant. We also study the polarizations in B→D^*D_(s)^* decays. The power law shows that the transverse perpendicular polarization fraction is small. The effects of the heavy quark symmetry breaking caused by the perturbative QCD and power corrections on the transverse polarization are also investigated.