Two-pseudoscalar-meson decay ofχcJwith twist-3 corrections

Abstract

The decays of χ cJ → π + π − , K + K − (J = 0, 2) are discussed within the standard and modified hard scattering approach when including the contributions from twist-3 distribution amplitudes and wave functions of the light pseudoscalar meson. A model for twist-2 and twist-3 distribution amplitudes and wave functions of the pion and kaon with BHL prescription are proposed as the solution to the end-point singularities. The results show that the contributions from twist-3 parts are actually not power suppressed comparing with the leading-twist contribution. After including the effects from the transverse momentum of light meson valence-quark state and Sudakov factors, the decay widths of the χ cJ into pions or kaons are comparable with the their experimental data.The factorization form in the framework of the hard-scattering picture [1] is usually used in hadronic processes with large momentum transfer. In this picture, the full amplitude is factorized as a convolution of process independent distribution amplitudes of hadrons and process-dependent hard-scattering amplitude. However, the applicability of this approach at experimentally accessible momentum transfers, typically a few GeV, is questionable[2]. One of the reasons is the large contributions from the soft end-point regions. A modified perturbative approach, so-call modified hard-scattering approach(mHSA), has been proposed by Li and Sterman [3], where quark transverse momenta and Sudakov suppressions are taken into account. The advantage of this modified perturbative approach is the strong suppression of the soft end-point regions where the pQCD can not be applied.The exclusive charmonium decays have attracted interest for decades as they are an excellent laboratory for studying quark-gluon dynamics at relatively low energies. In the decay of P-wave charmonium χ c0,2 to a pair of pseudoscalars, one finds that the lowest Fock state, the color-singlet contribution, alone is not sufficient to accommodate the experimental data. This discrepancy provides an important arena in which to test our understanding of the boundary domain between perturbative and non-perturbative QCD. From a naive point of view, QCD radiative correction is suppressed by the factor α s (Q 2 ) and the contribution from higher Fock states, higher twist distribution amplitudes are suppressed by the factor 1/Q 2 . But this is not always the real case. In Ref. [4], the author showed that in the decay of χ c0,2 → P P (where P represents a light pseudoscalar meson.) the color-octet contribution from the higher Fock state contributes the same level as the color singlet state.To reveal the decay mechanism more clear, the systemic reanalysis on the contributions from higher twist distribution amplitudes will be significative and interested. When the amplitude of a physical process with large momentum transfer Q 2 is only related to one hadron wave function, there is a suppression for the contribution from higher Fock states and higher twist distribution amplitudes. For example, the dominating con...

$$\gamma \gamma \rightarrow M^{+}M^{-}(M=\pi , K)$$ γ γ → M + M - ( M = π , K ) processes with twist-3 corrections in QCD

“…From the naive point of view, the contribu- tions of high twist distribution amplitudes are suppressed by the factor 1/Q 2 for exclusive processes with large momentum transfer Q, but that has not always been the case. For example, the contributions from twist-3 distribution amplitudes are comparable with or even larger than the one from the leading-twist distribution amplitude of light pseudoscalar meson in the χ cJ → π + π − , K + K − decay channels [19] and the pion/kaon electromagnetic form factor [20,21]. More discussion of the high twist corrections of vector mesons is presented in Refs.…”

“…The constituent quark masses m q = 0.30 GeV (q = u, d) and m s = 0.45 GeV [19] are given in the above formulas. To simplify the following numerical analysis, we write the twist-3 wave functions as…”

Characterizing Ground and Thermal States of Few-Body Hamiltonians

“…Consequently, the observation of a negative expectation value proves that a state is outside of the set. We will see below that such witnesses can be used to certify quantum simulation.Quantum exponential families.-We recall some results on the characterization of quantum exponential families [10,11]. Given a state , consider its distance from the exponential family Q 2 in terms of the relative entropy (or divergence) S( ||τ ) = tr[ (log( ) − log(τ ))].…”

“…Quantum exponential families.-We recall some results on the characterization of quantum exponential families [10,11]. Given a state , consider its distance from the exponential family Q 2 in terms of the relative entropy (or divergence) S( ||τ ) = tr[ (log( ) − log(τ ))].…”

“…As the closest state to in Q 2 , one obtains the so-called information projection˜ 2 . It has been shown that the following three characterizations for the information projection˜ 2 ∈ Q 2 are equivalent [10]: (a)˜ 2 is the unique minimizer of the relative entropy of from the set Q 2 ,…”