Model-independent study of magnetic dipole transitions in quarkonium

Abstract

We study magnetic dipole (M1) transitions between two quarkonia in the framework of nonrelativistic effective field theories of QCD. Relativistic corrections of relative order v 2 are investigated in a systematic fashion. Nonperturbative corrections due to color-octet effects are considered for the first time and shown to vanish at relative order v 2 . Exact, all order expressions for the relevant 1=m and 1=m 2 magnetic operators are derived. The results allow us to scrutinize several potential model claims. In particular, we show that QCD excludes both contributions to the anomalous magnetic moment of the quarkonium induced by low-energy fluctuations and contributions to the magnetic dipole operators of the type induced by a scalar potential. Finally, we apply our results to the transitions J= ! c ,, and b2 1P ! h b 1P by assuming these quarkonium states in the weak-coupling regime. Our analysis shows that the J= ! c width is consistent with a weak-coupling treatment of the charmonium ground state, while such a treatment for the hindered transition 2S ! b appears difficult to accommodate within the CLEO III upper limit.

Lattice QCD estimate of the η c (2S) → J/ψγ decay rate

“…non-relativistic QCD (pNRQCD) [12], lead to a very good agreement with lattice QCD results [13]. Therefore, as of today, the theoretical estimate of Γ(J/ψ → η c γ) is very solid.…”

“…Quark model predictions of the hadronic matrix element governing this decay are difficult to control because the leading term vanish due to orthogonality of the meson wave functions and the relativistic corrections are highly sensitive to the form of the used potential. Phenomenology of this decay mode has not been considered in the effective theory approach [12]. It is often assumed to be similar in size to Γ(ψ(2S) → η c γ) which has been measured and found to be small.…”

Lattice QCD study of the radiative decays J/ψ → η c γ and h c → η c γ

“…The effective theory approach of ref. [47] and the QCD sum rule analyses [48,49] succeeded at getting lower value for the decay rate of this decay, but with large uncertainties. Note that the dispersive (model independent) approach of ref.…”

Hadronic loop contributions to J/ψ and ψ′ radiative decays into γLi1, Zhao2 2008Physics Letters B430161View full textAdd to dashboardCite

“…Systematic investigation of the M1 transitions in the framework of nonrelativistic effective field of QCD has been reported in Ref. [30], where relativistic corrections of relative order v 2 are included. For J/ψ → γη c the authors found Γ J/ψ→γηc = (1.5 ± 1.0) keV, which is in a good agreement with the data, but with quite large estimated uncertainties from higher-order relativistic corrections.…”

“…Theoretical studies of the heavy quarkonium M1 transitions with relativistic corrections are various in the literature [24,25,26,27,28,29,30,31]. Relativistic quark model calculations show that a proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for explaining the J/ψ → γη c data [27].…”