Scalar mesons in φ radiative decay: Their implications for spectroscopy and for studies of CP violation at φ factories

Abstract

Existing predictions for the branching ratio for φ → KKγ via φ → Sγ (where S denotes one of the scalar mesons f 0 (975) and a 0 (980)) vary by several orders of magnitude. Given the importance of these processes for both hadron spectroscopy and CP-violation studies at φ factories (where φ → K 0K 0 γ poses a possible background problem), this state of affairs is very undesirable. We show that the variety of predictions is due in part to errors and in part to differences in modelling. The latter variation leads us to argue that the radiative decays of these scalar states are interesting in their own right and may offer unique insights into the nature of the scalar mesons. As a byproduct we find that the branching ratio for φ → K 0K 0 γ is < ∼ 0(10 −7 ) and will pose no significant background to proposed studies of CP-violation. * For an historical perspective see Ref. [8]; for a more recent study see Ref. [9].

The a0(980), a0(1450) and scalar decay constants and the isovector scalar spectrum

“…One should bear in mind, however, that an alternate quark model approach, whose γγ model dynamics are constrained by an analogous treatment of π 0 , η → γγ, allows widths compatible with experiment for a conventional quark model assignment [19], and that small γγ widths are also claimed in the four-quark picture, based on a schematic estimate loosely motivated by the MIT bag model [20]. An alternate means of testing the molecule scenario is via the processes φ → f 0 γ , a 0 γ [21]. Recent experimental determinations [22,23] give branching ratios larger than predicted in the molecule picture [21,24] but, since the predictions of Refs.…”

Radiative decays with scalar mesons and in Resonance Chiral Theory

“…The expression for the invariant mass distribution in the KL model is obtained in Ref. [10], and its physical meaning is explained in terms of the SP P and φP P couplings [6]. Taking into account the momentum-dependent vertices we obtain…”

“…The factor 1/2 takes into account the identity of the neutral pions. The formula for the π 0 η case is analogous to (10).…”

Radiative ϕ decays with derivative interactions

“…While it is not yet clear to which extent large-N c is reliable in this context -see also Ref. [3] for a discussion of this point-, we consider this fact as a motivation to study in detail the effects of the mechanism (a) on radiative decays and thus to test an alternative scenario for the description of radiative φ decays. Moreover, in this work we restrict to the chiral limit dominant mechanism a.1 where only derivatives are involved (corresponding to setting d f0ππ = d f0KK = d a0πη = d a0KK = 0).…”

“…The radiative decays of the φ meson are a valuable tool to study the nature of light scalar states below 1 GeV [1,2,3]. It is still debated if the latter are quarkonia [4], tetraquark [5,6], molecular states [7] or a mixing of these configurations [8,9].…”