Two-photon decays of hadronic molecules

Abstract

In many calculations of the two-photon decay of hadronic molecules, the decay matrix element is estimated using the wave function at the origin prescription, in analogy to the two-photon decay of parapositronium. We question the applicability of this procedure to the two-photon decay of hadronic molecules for it introduces an uncontrolled model dependence into the calculation. As an alternative approach, we propose an explicit evaluation of the hadron loop. For shallow bound states, this can be done as an expansion in powers of the range of the molecule binding force 1/β. In the leading order one gets the well-known pointlike limit answer. We estimate, in a self-consistent and gauge invariant way, the leading range corrections for the two-photon decay width of weakly bound hadronic molecules emerging from kaon loops. We find them to be small, of order O(mε/β 2 ), where m and ε denote the mass of the constituents and the binding energy, respectively. The role of possible shortranged operators and of the width of the scalars remains to be investigated.

Amplitude analysis of high statistics results on γγ→π+π- and the two photon width of isoscalar states

“…His calculation [44] of a KK composition in the molecular model of Weinstein and Isgur [45,46] gives ∼ 600 eV. In contrast, more recently Hanhart et al [47] predict 220 eV in a KK-molecular picture. This is comparable to the much earlier calculation of Achasov et al [48][49][50], who find, with a qqqq composition, a prediction of ∼ 270 eV, using Achasov's kaon loop model.…”

Light meson mass dependence of the positive-parity heavy-strange mesons

“…Note that the mentioned relation between the coupling and the structure of the state holds only in leading order in an expansion in √ M K ǫ/β (see Ref. [35] for a detailed discussion), with the inverse range of forces β ∼ m ρ . For the scalar and axial vector open charm mesons this gives an uncertainty of the order of 20%.…”

Masses of di-mesonic molecular states

“…The two-photon decay of the hadronic (di-mesonic) molecules are estimated, using the wave function at the origin, in analogy to the two photon decay of parapositronium [16]. The di-gamma width for…”

“…[16], m is the mass of meson and the factor ξ takes the value different from 1, if all constituents is not participate in the decay.…”

“…Here we briefly study the light di-mesonic masses by semi relativistic approach. The di-gamma decay width has been calculated for equal masses [16]. We have used hydrogen-like trial wave function.…”