Radiative corrections to double Dalitz decays: Effects on invariant mass distributions and angular correlations

Abstract

We review the theory of meson decays to two lepton pairs, including the cases of identical as well as non-identical leptons, as well as CP-conserving and CP-violating couplings. A complete lowestorder calculation of QED radiative corrections to these decays is discussed, and comparisons of predicted rates and kinematic distributions between tree-level and one-loop-corrected calculations are presented for both π 0 and K 0 decays. PACS numbers: 12.15.Lk, 13.20.Cz, 13.20.Eb, 13.40.Gp, 13.40.Hq I. BACKGROUNDMeson decays to two photons should exhibit interesting correlations between the photon polarizations [1]. Although existing particle detectors cannot measure photon polarizations directly, it has long been known that the polarization correlations can be measured indirectly by studying angular correlations in the related double Dalitz decays [2] in which both photons undergo internal conversion to a lepton pair. More recently, it has been pointed out [3] that a detailed study of these correlations can be used to determine the relative amount of two possible meson-γγ couplings (one CP-conserving and one CP-violating for mesons that are CP eigenstates) that can contribute to this process.Dalitz and double Dalitz decays are also of interest because they can be exploited to perform a measurement of the electromagnetic form factor of the decaying mesonthat is, how the meson couples to one real and one virtual photon (Dalitz decay) or two virtual photons (double Dalitz) depends on the q 2 values of the photon(s). An accurate knowledge of this form factor is essential, for example, to calculate the so-called long-distance contribution to the rare decay K L → µ + µ − . The short-distance contribution to this process, mediated by loops involving heavy quarks and massive vector bosons, is sensitive to the CKM matrix element V td , but this contribution cannot be extracted from the accurate experimental measurement of the partial width unless the long-distance amplitude is precisely known.The tree-level rates for several double Dalitz processes have been published in various forms [2,3,4,5]. The first experimental observation of a double Dalitz decay was published in 1962 [6,7]. A total of 206 examples of the decay π 0 → e + e − e + e − were observed by Samios in a sample of some 800,000 bubble chamber photographs. Based on the observed angular correlations, Samios was * E-mail: tonyb@cuhep.colorado.edu † Current address: Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, PA 16802-6300. able to exclude the possibility that the π 0 was a scalar particle (with a CP-conserving decay) at the 3.3σ confidence level. His measurement of the branching ratio for that process remains the only one published to date.Experimental observations of the much rarer kaon double Dalitz decays began to appear in the 1990's. Several measurements have been made of the decay K L → e + e − e + e − [8,9,10,11,12,13,14], the most recent of which are based on several hundred observed events. The still rarer doub...

Determination of the Parity of the Neutral Pion via Its Four-Electron Decay

“…For normalization, the decay π 0 → e + e − γ is understood to include all radiative final states, for consistency with previous measurements of this decay [16]. Radiative corrections in this analysis are taken from an analytic calculation to order O(α 2 ) [8].…”

“…The parameters of the π 0 γ * γ * coupling are found by maximizing an unbinned likelihood function composed of the differential decay rate in terms of ten phase-space variables. The first five are (x 1 , x 2 , y 1 , y 2 , φ), where x 1 , x 2 , and φ are described above and the remaining variables y 1 and y 2 describe the energy asymmetry between the electrons in each Dalitz pair in the π 0 center of mass [8]. The remaining five are the same variables, but calculated with the opposite choice of e + e − pairings.…”

“…This yields B x>0.9 eeee = (3.26 ± 0.18) × 10 −5 , where the error is dominated by the uncertainty in the π 0 → e + e − γ branching ratio. Using our radiative corrections model [8] to extrapolate to all radiative final states, we find:…”

Digamma, what next?

“…The kinematical distributions of pp → → γ * γ * → + − + − decay allow us to measure whether is scalar or pseudo-scalar, in analogy with pion π 0 physics [129,130]. Note that these techniques find little prospects of realisation in the context of Higgs physics, due to the large di-photon background; at 750 GeV, the situation is more favourable.…”

Measurements of the DecayKL→e+e−μ+μ−

“…Theoretical predictions for the branching ratio are also calculated as a function of α. Full single-loop QED radiative corrections are included [13] with a cutoff at M 2 eeµµ /M 2 K > 0.95, and the quadratic DIP parameter β is assumed to be zero. The intersection of these two curves, shown in Fig.…”