On the electron–positron energy asymmetry in KL→π0e+e−

Abstract

Motivated by some new experimental and theoretical efforts, we update the theoretical analysis of the electron-positron energy asymmetry, which arises, in K L → π 0 e + e − , from the two-photon intermediate state in the standard model. It is found that the measurement of this asymmetry in future experiments may increase our understanding of the K L, S → π 0 e + e − decays, which would thus provide some useful information on quark flavor physics. Meanwhile, in the standard model the electron-positron energy asymmetry in the decay of K S → π 0 e + e − is expected to be vanishingly small, therefore the asymmetry in K S → π 0 e + e − might be a very interesting quantity to explore new physics scenarios. †

Binding energy and scattering length for diatomic systems

“…The physical meaning is clear. An s wave scattering length that is less than, but close to 2 ā0s corresponds to having bound states of l = 4j + 1 close to the threshold [22,23]. The same expansion in 2 ā0s − a 0s can also be obtained by using in equation ( 17) the following more general result:…”

“…Equation ( 14) is applicable over a wide range of scattering lengths where a 0s is not necessarily much greater than ā0s . In fact, figure 1 shows it to be an excellent approximation for all a 0s > 2 ā0s , namely for all Class 0 systems according to the classification of [23]. Rewriting it as an expansion to the fourth order in 1/a 0s would destroy its accuracy and range of applicability.…”

“…The angular-momentum-insensitive quantum defect theory (AQDT) [21][22][23] provides a systematic understanding of highly-excited molecular rovibrational states and cold-atom collisions. Here we apply it specifically to the binding energy of the least-bound state of an arbitrary angular momentum l and derive simple analytic results that are easily accessible.…”

“…If the p wave scattering length is not known explicitly, it can be derived from the s wave scattering length by taking advantage of the approximate l-independence of µ c . This was left as an exercise in [23], and the answer is…”

“…The corresponding expansions, including the expansions in scattering lengths for both s and p partial waves and the generic expansions with the µ c ( , l) ≈ µ c (0, l) approximation, have essentially the same accuracy. Other expansions that make use of both the energy-and the l-independence of µ c are examples of universal properties at length scale β 6 [21,23,26,28] described by a single parameter, be it µ c (0, 0) or a 0s . They are very useful for qualitative understanding, and should also work well quantitatively for the first few partial waves.…”