Measuring the Photon Polarization inB→Kππγ

Abstract

We propose a way of measuring the photon polarization in radiative B decays into K resonance states decaying to Kππ, which can test the Standard Model and probe new physics. The photon polarization is shown to be measured by the up-down asymmetry of the photon direction relative to the Kππ decay plane in the K resonance rest frame. The integrated asymmetry in K1(1400) → Kππ, calculated to be 0.34 ± 0.05 in the Standard Model, is measurable at currently operating B factories.The Standard Model (SM) predicts that photons emitted in rare b → sγ decays are left-handed [1], up to small corrections of order m s /m b , while being righthanded inb →sγ. This feature is common to inclusive and exclusive radiative decays, also when including long-distance effects in the latter case [2]. While measurements of the inclusive rate agree reasonably well with SM calculations [1], no evidence exists for the helicity of the photons in these decays. In several models beyond the SM the photon in b → sγ acquires an appreciable right-handed component due to the exchange of a heavy fermion in the electroweak loop process. For instance, in SU (2) L × SU (2) R × U (1) left-right symmetric models [3] this component may be comparable in magnitude to the left-handed component, without affecting the SM prediction for the inclusive radiative decay rate. An independent measurement of the photon helicity is therefore of interest.Several strategies have been proposed to look for signals of physics beyond the SM through helicity effects in B → X s γ. In one method the photon helicity is probed through mixing-induced CP asymmetries [4]. In two other schemes one studies angular distributions in radiative decays of Λ b baryons [5,6] and in B → γ(→ e + e − )K * (→ Kπ) [7,8]. The methods using B mesons are sensitive to interference between amplitudes involving photons with left and right-handed polarization. In the SM the interference is at a level of a few percent, and these methods become unfeasible at present B factories also for larger interference due to insufficient luminosities. The methods using Λ b decays, measuring directly the photon polarization, rely on future hadron colliders or on extremely high luminosity e + e − Z factories.

Future prospects for the determination of the Wilson coefficient $ C_{{^{{7\gamma }}}}^{\prime } $

“…[17,18] and improved in [19]. Our study shows that the photon polarization parameter λ γ can be measured at super B factories with an accuracy ∼ 20%, with integrated luminosity of 75 ab −1 .…”

“…For example, p γ · ( p π × p K ) is a pseudo-scalar; then applying the parity transformation it will have the different sign for left-and right-handed photons. Gronau et al [17,18] proposed to study the angular distribution in the B → K 1 (→ Kππ)γ decay and extract the polarization parameter λ γ ,…”

“…Contrary to refs. [17,18] we pointed out the complex hadronic structure of K 1 (1270) → Kππ, that we studied in great detail in ref. [42].…”

RadiativeBdecays to the axialKmesons at next-to-leading order

“…In addition to K * , higher resonances of Kaon also deserve much attention. Especially, it was suggested that B → K res (→ Kππ)γ can provide a direct measurement of the photon polarization [15]. In particular, it was shown that B → K 1 (1400)γ can produce large polarization asymmetry of ≈ 33% in the standard model.…”

RadiativeBMeson Decays intoKπγandKππγFinal States

“…[4]. Exclusive decays, such as B → K 1 (1400)γ, can also be used to measure the photon helicity, which may differ from the SM prediction in some new physics models [5].…”