decay: A Stringent Test of Right-Handed Quark Currents

Clean tests of a small admixture of right-handed quark currents directly coupled to the standard W are still lacking. We show that such non-standard couplings can be significantly constrained measuring the value of the scalar Kπ form factor at the Callan-Treiman point to a few percent. A realistic prospect of such a measurement in K μ3 decay based on an accurate dispersive representation of the scalar form factor is presented. The inadequacy of the currently used linear parametrisation is explained and illustrated using recent KTeV data. Email: [email protected] Email: [email protected] Email: [email protected] Email: [email protected] I. In this letter we propose a new dedicated test of (the absence of) charged right-handed currents (RHCs) involving light quarks. We show how high statistics measurements [1, 2] of Dalitz distributions in the K μ3 decay, KL → π μν, can be used to extract the value C = f(∆Kπ) of the scalar Kπ form factor at the Callan-Treiman point ∆Kπ = m 2 K0 −m π+ and how this information constrains the effect of ūd and ūs RHCs. The method is model independent. It is based on the observation that standard dispersive technics and the known low-energy Kπ phases lead to an accurate parametrization of the scalar Kπ form factor in terms of a single parameter C subject to experimental determination. The related theoretical uncertainties are under control and they remain small compared with the possible signal of RHCs. II. In the past, tests of RHCs have often been considered in connection with left-right symmetric extensions of the Standard Model (SM) [3], yielding a lower bound on the mass MWR of the hypothetical vector boson mediating the RH weak interactions [4]. Different models leading to RHCs through mixing with heavy exotic fermions [5] have been considered, too. Independently of any specific models, RHCs naturally arise in Low Energy Effective Theories which below some scale ΛW operate with SM degrees of freedom and symmetries. Such RHC interactions are not necessarily mediated by an extra gauge boson WRμ and they need not be concerned by phenomenological lower bounds on MWR . Indeed, there exists a unique SU(2) ×U(1) gauge-invariant operator [6] ORHC = 1 Λ2 (ŪRγ DR)φrǫ (Dμφ)s (1) describing a direct coupling of W μ with the RHC ŪRγμDR. The presence of the Higgs doublet φr(r = 1, 2) in Eq. (1) suggests that the actual strength of this operator depends on the mechanism of electroweak symmetry breaking. If the symmetry is linearly realized and the light Higgs particle exists, the operator Eq. (1) is just one among the 80 independent gauge invariant operators of the mass (or UV) dimension D = 6 [6] and it is not easy to disentangle their respective dimensional suppression. In the opposite case of a Higgs-less effective theory [7,8], only the three Goldstone bosons contained in the complex Higgs doublet φr remain in Eq. (1) and the operator ORHC becomes of the chiral (infrared) dimension d = 2, i.e., it is not dimensionally suppressed anymore. Instead, its suppression is now related to its symmetry properties with respect to the higher non-linearly realized gauge symmetry characteristic of Higgsless vertices of the SM [7]. As a result the RHC interaction now appears already at the NLO: it represents a genuine effect beyond the SM that is potentially more important than the loop corrections. In the framework of a systematic low-energy expansion, one should first consider observables that Notice that in the SM 1PI vertices bewteen the W and right-handed fermions i, j are induced at one-loop order and are proportional to mimj . This is the reason why we are particularly interested in RHC of light quarks.