Z. Phys. C - Particles and Fields 20, 305-312 (1983) Zei~,chrift F ~ t i c ~ forI~ysik C and FE Ls 0 Springer-Verlag 1983 The KL-K s Mass Difference in Left-Right Symmetric Models and the Right-Handed Kobayashi-Maskawa Matrix Parbati Basak Raja Peary Mohan College, Uttarpara, Hooghly, West Bengal, India Amitava Datta Department of Physics, Jadavpur University, Calcutta--700 032, India Amitava Raychaudhuri Department of Pure Physics, University of Calcutta, 92, A.P.C. Road, Calcutta--700 009, India Received 12 April 1983 Abstract. K L K s mass difference is computed in a left-right symmetric model with three generations of quarks. Under the assumption of "manifest" left-right symmetry the mass of the right-handed charged gauge boson consistent with Ke-K s constraint appears to be rather high. A low mass right-handed gauge boson can be accommodated in models with broken "mani- fest" left-right symmetry. The latter scenario has many non-trivial predictions for the decay of heavy (c, t, b) quarks. 1. Introduction The standard model [1] of the electroweak interac- tions has been very successful in explaining the cur- rently available low energy experimental results. There are now preliminary results that even indicate that the charged vector bosons mediating the weak interactions may already have been detected [2]. Yet an alleged defficiency (albeit somewhat philosophical) of the standard model is that parity violation in this model is rather artificial and put in by hand. Some authors have therefore considered models which are left-right sym- metric (LRS) at the fundamental level [3]. Obviously, if the right-handed gauge bosons are very heavy com- pared to the left-handed ones (MR >>ML) then at low energies the LRS model will be indistinguishable from the standard model. Another intriguing possibility, also allowed by the data, corresponds to LRS models * For a different point of view see [5] with a heavy right-handed Majorana neutrino and restoration of parity at low energies (M R ~ ML) [4]*. In this paper we focus on this last alternative. One standard test of electroweak models is the prediction for the Ke-K s mass difference. Historically, it was first used to obtain a crude estimate of the mass of the charmed quark [6]. Later on the determination of the Kobayashi Maskawa (K-M) quark mixing angles was carried out using the KEK s system [7]. More recently [8] it has been used in the context of the LRS model to set a lower bound on the right-handed gauge boson mass (MR > 1.6 Tev) under the assumption of "manifest" left-right symmetry (Sect. 2). It was subsequently noted that a complementary possibility exists in which MR ~ ME but "manifest" left-right symmetry is broken [9]. The two alternatives may be distinguished, for example, through the decay of the charmed mesons and baryons [9]. The calculations in [8] and [-9] are based on a four quark (u, d, s and c) model. The fifth quark--b has now been around for quite some time and it is generally expected that its charge + 2 partner--the t-quark-- will soon be found. In view of the uncertainties in its mass and mixing angles it is not possible to un- ambiguously estimate its effect on the KL-K s scena- rio. However, the leading contribution to the K e K s mass difference is proportional to 2 2 Mq/ML, and the t-quark contribution may actually dominate over all other contributions unless its mixing angles are small enough. With this as our motivation we have in- vestigated the K o /(o problem in an LRS model with six quarks. One non-trivial complication that we are im- mediately led into is the effect of charged Higgs scalar