Right-Handed Quark Mixing in Left-Right Symmetric Theory

Abstract

We give exact formulas for the right-handed analog of the CKM matrix in the minimal Left-Right symmetric theory, for the case when the Left-Right symmetry is generalized Parity as in the original version of the theory. We derive its explicit form and give a physical reason for the known and surprising fact that the right-handed mixing angles are close in value to the CKM ones, in spite of the Left-Right symmetry being badly broken in nature. We exemplify our results on the production of the right-handed charged gauge boson and the computation of KL − KS mass difference.I. Introduction. The Left-Right (LR) symmetric theory [1] prophetically implied non-vanishing neutrino mass whose smallness, through the seesaw mechanism [2-4], is related [2,3] to parity violation at low energies. The theory leads to neutrinoless double beta decay [5] through both left handed (LH) and heavy right handed (RH) neutrinos [3]. One can in principle observe lepton number violation at hadronic colliders and probe directly the Majorana nature of heavy neutrinos through the so-calleed KS process [6]. Moreover, the knowledge of neutrino masses allows one to predict the Dirac Yukawa couplings [7] and the associated decays of RH neutrinos.The small K L − K S mass difference implies a lower limit [8] on the LR scale in the minimal model around 3 TeV [9], and the LHC has come close to it for some channels [10]. This limit could go up to 20 TeV [11], but that depends on the UV completion of the theory.Detailed studies [12] support the feasibility of the KS process at the LHC connected to neutrinoless double beta decay and lepton flavor violation [13]. Recently CMS reported a 2.8 sigma excess [10] in the KS process that could be a manifestation of the LR symmetry [14]. It would require, however, the RH gauge coupling to be appreciably smaller that the LH one, not discussed here.In the limit of unbroken LR symmetry, left and right mixings are equal. The situation after the LR symmetry breaking depend on its nature, which can be either generalized charge conjugation C or generalized parity P. In the case of C, quark mass matrices are symmetric and the mixing angles remain the same, the only difference lying in phases.In the case of P, quark mass matrices are neither symmetric nor hermitian in general, yet it turns out that the left and right mixing angles are close to each other, as shown first numerically in a portion of the parameter space in [15]. An analytical study in the same approximation was made in [16], and [17] established this result over the entire parameter space by combining analytical and numerical computations.In this Letter we shed new light on this old issue by finding the explicit form of the right-handed quark mixing matrix, essential for high precision phenomenological studies of the theory. In the process we offer a physical explanation behind the approximate equality of left and

Non-minimal flavored $${S}_{3}\otimes {Z}_{2}$$ S 3 ⊗ Z 2 left–right symmetric model

“…Additionally, the see-saw mechanism comes in rather naturally in the context of left-right symmetric scenarios; aside from other nice features, as for instance the recovery of parity symmetry, and the appearance of right-handed currents at high energy, which also makes such extensions very appealing. Recently, the left-right scenarios have been revised [15][16][17][18][19][20][21][22][23][24][25] in order to make contact with the latest experimental data of LHC. Moreover, the dark matter problem [26][27][28] and the diphoton excess anomaly [29][30][31][32][33] have been explored in this kind of scenarios.…”

Lepton Number Violation in Higgs Decay at LHC

“…After pair-production from Higgs decay, each N decays to a charged lepton and two jets via W R , with a RH charged current quark flavour structure essentially identical to the left-handed one [42]. Due to the Majorana nature of N , 50% of events will result in a final state of two same-sign leptons and four jets with no missing energy, explicitly signalling LNV.…”

Is left–right symmetry the key?

“…First, finally the LHC has a potential of observing it which makes it more timely than ever. Second, there have been two fundamental developments in recent years that make the theory self-contained and predictive: (i) the testable Higgs origin of neutrino mass [6], in complete analogy with the Standard Model case of charged fermions (ii) the analytic expression for the right-handed quark mixing matrix [7], a challenge that lasted some forty years. Moreover, there has been a furry of activity devoted to the LHC potential and the low energy processes such as neutrinoless double beta decay, lepton flavor violation and such.…”

“…Numerical calculations indicated that the LH and RH mixing angles were similar, but the first serious attempt to compute V R was made only some ten years ago [37], in a limited portion of parameter space and not as clearly as one would have hoped for direct application. The task was finally completed two years ago, when the analytic form valid in the entire parameter space was finally obtained [7] The leading form is given by simple (4), used in Introduction to anticipate the discussion. For a complete form and extensive discussion see [7] where the leading terms are derived for the differences between mixing angles …”

“…(ii) The right-handed quark mixing matrix V R has a simple approximate form [7] as a function of the usual…”