Advances in High Energy Physics

Volume 2018, Article ID 4176840, 20 pages

https://doi.org/10.1155/2018/4176840

## Study of Rare Mesonic Decays Involving Di-Neutrinos in Their Final State

^{1}Physics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan^{2}Air University, PAF Complex, Service Road, E-9, Islamabad, Pakistan^{3}CIDETEC, Instituto Politécnico Nacional, Unidad Profesional, Adolfo López Mateos, CDMX 07700, Mexico

Correspondence should be addressed to Shakeel Mahmood; moc.liamtoh@doomham_leekahs

Received 1 December 2017; Revised 15 March 2018; Accepted 11 April 2018; Published 1 August 2018

Academic Editor: Adrian Buzatu

Copyright © 2018 Azeem Mir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We have studied phenomenological implication of R-parity violating () Minimal Supersymmetric Model (MSSM) via analyses of pure leptonic () and semileptonic decays of pseudoscalar mesons (). These analyses involve comparison between theoretical predictions made by MSSM and the Standard Model (SM) with the experimental results like branching fractions of the said process. We have found, in general, that contribution dominates over the SM contribution, i.e., by a factor of for the pure leptonic decays of and by and in case of and , respectively. Furthermore, the limits obtained on Yukawa couplings by using are used to calculate This demonstrates the role of MSSM as a viable model for the study of new physics contribution in rare decays at places like Super B factories, KOTO (J-PARC) and NA62 at CERN.

#### 1. Introduction

Flavor Changing Neutral Currents (FCNC) that mediate different flavored fermions (quarks) of the same charge are one of the most important tools searching for physics beyond the Standard Model (SM). This is due to their rarity owing to the GIM mechanism [1]. FCNC processes involving leptons are strictly forbidden in SM due to lepton family number conservation contrary to established experimental facts [2–13], and such processes can only be accommodated through physics beyond the SM. However,* lepton flavor* conserving processes can proceed through both universal and non-universal weak neutral current interactions. Here, universal weak neutral current interactions correspond to the SM interactions, which are flavor as well as generation blind, and non-universal weak neutral current interactions represent new physics (NP) interactions which are flavor as well as generation sensitive. Analyses, involving the bounds on NP couplings, of such type of processes are good for comparative study of different models. In this paper, we have presented one class of such type of pure leptonic and semileptonic decays of pseudoscalar mesons involving di-neutrinos in their final state in the framework of SM and R-parity violating () supersymmetric (SUSY) model.

Leptonic and semileptonic decays of beauty and strange mesons have played an important role in measuring parameters related to Cabibbo-Kobayashi-Maskawa (CKM), unitary angles, and also in probing CP-violation [14–16]. Many NP models like 2HDM [17] and Minimal Supersymmetric Standard Model (MSSM) [18–20] have been explored in these processes [21–33] as well. Super B factories [34, 35] and experimental set-ups like KOTO at J-PARC and NA62 at CERN [36–39] hold a lot of potential in this regard. LHCb also holds a lot of promise for discovering prospects of NP in B decays [40, 41].

MSSM [42–47] is the most economical version of SUSY. It is also the minimal extension of SM [42–47]. MSSM allows processes that violate baryon and lepton number. It also allows Lepton flavor violating (LFV) processes (that do violate lepton family number). R-parity, a discrete symmetry, is imposed to prevent baryon number, lepton number, and flavor violating processes. It is defined as [42, 48, 49]. R-parity conservation is phenomenologically motivated and if relaxed carefully allows one to analyze rare and forbidden decays while maintaining the stability of matter [46, 50–52]. The R-parity violating gauge invariant and renormalizable superpotential is [42, 48, 49]where are generation indices, and are the lepton and quark left-handed doublets, and , are the charge conjugates of the right-handed leptons and quark singlets, respectively. Here , , and are the Yukawa couplings. The term proportional to is antisymmetric in first two indices and is antisymmetric in last two indices , implying independent coupling constants among which 36 are related to the lepton flavor violation (9 from and 27 from ). We can rotate the last term away without affecting things of our interest.

In this scenario for detailed illustration we will use the pure and semileptonic rare decays of pseudoscalar mesons with neutrinos in the final state, i.e., , and , where and . At the quark level, all decays are represented by and (all these processes can be) divided into two categories on the bases of lepton flavors, i.e.,(1)*lepton flavor conserving *,(2)*lepton flavor violating * decays.

The* first type* of decays () is absent in the SM at tree level and is however induced by GIM mechanism [1] at the quantum loop level [53] which makes their effective strength very small, further suppression caused by the CKM matrix [54, 55]. These two suppressions make FCNC decays very rare. Furthermore, these processes will provide indirect test of high energy scales through a low energy process. Such type of processes has only short distance dominant contribution whereas long distance contribution is subleading [56], as we are taking pure and semileptonic decays, which can be accurately predicted in the SM due to the fact that the only relevant hadronic operators are just the current operators whose matrix elements can be extracted from their respective leading decays [57–61].

The* second type* of decays is strictly forbidden to all orders in the SM due to lepton flavor violation, so their detection can clearly signal the presence of new interactions. Hence one can say that these are the “golden channels” for the study of NP.

In this paper, we have analyzed the above-mentioned decays in the SM (first case) and then in violating MSSM. Our focus is to compare the NP contribution to the branching fraction of decay processes (under consideration) with the SM prediction and also with the experimental limits. In the forthcoming section, we will discuss these processes one by one.

#### 2.

In the SM, the effective Hamiltonian for the semileptonic and pure leptonic processes is given by [62, 63]

In this case, all leptons couple universally with the electroweak gauge bosons, wherewhere and

and , and are penguin and box diagrams, respectively. are CKM matrix elements and is the coupling strength of strong interactions.

In MSSM, the relevant effective Lagrangian for the decay process is given by [57–61]where . The first term in (2) comes from the down squark exchange (where and are down type quarks). The dimensionless coupling constant is related to Yukawa couplings by

The differential decay rate for the semileptonic decay processes is given by [62–64]where with and , ; is the general parameter. We have used the value for the form factor for the above decay processes of and as given in [65]. Since this work focuses on MSSM, we will shift our focus to (for the calculation of limits on couplings) and Yukawa couplings (for the predictions of branching fraction). The decay rate for pure leptonic decay processes is given byThe form factor is given by [66]. represents the mass of strange meson and is the mass of lepton, where is same as that of semileptonic decays.

#### 3.

In MSSM, the relevant effective Lagrangian for the decay process is given by [57–61]where . The first term in (2) comes from the down squark exchange (where and are down type quarks). The dimensionless coupling constant is given by

The differential decay rate for semileptonic decay processes is given by [62–64]where

with

with

and as explained in the above section is the general NP parameter and . We have used the form factor for the above decay processes of as given in [67]. The decay rate for pure leptonic decay processes is given by [46, 50–52]

The form factor is given by [66], represents the mass of beauty meson and is the mass of lepton.

#### 4. Results and Discussions

We have carried out study of hypercharge changing two and three body decay processes of pseudoscalar mesons (), where and . This study considers two types of processes: polarized and unpolarized flavor of the lepton. The analysis carried out involves comparison of branching fraction of a certain decay process (mentioned above) calculated from both theoretical and experimental ground. This comparison not only helps to place bounds (listed in Tables 2, 4, and 5) on Yukawa couplings but also enables to predict (listed in Tables 3, 6–9) the enhancement of similar processes (having identical FCNC). The enhancement is given in three forms, namely, NP (contribution from Yukawa couplings only), Interference (product of SM contribution, coming from and Yukawa couplings), and combined (NP+Interference). All the results are displayed in graphs plotted in Figures 2–13, which are composed of simple (variation of branching fraction with respect to the magnitude of NP parameter, i.e., ) and contour plot (region plot of magnitude and phase of NP parameter at different values of branching fraction within limits of experimental measurements). A visual error analysis for the experimental measurement of branching fraction is also presented in these graphs by constraining lines at mean and level. Similar error analysis is repeated in tables. The Feynman diagrams and table listing experimental data [68] related to these processes are given in Figure 1 and Table 1, respectively. The Yukawa couplings involved are normalized to the square of in all these tables and figures.