R-parity revisited!

In Minimal Supersymmetric Standard Model (MSSM), we generally assume the existence of an additional discrete symmetry called R-parity defined as

where B, L corresponds to baryon and lepton number respectively whereas s denotes spin. The advantage of this ad-hoc discrete symmetry is that it keeps all the B and L violating interactions away from the superpotential and the lightest super-particle(LSP) becomes stable which can be a good dark matter candidate provided it satisfies other criteria as well. There are some models where this discrete symmetry gets spontaneously broken and we loose some of its benefits. Although the most dangerous B violating terms (leading to proton decay) remain still away, but L violating terms come into the model as a result of spontaneous symmetry breaking. These terms are not very dangerous if parametrically put under control. We can in fact see some signatures of these in ongoing experiments like Tevatron and LHC. But the LSP will no longer be stable in this case and we loose a dark matter candidate. But it is not a very serious problem that gravition (superpartner of graviton) is always there to satisfy the criteria of a good dark matter candidate in any R-parity violating model. Since gravity is very weak, gravitino can have a long life time even if R-parity is broken in the model. In fact such spontaneously broken R-parity models are much better than R-parity conserving MSSM. Initially what I used to assume that R-parity conserving models are good enough to explain the low energy phenomena as well as dark matter. But when I was trying to arrive at non-zero neutrino masses by adding right handed singlet neutrinos, R-parity gets explicitly violated at the superpotential level. Of course if we break R-parity explicitly at the superpotantial level, we can not keep the other B and L violating terms away from the superpotential. The only way to get rid of this problem is to fine tune the B-violating terms to make proton stable enough and keep L-violating terms so as to give rise to neutrino mass. This fine-tuning does not look elegant but we need to do this to explain another hierarchy problem in case of neutrino mass (why it is so small compared to other leptons and quarks). We could have realized spontaneously broken R-parity in MSSM (without right handed singlet neutrinos) by sneutrino (superpartner of left handed neutrino) vev. But that will break lepton number (a global symmetry) spontaneoysly and will give rise to Majoron which will couple to Z-boson and hence ruled out from precision measurement of Z-decay width. Thus R-parity conserving and spontaneous R-parity violating MSSM are not good enough to explain all the low energy phenomena. We need to consider either explicit R-parity violating MSSM (which needs lots of fine tuning in the R-parity breaking sector) or go beyond MSSM by enlarging the Higgs sector or gauge symmetry.

Reviewer's comments I

Today I got the first set of comments from reviewers of Physics Letters B. They have sent eight comments. Most of them are minor ones which can be fixed by rephrasing some sentences. Some sentences are communicating a different meaning than what we want. So fixing them is not a big deal. However there is a serious conceptual issue which needs some careful study. I need to go to PRL, Ahmedabad soon to work with my collaborator on this issue and resubmit the paper again. I am quite sick of working alone and communicating via emails. There always remain a communication gap in this process. The issue we need to study is regarding R-parity violation in our model and the stability of dark matter candidate. Although any R-parity violating supersymmetric model will rule out a stable dark matter candidate, in our model I still think we can have a stable dark matter candidate which is basically the LSP (Lightest supersymmetric particle). Since our model has $ U(1)_{B-L} $ gauge symmetry, all the R-parity $ R_p = (-1)^{3(B-L)+2s} $ violating dimension four terms are absent from the lagrangian. However the terms which is responsible for mixing the standard model neutrinos with the singlet sterile neutrinos violate R-parity which we are calling as accidental breaking. Since neutrinos are even and the sterile gauge singlet fermions are odd under R-parity, their mixing will of course violate R-parity. But although the sterile neutrino need not be stable unless we incorporate some other discrete symmetries, its superpartner can be stable if its the LSP. Because there is no term in the superpotential which makes this LSP decay into two standard model particles. Hence if the superpartner of the sterile singlet neutrino becomes the LSP, it can be a stable dark matter candidate. I hope we will be able to convince the reviewers through these arguments, without calculating the life time of the dark matter candidates. The following video tells how embarrasing reviewer's comments are sometimes :D

A purely supersymmetric origin of neutrino mass

Yesterday I came to know about a completely supersymmetric(SUSY) origin of tiny neutrino mass, that is, in the non-SUSY version of the model neutrino mass remains either zero or comparable to lepton/quark masses. This comes when neutrino mixes with the neutralinos in the Supersymmetric model. The neutralinos are the mass eigenstates of neutral gauginos as well as Higgsinos. Neutrinos can mix with the neutralinos only if the sneutrino field get a vacuum expectation value (vev). Diagonalizing the mixing mass matrix will give rise to a small neutrino mass by sutable adjustment of different scales. However since neutrino/sneutrino carry a lepton number whereas neutralinos do not, such mixing violate R-parity. This R-parity violation however should not lead to dangerous proton decay, but it will make the standard neutralinos decay into neutrinos. If neutralino is to be a dark matter candidate, the relic abundance will put a constraint on the R-parity violation. Thus this scenario will be tightly constrained by smallness of neutrino mass as well as dark matter relic abundance. I am trying to see if there is any other advantage of this approach, say from the point of view of recent positron excess measured by various dark matter indirect detection probes.

Oops!!...my model violates R-parity

Yesterday I got a very important remark on the paper I am writing from my supervisor. He mentioned that some of the terms in the lagrangian violates R-parity. By the way R-parity is a discrete symmetry defined as $ R_p = (-1)^{2s+3(B-L)}$ where s is the spin, B and L are baryon and lepton number of the particle respectively. Although in the model there is an overall B-L gauge symmetry, there arises R-parity violation in some mass terms. These mass terms however are not coming from the soft SUSY breaking lagrangian, but from the superpotential itself. The mass lagrangian actually mixes two different fermions with odd and even R-parities. However there is no vertex (as far as I know) in the model which leads to R-parity violation and hence I don't think these R-parity violating mass terms would lead to any dangerous proton decay type of consequences. I am still waiting for supervisor's comments on this. I hope it will be enough to mention this in the paper without exploring further details. Just keeping my fingers crossed...:)