We have come across several works , where some discrete symmetries is invoked for the stability of a potential DM candidate. That we do by assigning Z_n charges on the respective particles whom we want to call as Dark (and obviously seeing that they are not decaying to some known SM particles). But how the scenario goes when we need to invoke accidental symmetries to stabilize the potential DM ?
Dear Mukta,
I am not sure whether I entirely understand your question... nobody can "invoke" an accidental symmetry, as it is by it nature "accidental". Furthermore, accidental symmetries generically appear in a different context: usually, one imposes a symmetry which has to be spontaneously broken for phenomenological reasons. However, if this is done without sufficient care, it may be that even after the breaking some subgroup of the original symmetry remains intact, in a way that it forbids certain things one actually wanted to achieve by the breaking (e.g. a certain particle remains massless even though the original plan was to give it a mass).
In that sense, an accidental symmetry has always been put in implicitly by hand at some point (although often not by intention). But ultimately it was imposed on a certain model and is thus, from a technical point of view, not different compared to directly putting in some stabilising symmetry.
Best regards,
Alexander
Suppose we write a Lagrangian density using a gauge symmetry and Lorentz invariance, and then discover that there is some other symmetry which is also accidentally respected by the Lagrangian; we then generally say that it is accidental. In standard model Lagrangian density, we see that Baryon number and Lepton number are conserved accidentally.
While addressing dark matter problem, one possibility is to add exotic scalars to SM particle content and write down all gauge invariant terms in the scalar potential and also check whether exotic scalars couple to standard model fermions. After this check whether there is a symmetry such as Z2 which will keep Lagrangian invariant but will change the sign of exotic scalar fields. If you are lucky such a symmetry may exist, which will make the neutral members of exotic multiplets stable.
ref:Amine Ahriche et al: http://arxiv.org/abs/1504.05755
all light fermionic degrees of freedom, including the Standard Model (SM) fermions and all possible light beyond-the-standard-model fields, are chiral with respect to some spontaneously broken abelian gauge symmetry. Hypercharge, for example, plays this role for the SM fermions. If you ıntoduce a new symmetry, U(1) ν , for all new light fermionic states. Anomaly cancellations mandate the existence of several new fermion fields with nontrivial U(1) ν charges. If we develop a concrete model of this type, for which we can show that (i) some fermions remain massless after U(1) ν breaking — similar to SM neutrinos — and (ii) accidental global symmetries translate into stable massive particles — similar to SM protons. These ingredients do provide a solution to the dark matter and neutrino mass puzzles assuming we also postulate the existence of heavy degrees of freedom that act as “mediators” between the two sectors.
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