### Epistemology and phenomenology of B-L gauged extension of the Standard Model

**Gauging a global symmetry and fixing the electric charge**

Many attempts were made to combine space-time symmetries with internal symmetries, e.g., theories based on SU(6) and in the 1970s the emergence of supersymmetry, which from 1980’s became the dominant theme in both theory and experiment. Although experiments ultimately decide which symmetries live and which die, either way they leave a lasting impact on the ﬁeld.In this article, I will focus on a new symmetry of particle physics, the B−L symmetry, which is a global symmetry of the standard model and appears to be emerging as a local symmetry designed for understanding the physics of neutrino masses...

A key prediction of the standard model (SM) is that neutrino masses vanish since, unlike other fermions, which have both left and right handed chiralities in the theory, there is no right handed neutrino but just the left handed SU(2)partner of e_{L}._{L}Because several experiments have conﬁrmed since 1990’s that neutrinos have mass, the simplest extension of SM is to add to it one right handed neutrino per generation to account for this fact. As soon as this is done, one not only has Tr(U(1)[SU(2)_{B-L}]_{L}^{2})=0 and Tr(U(1)[U(1)_{B-L}_{Y}]^{2})=0 but also Tr(B-L)=0. This allows for the possibility of gauging the U(1)^{3}..quantum number, which gives B−L a dynamical role._{B-L}

... it was pointed out independently by Marshak and me [11] and Davidson [12], that the electric charge formula now becomes

Q = I+_{3L}I+ (_{3R}B−L) / 2...

This is a considerable improvement over the SM electric charge formula... in the sense that all terms in the formula are determined through physical considerations of weak, left and right isospin, and baryon and lepton number, that reﬂect independent characteristics of the various elementary particles. No freely ﬂoating parameters are needed to ﬁx electric charges as in the standard model. Electric charge is no more a free parameter but is connected to other physical quantum numbers in the theory. As a result, a number of interesting implications follow...

(Submitted on 26 Sep 2014)

**Looking for neutron oscillations, Majorana fermions, new gauge bosons...**

The question that has to be tackled is whether there exist a theory that combines neutrino mass via the seesaw mechanism which predicts an observable [neutron-antineutron oscillation] and yet keeps the proton ... stable. One example of such a theory was presented in 1980 in [16]. This model presents an embedding of the left-right seesaw model into a quark lepton uniﬁed framework using the gauge group ... SU(2)L×SU(2)R×SU(4)c with the symmetry breaking suggested in [the Pati-Salam model] rather than in Ref.13... The sixteen chiral fermions of the SU(2)L×SU(2)R×SU(4)c model ﬁt into the sixteen dimensional spinor representation of the SO(10) group [20] which can be the ﬁnal grand uniﬁcation group for left-right symmetry as well as B−L gauge symmetry...

... we have provided a broad brush overview of the history of B-L as a new symmetry in particle physics and how in recent years following the discovery of neutrino masses, interest in this possible new symmetry has grown enormously. In particular, its connection to both neutrino mass and baryon number violation have provided new insights into physics beyond the standard model. All these have to be conﬁrmed experimentally. At the same time, there are phenomenological studies of many different aspects of this symmetry. To summarize the efforts to unravel the degree of freedom corresponding to local B-L symmetry experimentally, I mention only a few topics.Deciphering whether neutrinos are Majorana fermions is a direct conﬁrmation of whether B-L symmetry is broken or not. This does not say whether it is a global or local symmetry. Furthermore, by itself, discovery of ββ. Such searches are currently under way at the LHC [30a, 30b].decay cannot tell where the scale of B-L symmetry breaking is. Supplemented by a discovery (or non-discovery) of neutron oscillation, one can get an idea about a possible range (or exclude a possible range) of this scale but not the actual scale. The most deﬁnitive way to discover the scale of B-L symmetry is to directly search for the gauge boson associated with this in the collider such as the LHC [29]. The same could also be inferred from a discovery of the W_{0ν}_{R}combined with a Majorana right handed neutrino

Id.

To deepen the historical perspective on our forty year-old Standard Model the interested reader may also benefit from reading an already twenty year old other Mohapatra paper :

Freedom from Adler-Bell-Jackiw anomalies is a primary requirement for the renormalizability of a gauge theory of chiral fermions, which forms the basis of the successful standard model of electroweak interactions and its many extensions. In this article,we explore to what extent, the assumptions behind the standard model as well as the observed quantization of electric charges of quarks and leptons can be understood using the various anomaly constraints and how the situation changes as one tries to incorporate a nonvanishing neutrino mass.

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