Abstract
We discuss the selection rules for baryon number nonconserving processes in the context of various gauge models with partial and complete unification of all elementary particle forces. Three separate cases are discussed: (a) Δ(B−L) = 0, Δ(B+L) ≠ 0; (b) Δ(B−L) ≠ 0, Δ(B+L) = 0; and (c) Δ(B−L) ≠ 0 and Δ(B+L) ≠ 0. Observation of \(n - \bar n\) “oscillation” without proton decay with a life-time of ≳ 1030 years would be evidence of “partial unification” with an intermediate mass scale of ~108–109 GeV.
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References and Footnotes
For a review and earlier references, see M. Goldhaber, “Unifi-cation of Elementary Forces and Gauge Theories”, ed. by D. Cline and F. Mills, Academic Press (1977), p. 531. H.S. Gurr, W.R. Kropp, F. Reines and B.S. Meyer, Phys. Rev. 158, 1321 (1967): F. Reines and M.F. Crouch, Phys. Rev. Lett. 32_, 493 (1974).
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In the Pati-Salam model with integer charge quarks, this theorem is not respected since SU(3)C is only an approximate symmetry at low energies. Since their model has an absolutely conserved B+3L quantum number (called by them fermion number), it allows for decays of the type p →π++3V. For a review and detailed predictions, see J.C. Pati, University of Maryland Technical Report No. 79-066 (1979) (unpublished).
The question of B-L violation in the framework of grand unifi-cation has been considered by F. Wilczek and A. Zee, University of Pennsylvania Preprint, (1979).
R.N. Mohapatra and R.E. Marshak, VPI-HEP-80/1.
J.C. Pati and A. Salam, Phys. Rev. D10, 275 (1974). R.N. Mohapatra and J.C. Pati, Phys. Rev. Dll, 566, 2558 (1975). G. Senjanovic and R.N. Mohapatra, Phys. Rev. D12, 1502 (1975). For a review, see R.N. Mohapatra, “New Frontiers in High Energy Physics”, ed. by A. Perlmutter and Linda Scott, ( Plenum, 1978 ), p. 337.
This yields ΔL processes such as neutrinoless double β decay and an interesting correlation between neutrino mass and the right-handed W boson, i.e. \({m_\upsilon } \simeq \frac{{{m_\ell }^2}}{{{g_{{m_{{w_r}}}}}}}.\) See R.N. Mohapatra and G. Senjanovic, CCNY-HEP-79/10 (1979).
The equivalent of this relation was suggested by A. Gamba, R.E. Marshak and S. Okubo (Proc. Nat. Acad, of Sci.? (1959)) when the consequences of the baryon-lepton symmetry of the weak interaction were first examined. See also paper by R.E. Marshak and R.N. Mohapatra for Maurice Goldhaber Festschrift (New York, 1980 ).
We have used the same notation as J.C. Pati and A. Salam (ref. 9) but it is important to stress that the fourth color in our case is (B–L) not L.
For a review of the proposed experiments, see L. Sulak, Proceedings of “Weak Interaction” Workshop at Virginia Polytechnic Institute (1979).
The extended SU (5) model has also been considered in detail by L.N. Chang and N.P. Chang (to be published).
H. Fritzsch and P. Minkowski, Ann. of Phys. 93, 193 (1975). H. Georgi, in “Particles and Fields, 1975” (AIP Press, N.Y.).
M. Chanowitz, J. Ellis and M.K. Gaillard, Nuc. Phys. B129, 506 (1977). For recent discussions on the subject see H. Georgi and D.V. Nanopoulos, Nuc. Phys. B155, 52 (1979). R.N. Mohapatra and B. Sakita, Phys. Rev. D (to appear). M. Ge11-Mann, P. Ramond and R. Slansky - unpublished.
This is the subject of a forthcoming paper by R.N. Mohapatra and G. Senjanovic, to appear as a City College Preprint (1980). It is shown in this paper that to get sin2 0W(mwL) to be about 0.23, while at the same time getting an intermediate mass scale, requires the value mX,Y ≈ 1019 GeV and mWR ≈10 GeV, as well as mX,Y.. mPS. In this case, the proton decay mediated by the gauge bosons is completely suppressed leaving n–n oscillation as a possible dominant mode of baryon non- conservation.
HUTP-79/AO29 and HUTP-79/A059. These preprints discuss modifications of the minimal SU(5) model and reach similar conclusions to ours as summarized in Table 1; however, we stress that the new result highlighted by Table 1 is the predicted dominance of the “neutron oscillation” mode in a partial unification model incorporating B-L local symmetry on the electroweak level.
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Marshak, R.E., Mohapatra, R.N. (1980). Selection Rules for Baryon Number Nonconservation in Gauge Models. In: Perlmutter, A., Scott, L.F. (eds) Recent Developments in High-Energy Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3165-0_18
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