Seesaw Neutrino mass and U(1) symmetry Rathin Adhikari Centre for Theoretical Physics Jamia Millia Islamia Central University New Delhi : arXiv: [hep-ph] Based on : e-Print: arXiv: [hep-ph] R. Adhikari, J. Erler and E. Ma R. Adhikari, J. Erler and E. Ma

22:33 2 Effective Dimension five operator which generates neutrino mass : There are three tree level realization : E. Ma, Phys. Rev. Lett, 81, 1171 (1998) (I) (II) (III) Replacing in (I) by heavy Majorana fermion triplet S. Weinberg, Phys. Rev. Lett, 43, 1566 (1979)

22:33 3 U(1) gauge symmetry Consider fermion of Standard Model plus and under new gauge symmetry Ref: E. Ma, Mod Phys Lett A17, 535 (2002); E. Ma & D. P. Roy, Nucl. Phys B644,290 (2002); S.M. Barr & I. Dorsner, Phys. Rev.D 72, (2005)

22:33 4 Condition for absence of axial vector anomaly : Condition for absence of mixed gravitational-gauge anomaly : (1) (2) (3) (4) (5) (6) Ref: Adler, Phys. Rev 177, 2426 (1969); Bell & Jackiw, Nuovo Cemento, A60, 47 (1969); Bardeen, Phys Rev, 184,1848 (1969) Ref: Delbourgo & Salam, PLB 40, 381 (1972); Eguchi & Freund, PRL, 37, 1251 (1976); Alvarez-Gaume & Witten NPB, 234,269 (1984)

22:33 5 From (1), (3) & (4) (which are independent of) two solutions: For, (2) impliesNo new gauge symmetry Solution (I): Gauge symmetry are possible Solution (II) : From (5) & (6) one solution is (a)

22:33 6 However, in this case to cancel anomalies additional singlets are to be considered. Four possible models in this case: Another solution (b)

22:33 7 Radiative neutrino masses are possible here

22:33 8 Model B Model C

22:33 9 For zero mass mixing X gauge boson mixes with Z boson

22:33 10

22:33 11 If X gauge boson is observed at LHC, then r may be determined from its decay branching fraction :

22:33 12 One loop radiative contribution to neutrino mass In Model C the 3X3 Majorana neutrino mass matrix receives tree level contribution from the coupling of to a linear combination of through as well as radiative contribution from and. This is a natural hierarchical scenario.

22:33 13 Lightest particle of odd is dark matter candidate. It may be a scalar boson - the lighter of and Conclusion : (1) In the context of U(1) extension of the Standard Model we have discussed consequences of having one or more Majorana fermion triplets generating neutrino mass through Seesaw mechanism. (2) Associated neutral gauge boson has prescribed couplings to the usual quarks and leptons in terms of and The exclusion limit of from low energy data has been obtained showing that may be accessible to LHC if is of the order of

22:33 14 (3) In case of one triplet (Model B) one Higgs doublet couples to quark and the other to leptons; in case of two triplet (Model C) there is third scalar doublet which allows natural implementation of radiative neutrino mass and dark matter. Thank You