Neutrino Masses in the Lepton Number Violating MSSM

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1 Neutrino Masses in the Lepton Number Violating MSSM Steven Rimmer Institute of Particle Physics Phenomenology, University of Durham

2 A supersymmetric standard model Find the most general Lagrangian which is invariant under Lorentz, SU(3) C SU(2) L U(1) Y and supersymmetry transformations; renormalizable minimal in particle content Neither lepton number (L) nor baryon number (B) are conserved Two options: constrain Lagrangian parameters impose a further discrete symmetry when constructing the lagrangian

3 Superpotential The most general superpotential is given by W = Y E LH 1 E + Y D H 1 QD c + Y U QH 2 U c µh 1 H λllec + λ LQD c κlh λ U c D c D c Dreiner et al, building on work of Ibanez & Ross, show that there are three preferred discrete symmetries; R-parity, a Z 3 allowing /L and P 6, referred to as proton-hexality. L. E. Ibanez and G. G. Ross, Nucl. Phys. B 368, 3 (1992) H. K. Dreiner, C. Luhn and M. Thormeier, Phys. Rev. D 73 (2006)

4 L violating minimal supersymmetric standard model (/L-MSSM) Without imposing the conservation of L on the Lagrangian, bilinear terms exist between (and hence, mixing occurs between) charged gauginos, charged higgsinos and charged leptons neutral gauginos, neutral higgsinos and neutrinos Higgs bosons, sneutrinos... giving rise to some attractive features. B. C. Allanach, A. Dedes and H. K. Dreiner, Phys. Rev. D 69, (2004)

5 Vanishing sneutrino vev basis Notice that if L is not imposed, h 0 1 and ν Li carry the same quantum numbers, even before symmetry breaking. Define ν Lα = (h 0 1, ν Li ) µ α = (µ, κ i ) Solving the minimisation conditions defines a direction in this (h 0 1, ν Li ) space. In the interaction basis, we are free to define any direction in (h 0 1, ν Li ) to be the Higgs. Had the basis been rotated such that the Higgs points in this direction, a basis would have been chosen such that the sneutrino vevs are zero. M. Bisset, O. C. W. Kong, C. Macesanu and L. H. Orr, Phys. Lett. B 430, 274 (1998) Y. Grossman and H. E. Haber, Phys. Rev. D 59, (1999) A. Dedes, SR, J. Rosiek and M. Schmidt-Sommerfeld, Phys. Lett. B 627 (2005) 161

6 Neutrino Masses in /L-MSSM The mixing between neutrinos and neutral gauginos/higgsinos produces one tree-level, see-saw suppressed, neutrino mass. where m tree ν m tree ν = v 2 d ( M1 g2 2 + M 2 g 2) ( κ1 2 + κ 4Det[M χ 0] κ 3 2) A. S. Joshipura and M. Nowakowski, Phys. Rev. D 51, 2421 (1995) M. Nowakowski and A. Pilaftsis, Nucl. Phys. B 461, 19 (1996)

7 Neutrino Masses in /L-MSSM Loop corrections lift the degeneracy between the two massless neutrinos. The neutrino masses, and hence mass squared differences, are dependent on the values of lepton number violating couplings. Values for lepton violating couplings exist which reproduce experimental results for mass squared differences and mixing angles. d ν λ λ ν d L d R F. M. Borzumati et al, Phys. Lett. B 384, 123 (1996) ; A. S. Joshipura et al, Phys. Rev. D 60, (1999) K. Choi et al, Phys. Rev. D 60, (1999) ; D. E. Kaplan et al, JHEP 0001 (2000) 033 M. Hirsch et al, Phys. Rev. D 62, (2000) ; A. Abada et al, Phys. Rev. D 65, (2002) Y. Grossman et al, Phys. Rev. D 69, (2004) A. Dedes, SR and J. Rosiek, hep-ph/ to appear JHEP

8 Neutrino masses generated via λ couplings m 2 ATM [ev2 ] 6x10-3 5x10-3 4x10-3 3x10-3 2x10-3 a) All LNV=0 except λ i33 m 2 SOL [ev2 ] 1x10-4 9x10-5 8x10-5 7x10-5 All LNV=0, λ i33 fixed, λ i11 varied b) 1x x x x10-5 λ i33 6x x x10-2 λ 111 m 2 SOL [ev2 ] 1x10-4 9x10-5 8x10-5 7x10-5 All LNV=0, λ i33 fixed, λ i22 varied c) m 2 SOL [ev2 ] 1x10-4 9x10-5 8x10-5 7x10-5 All LNV=0, λ i33 fixed, λ i33 varied d) 6x x x x10-4 λ 122 6x x x10-5 λ 133 A. Dedes, SR and J. Rosiek, hep-ph/ to appear JHEP

9 Interplay between µ-decays and neutrino masses In certain cases lepton number violating couplings which give rise to the mass squared differences observed in neutrino experiments will be correlated with the branching ratios for rare lepton decays.

10 Interplay between µ-decays and neutrino masses Generate atmospheric mass difference h 0 2 h 0 2 B κ 1 h 0 2 h 0 2 κ 1 Generate µ eγ ẽ γ ν 1 ν 1 µ L λ 121 ẽ Generate solar mass difference ẽ ν1 B e R λ ν 121 λ ν 2 el er A. Dedes, SR and J. Rosiek, in progress

11 Bounds m 2 solar = ( ) 10 5 ev 2 m 2 atm = ( ) 10 3 ev 2 (hep-ph/ ) B(τ µγ) < BaBar (hep-ex/ ) B(µ eγ) < MEGA (hep-ex/ ) T. Schwetz, Acta Phys. Polon. B 36 (2005) 3203 B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett. 95, (2005) M. Ahmed et al. [MEGA Collaboration], Phys. Rev. D 65, (2002)

12 Solar mass sqaured difference against λ m 2 atm e-05 6e-05 4e-05 2e λ 121 All low energy parameters reproduced correctly SPS1a parameters, plus κ i chosen to give matm λ 121 varied Preliminary results

13 Br(µ eγ) against λ 121 2e e-11 Br(µ -> e γ) 1.6e e e-11 1e-11 8e-12 6e λ 121 All low energy parameters reproduced correctly SPS1a parameters, plus κ i chosen to give matm λ 121 varied Preliminary results

14 Summary and Conclusions The one-loop corrections to the neutrino masses in the /L-MSSM have been calculated, and it has been shown that the current values for mass squared differences and leptonic mixing angles can be reproduced. In some cases, the operators which determine neutrino masses, either at tree or loop level, will also give rise to flavour violating leptonic decays. Future experiments, B-factories in particular, will improve current bounds. It will be possible to correlate results from neutrino experiments with flavour violation and neutrinoless double beta decay experiments, providing useful information in determining the phenomenology of physics beyond the Standard Model.

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18 Effective Operators LFV events can be derived in terms of effective operators, in a model independent manner. Leading contributions to the effective operators arise from d = 6, SU(2) L U(1) Y invariant operators. For example, the τ µ γ vertex, with an on-shell photon, arises from the following terms in the effective Lagrangian. τ L D γ R µ R τ R D γ L µ L γ γ L eff = em τ [id γ L µ L σ µν τ R + id γ R µ Rσ µν τ L + H.c.] F µν A. Brignole and A. Rossi, Nucl. Phys. B 701 (2004) 3