# R–Parity Breaking in Minimal Supergravity

• Marco Aurelio Dı́az
• Published 1997

#### Abstract

We consider the Minimal Supergravity Model with universality of scalar and gaugino masses plus an extra bilinear term in the superpotential which breaks R– Parity and lepton number. We explicitly check the consistency of this model with the radiative breaking of the electroweak symmetry. A neutrino mass is radiatively induced, and large Higgs–Lepton mixings are compatible with its experimental bound. We also study briefly the lightest Higgs mass. This one–parameter extension of SUGRA–MSSM is the simplest way of introducing R–parity violation. † Talk given at the International Europhysics Conference on High Energy Physics, EPS– HEP–1997, 19–26 August 1997, Jerusalem. The Minimal Supersymmetric Standard Model (MSSM) [1] contains a large number of soft supersymmetry breaking mass parameters introduced explicitly in order to break supersymmetry without introducing quadratic divergencies. When the MSSM is embedded into a supergravity inspired model (MSSM–SUGRA), the number of unknown parameters can be greatly reduced with the assumption of universality of soft parameters at the unification scale. In addition, in MSSM–SUGRA the breaking of the electroweak symmetry can be achieved radiatively due to the large value of the top quark Yukawa coupling. The most general extension of the MSSM which violates R–parity [2] contains almost 50 new parameters, all of them arbitrary although constrained by, for example, proton stability . The large amount of free parameters makes R–parity violating scenarios less attractive. Nevertheless, models of spontaneous R–parity breaking do not include trilinear R–parity violating couplings, and these models only generate bilinear R–parity violating terms [3]. Motivated by the spontaneous breaking of R–parity, we consider here a model where a bilinear R–parity violating term of the form ǫiL̂ a i Ĥ b 2 is introduced explicitly in the superpotential [4]. We demonstrate that this “ǫ–model” can be successfully embedded into supergravity, i.e., it is compatible with universality of soft mass parameters at the unification scale and with the radiative breaking of the electroweak group [5]. For simplicity we consider that only the third generation of leptons couples to the Higgs. Therefore, our superpotential is W = εab [ htQ̂ a 3 Û3Ĥ b 2 + hbQ̂ b 3 D̂3Ĥ a 1 + hτ L̂ b 3 R̂3Ĥ a 1 − μĤ 1 Ĥ 2 + ǫ3L̂ a 3 Ĥ 2 ] (1) where the last term is the only one not present in the MSSM. This term induces a non–zero vacuum expectation value of the tau sneutrino, which we denote by 〈ν̃τ 〉 = v3/ √ 2. The ǫ3–term cannot be rotated away by the redefinition of the fields Ĥ ′ 1 = μĤ1 − ǫ3L̂3 √ μ + ǫ23 , L̂ 3 = ǫ3Ĥ1 + μL̂3 √ μ + ǫ23 , (2) and in this sense the ǫ3–term is physical. If the previous rotation is performed, the bilinear R–Parity violating term disappear from the superpotential. Nevertheless, a trilinear R– Parity violating term is reintroduced in the Yukawa sector and it is proportional to the bottom quark Yukawa coupling. In addition, bilinear terms which induce a non–zero vacuum expectation value of the tau sneutrino reappear in the soft terms, and therefore, the vacuum expectation value of the tau sneutrino is also non–zero in the new basis: 〈ν̃ ′ τ 〉 = v 3 6= 0. These terms are Vsoft = (B2 − B) ǫ3μ μ′ L̃ 3 H2 + (m 2 H1 −M L3) ǫ3μ μ′2 L̃ 3 H ′ 1 + h.c.+ ... (3)

### Cite this paper

@inproceedings{Daz1997RParityBI, title={R–Parity Breaking in Minimal Supergravity}, author={Marco Aurelio Dı́az}, year={1997} }