Spontaneous breaking of the left-right symmetry and quantum corrections
Cvetič, Mirjam ; Sher, Marc
In this paper we study new features of spontaneous symmetry breaking (SSB) of the left-right (LR) symmetry based on a model with gauge symmetry SU(2)R * SU(2)L * U(1)B-L that arise when we include ...quantum corrections to the tree-level Higgs potential. First, an instructive toy model, with fermions remaining massless, is considered in which the gauge symmetry breaks via SU(2)L * U(1)Y down to U(1)EM through the vacuum expectation value (VEV) of just two scalar doublet fields ?L (2, 1, 1) and ?R (1, 2, 1). We show that while the tree-level solution yields ?R ? 0 and ?L = 0, inclusion of quantum corrections can induce ?R? 0 and provide a hierarchy mWR > mWL ? 0 for masses of the left-handed and right-handed vector bosons. The striking prediction of the model, following from the minimization of the potential, is a result of R = mWR/mWL being bounded above the expression exp(1+ß/2?2 where ?=g2/4? with g a gauge coupling constant and ß depends on the tree-level Higgs potential parameter and ß<O(?2). Thus in this model there is a natural bound for R 2 to4. The model also predicts a light neutral pseudo-Goldstone particle, which is indeed a Higgs particle of the Weinberg-Salam model, and whose mass cannot exceed 10 GeV. This approach represents a viable way for breaking a discrete LR symmetry by quantum corrections and evades a constraint which states: the symmetry of the VEV obtained at the tree level cannot be broken by quantum corrections unless some ĆaccidentalĆ symmetry is present at the tree-level Higgs potential. We also consider a realistic model where we include together with the doublet fields ?L,R, also the field ? (2, 2, 0) giving Diracmasses to fermions. In this model we observe that the LR symmetry can be broken spontaneously at the tree level as before, but in contrast to the toy model, also SU(2)L symmetry is necessarily broken at the tree level consistent with a hierarchy requirement mWR > mWL ? 0. Including quantum corrections the ratio R is still found to be bound above by the same expression as the one obtained in the toy model. However, now ß can range from|O(?2| to |O(?)| which permits the ratio R to span the entire range from 2to exp[|O(1/?)|]. Also, the spectrum of pseudo-Goldstone particles is studied, and it is found compatible with experiment.
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