Perturbative and non-perturbative infrared behavior of ...

7.4. R-parity and R-symmetry
model dependent, we can add a new discrete symmetry to the visible sector which eliminates the
possible baryon and lepton violating terms in the renormalizable superpotential. This symmetry
is called R-parity or matter parity. The matter parity quantum numbers are given by
PM = (−1) 3(B−L)
(7.4.26)
under which the quark and lepton supermultiplets have PM = −1 and the Higgs and vector
supermultiplets have PM = 1. It is easy to check that it is equivalent to the R-parity
PR = (−1) 3(B−L)+2s
(7.4.27)
where s is the spin of the particle. The advantage of this definition is that the Standard Model
particles have PR = 1 while their supersymmetric superpartners have PR = −1.
Supersymmetric field theories also possess the continuous R-symmetry, under which the gaugino
is usually assigned to have charge 1. This continuous symmetry has nothing to do with the
discrete R-parity. It is of phenomenological interest that R-symmetry is broken in the hidden
sector. By looking at the gaugino mass term in (7.2.23) it is easy to see that it does not preserve
R-symmetry. Hence if a supersymmetric theory have a vacuum which breaks supersymmetry
but preserves R-symmetry, the radiative corrections which generate the non-renormalizable soft
interactions (7.2.23) cannot generate a gaugino mass term. Then, the low energy spectrum would
have a massless fermion in the adjoint representation, which is not observed.
Even if the R-symmetry is anomalous and broken by quantum effects to a discrete subgroup,
this problem is not solved unless this discrete subgroup is reduced to Z2, and in R-symmetry
preserving vacua a gaugino mass is forbidden.
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