Chiral symmetry breaking and effective Lagrangians for softly broken supersymmetric QCD

Abstract

We study supersymmetric QCD with N f < N c in the limit of small supersymmetrybreaking masses and smaller quark masses using the weak-coupling Kähler potential. We calculate the full spectrum of this theory, which manifests a chiral symmetry breaking pattern similar to that caused by the strong interactions of the standard model. We derive the chiral effective lagrangian for the pion degrees of freedom, and discuss the behavior in the formal limit of large squark and gluino masses and for large N c . We show that the resulting scalings of the pion decay constant and pion masses in these limits differ from those expected in ordinary nonsupersymmetric QCD. Although there is no weak coupling expansion with N f = N c , we extend our results to this case by constructing a superfield quantum modified constraint in the presence of supersymmetry breaking. †

θ and the η ′ in large N supersymmetric QCD

“…In Secs. 2 and 3, we observe a number of properties consistent with the large N conjectures for ordinary QCD, including, as noted previously in [7,17], branched behavior (associated with the gaugino condensate in the SUSY limit, as well as FF in the presence of soft breakings), and, as noted in [16,19], a supersymmetric version of the η ′ with mass of order 1/N in certain regions of parameter space.…”

“…Turning on general soft breakings gives a set of theories which, in certain limits, should reduce to SU(N) QCD with N f flavors of fermionic quarks. For small values of the supersymmetric mass terms and the soft breaking terms, the system can be studied in a systematic perturbative/semiclassical approximation [16,19]. Consider first adding only soft squark and gaugino masses:…”

R -Axion at Colliders

“…where r ϵ is the R charge of the explicit-breaking spurion ϵ R , with ϵ R =F ≪ 1 technically natural. Explicit examples of this mass hierarchy arise by adding suitable R-symmetry breaking deformations in calculable models of dynamical SUSY breaking like the 3-2 model [1,13,14] or in SUSY QCD at large N once the hidden gauginos and squarks get soft masses [15,16]. Moreover, in SUSY-breaking models like the one in [5], the explicit breaking of the R-symmetry is generically bounded from above (ϵ R =F ≪ 1) by requiring the SUSY-breaking vacuum to be metastable.…”

Superheavy dark matter from string theory

“…Hence we need to discard the pure SYM case. For N f > 0 with soft supersymmetry breaking terms, squarks and quarks form scalar and fermionic condensates which all develop a mass of order m 0 M 1/2 m σ [53], except for pion-like mesons which are exactly massless in the absence of a supersymmetric quark mass term in W . Therefore σ could decay into these heavy condensates but some of them would be stable in the absence of EW interactions.…”