Abstract
We discuss the role of a class of higher dimensional operators in 4D N=1 super-symmetric effective theories. The Lagrangian in such theories is an expansion in momenta below the scale of “new physics” (Λ) and contains the effective operators generated by integrating out the “heavy states” above Λ present in the UV complete theory. We go beyond the “traditional” leading order in this momentum expansion (in ∂/Λ). Keeping manifest supersymmetry and using superfield constraints we show that the corresponding higher dimensional (derivative) operators in the sectors of chiral, linear and vector superfields of a Lagrangian can be “unfolded” into second-order operators. The “unfolded” formulation has only polynomial interactions and additional massive superfields, some of which are ghost-like if the effective operators were quadratic in fields. Using this formulation, the UV theory emerges naturally and fixes the (otherwise unknown) coefficient and sign of the initial (higher derivative) operators. Integrating the massive fields of the “unfolded” formulation generates an effective theory with only polynomial effective interactions relevant for phenomenology. We also provide several examples of “unfolding” of theories with higher derivative interactions in the gauge or matter sectors that are actually ghost-free. We then illustrate how our method can be applied even when including all orders in the momentum expansion, by using an infinite set of superfield constraints and an iterative procedure, with similar results.
Highlights
Replaces non-local interactions with virtual particles exchange by a set of local interactions such as to give the same low energy physics
The Lagrangian in such theories is an expansion in momenta below the scale of “new physics” (Λ) and contains the effective operators generated by integrating out the “heavy states” above Λ present in the UV complete theory
We obtain in this way a two-derivative, ghost free Lagrangian that generates in the low energy the Dirac gaugino mass term
Summary
Let us first consider the case the -operators, eqs. (1.3), (1.4) in the matter sector [15]. One due to the operator , the second because auxiliary F1 of Φ1 became dynamical, an extra d.o.f. is present which, by supersymmetry, demands the presence of an extra (ghost) superfield. The notation ν3 ∼ −ρ means ν3 has the sign of (−ρ) and is 0 if ρ = 0 The effect of the original higher dimensional operators was to introduce ghost superfields, of large mass (of order Λ) as shown by the F-terms in the last two equations.. Using the equations of motion one can integrate out the massive ghost superfields. This is the formulation that can be used for phenomenology In both examples there are no ghost superfields as asymptotic (final) states in the approximation O(1/Λ3). An alternative to our approach that leads to results identical to those in eqs. (2.13), (2.14), is to use in eq (2.1) non-linear field redefinitions to “remove” the derivative operators [18]
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