Linear delta expansion applied to the O’Raifeartaigh model

Abstract

We reassess the method of the linear delta expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules in the framework of the O'Raifeartaigh model for spontaneous supersymmetry breaking. The effective potential is calculated using both the fastest apparent convergence and the principle of minimal sensitivity criteria and the consistency and efficacy of the method are checked in deriving the Coleman-Weinberg potential. DOI: 10.1103/PhysRevD.80.065002 PACS numbers: 11.10.Ef, 11.30.Pb O'Raifeartaigh-type models for spontaneous breaking of supersymmetry (SUSY) have recently received renewed attention. According to the Nelson-Seiberg theorem [1], all these models have an R symmetry, which plays an important role in SUSY breaking. However, in order to have nonzero Majorana gaugino masses, R symmetry needs to be broken [2]. Since the simplest original O'Raifeartaigh model [3] does not spontaneously break R symmetry, generalized O'Raifeartaigh models, which spontaneously violate R symmetry, have been constructed [2,4,5].In many generalized O'Raifeartaigh models, R symmetry is spontaneously broken by the pseudomoduli, which are charged under R symmetry and acquire a nonzero vacuum expectation value via effective potential. Using this approach, it was shown how to build up models that break R symmetry at one-loop via the Coleman-Weinberg potential [6,7].Since the Coleman-Weinberg potential [8] is a sum of all one-loop diagrams of the theory, it is very interesting to develop methods that account for higher loop corrections in the effective potential of O'Raifeartaigh-type models and go beyond the approximation used in [6]. There are two traditional ways to make resummations in supersymmetric and nonsupersymmetric quantum field theories: the diagrammatic calculation and the functional calculation [8,9]. Both are very difficult to use if we are interested in going beyond the Coleman-Weinberg approximation. Mainly because it is necessary to work with infinite diagrams, which turns the renormalization procedure into a heavy task.Over the past years, an alternative resummation method has been developed, namely, the linear delta expansion (LDE) [10]. This method can easily reproduce the Coleman-Weinberg potential, and the use of the LDE in various quantum field theory models has proven to be a powerful tool to derive new nonperturbative results [11,12]. In [13], the method was further developed to be applied to supersymmetric theories in superspace, where the Coleman-Weinberg potential has been derived and twoloop corrections for the Kähler potential of the WessZumino model have been computed. The main characteristic of the method is to use a traditional perturbative approach together with an optimization procedure. So, in order to derive a nonperturbative result, it is just necessary to work with a few diagrams and use perturbative renormalization techniques.The main goal of this paper is to show that the LDE can also be a powerful method to derive nonpe...

Supergraph approach in a higher-order linear delta expansion calculation of the effective potential forF-type broken supersymmetry

“…This naturally brings nonlinear g contributions and generates nonperturbative results that go beyond the one-and two-loop results derived in Refs. [13,31]. The parameters were chosen so that spontaneous SUSY breaking appears in the O'Raifeartaigh model.…”

“…The above result represents the Coleman-Weinberg-type potential [29,30] for the O'Raifeartaigh model [13,28], and it accounts for the sum of all one-loop diagrams. It is a nonperturbative result in that it takes into account all orders (actually infinite orders) in the original coupling constant.…”

“…We adopt a superfield approach and follow Refs. [13,14,26]. Building up our superspace action in terms of chiral and antichiral supermultiplets, we start off from what we call the interpolated Lagrangian L :…”

“…With our super-Feynman rules and the results of Ref. [13], the effective potential up to the order 1 reads as given below:…”

“…In a series of previous works [13,14], we have adopted the minimal O'Raifeartaigh model [1], which realizes SUSY violation by means of the so-called F terms, and we have devised a technique to approach the problem with the use of superfield and supergraph techniques. To get a richer perturbative series, we have chosen the so-called linear delta expansion (LDE) 1 and we have coupled this method to our superfield methods.…”