Abstract
We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green’s functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.
Highlights
The current intensive searches for Physics Beyond the Standard Model (BSM) are becoming a very timely endeavor, given the precision experiments at LHC and elsewhere; at the same time, numerical studies of BSM Physics are more viable due to the advent of lattice formulations which preserve chiral symmetry
As a forerunner to a long-term prospect of addressing numerically supersymmetric extensions of the Standard Model, we have undertaken an investigation of SQCD, in order to address some of the fundamental difficulties which must be resolved before further progress can be made
Quarks, squarks and gluinos live on the lattice sites, and gluons live on the links of the lattice: Uμ(x) = eigaTαuαμ(x+aμ/2). This formulation leaves no SUSY generators intact, and it breaks chiral symmetry; it represents a “worst case” scenario, which is worth investigating in order to address the complications [5] which will arise in numerical simulations of SUSY theories
Summary
The current intensive searches for Physics Beyond the Standard Model (BSM) are becoming a very timely endeavor, given the precision experiments at LHC and elsewhere; at the same time, numerical studies of BSM Physics are more viable due to the advent of lattice formulations which preserve chiral symmetry. The lattice formulation of various supersymmetric models is currently under active study [1, 2]. As a forerunner to a long-term prospect of addressing numerically supersymmetric extensions of the Standard Model, we have undertaken an investigation of SQCD, in order to address some of the fundamental difficulties which must be resolved before further progress can be made. Within the SQCD formulation we compute the quark (ψ), gluino (λα), gluon (uαμ), squark (A) propagators and the gluon-antighost-ghost Green’s function. The details of our work, along with a longer list of references, can be found in Ref.[3]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
