A dilaton near the conformal window?

In a project supported by the National Science Foundation, we are developing computer code to study scalar resonances in QCD-like theories, harvesting the significant computing power of GPUs. This has an application to the so-called dilaton in a "walking" theory. While the evidence from the Large Hadron Collider strongly favors an elementary Higgs boson with Standard Model couplings, it is still an interesting theoretical question as to whether or not approximate scale invariance over some range of scales can produce an anomalously light scalar resonance in the QCD-like theory. The calculation is quite similar to that for the sigma resonance in QCD. Lattice QCD is still attempting to extract this state, because of significant difficulties.

The underlying theory The theory that we are studying is the one with three Majorana fermions in the adjoint representation of gauge group SU(2). Because four Majorana fermions is believed to be inside the conformal window, and because two Majorana fermions is believed to be "more confining" than N=2 super-Yang-Mills due to the absence of elementary scalars, it would seem that three Majorana fermions stands a good chance to be right on the edge of the conformal window. In this case it may be a walking theory.

Pseudo-Nambu-Goldstone boson If chiral symmetry spontaneously breaks for a value of the running coupling which is near the approximate fixed point, then the beta function is quite small at the scales relevant for chiral symmetry breaking. Thus there is an approximate scale invariance at the corresponding energy regime and one can expect by this argument that there is an anomalously light scalar resonance in the spectrum, the so-called dilaton.

Method for extraction As with our similar study of the QCD sigma state, the problem that we encounter with standard methods is that in the chiral limit there is a two-pion continuum in the same channel as the scalar resonance. This continuum will dominate correlation functions, making it impossible to see the signal if the "pions" are light. For this reason we use the Lüscher method to extract the resonance properties.

GPU code We have integrated the GPU inverter package QUDA with the physics application package CPS in order to conduct our measurements. This makes it straightforward to compute our correlation functions, using the tools in CPS, while having the acceleration of QUDA.

Variational methods In order to get accurate estimates of the two-pion energy states in the two-pion correlation function, we will variational methods. This involves building a large set of operators and then solving a generalized eigenvalue problem.