V. Ayyar, T. DeGrand, M. Golterman, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. SvetitskySpectroscopy of SU(4) composite Higgs theory with two distinct fermion representations, arXiv:1710.00806 [hep-lat], October 2017. Submitted to Physical Review D.
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously.  Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the non-anomalous U(1) symmetry of the model. Our results are broadly consistent with large-Nc scaling and vector-meson dominance.
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V. Ayyar, T. DeGrand, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. SvetitskyChiral Transition of SU(4) Gauge Theory with Fermions in Multiple Representations, talk given by D. Hackett at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, June 2017, to appear in proceedings (arXiv:1709.06190 [hep-lat], September 2017).
We report preliminary results on the finite temperature behavior of SU(4) gauge theory with dynamical quarks in both the fundamental and two-index antisymmetric representations. This system is a candidate to present scale separation behavior, where fermions in different representations condense at different temperature or coupling scales. Our simulations, however, reveal a single finite-temperature phase transition at which both representations deconfine and exhibit chiral restoration. It appears to be strongly first order. We compare our results to previous single-representation simulations. We also describe a Pisarski-Wilczek stability analysis, which suggests that the transition should be first order.
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B. SvetitskyLooking behind the Standard Model with lattice gauge theory, plenary lecture given at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, June 2017, to appear in proceedings (arXiv:1708.04840 [hep-lat], August 2017).
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to address fundamental dynamical questions. I survey recent work in this area.
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T. DeGrand, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. SvetitskyTowards partial compositeness on the lattice: Baryons with fermions in multiple representations, talk given by W. I. Jay at Lattice 2016, the 34th International Symposium on Lattice Field Theory, University of Southampton, UK, July 2016, published in proceedings, Proc. Sci. (LATTICE2016) 219 (arXiv:1610.06465 [hep-lat], October 2016).
We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these “chimera baryons” has a straightforward interpretation in terms of a non-relativistic quark model based on SU(4). Our results are particularly relevant to composite Higgs models in which the top quark is partially composite.
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T. DeGrand, M. Golterman, W. I. Jay, E. T. Neil, Y. Shamir, and B. SvetitskyRadiative contribution to the effective potential in a composite Higgs model, talk given at Lattice 2016, the 34th International Symposium on Lattice Field Theory, University of Southampton, UK, July 2016, published in proceedings, Proc. Sci. (LATTICE2016) 216 (arXiv:1610.06121 [hep-lat], October 2016).
The SU(4) gauge theory with two flavors of Dirac fermions in the sextet representation shares features of a candidate for a composite Higgs model. The analogue of the Higgs multiplet of the Standard Model lives in the Goldstone manifold resulting from spontaneous breaking of the global symmetry SU(4) to SO(4). The Higgs potential arises from interaction with the particles of the Standard Model. We have computed the gauge boson contribution to the Higgs potential, using valence overlap fermions on a Wilson-clover sea. The calculation is similar to that of the electromagnetic mass splitting of the pion multiplet in QCD.
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T. DeGrand, M. Golterman, W. I. Jay, E. T. Neil, Y. Shamir, and B. SvetitskyRadiative contribution to the effective potential in composite Higgs models from lattice gauge theory, Phys. Rev. D 94 (2016) 054501 (arXiv:1606.02695 [hep-lat], June 2016).
We develop methods to calculate the electroweak gauge boson contribution to the effective Higgs potential in the context of composite Higgs models, using lattice gauge theory. The calculation is analogous to that of the electromagnetic mass splitting of the pion multiplet in QCD. We discuss technical details of carrying out this calculation, including modeling of the momentum and fermion-mass dependence of the underlying current-current correlation function; direct integration of the correlation function over momentum; and fits based on the minimal-hadron approximation. We show results of a numerical study using valence overlap fermions, carried out in an SU(4) gauge theory with two flavors of Dirac fermions in the two-index antisymmetric representation.
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