Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions

Abstract

We consider the Sp(4) gauge theory coupled to N f = 2 fundamental and n f = 3 antisymmetric flavours of Dirac fermions in four dimensions. This theory serves as the microscopic origin for composite Higgs models with SU (4)/Sp(4) coset, supplemented by partial top compositeness. We study numerically its lattice realisation, and couple the fundamental plaquette action to Wilson-Dirac fermions in mixed representations, by adopting a (rational) hybrid Monte Carlo method, to perform non-trivial tests of the properties of the resulting lattice theory.We find evidence of a surface (with boundaries) of first-order bulk phase transitions in the threedimensional space of bare parameters (one coupling and two masses). Explicit evaluation of the Dirac eigenvalues confirms the expected patterns of global symmetry breaking. After investigating finite volume effects in the weak-coupling phase of the theory, for the largest available lattice we study the mass spectra of the lightest spin-0 and spin-1 flavoured mesons composed of fermions in each representation, and of the lightest half-integer spin composite particle made of fermions in different representations-the chimera baryon. This work sets the stage for future systematical studies of the non-perturbative dynamics in phenomenologically relevant regions of parameter space.

Color dependence of the topological susceptibility in Yang-Mills theories

“…In the case of Sp(N c ) gauge theories, we borrow the results from a companion publication, Ref. [50], which is part of the ongoing programme of study of Sp(N c ) lattice gauge theories [11,13,[60][61][62], and uses the HiRep code [63], adapted to Sp(N c ) groups [11]. The lattice topological charge is obtained from Wilson-flowed configurations [64,65], and correction-and-rounding is used to assign integer topological charge.…”

Holographic models of composite Higgs in the Veneziano limit. Part II. Fermionic sector

“…As the latter have not been observed, a realistic model requires a (+) IR boundary condition, to remove these components from the chiral content of the theory. 15 Given such large, composite vector-like multiplet, an elementary SM chiral fermion can have a linear coupling to the corresponding component of the multiplet, i.e. the one carrying the conjugate quantum numbers: this results in a partially composite chiral fermion, as well as a state with mass raised with respect to the other components of the multiplet.…”

“…However, so far little is known about the spectrum of such fermionic states. On the lattice, the fermionic spectra of SU(4) and Sp(4) gauge theories have been studied in [12] and [13][14][15], respectively, while consequences for partial compositeness have been further explored in [16].…”

Composite two-Higgs doublet model from dilaton effective field theory

“…Here the Higgs fields appear within the low energy EFT description of pseudo-Nambu-Goldstone bosons (PNGBs), themselves originating from a new, strongly coupled field theory. Lattice studies have begun to provide non-perturbative information about the dynamics of such strongly coupled systems, and their spectroscopy [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”