Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond)
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Received: December 18, Revised: March 9, Accepted: March 21, Published: March 29,
2017 2018 2018 2018
Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond)
a
Department of Physics, College of Science, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales, U.K. b Swansea Academy of Advanced Computing, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales, U.K. c Department of Physics, Pusan National University, Busan 46241, Korea d Extreme Physics Institute, Pusan National University, Busan 46241, Korea e Institute of Physics, National Chiao-Tung University, 1001 Ta-Hsueh Road, Hsinchu 30010, Taiwan f Department of Mathematics, College of Science, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales, U.K. g INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: The Sp(4) gauge theory with two Dirac fundamental flavours provides a candidate for the microscopic origin of composite-Higgs models based on the SU(4)/Sp(4) coset. We employ a combination of two different, complementary strategies for the numerical lattice calculations, based on the Hybrid Monte Carlo and on the Heat Bath algorithms. We perform pure Yang-Mills, quenched computations and exploratory studies with dynamical Wilson fermions. We present the first results in the literature for the spectrum of glueballs of the pure Sp(4) Yang-Mills theory, an EFT framework for the interpretation of the masses and decay constants of the lightest pion, vector and axial-vector mesons, and a preliminary calculation of the latter in the quenched approximation. We show the first numerical evidence of a bulk phase transition in the lattice theory with dynamical Wilson fermions, and perform the technical steps necessary to set up future investigations of the mesonic spectrum of the full theory. Keywords: Lattice Quantum Field Theory, Confinement, Spontaneous Symmetry Breaking, Wilson, ’t Hooft and Polyakov loops ArXiv ePrint: 1712.04220
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)185
JHEP03(2018)185
Ed Bennett,a,b Deog Ki Hong,c Jong-Wan Lee,c,d C.-J. David Lin,e Biagio Lucini,f Maurizio Piaia and Davide Vadacchinoa,g
Contents 1 Introduction and motivation 1.1 The Sp(2N ) research programme 1.2 Laying the foundations of the Sp(4) lattice studies
2 2 3 4 5 5 7 9 10 12 12
3 Numerical lattice treatment 3.1 Lattice action 3.2 Heat bath 3.3 Hybrid Monte Carlo
14 15 15 16
4 Lattice calibration 4.1 Scale setting and gradient flow 4.2 Topological charge history
19 19 23
5 The 5.1 5.2 5.3
24 24 29 32 33 36 40
spectrum of the Yang-Mills theory Of glueballs and strings A variational approach to the mass spectrum Lattice results 5.3.1 The string tension 5.3.2 The mass spectrum of glueballs 5.3.3 Epilogue
6 Of quenched mesons: masses and decay constants 6.1 Observables 6.2 N
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