Study of meson spectroscopy of a lattice SU(4) gauge BSM model. Venkitesh Ayyar 1 Thomas Degrand 1 Daniel Hackett 1 William Jay 1 Ethan Neil 1 , 3 Benjamin Svetitsky 2 Yigal Shamir 2 . 1 University of Colorado, Boulder, 2 Tel Aviv University, 3 RIKEN-BNL Research Center. TaCo collaboration Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, USA. Work supported by grants from the DOE. Computational work done using resources provided by Fermilab and local Janus cluster. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Introduction Hierarchy problem Unaesthetic features of SM Higgs potential introduced for SSB. Higgs is light ( ∼ 100GeV) compared to Λ Planck . Higgs is a scalar. Higgs mass Hierarchy problem Higgs mass ∼ Λ EW . Any coupling to the Higgs introduces corrections O (Λ 2 UV ) to Higgs mass, due to radiative corrections. At higher scales, parameters have to be fine-tuned to get observed Higgs mass. Is Higgs a composite pNGB in a new strong sector? Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Introduction Composite Higgs 2 Introduce a new strong sector (Hypercolor). Induce chiral symmetry breaking to get pNGBs one of which is the Higgs. Symmetry breaking G → H , with Higgs doublet in the G / H coset. Weak sector SU (2) L × U (1) Y ⊂ H . Higgs potential generated dynamically by coupling to SM fields. Partial compositeness 1 Linear couplings of top quark to a baryon in the new sector gives fermion mass. Ferretti-Karateev in 2014 classified UV completions. 2 Dugan, Georgi, Kaplan, Nucl. Phys. B254, 299 (1985) 1 Kaplan, Nuclear Physics B365, (1991) Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Introduction Ferretti’s model(1404.7137) UV completion with partial compositness. SU(4) gauge theory with 2 representations. Fermion content 5 sextet( A 2 ) Majorana fermions. 6 fundamental(F) Weyl fermions. Symmetry breaking SU (5) / SO (5) in A 2 rep. ( SU (3) L × SU (3) R ) / SU (3) in F rep. The Higgs doublet lives in the SU (5) / SO (5) coset. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Lattice model Our Lattice model SU(4) gauge theory with modified fermion content 2 flavors of sextet A 2 Dirac fermions. 2 flavors of fundamental F Dirac fermions. Symmetry breaking SU (4) / SO (4) in A 2 rep. ( SU (2) L × SU (2) R ) / SU (2) in F rep. 3 coupling constants : β, κ 4 , κ 6 . Expected to capture qualitative features of Ferretti’s model. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Lattice model Lattice details Simulations on lattice sizes 16 3 × 32 and 16 3 × 18. About 40 ensembles. Multi-rep MILC code by Yigal Shamir Studied Pseudo-scalar and vector mesons. Extract meson masses using two-point correlation functions. Using Wilson flow method to set the scale. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Meson spectroscopy Ensemble overview Lattice results obtained in terms of lattice spacing a . Using Wilson flow scale t 0 to remove a 0.8 dependence. 0.6 Look at M P / M V vs M P, r /M V, r m q . 0.4 Quark mass m q 0.2 obtained using Axial Fundamental Ward identity. Sextet 0.0 0.00 0.02 0.04 0.06 0.08 0.10 Relatively heavy p m q, r t 0 mesons. Similar behavior for both representations. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Meson spectroscopy Leading order ChiPt Upto leading order in ChiPt, M 2 pi ∼ m q . Removed lattice artifacts obtained using Wilson ChiPt. Linear behavior for both reps. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Meson spectroscopy Comparison with NLO ChiPT Useful to compare lattice results to NLO ChiPT. Multirep NLO ChiPT worked out by DeGrand, Goltermann, Neil, Shamir (1605.07738). M P 4 , F P 4 , M P 6 , F P 6 depend on a set of low energy constants(LECs). Simultaneous fit to all four quantities. Find a good fit ( χ 2 / DOF ∼ 0 . 5) Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Meson spectroscopy Condensates Two condensates, one for each representation. 0.35 Fundamental Compute it indirectly using 0.30 Sextet M 2 P , r F 2 ˆ Σ r = P , r 0.25 2 m q , r t 0 ) 3 0.20 Chiral limit values computed p 0.15 using ChiPt. Σ r ( 0.10 Condensate ratio Σ 6 / Σ 4 0.05 ◮ Lattice calc → 2.2 0.00 ◮ Large N scaling 0.00 0.02 0.04 0.06 0.08 0.10 0.12 p dim ( F ) ∼ N 2 / 2 → dim ( A 2 ) t 0 m q, r ∼ 2. N Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Comparison with KSRF Decay constants KSRF 3 , 4 related F V and F P using current algebra and 1.8 vector meson dominance. √ F V = 2 F P . 1.6 F V, r /F P, r Can compare F V and F P in 1.4 a fixed representation. QCD 1.2 KSRF QCD experiment: F V / F P = F V, 4 /F P, 4 216 MeV / 130 MeV = 1 . 66. 1.0 F V, 6 /F P, 6 For both reps, our results 0.02 0.04 0.06 0.08 0.10 p similar to QCD. m q, r t 0 3 Kawarabayashi and Suzuki, PRL 16, 255 (1966). 4 Riyazuddin and Fayyazuddin, PRL 147, 1071 (1966). Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Comparison with KSRF Decay widths KSRF also predicted coupling strength g VPP = M V F P . 0.35 KSRF 0.30 Allows tree-level estimation Γ V, 4 /M V, 4 of vector decay width: 0.25 Γ V, 6 /M V, 6 Γ V = g 2 VPP M V / 48 π . 0.20 Γ V /M V KSRF prediction 0.15 M 2 Γ V M V ∼ P . V 0.10 48 π F 2 0.05 Γ V M V QCD = 0 . 19. 0.00 0.02 0.04 0.06 0.08 0.10 p Our states narrower than m q t 0 QCD. Γ V 6 Γ V 4 M V 6 = 0 . 13 , M V 4 = 0 . 18. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Conclusions Conclusions and Outlook Conclusions Zero temperature study of lattice SU(4) gauge theory BSM model with fermions in multiple reps. Meson spectroscopy data consistent with ChiPT. KSRF relations hold similar to QCD. Theory appears QCD-like. Future direction Baryon spectroscopy. Coupling between the two irreps. ◮ LECs unconstrained. ◮ Greater precision might help constrain these. Existence of exotic pNGB ζ meson. ◮ Theory has non-anomalous U (1) A ◮ SSB = ⇒ scalar, singlet ζ meson. Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Conclusions THANK YOU Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Back-up slides Back-up slides Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
Back-up slides Wilson flow to set the scale Wilson flow: a smearing technique to smooth-out configurations. Also, a method to set the scale 5 , . t 0 � E ( t 0 ) � = M ( N ), where E ( t ) = 1 4 G t ,µν G t ,µν . � For QCD (N=3), M = 0.3, corresponding to ( t 0 ) = 0 . 14 fm . For SU(4), t 0 � E ( t 0 ) � = 0 . 3 × 4 3 = 0 . 4, 6 M. Luscher, JHEP 08, 071 (2010) Tue, Aug 1, DPF 2017, Fermilab, Batavia, IL, V. Ayyar (CU, Boulder) Spectroscopy of lattice BSM model. / 16
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