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Lattice Gauge Theories and the Composite Higgs

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Lattice Gauge Theories and the Composite Higgs Lattice gauge theories and the composite Higgs (on behalf of the USQCD BSM group) Snowmass on the Pacific @ KITP Julius Kuti University of California, San Diego Snowmass on the Pacific @ KITP, May 29-31, 2013 1 Large Hadron Collider - CERN primary mission: - Search for Higgs particle - Origin of Electroweak symmetry breaking • A Higgs-like particle is found Is it the Standard Model Higgs? • Or, new strong dynamics? • Composite Goldstone-like Higgs? • SUSY? 2 Large Hadron Collider - CERN primary mission: - Search for Higgs particle - Origin of Electroweak symmetry breaking • A Higgs-like particle is found Is it the Standard Model Higgs? • Or, new strong dynamics? • Composite Goldstone-like Higgs? • SUSY? Primary focus of USQCD BSM effort and this short talk 2 LATTICE GAUGE THEORIES AT THE ENERGY FRONTIER Thomas Appelquist, Richard Brower, Simon Catterall, George Fleming, Joel Giedt, Anna Hasenfratz, Julius Kuti, Ethan Neil, and David Schaich (USQCD Collaboration) (Dated: March 10, 2013) USQCD BSM White Paper - community based effort: 3 1 LATTICE GAUGE THEORIES AT THE ENERGY FRONTIER Thomas Appelquist, Richard Brower, Simon Catterall, George Fleming, Joel Giedt, Anna Hasenfratz, Julius Kuti, Ethan Neil, and David Schaich (USQCD Collaboration) (Dated: March 10, 2013) USQCD BSM White Paper - community based effort: • to identify most significant lattice results of last few years • to identify major research directions for planning • to describe BSM lattice toolset with phenomenological applications • estimate resources needed for the plan New hardware proposal submitted including USQCD BSM plans 3 1 Introducing USQCD BSM groups with highlighted publications: (approximately 1/5 of USQCD community) select publications of Lattice Strong Dynamics (LSD) collaboration: WW Scattering Parameters via Pseudoscalar Phase Shifts Thomas Appelquist (Yale U.), Ron Babich, Richard C. Brower (Boston U.), Michael I. Buchoff, Michael Cheng (LLNL, Livermore), Michael A. Clark (Harvard-Smithsonian Ctr. Astrophys.), Saul D. Cohen (Washington U., Seattle), George T. Fleming (Yale U.), Joe Kiskis (UC, Davis), Meifeng Lin (Yale U.) et al.. Jan 2012. 8 pp. Published in Phys.Rev. D85 (2012) 074505 select publication from Lattice Higgs Collaboration (LHC): Can the nearly conformal sextet gauge model hide the Higgs impostor? Zoltan Fodor (Wuppertal U. & IAS, Julich & Eotvos U.), Kieran Holland (U. Pacific, Stockton), Julius Kuti (UC, San Diego), Daniel Nogradi (Eotvos U.), Chris Schroeder (LLNL, Livermore), Chik Him Wong (UC, San Diego). Sep 2012. 10 pp. Published in Phys.Lett. B718 (2012) 657-666 select publications of SUSY group: Phase Structure of Lattice N=4 Super Yang-Mills Simon Catterall, Poul H. Damgaard, Thomas Degrand, Richard Galvez, Dhagash Mehta. Sep 2012. 28 pp. Published in JHEP 1211 (2012) 072 Neutralino-hadron scattering in the NMSSM Sophie J. Underwood (Adelaide U.), Joel Giedt (Rensselaer Poly.), Anthony W. Thomas, Ross D. Young (Adelaide U.). Mar 2012. 4 pp. Published in Phys.Rev. D86 (2012) 035009 select publication of Boulder BSM collaboration: MCRG study of 8 and 12 fundamental flavors Gregory Petropoulos, Anqi Cheng, Anna Hasenfratz, David Schaich (Colorado U.). Dec 2012. 7 pp. Published in PoS LATTICE2012 (2012) 051 To appear in the proceedings of Conference: C12-06-24 Proceedings e-Print: arXiv:1212.0053 [hep-lat] | PDF select publication of BSM finite temperature studies: QCD with colour-sextet quarks D.K. Sinclair, J.B. Kogut. Nov 2012. 7 pp. Published in PoS LATTICE2012 (2012) 026 4 Rational for BSM: voices: a light Higgs-like scalar is found which is consistent with SM within errors and no composite states have been seen below 1 TeV, ergo no need for BSM based compositeness. Besides, how do you get a light Higgs from compositeness? facts: Compositeness and a light Higgs scalar are not incompatible; search for composite states in the LHC7/8 runs was not based on solid predictions but on naively scaled up QCD and on unacceptable old technicolor guessing games. This alone does not make compositeness right! plans: LHC14 will search for new physics from compositeness and SUSY, and the USQCD BSM group is preparing quantitative lattice based predictions to rule in or rule out 5 Rational for BSM: three USQCD BSM directions based on gauge force: • strongly coupled near-conformal gauge theories - light scalar is expected from approximate scale invariance (dilaton, or just light scalar?) - QCD is NOT approximately scale invariant making old technicolor guessing games irrelevant • light pseudo-Goldstone boson (like little Higgs) - starts from a scalar massless Goldstone boson - expects to make quantitative predictions about composite spectrum above 1 TeV • SUSY - for better understanding of dynamical symmetry breaking and to explore susy theory scenarios - We are calculating quantitative predictions for LHC14 (e.g. sextet model) 6 Rational for BSM: three USQCD BSM directions based on gauge force: • strongly coupled near-conformal gauge theories - light scalar is expected from approximate scale invariance (dilaton, or just light scalar?) - QCD is NOT approximately scale invariant making old technicolor guessing games irrelevant • light pseudo-Goldstone boson (like little Higgs) - starts from a scalar massless Goldstone boson compositeness - expects to make quantitative predictions about composite spectrum above 1 TeV • SUSY - for better understanding of dynamical symmetry breaking and to explore susy theory scenarios - We are calculating quantitative predictions for LHC14 (e.g. sextet model) 6 Rational for BSM: three USQCD BSM directions based on gauge force: • strongly coupled near-conformal gauge theories - light scalar is expected from approximate scale invariance (dilaton, or just light scalar?) from approximate scale invariance TeV - QCD is NOT approximately scale invariant A1 ~ 2.4 making TeV old technicolor guessing games irrelevant Rho~1.7• light TeV pseudo-Goldstone boson (like little Higgs) - starts from a scalar massless Goldstone boson compositeness 5 - expects to make quantitative predictions5 about where FΠ is the TC pion decay constant and ⇥ scales like 1/ d(RTC) if the cuto⇥ is identified composite spectrum above 1 TeV 4 where FΠ is the TC pion decay constantscalar and composite⇥ scales like at 1/ 500d(R TCGeV?) if the cuto⇥ is identifiedWZwith the technirho mass, or is a constant if the cuto⇥ is of the order of 4⇤FΠ. Provided rt is also with the technirho mass, or is a constant if the cuto⇥ is of the order of 4⇤ . Providedt is also EW self-energy• SUSY FΠ rt of order one, the dominant radiative correction is due to the top quark. For instance, if FΠ = v, 2 2 2 2 of order one, the dominant radiative correction is due to the top quark. For instance, if FΠ = v, which is appropriate for a TC theory with one weak technidoublet, then δMH 12⇥ rt mt observed - for Higgs-like better understandingFIG. 1: Quadratically of divergent dynamical diagrams contributing to the Higgs symmetry mass, with the interaction vertices ⌅ ⌅ given by (2).2 The gauge boson exchanges2 2 are computed2 in Landau⇥ gauge:2r2 then(600 the seagull GeV) diagrams,2. This demonstrates that the dynamical mass of the TC Higgs can be substantially which is appropriate for a TC theory with one breaking weak technidoublet, and to explore thenwithδ a singleMHW andsusyZ exchange,12 are⇥theory ther onlyt m quadraticallyt divergentscenarios one-loopt diagrams with gauge boson exchanges. ⌅ ⌅ − ⇥2r2(600 GeV)2. This demonstrates that the dynamical mass of the TC Higgs can be substantially heavier than the physical mass, MH 125 GeV. t a a by the breaking of the electroweak symmetry, U = exp i⇤ T /v , with covariant derivative DµU ⇧ − ⇥ a a 3 a ∂µU igWµT U + ig⇧UBµT ,2T are the Pauli matrices, with a ⇥= 1, 2, 3, and V[H] is the TC Higgs heavier than the physical mass, MH 125 - GeV. We are calculating quantitative− predictions ⇧ potential. ∆S is the contribution to the S parameter from the physics at the cuto⇤ scale, and is assumed to vanish in the M limit. The interactions contributing to the Higgs self-energy ⌅ ⌅⌃ for LHC14 (e.g. sextetare model) III. THE DYNAMICAL MASS OF THE TC HIGGS 2 2 2 mW r⇤ + µ mZ r⇤ µ mt rt HW W− + HZ Z H tt¯ 6 LH ⇤ v µ v µ − v 2 2 mW s⇤ 2 + µ mZ s⇤ 2 µ III. THE DYNAMICAL MASS OF THE TC HIGGS + H W W− + H Zµ Z . (2) v2 µ 2 v2 In QCD the lightest scalar is the ⌅ meson (also termed f0(500) in PDG), with a measured mass The tree-level SM is recovered for r⇤ = s⇤ = rt = rb = 1 between. 400 and(3) 550 MeV [23] in agreement with early determinations [11]. Scaling up two-flavor In QCD the lightest scalar is the ⌅ meson (also termed f (500) in PDG), with a measured mass 0 We divide the radiative corrections to the TC Higgs mass into two classes: external contributions, 0 corresponding to loop corrections involving elementary SMQCD fields, and yields TC contributions, a TC corre- Higgs dynamical mass in the 1.0 TeV MH 1.4 TeV range. This estimate between 400 and 550 MeV [23] in agreement with early determinations [11].sponding Scaling to loop corrections up involvingtwo-flavor TC composites only. The latter contribute to the dynamical mass M0 , whose size will be estimated in the next section by non-perturbative analysis. In order 0 H changes when considering TC theories which are not an exact replica of two-flavor QCD. Here we QCD yields a TC Higgs dynamical mass in the 1.0 TeV MH 1.4 TeVto isolate range. the SM contributions This we estimate work in Landau gauge. Here transversely polarized gauge boson propagators correspond to elementary fields, and masslessdetermine Goldstone boson the propagatorsgeometric scaling of the TC Higgs dynamical mass, i.e. the value of M0 as function of changes when considering TC theories which are not an exact replica of two-flavorcorrespond to TC composites.
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