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Lattice Gauge Theory for Physics beyond the Standard Model

Lattice Gauge Theory for Physics beyond the Standard Model. Richard C. Brower Moriond: QCD and High Energy Interactions March 19, 2009. Problem: Theorists have propose a myriad of models for TeV physics, often dependent on heuristics for non-perturbative effects in gauge theories.

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Lattice Gauge Theory for Physics beyond the Standard Model

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  1. Lattice Gauge Theory for Physics beyond the Standard Model Richard C. Brower Moriond: QCD and High Energy Interactions March 19, 2009

  2. Problem:Theorists have propose a myriad of models for TeV physics, often dependent on heuristicsfor non-perturbative effects in gauge theories Triage is needed! Experimental data is needed! • Lattice field theory can help to • narrow the options & • make prediction for specific models.

  3. New opportunity in LHC era:Use lattice to explore Theory Landscape! Typical QCD Lattice Calculation: 1 Teraflop/s-year = 8 hour job on sustained Petaflop/s

  4. Faster & Cooler & Cheaper on Nvidia GPU cluster Fully configured comparison with 1 rack of BG/L Flop/s Watts $’s

  5. Rough classification of EWSB models • SM Higgs (or multiple Higgs) • Super Symmetry • TeV strong dynamics (QCD-like, techni-color, extra dimensions,...) • Preparations and some early results for all 3 • Lattice Gauge Theory for LHC Physics, LNLL, May 2-3, 2008, http://www.yale.edu/LSD/workshop.html • Dynamical Electroweak Symmetry Breaking, Odense, Denmark, Sept 9-13,2008, http://hep.sdu.dk/dewsb/tp:htm • What can/should Lattice Gauge Theory contribute? • Existence of Theory: as cut-off is removed (a ! 0) • Mechanisms: assumed by model builders • Prediction: spectra for specific theories

  6. Does NATURE abhor a fundamental SCALAR ? I. NO: Only a scalar Higgs II. SORT OF: Give the Higgs a “super partner” Spin = 0 & 1/2 III. YES: Build at Higgs from Heavy techni-Quarks! LHC

  7. I. Higgs dynamics in the Standard Model Theory does not exist! Lattice “proves” it is a trivial free theory as a ! 0

  8. Higgs mechanism failure requiresa cut-off and places upper/lower bounds on MH PDG perturbative bounds: Re-evaluate PDG figure be non-perturbatively? Lattice provides a Lorentz violating cut-off (¼/a) = ¼/a

  9. Message from the Higgs Mass: MH • MH in “allowed” region: • Mass in a narrow band (140-180 GeV) hints ofcutoff not far from the Planck scale. • MH outside “allowed” region: • Large mass Higgs implies new non-perturbative physics. • Low mass Higgs can trigger an instability due to its large Yukawa coupling to the top quark. • Both imply thepresence of higher dimensional non-renormalizable operators on the TeV scale, but with constraintsfrom electroweak precision data.

  10. Lattice cut-off provides high dim operator: (Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder arXiv:0710.3151) av = 2.035(1) Continuum (Red)and lattice (Green) perturbation theory. Plot on right is a close-up of the behaviornear the origin. Ueff

  11. Lattice Higgs lower bound with (overlap) Top quark • Need to consider specific higher dimensional operators to give Lorentz invariant cut-off and explore role of physics above electroweak scale.

  12. II. Super symmetric field theories Spin = 0 & 1/2

  13. Super symmetric field theories • (MSSM) Minimal SUSY extension to the Standard Model • cancels quadratic divergence by Boson/Fermion pairing. • N=1 super Yang-Mills. • Constitutes non-perturbative sector of MSSM • On the lattice “accidental” SUSY • No fine tuning and positive definite Pfaffian -- gold plated SUSY laboratory. • First generation with DW fermions (Fleming, Kogut, Vranas)

  14. Gluino condensate in N = 1 SUSY SU(2) Yang Mills (Geidt, Brower Catterall, Fleming and Vranas arXiv:0810.5746) Zero mass gluino Domain Wall Fermions at Ls and beta = 2.4.

  15. Formulation of SUSY theories on Lattice • Larger range of “accidental” SUSY lattices. • Using ideas from orbifolding in string theory and the twisting in constructing topological field theories. • . They lead to surprising lattice geometries • Like staggered fermions, but with no unphysical degrees of freedom. 2-d 3-d

  16. III. New strong dynamics

  17. Suppose you drop the Higgs from the SM? • QUIZZ: • What is the mass of W and Z in SM without the Higgs? • HINT: • Higgless Lagrangian is scale invariant! • ANSWER: Dimensional transmutation + chiral symmetry breaking! • QCD provides a (small) Electroweak Sym Breaking (EWSM)! MW = g F¼/2 = 30MeV & MZ = (g2 + g’2)1/2 F¼ /2 = 34 MeV • Problem solved! • Boost ¤QCD to ¤Technicolor by 103

  18. ETC: Extended Technicolor A new strong force Techni-quarks Massless SUL(2) x UR(1) Gauge fields Massless quarks and leptons Techni-gluons ¤TC» 1 TeV ¤ETC» 100TeV Spontaneous chiral symmetry breaking by the strong dynamics

  19. The virtues of TC/ETC • Dynamical explanation of EWS breaking • Asymptotically free: • no unnatural fine tuning needed • no hierarchy problem (breaking scale naturally much smaller than cutoff) • it is not trivial • ETC provides insights to flavor physics The problems of TC/ETC • Flavor changing neutral currents (ETC) • Precision electroweak measurements (TC) • Large top quark mass Possible solution: Walking TC • Add flavor to approach conformal window • Naive QCD scaling in flavors fails • Must do non-perturbative (lattice) calculation.

  20. Adding flavors to QCD: Conformal Window • An IR fixed point can emerge already in the two-loop ¯function as you increase the number Nf of fermions. (Gross and Wilczek, Banks and Zaks, ... ) • Walking: Nf < N*f , but close to N*f • Spontaneous breaking of chiral symmetry SU(Nf) x SU(Nf) • Confinement • Spontaneous breaking of an approximate (IR) conformal symmetry ¯ ¯ g* g* g g • Conformal: Nf > N*f • Long distance (IR) Conformal theory. • Chiral symmetry SU(Nf) x SU(Nf) • No Confinement • But asymptotical free in the UV.

  21. Conformal Window (Sanino:DEWSB Odense 2008)

  22. How to make Finite Volume Errors your Friend? • Old idea from stat mechanics: • Understand phase transition and critical by finite volume scaling. • Techni-color lattice studies • Step scaling using the Schrödinger Functional approach(T. Appelquist, G. Fleming, E. Neil arXiv:0901.3766) • Epsilon Regime:1/F¼ < L a < 1/m¼(Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder arXiv:0809.4888) • Model conformal Field Theory in a box?

  23. Conformal Window for Lattice: • Schrödinger Functional Results: (coupling constant is determined by response of Action to applied E fields and the beta function bye step scaling) ¤TC ¤ETC Compare Nf =8 and 12 staggered quarks

  24. The LSD (Lattice Strong Dynamics) collaboration http://www.yale.edu/LSD/ • T. Appelquist (Yale U.), R. Babich (Boston U.), R. Brower (Boston U.), M. Cheng (LLNL), M. Clark (Boston U.), G. Fleming (Yale U.), J. Kiskis (UCD), T. Luu (LLNL), A. Martin (Yale U.), E. Neil (Yale U.), J. Osborn (ANL), C. Rebbi (Boston U.), D. Schaich (Boston U.), R. Soltz (LLNL), P. Vranas (LLNL). Generating DWF lattices for nf = 2, 4, 6 and 8 flavors All lattice made available after first publication

  25. Work in progress (FYEO) nf = 6

  26. Precision EW constraints The S parameter of Peskin & Takeuchi assumes a scaled QCD with Nf and Nc

  27. Many other projects: For example • Existence of Chiral Gauge Theories • Does SM exist even w.o. elementary Higgs ? • Large Nc Yang Mills (Narayanan and Neuberger) • String/gravity duals to non-SUSY YM theories. • AdS/CFT extra dimension models • Strangeness content of proton: • Detection efficiency of MSSM dark matter candidate

  28. Direct detection of dark matter • In SUSY, the neutralino scatters from a nucleon via Higgs exchange: • The strange scalar matrix element is a major uncertainty: • Uncertainty in fTs gives up to a factor of 4 uncertainty in the cross-section! • Bottino et al., hep-ph/0111229; • Ellis et al., hep-ph/0502001

  29. Higgs coupling to nuclear • See http://conferences.jlab.org/lattice2008/parallel-bytopic-struct.htmlS.Collins, G. Bali, A.Schafer“Hunting for the strangeness ... nucleon”Takumi Doi et al “Strangeness and glue in the nucleon from lattice QCDRon Babich et al “Strange quark content of the nucleon” VERY priliminary! No chiral/continuum extrap

  30. Conclusions • Basic Tools modified form lattice QCD are being developed • Chiral Fermions, • RHMC evolution • SciDAC software API extend to general Gauge & Fermion reps. • Real Needs: • Manpower & more flexible software libraries • Theoretical tools (renormalization, eff. theories, finite size scaling) • Guidance from model builders and signatures from LHC!

  31. Commercial Break: Second USQCD workshop on Lattice Field Theory beyond the Standard Model in Boston Fall 2009

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