Lattice Gauge Theory for Physics beyond the Standard Model

1
Lattice Gauge Theory for Physics beyond the
Standard Model

• Richard C. Brower
• Moriond QCD and High Energy Interactions
• March 19, 2009

2
ProblemTheorists have propose a myriad of models
for TeV physics, often dependent on heuristics
for 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 eraUse 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/t
  phtm
• 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 of
  cutoff 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 the presence of higher dimensional
  non-renormalizable operators on the TeV scale,
  but with constraints from electroweak precision
  data.

10
Lattice cut-off provides high dim operator
(Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C.
Schroeder arXiv0710.3151)
av 2.035(1)
Continuum (Red)and lattice (Green) perturbation
theory. Plot on right is a close-up of the
behavior near 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.
• N1 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
arXiv0810.5746)
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
  g2)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, ... )

g
g
g
g

• Walking Nf lt Nf , but close to Nf
• Spontaneous breaking of chiral symmetry SU(Nf) x
  SU(Nf)
• Confinement
• Spontaneous breaking of an approximate (IR)
  conformal symmetry

• Conformal Nf gt Nf
• Long distance (IR) Conformal theory.
• Chiral symmetry SU(Nf) x SU(Nf)
• No Confinement
• But asymptotical free in the UV.

21
Conformal Window
(SaninoDEWSB 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
  arXiv0901.3766)
• Epsilon Regime1/F¼ lt L a lt 1/m¼ (Z. Fodor, K.
  Holland, J. Kuti, D. Nogradi, C. Schroeder
  arXiv0809.4888)
• 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
(No Transcript)
29
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

30
Higgs coupling to nuclear
VERY priliminary! No chiral/continuum extrap

• See http//conferences.jlab.org/lattice2008/parall
  el-bytopic-struct.htmlS.Collins, G. Bali,
  A.Schafer Hunting for the strangeness ...
  nucleonTakumi Doi et al
  Strangeness and glue in the nucleon from
  lattice QCDRon Babich et al
  Strange quark content of the nucleon

31
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!

32
Commercial Break

• Second USQCD workshop on
• Lattice Field Theory beyond the Standard Model
• in Boston Fall 2009