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
Triage is
needed!


Experimental data
is needed!
Lattice field theory can help to
narrow the options &
make prediction for specific models.
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
Faster & Cooler & Cheaper on Nvidia GPU cluster
Fully configured comparison with 1 rack of BG/L
Flop/s
 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 913,2008, 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
Does NATURE abhor a fundamental SCALAR ?
I. NO: Only a scalar Higgs
II. SORT OF: Give the
Higgs a “super partner”
III. YES: Build at Higgs from
Heavy techni-Quarks!
LHC
I. Higgs dynamics in the Standard Model
Theory does not exist!
Lattice “proves” it is a trivial free theory as a ! 0
Higgs mechanism failure requires
a cut-off and places upper/lower bounds on MH
PDG perturbative
bounds:
Re-evaluate PDG
figure be
non-perturbatively?
= ¼/a
Lattice provides a
Lorentz violating
cut-off (¼/a)
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 nonrenormalizable operators on the TeV scale, but with constraints
from electroweak precision data.
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 behavior near the origin.
Ueff
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.
II. Super symmetric field theories
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)
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.
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

2-d
Like staggered fermions, but with no unphysical degrees of freedom.
3-d
III. New strong dynamics
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
ETC: Extended Technicolor
A new strong force
Massless SUL(2) x UR(1)
Gauge fields
¤TC » 1 TeV
Techni-quarks
Techni-gluons
Massless quarks and
leptons
¤ETC » 100TeV
Spontaneous chiral symmetry breaking by the strong dynamics
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
o Flavor changing neutral currents (ETC)
o Precision electroweak measurements (TC)
o Large top quark mass
Possible solution: Walking TC
o Add flavor to approach conformal window
o Naive QCD scaling in flavors fails
o Must do non-perturbative (lattice) calculation.
Adding flavors to QCD: Conformal Window
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, ... )
 An
¯
¯
g*
g*
g
g
Conformal: Nf > N*f

Long distance (IR) Conformal theory.

Chiral symmetry SU(Nf) x SU(Nf)


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
No Confinement
But asymptotical free in the UV.
Conformal
Window
(Sanino:DEWSB Odense 2008)
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?
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)
¤ETC
¤TC
Compare Nf =8 and 12 staggered quarks
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
Work in progress (FYEO)
nf = 6
Precision EW constraints
The S parameter of
Peskin & Takeuchi
assumes a scaled QCD
with Nf and Nc
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
QuickTime™ and a
decompressor
are needed to see this picture.
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
X
t = tf
t=0
t = t'
VERY priliminary!
No chiral/continuum extrap
See http://conferences.jlab.org/lattice2008/parallel-bytopic-struct.html
S.Collins, G. Bali, A.Schafer “Hunting for the strangeness ... nucleon”
Takumi Doi et al
Ron Babich et al
“Strangeness and glue in the nucleon from lattice QCD
“Strange quark content of the nucleon”
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!
Commercial Break:
QuickTime™ and a
decompressor
are needed to see this picture.
Second USQCD workshop on
Lattice Field Theory beyond the Standard Model
in Boston Fall 2009