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

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

Problem:Theorists have propose a myriad of models for TeV physics, often dependent on heuristics for

non-perturbative effects in gauge theories

Lattice field theory can help to narrow the options & make prediction for specific models.

Lattice field theory can help to narrow the options & make prediction for specific models.

Triage is needed! Experimental data

is needed!

New opportunity in LHC era:New opportunity in LHC era:Use lattice to explore Theory Landscape!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

Faster & Cooler & Cheaper on Nvidia GPU cluster

Fully configured comparison with 1 rack of BG/L

Flop/s

$’sWatts

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

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

Does NATURE abhor a fundamental SCALAR ? Does NATURE abhor a fundamental SCALAR ?

I. NO: Only a scalar Higgs

LHC

II. SORT OF: Give the Higgs a “super partner”

III. YES: Build at Higgs from Heavy techni-Quarks!

I. Higgs dynamics in the Standard ModelI. Higgs dynamics in the Standard Model

Theory does not exist!Lattice “proves” it is a trivial free theory as a ! 0

Theory does not exist!Lattice “proves” it is a trivial free theory as a ! 0

Higgs mechanism failure requiresa cut-off and places upper/lower bounds on MH

Higgs mechanism failure requiresa cut-off and places upper/lower bounds on MH

PDG perturbative bounds:

= ¼/a

Lattice provides a Lorentz violating cut-off (¼/a)

Re-evaluate PDG figure be non-perturbatively?

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.

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.

Message from the Higgs Mass: MHMessage from the Higgs Mass: MH

Lattice cut-off provides high dim operator:

Lattice cut-off provides high dim operator:

Continuum (Red)and lattice (Green) perturbation theory. Plot on right is a close-up of the behavior near the origin.

Continuum (Red)and lattice (Green) perturbation theory. Plot on right is a close-up of the behavior near the origin.

Ueff

(Z. Fodor, K. Holland, J. Kuti, D. Nogradi, C. Schroeder arXiv:0710.3151)

av = 2.035(1)

Need to consider specific higher dimensional operators to give Lorentz invariant cut-off and explore role of physics above electroweak scale.

Lattice Higgs lower bound with (overlap) Top quark

Lattice Higgs lower bound with (overlap) Top quark

II. Super symmetric field theories

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)

(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

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 LatticeFormulation 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

III. New strong dynamicsIII. New strong dynamics

Suppose you drop the Higgs from the SM?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 TechnicolorETC: Extended TechnicolorA new strong force

Techni-quarks

Techni-gluons

Spontaneous chiral symmetry breaking by the strong dynamics

Massless SUL(2) x UR(1)Gauge fields

Massless quarks andleptons

¤TC » 1 TeV ¤ETC » 100TeV

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 windowo Naive QCD scaling in flavors failso Must do non-perturbative (lattice) calculation.

Adding flavors to QCD: Conformal WindowAdding flavors to QCD: Conformal Window

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

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, ... )

¯

gg*

¯

gg*

Conformal: Nf > N*f

Long distance (IR) Conformal theory.

Chiral symmetry SU(Nf) x SU(Nf)

No Confinement

But asymptotical free in the UV.

(Sanino:DEWSB Odense 2008)

ConformalWindowConformalWindow

How to make Finite Volume Errors your Friend?

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: 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)

Compare Nf =8 and 12 staggered quarks

¤TC ¤ETC

The LSD (Lattice Strong Dynamics) collaboration

http://www.yale.edu/LSD/

The LSD (Lattice Strong Dynamics) collaboration

http://www.yale.edu/LSD/

All lattice made available after first publication

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).

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

Work in progress (FYEO)Work in progress (FYEO)

nf = 6

Precision EW constraints

The S parameter of Peskin & Takeuchi assumes a scaled QCD

with Nf and Nc

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

Many other projects: For exampleMany other projects: For example

QuickTime™ and a decompressor

are needed to see this picture.

29

Direct detection of dark matterDirect 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

Higgs coupling to nuclearHiggs coupling to nuclear

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 “Strangeness and glue in the nucleon from lattice QCDRon Babich et al “Strange quark content of the nucleon”

t = 0t = tf t = t'

X

VERY priliminary!

No chiral/continuum extrap

VERY priliminary!

No chiral/continuum extrap

Conclusions 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!

QuickTime™ and a decompressor

are needed to see this picture.

Commercial Break:

Second USQCD workshop on

Lattice Field Theory beyond the Standard Model

in Boston Fall 2009