The LHC Rap (Large Hadron Collider). Lattice QCD in the Era of the Large Hadron Collider Anna...

The LHC Rap(Large Hadron Collider)

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Lattice QCD in the Era of the Large Hadron Collider

Anna HasenfratzUniversity of Colorado, Boulder

University of Kansas, November 3 2008



The science goal of LHC • Find the Higgs boson & study the electroweak symmetry breaking• Search beyond the Standard Model: Supersymmetry, • Grand Unification, extra dimensions, dark matter candidates, ….

The primary science goal of LHC is to “break” the Standard Model of particle physics, i.e. find

experimental deviation from the theoretical predictions. – Why would we want to “break” something? – Is that so difficult?– The role of Lattice QCD calculations – LQCD and beyond-Standard-Model theories

Elementary interactions



TheoryElectromagnetic Interaction : QED - U(1) gauge model

- mediating gauge boson: photon -- massless vector particle- extremely well tested

® = e2 /4¼ ¼ 1/137 : perturbation theory works well

Running coupling : ® depends on the interaction energy

If ®=1/137 at the electron mass, ®=1 at q¼ 10277 MeV

The Standard Model

The Standard Model



TheoryStrong Interaction : QCD - SU(3) color gauge model

- mediating gauge boson:gluons - massless- describes all hadrons (proton, neutron, pion, …..)

- ®s is large: perturbation theory does not work at all

Running coupling :

®s vanishes at small distance (asymptotic freedom) ,but large at large distance (confinement)

Quarks

• Each quark comes in 3 colors (r,g,b)• 8 massless gluons, carry color charge

Generation Flavor Charge Mass [GeV]

first u (up)

d (down)

-1/3

2/3

7

3

second s (strange)

c (charm)

-1/3

2/3

120

1200

third b (bottom)

t (top)

-1/3

2/3

4300

174,000

Light Baryons



Light Mesons



Lights mesons (cont)



The Standard Model



TheoryWeak Interaction : SU(2) gauge model

- ®w is small: perturbation theory works

- mediating gauge bosons : W+/-, Z -- massive, mW,Z¼ 90 GeV

- Massless vector bosons have only 2 dof, massive ones have 3 - gauge symmetry forbids mass for the gauge bosons

- Higgs mechanism explains mass generation

Higgs Mechanism,Spontaneous symmetry breaking

Take a complex scalar field Á=Á1 + iÁ2 with potential

¸>0

m2 >0 : symmetric shape,

2 degenerate modes, Á1, Á2

m2<0 : broken symmetry

1 massless, 1 massive mode

(Nambu-Goldstone boson and

massive Higgs boson)



In general, each broken symmetry brings in a massless mode

Higgs Mechanism

Spontaneous symmetry breaking of a 4-component scalar field leads to 3 massless gauge bosons and a heavy Higgs

Couple it to the SU(2) gauge fields:– the gauge bosons “eat” the Goldstone bosons, absorbing their dof

and become massive– the massive Higgs boson is left behind to tell the tale

Electroweak Standard Model:

combine U(1) x SU(2) ; photon = mix of U(1) and SU(2) neutral boson

Z = orthogonal mix

W = charged SU(2) boson

Electroweak Symmetry Breaking W+/- and Z bosons’ masses can be predicted, experimentally observed

Higgs is still missing (after 30 years!) Experimental constraint: 114.4 GeV < mH < 167 GeV (95% CL)



All experimental data are described well with the MSM - no compelling evidence (or need) for beyond-SM physics.



ind

irec

t

d

irec

t

Running couplings of the Standard Model

U(1) x SU(2) x SU(3) : 3 very different gauge couplings at low energy

will they unify at a higher scale?

Minimal Standard Model misses the mark, but supersymmetry can fix it



The Standard Model cannot stand-aloneMSM

• does not describe gravity, dark matter, …• requires new physics for unification• requires fine tuning of the parameters (naturalness)• has too many parameters: masses, mixing angles

MSM is mathematically inconsistent: the scalar coupling ¸(q) increases with q

• either ¸phys =0 (no Higgs)

• or there is a maximal energy ¤cut-off for the SM

(lattice calculations in ~1990 proved even gave an upper bound for mH)

Yet the MSM is maddeningly good…..Where to look for deviation from the SM?

Higgs particle - does it exist ??

precision electroweak measurements vs

theoretical data from lattice QCD calculation

• QCD is the only non-perturbative part of the SM, but it enters at every level.

Lagrangean: SU(3) “color” gauge group

8 massless gauge bosons (gluons) (F¹º field strength)

3 generations of quarks Ã f : (u,d) : m=(2MeV, 4MeV)

(s,c) : m=(100MeV, 1.5GeV)

(b,t) : m=(4.2GeV,172GeV)

®s(q) is

• weak at short distances (asymptotic freedom) • strong at large distances (confinement)

• Dimensionfull quantities are non-analytic in ®s

Lattice simulations are (at present) the only way to do non-perturbative calculations form first principes.

QCD

• Discretize LQCD : ¹Ã(x) (Ã(x+a)-Ã(x))/a , etc

• finite number of degrees of freedom• Statistical physics simulation techniques are available

• Create configurations with Monte Carlo method “snapshots” of the vacuum

• Measure expectation values

Lattice QCD


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Lattice QCD : why is it difficult?Discretize LQCD : ¹ Ã(x) (Ã(x+a)-Ã(x))/a

finite number of degrees of freedom

Statistical physics simulation techniques are available

• There are many ways to discretize, some better than others

improved actions have smaller discretization errors but are more difficult to simulate

• Finite dof finite volume:In an N4 box we deal with 12*6*N4 gauge dof.

“Large volume” is L ~ 3-4 fm!

Lattice QCD : why is it difficult?Create configurations with Monte-Carlo method

Boltzman factor ~ exp(-s d4 x LQCD )

Fermions are problematic: – Ã are Grassmann variables - have to be integrated out complicated

non-local action; computational cost ~ L7 m-10 – Lattice fermion actions are either

a) break chiral symmetry explicitly or b) very expensive

Only the combined continuum (a 0) and chiral (mq 0) limits give physical predictions

Measure expectation values

Not always that simple…

Analysis requires theoretical input (chiral perturbation theory) to control systematical errors.

Use of different lattice actions, operators are imperative.

Lattice QCD : why is it difficult?



Lattice QCD : the solution

Lattice QCD: where do we stand now ?

• “Gold plated” quantities : can be measured better than 3% accuracy. They test the actions, simulations, extrapolations, etc.

(Davies at al)



Lattice QCD : what experimentalists care about

• Present: ®s(mZ), quark masses


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Decay constants: D meson



Asqtad/HISQ action mix

3 lattice spacings continuum limit (a 0)

3-5 quark masses each chiral limit (m 0)

Systematic errors have to be checked

Follana at al, 2007

Could the 2.5¾ deviation in fDs show

to beyond-SM ?

The race is on….

Major LQCD collaborations:

• USQCD (staggered fermions + domain wall fermions) In the next 5 years, expect better than 1% results for – Quark flavor mixing / CKM matrix elements. Need <1% precision

– Decay constants fD, fDs

– ²/²’, muon anomalous magnetic moment,….

• JLQCD (Wilson +overlap fermions) (Japan)• ETMC (Twisted mass fermions) (Europe)• BMW (improved Wilson) (Europe)

basic tests for now, gearing up for precision measurements

Beyond Standard Model physics the future of Lattice QCD

Many of the ideas considered for beyond-Standard-Model physics are based on non-perturbative properties of Quantum Field Theories

Supersymmetric models

some progress with lattice calculations; difficult to formulate

Technicolor models

Alternative to scalar Higgs mechanism for electroweak symmetry breaking

Based on QCD like theories with different number of fermions, representations

The Goldstone boson of QCD

We need 3 Goldstone bosons for electroweak breaking. QCD like theories with massless quarks have them - the pions!

f¼ = 93 MeV -- too light. We need parameters that give fTC~100GeV

´’TC will be the Higgs



Symmetry: chiral

Ã ei°5Ã

When broken :

<ÃÃ> 0 vacuum condensate

Couple to the gauge fields: Goldstones become the longitudinal component of the gauge bosons, giving mass

mW ~ f¼

Walking Technicolor

TC idea has been around for decades. Many are excluded by electroweak precision measurements. Those that are viable require a walking, not running coupling:



What models can do that?

SU(N) with more fermions or higher representations, just under the Banks-Casher IR fixed point.

The ¯ function of the running coupling

( ¯0 >0 : asymptotic freedom )

QCD like IR fixed point “walking”

confining deconfined confining

chirally broken chiral symmetric chirally broken

conformal QF technicolor?

“unparticle theory”




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Which models exhibit walking/IRFP ?

Perturbative map (Catterall, Sannini) as the function of Nf, Nc

Lattice studies are preliminary, but we have the methods, observables, expertise to do it. No walking so far. But it is nevertheless fun!



SU(2) with adjoint fermions,

SU(3) with sextet fermions

SU(3) with 10-12 fundamental flavors

are candidates.

Lattice calculations could decide

Conclusion

• LHC will revolutionarize high energy physics and lattice calculations will play an essential role.

• The needed <1% systematical/statistical errors are within reach in LQCD, but they require– Coordinated, large scale calculations– Checks and balances: different actions, analyzing techniques,

approaches• LHC will point to new physics, triggering (even more) model building.

Any model with non-perturbative properties should be tested on the lattice

• There is no known non-perturbative fixed point in 4D QFT. It would be real fun to find one.

The LHC Rap (Large Hadron Collider). Lattice QCD in the Era of the Large Hadron Collider Anna...

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