1. The LHC Rap (Large Hadron Collider)

2. Lattice QCD in the Era of the Large Hadron Collider Anna Hasenfratz University of Colorado, Boulder University of Kansas, November 3 2008

3. 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, ….

4. 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

5. Elementary interactions Theory Electromagnetic Interaction : QED - U(1) gauge model - mediating gauge boson: photon -- massless vector particle -extremely well tested ® = e 2 /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 10 277 MeV The Standard Model

6. Theory Strong 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)

7. Quarks Each quark comes in 3 colors (r,g,b) 8 massless gluons, carry color charge GenerationFlavorChargeMass [GeV] firstu (up) d (down) -1/3 2/3 7373 seconds (strange) c (charm) -1/3 2/3 120 1200 thirdb (bottom) t (top) -1/3 2/3 4300 174,000

8. Light Baryons

9. Light Mesons

10. Lights mesons (cont)

11. The Standard Model Theory Weak Interaction : SU(2) gauge model - ® w is small: perturbation theory works -mediating gauge bosons : W +/-, Z -- massive, m W,Z ¼ 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

12. Higgs Mechanism, Spontaneous symmetry breaking Take a complex scalar field Á=Á 1 + iÁ 2 with potential ¸>0 m 2 >0 : symmetric shape, 2 degenerate modes, Á 1, Á 2 m 2 <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

13. 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

14. 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 < m H < 167 GeV (95% CL) All experimental data are described well with the MSM - no compelling evidence (or need) for beyond-SM physics. indirect direct

15. 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

16. The Standard Model cannot stand-alone MSM 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 m H ) 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

17. 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) (F ¹º field strength) 3 generations of quarks à 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

18. Discretize L QCD :  ¹ Ã(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 e -m t + e -m(T-t)

19. Lattice QCD : why is it difficult? Discretize L QCD :  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 N 4 box we deal with 12*6*N 4 gauge dof. “Large volume” is L ~ 3-4 fm!

20. Lattice QCD : why is it difficult? Create configurations with Monte-Carlo method Boltzman factor ~ exp(-s d 4 x L QCD ) Fermions are problematic: – Ã are Grassmann variables - have to be integrated out  complicated non-local action; computational cost ~ L 7 m -10 –Lattice fermion actions are either a) break chiral symmetry explicitly or b) very expensive Only the combined continuum (a  0) and chiral (m q  0) limits give physical predictions

21. 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?

22. Lattice QCD : the solution

23. 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)

24. Lattice QCD : what experimentalists care about Present: ® s (m Z ), quark masses

25. 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 f D s show to beyond-SM ?

26. 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 f D, f D s – 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

27. 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

28. The Goldstone boson of QCD We need 3 Goldstone bosons for electroweak breaking. QCD like theories with massless quarks have them - the pions! f ¼ = 93 MeV -- too light. We need parameters that give f TC ~100GeV ´’ TC will be the Higgs Symmetry: chiral à  e i° 5 à When broken :  0 vacuum condensate Couple to the gauge fields: Goldstones become the longitudinal component of the gauge bosons, giving mass m W ~ f ¼

29. 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.

30. 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”

31. Which models exhibit walking/IRFP ? Perturbative map (Catterall, Sannini) as the function of N f, N c 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

32. 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.