Video Games in Technicolor

Transcription

1 Lattice Studies of the Nearly Conformal Video Games in Technicolor Composite Higgs Mechanism Julius Kuti Jefferson Lab seminar April19, 21 With Lattice Higgs Collaboration members: Z. Fodor, K. Holland, D. Nogradi, C. Schroeder

2 Video Games in Technicolor Julius Kuti Jefferson Lab seminar April19, 21 With Lattice Higgs Collaboration members: Z. Fodor, K. Holland, D. Nogradi, C. Schroeder

3 Friday, April 1, 211 Last Update: 11:17 AM ET Physicists at CERN in Geneva find the Higgs particle with unexpected characteristics By Jane Ellis The properties of the newly found Higgs particle shook the foundations of modern particle physics. Although its decay properties are very similar to what was expected, the mass at 57 GeV is far too heavy and the width far too narrow to accommodate what is know to be the Standard Model of modern particle physics. Physicists are turning now to lattice gauge theorists who are trying to explain with nearly conformal gauge theories the experiments at the Large Hadron Collider. Continued on page U= m t = ± 2.9 GeV m h = GeV How to pull out the heavy Higgs particle to 57 GeV from the allowed oval region without violating EW precision data? T Nearly conformal gauge theories might work? -.2 m t m h 68 % CL Requires unusual nonperturbative properties which can be studied on the lattice with extreme computing resources Can the lattice be transformational when we do not know the answer?

4 Outline 1. Overview of three coordinated projects in our program - SU(3) color, fundamental rep, staggered Nf=4-2 - sextet representation with SU(3) color - Running coupling (new ideas, first results) 2. Chiral symmetry breaking - Finite volume p-regime, delta-regime, epsilon-regime - Goldstone spectra and staggered CHPT - New results at Nf=4,8,9,12 will be presented 3. Inside and above the conformal window - Zero momentum dynamics at Nf=16,2 4. Conclusions and Outlook - Prospects towards model building? - Can lattice studies be transformational? - Is peta-scale to exa scale power needed for definitive phenomenology?

5 Talk is based on published results last year: 1. Topology and higher dimensional representations. Published in JHEP 98:84,29. e-print: arxiv: [hep-lat] 2. Nearly conformal gauge theories in finite volume. Phys.Lett.B681: ,29. e-print: arxiv: [hep-lat] 3. Chiral properties of SU(3) sextet fermions e-print: arxiv: [hep-lat] 4. Chiral symmetry breaking in nearly conformal gauge theories e-print: arxiv: [hep-lat] posted 5. Calculating the running coupling in strong electroweak models e-print: arxiv: [hep-lat] and some unpublished new analysis

6 Phase diagram of TWO projects as nearly conformal gauge theories in flavor-color space? Unparticle world Project 1: Fundamental rep Nf=4,8-12,14,16,2 flavors and three colors with staggered fermions. Phenomenology goal: nearly conformal gauge theory with minimal realization of the composite Higgs mechanism Consistent with ElectroWeak Precision Data? They are fun lattice field theories anyway! Project 2: 2-index symmetric rep with Nf=2 flavors and three colors with overlap chiral fermions staggered (will be briefly discussed here, but quenched results with interesting topology are published and full dynamical simulations are running) Unified GPU/MPI code near the conformal window (walking): Higgs phenomenology with nearly vanishing beta function

7 Project 3: Important to complement the test of chirality with running coupling and beta function like QCD far below conformal window How to reach walking scale which is wanted for several reasons in BSM? Fundamental rep with Nf=4,8,9 should be similar Nf=1,11,12,14,16,2 under continued study Nf=16 inside weak coupling Is 2-index symmetric rep nearly conformal? DeGrand et al. (conformal?) our staggered simulations disagree with conformal phase Nf=12 controversial important in model building would be Banks-Zaks FP

8 Theory space and conformal windows Predictions from Schwinger- Dyson approximations not reliable Project 1: in fundamental rep with N=3 colors with Nf=4,8,9,1,11,12,14,16,2 flavors dynamical staggered Banks-Zaks Fixed Point 2-index antisymmetric Project 2: 2-index symmetric rep (sextet) N=3 colors and Nf=2 flavors dynamical overlap adjoint rep BZ FP We only run with N=3 colors Running on CPU clusters and GPU clusters Very demanding Unified code

9 We are supported by the Wuppertal hardware/software infrastructure We built on Wuppertal software library: Fodor, Szabo, Katz GPU Hardware GTX 28 Flops: single 1 Tflop, double 8 Gflops Memory 1GB, Bandwidth 141 GBs -1 For code development: 23 Watts, $35 Small UCSD Tesla cluster ARRA funded by DOE waiting for Fermi cards Very limited use of Wuppertal hardware We are USQCD!! Schroeder Tesla 16 Flops: single 1 Tflop, double 8 Gflops Memory 4GB, Bandwidth 12 GBs Watts, $12 CUDA code: Kalman Szabo Sandor Katz Chris Schroeder Daniel Nogradi Our new DYNQCD software mostly by Szabo, Nogradi, Tesla 17 Flops: single 4 Tflops, double 32 Gflops Memory 16GB, Bandwidth 48 GBs -1 9 Watts, $8

10 Chiral regimes to identify in theory space: 1 1 L s L t! chiral p-regime Goldstone dynamics is different in each regime We study δ and ε -regimes (RMT) and p-regime (probing chiral loops) 4 F 2 3 L s 3 2F 2 3 L s! rotator pion energy gap M = 2Bm q complement each other interpretation of rotator levels in m q limit: 1 F 2 L s 3 1 L s m q = m q (a M) N f = 4 β = x 32 symmetry. π π i5 Figure 1: The potential V (φ) foranunbrokenfigure 2: The potential V (φ) for Figure asponta- neously broken symmetry. The arrow small explicit indi- symmetry breaking tilted term. The condensate arrow indicates now the on 3: The potential V (φ) for a spontaneously broken symmetry arbitrary cates a possible orientation choice of vacuum. of condensate vacuum. The linear term in η can be removed by a small additional Since QCD describes a very large collection of phenomena at high energies extremely well, there shift. This hap must thus be another way to include this symmetry in the real world. This was found energy by state Goldstone is Not slightlyto [28] shifted misidentify compared to therotator value v = gaps µ 2 /λ. But m and is often called the Nambu-Goldstone mode, while a direct realization is referred expand to as the the exponentials, Wigner we now find that the π(x)-field has gotten a small or Wigner-Eckart mode. Nambu s papers for this are Ref. [29]. the mass of theas η-field, evidence and no longer of haschirally only derivative symmetric interactions. The π Let us first describe this mode for a simpler model. A complex scalar field with Lagrangian phase!! m 2 L = µ φ π 2 2β. µ φ V (φ). (22) v is small and can be expanded in the small symmetry breaking parameter β. T We first look at a potential of the type shown in Fig. 1 with a standard form of the type to it, is now called a pseudo-goldstone boson. As long as the explicit symm V (φ) =µ 2 φ φ + λ (φ φ) 2. can still use Goldstone s (23) theorem as a first approximation and then add the c This is precisely what we do in ChPT when the light quark masses are explic We choose here λ > to have a stable theory. phasetransformation Veff: chiral condensate in flavor space This Lagrangian has a U(1) symmetry under the 2.5 Spontaneous symmetry breaking in QCD

11 One-loop expansion in our analysis of p-regime: 1 L s Leutwyer, Gasser, P. Hasenfratz, Niedermayer, Hansen, Neuberger,... Mπ 2 = M L t! chiral p-regime M 2 8π 2 N f F ln Λ3, 2 M F π = F 1 + N f M 2 16π 2 F ln Λ4, 2 M 2B m and F B are four funda Note Nf scaling of pion mass! warning: 2-loop ~Nf^2 (Bijnens) 4 F 2 3 L s 3 2F 2 3 L s! 1 F 2 L s 3 rotator pion energy gap m q = 1 L s M = 2Bm q M π (L s, η) = M π M 2 2N f 16π 2 F g 1(λ, η), 2 F π (L s, η) = F π 1 N f M π 2 F g 1(λ, η), 2 ( ) describes the finite volume corrections We use staggered action with stout smearing λ = ML s Taste breaking included in staggered perturbation theory! structure changing as Nf grows

12 Nf=4 NLO chiral analysis in p-regime: N f = 4 6 Stout β = 3.5 ρ N f = 4 6 Stout β = N f = 4 6 Stout β = (a M) ρ (a M) ρ.2.1 a 4 Δ.13 π ij i5 π.2.1 a 4 Δ.88 π ij i5 π.2.1 a 4 Δ.44 π ij i5 π N f = 4 6 Stout β = a F π N f = 4 6 Stout β = a 3 < ψ ψ > N f = Stout β = (4) L (4) χ = F2 4 Tr( µσ µ Σ ) 1 2 Bm q F 2 Tr(Σ +Σ ) e fundamental parameters F and B measured on M π (T a ) 2 = 2Bm q + a 2 (T a ) + O(a 2 m q ) + O(a 4 ) +V χ (6) (ξ 5 ) =, (ξ µ ) = 8 F (C C 2 + C 3 + 3C 4 + C 5 + 3C 6 ), (ξ µ5 ) = 8 F (C C 2 + 3C 3 + C 4 C 5 + 3C 6 ), (ξ µν ) = 8 F (2C C 4 + 4C 6 ).

13 Nf=8 NLO chiral analysis in p-regime: (a M) N f = 8 6 Stout β = 1. ρ π ij π i5 π (a M) N f = 8 6 Stout β = 1.4 ρ π ij π i5 π (a M) N f = 8 6 Stout β = 1.8 ρ π ij π i5 π a M π 2 / mq N f = 8 6 Stout β = a F π N f = 8 6 Stout β = a 3 < ψ ψ > N f = 8 6 Stout β = (1) (m 1 loop ) 2 π + 5 2m = µ { π 2 f N F ( 2 N F [ ] l(m 2 η ) V l(m2 π V ) [ l(m 2 η A ) l(m2 π A ) + 16µ f (2L 2 8 L 5 ) (2m) + 32µ f 2 ] + 1 ) l(m 2 π 2N I ) F (2L 6 L 4 ) (4N F m) + a 2 C } Nf=8 staggered NLO

14 Nf=9 NLO chiral analysis in p-regime: (a M) N f = 9 4 Stout β = 1.6 ρ π ij π i5 (a M) N f = 9 4 Stout β = 2. ρ π ij π i5 (a M) N f = 9 4 Stout β = x 32 ρ.2.1 π.2.1 π.2.1 π ij π i5 π a M π 2 / mq N f = 9 4 Stout β = 2. a F π N f = 9 4 Stout β = 2. a 3 < ψ ψ > N f = 9 4 Stout β = (7) Testing rooting (nothing unusual happens) (useful for rooted sextet code, complete and running with Nf=2) Provides additional independent info on chiral condensate trend

15 Nf=12 runs are far away from crossover region a 3 < ψ ψ > N f = 12 2 Stout 2 3 x β=1. β=1.4 β=1.8 β=2. β=2.2 β=

16 Nf=12 NLO chiral analysis in p-regime: (a M) N f = 12 2 Stout β = 2. ρ π ij π i5 π (a M) N f = 12 2 Stout β = 2.2 m q <.33: 32 4 m q >.33: 24 3 x32 ρ π ij π i5 π (a M) N f = 12 2 Stout β = 2.4 ρ π ij π i5 π a M π 2 / mq N f = 12 2 Stout β = 2.2 m q <.33: 32 4 m q >.33: 24 3 x32 a F π N f = 12 2 Stout β = 2.2 m q <.33: 32 4 m q >.33: 24 3 x32 a 3 < ψ ψ > N f = 12 2 Stout β = 2.2 m q <.33: 32 4 m q >.33: 24 3 x (12) Similar pattern to Nf=9 case! All features exhibit chiral symmetry breaking more work is needed

17 Some features of Nf=4,8,9,12 runs: Nearly degenerate Goldstone spectra stout action performs very well (a M) N f = 8 6 Stout! = 1. Techni-rho meson " ij " i5 " Chiral condensate measured in F unit is enhanced as Nf increases Nf=4 B/F = 53(6) Nf=8 B/F = 157(17) Nf=9 B/F = 125(19) Nf=12 B/F = 29(64) < ψψ >1/3 ~ F renormalization scale is not set large errors, preliminary, limited to Ls=32! (a M) N f = 8 6 Stout! = 1.4 Techni-rho meson " ij " i5 " rho - A1 splitting N f = 8 6 Stout! = 1.8 Better separtaion of rho and Goldstones at Nf=12 would require (a M) Techni-rho meson " ij " i5 " bigger runs at smaller fermion masses

18 a M eff a M eff N f = 12 β = x64 =.2 2 Stout Nf=12 mq=.2 rho-a1 splitting a Δτ N f = 12 β = 2.2 =.15 2 Stout 32 3 x a Δτ pulled out from single correlator with two parity partners Nf=12 mq=.15 rho-a1 splitting pulled out from single correlator with two parity partners

19 Random Matrix Theory tests in epsilon regime:! n N f = 4 " = 3.6 = ! n N f = 4 " = 3.8 = ! n N f = 4 " = 4. = n n n integrated distribution N f = 4 " = 3.6 = integrated distribution N f = 4 " = 3.8 = integrated distribution N f = 4 " = 4. = a! a! a! integrated distribution = Integrated eigenvalue distrubutions of RMT N f = 8 " = 1.4 Dirac spectrum > quartet degeneracy --> RMT

20 First conclusions on our Nf sequence: Nf=4,8,9,12 all appear to be in chirally broken phase according to several tests: 1. chiral Goldstone dynamics 2. nonvanishing condensate in chiral limit 3. rho-a1 parity doublet splitting close to chiral limit 4. epsilon regime and RMT 5. string tension and running coupling from potential/force? Important warning is appropriate related to the size of F*L

21 Sextet representation with Nf=2 sextet nx = 16 nt = 32 beta = 3.4 sextet nx = 16 nt = 32 beta = stout stout.12.3 f pi.1.8 m pi m m Goldstone spectrum and Fpi-> chirally broken Will be easy 2 flavor analysis

22 m =.2 - compare with Kogut/Sinclair Figure 1 pbp = pbp KS /2 naive KS Code reproduces Kogut-Sinclair results with the 2 stout steps disabled m =.2 - compare with Kogut/Sinclair Figure 1 Polyakov loop 1.8 naive KS

23 Preliminary indications on our Nf=2 sextet model: It appears to be in chirally broken phase according to several tests like the ones discussed earlier: 1. chiral Goldstone dynamics 2. nonvanishing condensate in chiral limit 3. rho-a1 parity doublet splitting close to chiral limit? 4. epsilon regime and RMT? 5. string tension and running coupling from potential/force? More favorable to reach large enough F*L values

24 When is F*L large enough? This can be quantified (epsilon, delta and p regimes are all connected) E l = 1 l(l + 2) with l =,1,2,... rotator spectrum for SU(2) 2θ with θ = F 2 L 3 s(1 + C(N f = 2) F 2 L 2 s + O(1 / F 4 L 4 s )) (P. Hasenfratz and F. Niedermayer) there is overall factor N 2 f 1 N f for arbitrary N f C(N f = 2) =.45 expected to grow with N f At FL s =.8 the correction is 7% and grows with N f When expansion collapses in δ regime, the p-regime analysis needs more scrutiny Cross checks from several running coupling schemes is important

25 V(R) Our running coupling methods (important to have 3 methods) α W (R) SF, MCRG, Wilson loops (including, V(R), F(R)) We use Wilson loop ratios, V(r) potential, and F(r) force to get the running coupling g(r) in several schemes Looks promising We are running with R, or with L when R/L fixed (different schemes) Nf=16 Creutz coupling running N f =12, 2-stout 32 3 x64,!=2.2, m= g*^2 ~.5!=5!=7!=12!=15!=35.3 Not Coulomb-like g 2 (L) fit simulations L R

26 V(R) Our new calculation: use V(r) potential and F(r) force to get traditional running g(r) in several schemes just like in QCD Looks very promising N f =12, 2-stout 32 3 x64,!=2.2, m= loop univ loop SF.25 g 2 L fit simulations LogLL R

27 Quenched test works Necco-Sommer F(r)= C Fḡqq 2 (r) 4πr 2, C F = 4 3, r d 2 dr ḡqq = β(ḡ qq ) = b ν ḡqq 2ν+3, b = 11 16π 2, b 1 = 12 (16π 2 ) 2, ν= b 2 = 1 ( 347 (4π) π 2 4 ) 3 99π ζ(3). F(r)= σ + π 12r 2, σ r2 = 1.65 π 12 ch is in excellent agreement with our results Infinite volume, continuum extrapolated limited r/ro range between.15 and.3 we try to run with the volume!

28 Necco/Sommer Running coupling from force and SF running nicely match for Nf= and Nf=2 We have difficulties to match data from the Force/Creutz running coupling and the Yale SF running at Nf=12 in the relevant coupling range Will requires further careful studies α W (R) Very difficult to resolve fixed point from walking Interesting collection of renormalized running couplings

29 Running gauge coupling from RG on large Wilson loops two groups: our group and Bilgici et al. (generalization from earlier work) problem with Bilgici et al: implementation was not independent of Schrodinger functional method (corrected now) Important that our implementation is T L T define renormalized coupling from second derivative of Wilson loops running with L if R/L is kept fixed: 2 k g R (L, R L )= R 2! 2!R!T ln W(R,T ;L,T ) T =R a k is geometric factor (cutoff dependent on lattice) defined from tree level relation with the bare coupling g W (R, T ; L,T ; a; g )= R g g g R 2! 2!R!T ln W (R,T ;L ) tree = kg 2, T=R g k L /a = Lattice implementation requires the study of the step function together with its cutoff dependence Useful alternative to Schrodinger functional? Wilson loops could be replaced by Polyakov loop correlators R/L

30 We first tested the method at weak coupling for large Wilson loops. Rather than simulating Wilson loops with Monte Carlo, we calculated (simulated) them analytically using the boosted coupling procedure of Lepage and McKenzie which reproduces even large Wilson loops accurately The finite volume dependence was obtained from Urs Heller s code who calculated the Wilson loops in bare perturbation theory (thanks to Urs Heller and Paul Mackenzie for the help they provided) running renormalized coupling in the deep UV region agrees well with loop prediction beeing tested in quenched and dynamical simulations testing the cutoff dependence of the step function and its extrapolation to zero lattice spacing (same as for Schrodinger functional) Onto Monte Carlo now -->

31 Quenched SU(3) simulation extrapolating the step function renormalized coupling to zero cutoff at fixed finite physical box size: data 1/L 2 extrapolation extrapolation: 4.25(11) g 2 (2L) from g 2 (L)= g 2 (2L) /L 2

32 5 4.5 simulations 1-loop 2-loop Starting point g 2 (L )= g 2 (L) /3/9 11:52 ln(l/l ) The running coupling of our Wilson-Creutz scheme In quenched SU(3) simulation renormalized coupling is running with physical box size L without lattice cutoff effects Onto dynamical fermions: fairly strong cutoff effects but no sign of Nf=12 conformal fixed point

33 Conclusions and Outlook - Our focus shifted to Nf=1-16 range (and beyond?) Nf=12 chiral symmetry breaking and running coupling from V(r) and F(r) and Wilson loops - Nf=12 might be close enough to realize walking technicolor but otherwise (like the S-parameter) we do not know how it will perform - What is the fate of the Nf=2 sextet model? Next controversy is brewing? Walking Nf=2 sextet would be a favorite candidate for composite Higgs (mass generation?) - Zero mode dynamics important at weak coupling inside conformal window - Reliable EW precision quantities (S/T/U) will be important to get accurately once we settle on the candidate model(s)

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