Strongly-Coupled Signatures through WW Scattering

Transcription

1 Strongly-Coupled Signatures through WW Scattering Presented by Michael I. Buchoff Lawrence Livermore National Lab With the LSD Collaboration Based on work from Phys. Rev. D85 (2012) This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA LLNL- PRES

2 Lattice Strong Dynamics Collab. (as of Oct. 4, 2011) Argonne Berkeley Boston Heechang Na, James Osborn Sergey Syritsyn Ron Babich, Richard Brower, Michael Cheng, Claudio Rebbi, Oliver Witzel Colorado Fermilab Harvard Livermore UC Davis Washington Yale David Schaich Ethan Neil Mike Clark MIB, Pavlos Vranas, Joe Wasem Joe Kiskis Saul Cohen Tom Appelquist, George Fleming, Meifeng Lin, Gennady Voronov

3 Primary Questions (as of Today) In light of LHC discovery... how viable is technicolor? Using the lattice, which channels can composite EW breaking be tested? What is the best strategy to address these questions?

4 LHC Discovery CMS: ATLAS: Both experiments consistent with ~125 GeV scalar

5 Implications for technicolor? m 0 ++ f π 0.5 m 0 ++ f π 5 for QCD Very restrictive...two theoretical possibilities: 1. Pseudo-dilaton near conformal window m 0 ++ (N f N c f ) N c 2. Scalar, Goldstone di-quark in real/pseudo-real rep. - Need ext. sector to violate techni-baryon number?

6 Classic Question Using the lattice, which channels can composite EW breaking be tested? Goal: Address this question using pion scattering as probe Techni-pion Scattering W-W Scattering EW LECs

7 Why WW Scattering? Central to perturbative unitarity question Longitudinal Modes: A(W + L W L W + L W L ) g2 4m 2 W (s + t) E 2 Perturbative unitarity breaks down: s 2.2 TeV Two possibilities: 1) New particles emerge that protect perturbative unitarity 2) New strong dynamics emerge (ala QCD) - Pion-pion scattering unitarized by excited states, resonances, etc.

8 Our approach to WW Effective Field Theory (other approaches include Equivalence Theorem, etc.) QCD Parallel: Determines QCD Coefficients Chiral Pert. Theory (known d.o.f.: pions, kaons, etc.) BSM: Determines BSM EW Chiral Theory (known d.o.f.: W, Z, etc.) Coefficients

9 Hadronic Chiral Lagrangian EFT of Hadronic scale physics resulting from QCD Include all terms that respect: SU(2) L SU(2) R L LO = f 2 4 tr ( µ U) ( µ U)+χ + L NLO = 1 4 [tr(v µv µ )] [tr(v µv ν )] tr(χ +) tr(v µv µ χ + ) U =exp iτ π f χ + = U χu + Uχ U V µ =( µ U)U χ =2Bm

10 Electroweak Chiral Lagrangian EFT of EW scale physics resulting from TeV scale physics Include all terms that respect: SU(2) L U(1) Y At leading order: (Quite Simple) L LO = f 2 4 tr (D µ U) (D µ U) 1 4 B µνb µν 1 2 trw µνw µν β 1g 2 f 2 [tr(tv µ )] 2 D µ U = µ U + ig τ 2 W µ U ig U τ 3 2 B µ T = Uτ 3 U V µ =(D µ U)U

11 Electroweak Chiral Lagrangian EFT of EW scale physics resulting from TeV scale physics Include all terms that respect: SU(2) L U(1) Y Higgs VEV L LO = f 2 At leading order: (Quite Simple) 4 tr (D µ U) (D µ U) 1 4 B µνb µν 1 2 trw µνw µν β 1g 2 f 2 [tr(tv µ )] 2 D µ U = µ U + ig τ 2 W µ U ig U τ 3 2 B µ T = Uτ 3 U V µ =(D µ U)U

12 Electroweak Chiral Lagrangian EFT of EW scale physics resulting from TeV scale physics Include all terms that respect: SU(2) L U(1) Y Higgs VEV L LO = f 2 At leading order: (Quite Simple) SU(2) C 4 tr (D µ U) (D µ U) 1 4 B µνb µν 1 2 trw µνw µν β 1g 2 f 2 [tr(tv µ )] 2 T = Uτ 3 U V µ =(D µ U)U Custodial-violating term D µ U = µ U + ig τ 2 W µ U ig U τ 3 2 B µ

13 Electroweak Chiral Lagrangian EFT of EW scale physics resulting from TeV scale physics Include all terms that respect: SU(2) L U(1) Y At leading order: f β 1 At NLO: α 1 -α 5 α 6 -α α 1gg B µν tr(tw µν ) 1 4 β 1g 2 f 2 [tr(tv µ )) 1 4 α 8g 2 [tr(tw µν )] 2 S α 1 U α 8 T β 1 Dominant terms in WW: (other coefficients experimentally bound/small) α 4 [tr(v µ V ν )] 2 α 5 [tr(v µ V µ )] 2

14 Electroweak Chiral Lagrangian EFT of EW scale physics resulting from TeV scale physics Include all terms that respect: At leading order: f β 1 SU(2) L U(1) Y SU(2) C At NLO: α 1 -α 5 α 6 -α α 1gg B µν tr(tw µν ) 1 4 β 1g 2 f 2 [tr(tv µ )) 1 4 α 8g 2 [tr(tw µν )] 2 S α 1 U α 8 T β 1 Dominant terms in WW: (other coefficients experimentally bound/small) α 4 [tr(v µ V ν )] 2 α 5 [tr(v µ V µ )] 2

15 Hadron-EW Connection Hadronic EFT One Doublet EW EFT m d 0 α 5 = O(g) α 4 = O(g) g, g 0 f 2 4 tr( µu µ U)+α 5 tr( µ U µ U) 2 + α4 tr( µ U ν U) ~ α 4, α 5 O(g 2 ) O(g 4 ) O(g 4 )

16 Hadron-EW Connection Hadronic EFT Multiple Flavors EW EFT m d 0 p 2 M 2 ds,m 2 ss g, g 0 p 2 M 2 ds,m 2 ss f 2 4 tr( µu µ U)+α 5 tr( µ U µ U) 2 + α4 tr( µ U ν U) 2 O(g 4 ) ~ α 4, α 5 α 5 = O(g) α 4 = O(g)

17 Hadron-EW Connection Hadronic EFT Multiple Flavors EW EFT m d 0 p 2 M 2 ds,m 2 ss g, g 0 p 2 M 2 ds,m 2 ss f 2 4 tr( µu µ U)+α 5 tr( µ U µ U) 2 + α4 tr( µ U ν U) 2 O(g 4 ) ~ α 4, α 5 α 5 = O(g) α 4 = O(g) Interesting implication: Direct probe of strong dynamics!!!

18 LEC Scale Scorecard α 4,5 (M H,M ds ): 1,2 (µ, M ds ) 1) + 4 Integrated-out flavors + 2) 1 384π 2 log M 2 H µ 2 + Eaten W and Z - log M 2 dd µ 2 log M 2 H M 2 dd 3) O(10 3 )

19 Pi-Pi Scattering Cleanest and most understood hadronic scattering process: theoretically, experimentally, and numerically π + I = 2 π + Weinberg 1966: LO Prediction π + π + m π a I=2 ππ = m2 π 8πf 2 π Gasser and Leutwyler 1985: m π a I=2 ππ = m2 π 8πf 2 π 1+ m2 π 16π 2 f 2 π 3 log NLO Prediction m 2 π µ 2 1 I=2 ππ (µ)

20 Many Flavor Scattering Bijnens, Lu 2011: M P a PP = M 2 P 8πF 2 P 1+ M 2 P 16πF 2 P Maximal Isospin 4(1 N F + N 2 F ) N 2 F ln M 2 P µ 2 4(N F 1) N 2 F L PP (µ) Key Points: L PP = 512π 2 (L 0 +2L 1 +2L 2 + L 3 2L 4 L 5 +2L 6 + L 8 ) 1) No explicit flavor dependence in L PP 2) Reduces to two flavor result via matching conditions r 1(µ, M ds )= 2L r 0(µ)+4L r 1(µ)+2L r 3(µ)+ 2 N f 24(32π 2 ) log M ds 2 µ 2 r 2(µ, M ds )=4L r 0(µ)+4L r 2(µ)+ 2 N f 12(32π 2 ) log M ds 2 µ 2

21 Many Flavor Scattering Bijnens, Lu 2011: M P a PP = M 2 P 8πF 2 P 1+ M 2 P 16πF 2 P Maximal Isospin 4(1 N F + N 2 F ) N 2 F ln M 2 P µ 2 4(N F 1) N 2 F L PP (µ) Key Points: L PP = 512π 2 (L 0 +2L 1 +2L 2 + L 3 2L 4 L 5 +2L 6 + L 8 ) 1) No explicit flavor dependence in L PP - Can compare different flavor theories directly!! 2) Reduces to two flavor result via matching conditions r 1(µ, M ds )= 2L r 0(µ)+4L r 1(µ)+2L r 3(µ)+ 2 N f 24(32π 2 ) log M ds 2 µ 2 r 2(µ, M ds )=4L r 0(µ)+4L r 2(µ)+ 2 N f 12(32π 2 ) log M ds 2 µ 2

22 10 DWF Ensembles: Lattice Details x 64 x 16 lattices am ρ flavor: mq = 6 flavor: mq = Note: Neither theory expected to yield light enough scalar Table 1: 2 Flavor m q # Configs # Meas Table 1: 6 Flavor m q # Configs # Meas

23 Results F 6F 0.4 M P kcot M P 2 F P LO Weinberg dominance persists!!!!

24 15 Results L PP Μ 2 F P F 6F M P 2 F P L 2F ππ(µ = 2F P )=5.42 ± 2.28 L 6F ππ(µ = 2f P )=9.20 ± 1.87 χ 2 /d.o.f = 0.71 χ 2 /d.o.f = 0.54

25 Two Flavor WW LECs NLO calculations of M P F P M P a PP Three EQs, four unknowns α r 4 + α r 5 =(3.43 ± 0.31) 10 3 µ 246 GeV How robust is this result?

26 How Robust? 2 Different Chiral expansion 0.05 M P 2 / 2 m N f =2 LO+NLO N f =2 N f =6 F P N f =2 LO+NLO N f =2 N f =6 M P/ m k cot δ N f =2 LO+NLO N f =2 N f = m m m Subpar Fit Implies: Need smaller masses Need larger volume Need bigger computer Even Still: α r 4 + α r 5 =(3.34 ± 0.71) 10 3 (this fit) vs. α r 4 + α r 5 =(3.43 ± 0.31) 10 3 (previous fit)

27 Where we Stand Estimates for 99% CL bounds for 100 inverse fb: < α 4 < < α 5 < Eboli et. al Two Flavor results: α 4 (M H )+ α 5 (M H )=(3.34 ± ) 10 3 M log 2 H F + O(1) 2 128π 2 Six flavor shows early signs for enhanced values, but is currently inconclusive

28 Future Directions... 1) Ultimately need: - Different volume(s) - More statistics & mass point 2) Get W-W parameters in other ways! - I=2 pi-pi D-wave scattering (more stats, operators) - Pion form factors (more stats, mass points) - Eff. Range & Shape Param. (more stats, volumes) - NNLO analysis (more stats, mass points) - PQ analysis (more inversions, volumes)

29 ...More relevant directions 1) Lattice calculations of real or pseudo-real rep. - Lattice simulations of SU(2) underway 2) Theoretical work - Settle on viable SU(2) model - Include 125 GeV scalar in EW Chiral EFT - Connect SU(2) LECs to WW LECs Bottom line: Lattice + WW scattering can say final word on technicolor

30 This research was supported by the LLNL LDRD Unlocking the Universe with High Performance CompuBng 10- ERD- 033 and by the LLNL MulBprogrammaBc and InsBtuBonal CompuBng program through the Tier 1 Grand Challenge award that has provided us with the large amounts of necessary compubng power.