Lattices, Strong Dynamics. and. Warped Extra Dimensions. at the Frontier

Transcription

1 Frontier p.1/50 Lattices, Strong Dynamics and Warped Extra Dimensions at the Frontier Joel Giedt Fine Theoretical Physics Institute University of Minnesota

2 A wonderful model Frontier p.2/50 30 years of success for the Standard Model = Electroweak (EW) + Quantum Chromodynamics (QCD) 70s to 90s, confirmed by experiment. Aspects of the theory still being worked out: Mechanism of EW symmetry breaking. Phase diagram of QCD (T vs. µ). Difficult strong coupling problems ( I = 1/2, ɛ /ɛ,...). Confinement mechanism ($1 million q.).

3 Confinement Frontier p.3/50 QCD = theory of color charge (quarks, gluons). All states we observe are color neutral. Short distance: evidence of colored constituents. Color is confined within color neutral objects: mesons, baryons, glueballs, exotics... string tension L V ~ σ L

4 Lattice Yang-Mills: exact gauge invariance [Wilson 74] Frontier p.4/50 x+ ν^ x+ ν^ U µ ( ) U ν ( x) x+ µ^ U ν ( ) x U µ ( x ) x+ µ^ Link U µ (x) points in ˆµ direction from site x. The µν plaquette: U µν (x) = U µ (x)u ν (x + ˆµ)U µ(x + ˆν)U ν(x)

5 Continuum limit Frontier p.5/50 U µ (x) = exp(iaga µ (x)), A µ = n 2 1 a=1 A a µt a U µν (x) = exp[iag(a ν (x + ˆµ) A ν (x)) iag(a µ (x + ˆν) A µ (x)) + O(a 2 )] = exp[ia 2 gf µν (x) + O(a 4 )] F µν = µ A ν ν A µ ig[a µ, A ν ] ( E a, B a ). Color electric E a, color magnetic B a.

6 Continuum limit Frontier p.6/50 Continuum action obtained from: S = x,µν 2n g 2 [1 (1/n) Re Tr U µν(x)] = x,µν a 4 4 F µν(x)f µν (x) + O(a 8 ) a 4 d 4 x x

7 Gauge invariance Frontier p.7/50 U µ (x) g (x)u µ (x)g(x + ˆµ) Since U U = 1, g(x) = U µ (x), g(x + ˆµ) = 1 U µ (x) 1. N 4 sites N 4 g s. µ = 1, 2, 3, 4 4N 4 U s. Can only fix 1/4 of links to 1. E.g., U 4 (x) 1 A 4 (x) = 0 (temporal gauge).

8 Maximal gauges in SU(2) Frontier p.8/50 Maximal abelian gauge: max x,µ Tr [U µ (x)σ 3 U µ (x)σ 3] Direct maximal center gauge: max x,µ Tr [U µ (x)u µ (x)]

9 Direct maximal center gauge Frontier p.9/50 U µ (x) = exp(iag A µ (x) σ/2) Tr U 2 µ(x) = 2 cos(ag A µ (x) ) max ag A µ (x) = 0 mod 2π ( ) ag A U µ (x) = cos µ (x) 2 + i 2 σ µ(x) sin ±1 0 ( ag A µ (x) 2 )

10 Discovering Center Dominance [Del Debbio et al., 96] Frontier p.10/50 (1) Fix to maximal center gauge, U µ (x) ±1. (2) Project links U µ (x) ±1, exactly. (3) Measure confinement observable: string tension. [Del Debbio, Faber, JG, Greensite, Olejnik 98]

11 Frontier p.11/50 Effective electromagnetic coupling α [Mele, hep-ex/ ] 135 e + e e + e 1/α=constant= LEP 1/α GeV 2 < -Q 2 < 6.07GeV 2 OPAL 2.10GeV 2 < -Q 2 < 6.25GeV 2 L GeV 2 < -Q 2 < 3434GeV 2 L3 1800GeV 2 < -Q 2 < 21600GeV 2 L3 QED Q 2 (GeV 2 )

12 Strange predictions Frontier p.12/50 Some Standard Model interactions at E finite: (1) Weak hypercharge: B = cos θ W A sin θ W Z 0. photon Z-boson (2) Higgs self-coupling: H + H H + H.

13 Gravity turns strong too Frontier p.13/50 In theorists units = c = 1, Newton s constant G has dimensions: [G] = (mass) 2. The mass scale Planck scale is: m P = 1/ 8πG m Z. Effective gravitational coupling λ grav. E 2 G (E/m P ) 2. Becomes O(1) strong at E m P.

14 Scales of mystery Inverse coupling 0 m Z E Frontier p.14/50 Gravity Light Higgs Electroweak hypercharge m Z m Z m Z

15 What does this mean? Frontier p.15/50 unphysical approximation breaking down: triviality problem Standard Model (SM) = effective or cutoff theory = finite range of validity: 0 m cutoff E SM OK SM bad m cutoff < m P = unobtainable.

16 If cutoff so big, who cares? Frontier p.16/50 The classical Higgs mass in the Standard Model is: m 2 H m 2 Z. The quantum corrections shift this mass by: m 2 H m 2 cutoff. Physical mass = total: m 2 H + m 2 H m 2 cutoff < m2 P.

17 Experimental fit constraints Frontier p.17/ all data (90% CL) 200 M H [GeV] Γ Ζ, σ had, R l, R q asymmetries low-energy M W m t excluded m t [GeV] Particle Data Group, 2006

18 What gives? Frontier p.18/50 But the Standard Model quantum corrections predict a Higgs mass of the cutoff scale. What keeps the Higgs so light? This is the gauge hierarchy problem.

19 Keeping m 2 H small Frontier p.19/50 All solutions in a nutshell: (1) m cutoff < 1000 GeV = 1 TeV. Beyond the Standard Model at our fingertips! (2) New particles and symmetries such that: m 2 H < m2 H, in the Beyond the Standard Model theory.

20 Around the corner Frontier p.20/50 For m 2 H < m2 H to work: mass(new particles) m Z. We will be looking for these Beyond the Standard Model particles at the Large Hadron Collider.

21 LHC is coming... Frontier p.21/ MB of data will be recorded every second! (20000 GB = 4400 DVD s per day, full luminosity) It will be an EXCITING period in physics.

22 Solutions to the hierarchy problem Frontier p.22/50 Cancellations: supersymmetry (SUSY). Fluffiness: Composite Higgs, transparent to high frequencies. Old: Technicolor,... New: Warped extra dims. (via AdS/CFT),... Hierarchy is a fake: Large extra dimensions.

23 Supersymmetry Frontier p.23/50 It is a symmetry that transforms bosons fermions. If the symmetry is exact, the masses of particles show a Bose-Fermi degeneracy: m B = m F.

24 Superpartners Frontier p.24/50 Supersymmetry predicts superpartners: electron (fermion) scalar electron (boson) = selectron. Recall, however, that SUSY predicts: m B = m F. Because we have not observed superpartners, SUSY must be spontaneously broken. E.g., m selectron > m Z.

25 Tackling the nonperturbative Frontier p.25/50 Models for SUSY-breaking involve nonperturbative dynamics of SUSY gauge theories. Higgs effect at high scale frozen at weak coupling calculable models. Other scenarios: strongly interacting noncalculable models.

26 Gravity dual Frontier p.26/50 One approach: Find weakly coupled gravity dual. AdS/CFT correspondence: Yang-Mills dynamics (= CFT ) takes on a gravitational meaning (= AdS ). In recent work w/ T. Gherghetta (Minnesota), M. Gavella (Lausanne): MSSM in bulk. Deformed AdS 5. Susy-breaking from deformed metric, inspired by Type IIB supergravity solutions. [Borokhov, Gubser 02; Kuperstein, Sonnenschein 03]

27 Frontier p.27/50 RS1 [Randall, Sundrum 99] Slice of AdS 5 : ds 2 5 = A 2 (z) ( dt 2 + d x 2 + dz 2), A 2 (z) = 1 z dim s: t, x. 5th dim.: 1 z z IR. Warp factor: A 2 (z) (units of AdS curvature). UV brane: z UV = 1. IR brane: z IR = m P /(0.1 to 10 TeV).

28 Frontier p.28/50 Deforming AdS 5 Deform AdS according to the dim l reduc. of Kup.-Sonn. soln.: ds 2 5 = A2 (z) ( dt 2 + d x 2 + dz 2), A 2 (z) = 1 z 2 ( 1 ɛ (z/zir ) 4). Domain: 1 z z IR. Dial 1: ɛ 0.1. [ɛ = 0.05 in following.] Dial 2: z IR = m P /(1-100 TeV). SUSY lim.: ɛ 0. Interpretation: DSB in the SU(N c ).

29 A few per cent violence in the IR: Will it matter? Frontier p.29/50 * Ratio deformed/undeformed warp factor. * * Unchanged except very near IR brane. *

30 Scalars Frontier p.30/50 Solutions parameterized by boundary mass b. LO profile z b 1, unchanged. Zero modes lifted: m ɛ(b 1)(b + 10)z 1 IR (b > 1) m ɛ(1 b)(b + 10)(z IR ) b 2 (0 < b < 1)

31 Masses of quasi-zeromode scalars Frontier p.31/50

32 Fermions Frontier p.32/50 Exact zeromodes persist. 0 = (γ α α + γ 5 z + ca) ˆψ, ˆψ A 2 ψ, ˆψ = χ(x)a 2 (z)f(z), (± z + ca)(a 2 f) = 0 ( z ) = N ± A 2 (z) exp c dz A(z ). f ± Profile virtually unchanged: f ± N ± z 1 2 c ± [1 + ɛz4 (1 1 ] 2 c ±). 4z 4 IR 1

33 Generational hierarchies Frontier p.33/50 Higgses at UV brane. Use profiles z 1 2 c L, z 1 2 +c R for ferm. hier. m 4d = H 1 2 Y 2cL 1 + 2cR 5d z 1 2c L IR 1 z 1+2c R IR 1. IR "Brane" Gen. 1 Gen. 2 o Higgses UV "Brane"

34 Scalar-fermion correlation Frontier p.34/50 SUSY relates scalar/fermion masses: b = 3 2 c L. Scalar/fermion profiles approx. same. scalar partners of light fermions IR localized (b > 1), [HEAVY] partners of heavy fermions UV localized (b < 1). [LIGHT] Gauginos, stop, sbottom, stau: radiative mass.

35 Example spectrum Frontier p.35/50 E Gen. 1 sleptons (10.2 TeV) Gens. 1 & 2 squarks (5.9 TeV) Gen. 2 sleptons (5.1 TeV) Gravitino (2 ev) LHC Reach (few TeV) Gen. 3 spartners, gauginos, higgsinos, higgses (115 GeV 1.6 TeV)

36 Dual interpretation Frontier p.36/50 IR-localized: composites of new strong interaction. UV-localized: elementary. Composite fermions massless: SM chiral gauge symmetry. SUSY-breaking similar to: More minimal SSM. [Cohen, Kaplan, Nelson 96] Single-sector models. [Arkani-Hamed, Luty, Terning 97-98]

37 Example spectrum (5d numerical + 2-loop Softsusy [Allanach]) Frontier p.37/50 ẽ L, ẽ R, ν el 10160, 10150, GeV µ L, µ R, ν µl 5145, 5130, 5145 GeV d L, d R, ũ L, ũ R 5905, 5885, 5970, 5890 GeV s L, s R, c L, c R 5905, 5885, 5970, 5890 GeV g 1615 GeV b1, b 2, t 1, t , 1369, 1253, 1369 GeV τ 1, τ 2, ν τl 511, 630, 633 GeV χ ± 1, χ± 2 478, 593 GeV χ 0 1, χ 0 2, χ 0 3, χ , 480, 511, 598 GeV h 0, A 0, H 0, H ± 115, 646, 646, 651 GeV G 2.35 ev

38 LHC predictions Frontier p.38/50 Typical cascade decay from gg g g: ~g ~t1 ~chi1+ ~chi10 tbar b W+ l+ W bbar nu ~G gamma nubar l

39 LHC predictions Frontier p.39/50 NLSP decays χ 0 1 γ + G 288 GeV 2 ev give strong signal: p p γγ + E T +X hard lots

40 γγ+ E T in our model Frontier p.40/50 At Tevatron energy 1.96 TeV, PYTHIA says: σ BR = pb 0 events at D +CDF w/ 2 fb 1. No constraint.

41 γγ+ E T in our model Frontier p.41/50 At LHC energy 14 TeV, PYTHIA says: σ BR = pb times the rate of Tevatron! Obtain 35 events w/ 1 fb 1 ( 1st year). Backgrounds larger at LHC: Will we see the signal?

42 Backgrounds Frontier p.42/50 Real: pp {gg, q q} γγ, Fake: (mainly j π 0 ): pp γ j fake, pp j fake j fake. channel γγ γj jj cross section 0.15 µb 0.12 mb 55 mb Comparable since j fake /j 10 3

43 MET [SUSY = solid, SM(γγ) = dashed] Frontier p.43/50

44 pt [SUSY = solid, SM(γγ) = dashed] Frontier p.44/50

45 Cuts Frontier p.45/50 Distributions suggest: p T,γ 40 GeV, E T 60 GeV Don t lose much signal. Background eliminated.

46 MET w/ cuts [SUSY = solid, SM(γγ) = dashed] Frontier p.46/50

47 pt w/cuts [SUSY = solid, SM(γγ) = dashed] Frontier p.47/50

48 Summary w/cuts Frontier p.48/50 Integrated Luminosity SUSY SM 2γ SM 2γ + fakes 1 fb fb < 0.1 < 1

49 Summary Frontier p.49/50 Far fewer parameters than new particles: predictive. (2-loop evaluation with publicly avail. code.) Gravity dual for single-sector models of spontaneous SUSY-breaking. Our simulations imply 2γ+ E T is a very clean signal for the model at LHC. On edge of B-physics FCNC s and LFV s experiments, keep searching! (Upcoming experiments will test.)

50 Conclusions Frontier p.50/50 Interesting questions remain to be answered in the Standard model: EW symmetry breaking strong effects in QCD [Z 3 vortex confinement?] Problems of the Standard Model (triviality, hierarchy problem, etc.) imply new physics somewhere above 100 GeV. Example given: new strong dynamics and SUSY-breaking modeled with 5d warped extra dimension. Encouraging recent progress in strong SUSY & chiral gauge theory on lattice. [4d simulations needed]