LHC Signals of (MSSM) Electroweak Baryogenesis

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1 LHC Signals of (MSSM) Electroweak Baryogenesis David Morrissey Department of Physics, University of Michigan Michigan Center for Theoretical Physics (MCTP) With: Csaba Balázs, Marcela Carena, Arjun Menon, Carlos Wagner KITP, February 21, 2008

2 Baryons Baryon density of the universe: [WMAP 06] η = n B n γ = (6.5 ± 0.3) where n B = (# baryons) (# anti baryons). Only baryons, not anti-baryons. Baryon Asymmetry of the Universe (BAU). No Standard Model (SM) explanation. MSSM Electroweak Baryogenesis

3 Baryogenesis Mechanisms =

4 Electroweak Baryogenesis (EWBG) baryon production during the electroweak phase transition. [Kuzmin,Rubakov,Shaposhnikov 85] 1. Electroweak symmetry breaking as the universe cools. 2. Nucleation of bubbles of broken phase. 3. Baryon production near the expanding bubble walls. <ϕ> = 0 <ϕ> = 0 <ϕ> = 0 <ϕ> = 0

5 1. The Electroweak Phase Transition Order parameter = Higgs VEV φ : φ = 0 SU(2) L U(1) Y is unbroken. φ = 0 SU(2) L U(1) Y U(1) em. Effective potential: V eff = ( µ 2 + α T 2 )φ 2 γ Tφ 3 + λ 4 φ V eff Τ >> µ Τ << µ φ

6 2. Bubble Nucleation First order phase transition: V eff T > T c tunnel φ T = T T < T Bubbles of broken phase are nucleated at T < T c. c c <ϕ> = 0 <ϕ> = 0 <ϕ> = 0 <ϕ> = 0

7 3. Producing Baryons CP violation occurs in the bubble wall. Sphaleron transitions create baryons outside the bubbles. These baryons are swept up into the bubbles. CP χ R χ L + χ L Sphaleron B Bubble Wall <φ> = 0 <φ> = 0 Sphaleron

8 Aside: Sphalerons B + L is SU(2) L anomalous in the SM (and MSSM). Transitions between topologically distinct SU(2) L vacua: B = L = n g = # generations. [ t Hooft 76] T = 0 tunnelling (instantons). Γ inst e 16π2 /g T 0 thermal fluctuations (sphalerons).[klinkhamer+manton 84] Γ sp T 4 e 4π φ /g T φ = 0 [Arnold+McLerran 87] κ α 4 w T4 φ = 0 [Bodeker,Moore,Rummukainen 99].

9 EWBG in the Standard Model It doesn t work for two reasons: 1. The electroweak phase transition is first-order only if the Higgs boson is very light, [Kajantie et al. 98] m h 70GeV. LEP II experimental mass bound: m h > 114.4GeV (95% c.l.). 2. There isn t enough CP violation in the SM. [Gavela et al. 94]

10 EWBG in the MSSM SM Problem #1: No First-Order Phase Transition MSSM superpartners modify the Higgs potential. SM Problem #2: Not Enough CP Violation Soft SUSY breaking (and µ) introduces new CPV phases: Arg(µ M a ), Arg(µ A i ),... EWBG can work in the MSSM! These requirements fix much of the MSSM spectrum.

11 Requirement #1: A Strong First-Order EWPT V eff = ( µ 2 + α T 2 )φ 2 γ Tφ 3 + λ 4 φ Quantitative Condition: [Shaposhnikov 88] φ(t c ) T c γ λ > 1. γ 0 is generated by bosonic loops. The dominant MSSM contribution comes from a light mostly right-handed stop. [Carena,Quirós,Wagner 95] m h λ v

12 V eff = ( µ 2 + α T 2 )φ 2 γ Tφ 3 + λ 4 φ M 2 t = m2 Q + m 2 3 t + D L m t X t m t X t m 2 U 3 + m 2 t + D R MSSM cubic term : γ Tφ 3 T 4π [ m 2 t ] 3/2 (φ, T) 1 where m 2 t 1 (φ, T) y 2 t φ2 1 X t 2 + m 2 U 3 + ξ T 2 m 2 Q 3. }{{} δm 2 δm 2 0 maximizes the cubic term.

13 Implications A light right-handed stop: (100GeV) 2 m 2 U 3 0, X t /m Q GeV m t 1 170GeV m t. A heavy left-handed stop: m Q3 2TeV. A light SM-like Higgs: m higgs 120GeV. M a 200GeV, 5 < tan β < 10.

14 Requirement #2: New CP Violation Main source: Higgsinos. e.g. M χ ± M 2 g 2 v u (z) g 2 v d (z) e iφ µ, with φ = Arg(µ M 2 ). CPV source: J 0 H (z) = Hγ 0 H Im(µ M 2 ) z f(v u (z), v d (z)) ~ H g v(x) µ J ~ H (z) ~ H χ a g v(y)

15 B formation cartoon: CP H Q U Q U y t QH u U c SU(2) L sphaleron O sphal i(q i Q i Q i L i ) is sourced by the Q asymmetry.

16 Implications This is enough to generate the baryon asymmetry if: [Carena,Quirós,Seco,Wagner 02; Lee,Cirigliano,Ramsey-Musolf 04] Arg(µM 1,2 ) 10 2 µ, M 1,2 400GeV New CP violation electric dipole moments (EDM) Strict constraints: d e < e cm [Regan et al 02] d n < e cm [Baker et al 06] d Hg < e cm [Romalis et al 01]

17 e.g. Electron EDM d e One-loop contribution: [Ibrahim+Nath 98] ~ f γ f ~ χ 0 f +... Consistency with EWBG and EDM constraints requires m f 1,2 5 10TeV. decouple first and second generation sfermions.

18 e.g. Electron EDM d e (contd... ) Irreducible two-loop contribution ( Im(µ M 2 )): [Chang, Chang, Keung 02; Pilaftsis 02] 1.6 γ χ h, H, A γ d e 27 (10 e cm) M (GeV) A Upcoming experiments will probe the EWBG region. [Balázs,Carena,Menon,DM,Wagner 04, Lee,Cirigliano,Ramsey-Musolf 04]

19 Spectrum Summary Light mostly right-handed stop: m t 1 < m t. Heavy mostly left-handed stop: m t 2 > 2TeV. Light SM-like Higgs boson: m h 120GeV. Very heavy 1st and 2nd gen. sfermions: m f 1,2 5TeV. Light charginos and neutralinos: M 1,2, µ 400GeV.

20 Baryogenesis Mechanisms =

21 MSSM EWBG at the LHC

22 MSSM EWBG at the Tevatron? A visible light stop since m t 1 < m t? [Balázs,Carena,Wagner 04] m 0 (GeV) χ 1 t > c χ t > b W χ 1 m (GeV) t

23 Light Stop Decay Modes t 1 c χ 0 1 (m t 1 m χ 0 1 ) < 30GeV soft charm t 1 b W + χ 0 1, t 1 b χ + 1 Often kinematically impossible. Swamped by background for m χ 0 > 35GeV. (4 fb 1 ) 1 [Demina, Lykken, Matchev, Nomerotski 99] Metastable t 1 ( gravitino) Tevatron CHAMP searches imply m t 1 > 220GeV. [CDF 06; Diaz-Cruz, Ellis, Olive, Santoso 07]

24 t 1 c χ 0 1 and Dark Matter Stop coannihilation with a Bino LSP: [Balázs,Carena,Menon,DM,Wagner 04] m A = 1000 GeV 140 M 1 (GeV) Ω h 2 > < Ω h < 0.. h 2 Ω < m < 104 GeV χ m < m N t 60

25 LHC Picture ( t 1 cχ 0 1 ) A bit glum... t 1 c χ 0 1 is difficult to trigger on. Other scalars are very heavy. ( b R, τ R?) g t t 1, t t 1 dominates. Challenging electroweak-ino decays: [Carena+Freitas 06] χ ± 1,2 t 1 b (if possible) χ 0 (i>1) Z χ0, h χ 0, W ± χ

26 Same Sign Stops [Kraml+Raklev 05, 06] g g t t t 1 t 1 b b l+ l + + (jets) + /E T same sign tops same-sign leptons Discovery of light stops with 30 fb 1 for m g < 1000GeV. Parameter determination is difficult. No c-tags...

27 Stoponium [Drees+Nojiri 97; Martin 08] η t 1 = t 1 t 1 bound state. Γ t 1 cχ 0 1 }{{} ev η t 1 binding energy. }{{} GeV η t 1 γγ may be observable at the LHC with < 100 fb 1 for m η t 1 < 250GeV. [Martin 08] Very good absolute mass measurement of t 1!

28 Indirect Higgs Signals [in progress with Arjun Menon] A light stop can modify Higgs production and decay. [Kane,Kribs,Martin,Wells 95; Dawson,Djouadi,Spira 96;Djouadi 98;Dermisek+Low 07 Effective (EWBG) h t 1 t 1 coupling: g h t 1 t 1 m 2 t 1 X t 2 m 2 Q 3. same combination as in the EWBG phase transition...

29 Gluon Fusion: gg h σ(gg h) Γ(h gg) Loops: g t h + g ~ t h g g Constructive...

30 X t 0, tan β = 10, M a = large M 1 = 120GeV, µ = M 2 = 200GeV m h = 114 GeV m h = 120 GeV Γ(h -> gg) / Γ(h -> gg) SM m t1 (GeV)

31 Diphotons: h γγ Important search channel for a light Higgs. Loops: h W γ ~ t γ h γ γ Destructive...

32 X t 0, tan β = 10, M a = large M 1 = 120GeV, µ = M 2 = 200GeV BR(h -> γγ) / BR(h -> γγ) SM m h = 114 GeV m h = 120 GeV m t1 (GeV)

33 LHC Light SM Higgs (m h < 120GeV) Searches [ATLAS TDR 99; CMS TDR 07] (gg ) h γγ 5σ with about 10 fb 1 m h /m h < 0.2%. V BF h ττ 4.0σ with 30 fb 1, 5.5σ with 60 fb 1 V BF h γγ 3.1σ with 60 fb 1 Wh, Zh γγ 4.0 σ with 100 fb 1 (high L) (gg ) h ZZ 3.0 σ with 30 fb 1 (m h = 120GeV)

34 gg h γγ Total Rate Γ(h gg) BR(h γγ) m h = 114 GeV m h = 120 GeV σ BR / σ BR SM m t1 (GeV) 10 20% uncertainty on the rate with 300 fb 1 [Zeppenfeld 02]

35 Summary On top of everything else, the MSSM can account for the dark matter and the baryon asymmetry. Baryon production electroweak baryogenesis. EWBG requires a light stop, light -inos, heavy scalars. This scenario can be challenging at the LHC. Higgs boson production and decay gives an indirect probe. Connection between colliders and cosmology!?

36 MSSM EWBG at the LHC

37 Extra Slides

38 Sphalerons B + L is a symmetry of the classical SM and MSSM Lagrangians. This symmetry is broken by quantum effects. The only processes that violate B + L are transitions between topologically inequivalent SU(2) L gauge vacua. Each transition produces B = L = n g = #generations. At T = 0, these transitions proceed by tunnelling (instantons). Γ e 16π2 /g At T 0, these can go via thermal fluctuations. sphaleron transitions. The transition rate (per unit volume) is [Arnold+McLerran 87] Γ sp T 4 e 4π φ /g T φ = 0 α 4 w T 4 φ = 0.

39 The net rate of B violation due to the sphalerons is dn B dt = Γ sp T 3 A n g i=1 (3 n q i L + n l i L ) + B n B for positive dimensionless constants A and B. The first term corresponds to the chiral fermion charge: e.g. n ql = (# left-handed quarks) - (# right-handed antiquarks). In the absence of this asymmetry, baryon number relaxes to zero as n B (t) = n B (0) e B(Γ sp/t 3 ) t., When non-zero, the chiral charge acts as a source for baryon production.

40 Beyond the MSSM

41 Why? The minimal SUSY SM faces a few difficulties: The tree-level mass of the lightest CP-even Higgs is bounded by M Z : m 2 h M2 Z cos2 2β, but LEP II finds m h 114 GeV. On the other hand, a strongly first-order electroweak phase transition, needed for EWBG, is only obtained for µ problem: m h 120 GeV. The dimensionful superpotential coupling µ H 1 H 2, with µ O(TeV), is needed to break the electroweak symmetry. Why is µ M GUT or M Pl? (However, see [Giudice+Masiero 88].)

42 Adding a gauge singlet S helps: µ H 1 H 2 λ S H 1 H 2 solves the µ problem; S gets a VEV at a scale set by the soft terms. The upper bound on the lightest CP-even Higgs mass becomes m 2 h M2 Z ( cos 2 2β + 2λ2 ḡ 2 sin2 2β A new S H 1 H 2 trilinear soft term makes the electroweak phase transition more strongly first-order. [Pietroni 92, Davies et al 96, Schmidt+Huber 00, Kang et al 04.] ).

43 But... The singlet must be charged under some additional symmetry to forbid new dimensionful (d < 4) couplings. The most popular choice is a Z 3 symmetry, which yields the superpotential W = λ S H 1 H 2 + κ S 3 + (MSSM terms). This model is called the NMSSM, the Next-to-Minimal Supersymmetric Standard Model. When S gets a VEV, the Z 3 symmetry is broken producing cosmologically unacceptable domain walls. The domain wall problem can be avoided by including non-renormalizable operators that break Z 3. However, these generate a large singlet VEV which destabilizes the hierarchy. [Abel,Sarkar,+White 95]

44 A way out: the nmssm Both problems can be avoided by imposing discrete R-symmetries on both the superpotential and the Kähler potential. [Pangiotakopoulos+Tamvakis 98/ 99, Pangiotakopoulos+Pilaftsis 00, Dedes et al 00] The resulting model is the nmssm, the not-quite MSSM. Superpotential: W = m2 12 λ 2 S + λ S H 1 H 2 + (MSSM matter terms), Soft-breaking potential: V soft = t s (S + h.c.) + m 2 s S 2 + a λ (S H 1 H 2 + h.c.) + (MSSM terms). The same superpotential and soft-breaking terms also arise in the low-energy limit of the Fat Higgs model. [Harnik et.al. 03]

45 EWBG in the nmssm In the SM and MSSM, the effective potential has the form: V eff ( µ 2 + α T 2 )φ 2 γ T φ 3 + λ 4 φ γ drives the transition to be first order. γ = 0 at tree-level in the SM and MSSM. SM: the PT isn t strong enough. MSSM: one-loop corrections to V eff from a light stop can make the PT strong enough, but only for m h 120 GeV. [Carena et al 96, Laine 96, Losada 97, Laine+Rummukainen 00] nmssm: the trilinear soft term S H 1 H 2 contributes to γ at tree level making the PT first-order, even without a light stop, and for m h > 120 GeV.

46 Charginos, Neutralinos, and Dark Matter The chargino mass matrix is identical to the MSSM, but with µ λ v s. The fermion component of S, the singlino, produces a fifth neutralino state. MÑ = M 1 0 M 2 c β s w M Z c β c w M Z 0 s β s w M Z s β c w M Z λv s λv 2 λv 1 0 We relate M 1 to M 2 by universality and allow for a common phase; M 2 = M 2 e iφ α 2 α 1 M 1. λ(m Z ) 0.8 for perturbative unification. There is always a light neutralino: mñ1 60 GeV. e.g. mñ1 2 λ v 1 v 2 v s v v2 2 + v2 s for M 1, M 2, and tan β 1 or v s v.,

47 EWBG and DM Results Neutralino relic densities consistent with EWBG: 10 Ω h Exp. Value Z width e LSP Mass (GeV) Dots = parameter sets consistent with EWBG. Green line = WMAP result: Ω DM h 2 = Blue line = LEP Z-width constraint: Γ(Z Ñ 1 Ñ 1 ) < 2.0 MeV.

48 Higgs Bosons Physical states: 3 CP-even, 2 CP-odd, 1 charged. For M 2 a, the charged state, one CP-even state, and one CP-odd state decouple. The remaining CP-odd state is pure singlet with mass m 2 P = m2 s + λ2 v 2. The remaining CP-even states have mass matrix M 2 S = ( M 2 Z cos 2 2β + λ 2 v 2 sin 2 2β v(a λ sin2β + 2 λ 2 v s ) m 2 s + λ2 v 2 ). This is in the basis (S 1, S 2 ), where S 1 is SM-like, and S 2 is a singlet.

49 EWBG m 2 s + λ 2 v GeV. If so, there are two light CP-even and one light CP-odd Higgs bosons. The lightest CP-even and CP-odd states usually decay invisibly into pairs of the neutralino LSP. The CP-even states can still be detected at the LHC through vector boson fusion channels. Define η = BR(h inv) σ(v BF) σ(v BF) SM. The luminosity needed for a 5σ discovery is then [Eboli+Zeppenfeld 00] L 5σ 8fb 1 /η 2. η for the SM-like state. η for the mostly singlet state.