Implications of a Heavy Z Gauge Boson Motivations A (string-motivated) model Non-standard Higgs sector, CDM, g µ 2 Electroweak baryogenesis FCNC and B s B s mixing
References T. Han, B. McElrath, PL, hep-ph/0402064 (implications of Higgs sector) V. Barger, C. Kao, PL and H. S. Lee, hep-ph/0408120 (cold dark matter). V. Barger, C. Kao, PL and H. S. Lee, in preparation (g µ 2) J. Kang, T. Li, T. Liu, and PL, hep-ph/0402068 (electroweak baryogenesis) V. Barger, C. W. Chiang, J. Jiang and PL, hep-ph/0405108 (B s B s mixing).
Beyond the MSSM Even if supersymmetry holds, MSSM may not be the full story Most of the problems of standard model remain (hierarchy of electroweak and Planck scales is stabilized but not explained) µ problem introduced Could be that all new physics is at GUT/Planck scale, but there could be remnants surviving to TeV scale Specific string constructions often have extended gauge groups, exotics Important to explore alternatives/extensions to MSSM
Motivations Strings, GUTs, DSB, little Higgs, LED often involve extra Z (GUTs require extra fine tuning for M Z M GUT ) String models Extra U(1) and SM singlets extremely common Radiative breaking of electroweak (SUGRA or gauge mediated) often yield EW/TeV scale Z (unless breaking along flat direction intermediate scale) Breaking due to negative mass 2 for scalar S (driven by large Yukawa) or by A term
S f S ~ f _ f 1.1 0.9 0.7 0.5 0.3 0.1 0.25 0.20 0.15 0.10 0.05 t 0.1 0.3 0.5 0.7
Solution to µ problem (string-motivated extension of NMSSM) W hsh u H d, U(1) may forbid elementary µ or term in Kähler S = standard model singlet, charged under U(1) S breaks U(1), µ eff = h S Like NMSSM, but no domain walls (Alternative: nmssm) Singlets don t have W κs 3 (cf. NMSSM) in constructions studied SM-singlets usually have U(1) charges in constructions studied
Flat directions Two SM singlets charged under U(1). If no F terms, V (S 1, S 2 ) = m 2 1 S2 1 + m2 2 S2 2 + g 2 Q 2 ( S 2 1 2 S2 2 )2 Break at EW scale for m 2 1 + m2 2 > 0, at intermediate scale for m 2 1 + m2 2 < 0 (stabilized by loops or HDO) Small Dirac (or other fermion) masses from ( Ŝ ) PD W Ĥ 2 ˆL Lˆν c L M Secluded sector: lift F -flatness by small ( 0.05) singlet Yukawa
Models SUSY-breaking scale models (Demir et al) M Z M Z, leptophobic M Z > 10M Z by modest tuning Secluded sector models (Erler, PL, Li) Approximately flat direction, broken by small ( 0.05) Yukawa Z breaking decoupled from effective µ term Four SM singlets: S, S 1,2,3, doublets H 1,2 Off-diagonal Yukawas (string-motivated) Can be consistent with minimal gauge unification
Superpotential : W = hsh 1 H 2 + λs 1 S 2 S 3 Potential : V = V F + V D + V soft V F = h 2 ( H 1 2 H 2 2 + S 2 H 1 2 + S 2 H 2 2) + λ 2 ( S 1 2 S 2 2 + S 2 2 S 3 2 + S 3 2 S 1 2) V D = G2 8 ( H2 2 H 1 2) 2 + 1 2 g2 Z (Q S S 2 + Q H1 H 1 2 + Q H2 H 2 2 + ) 2 3 Q Si S i 2 i=1 where G 2 = g 2 1 + g2 2,
3 V soft = m 2 H 1 H 1 2 + m 2 H 2 H 2 2 + m 2 S S 2 + m 2 S i S i 2 i=1 (A h hsh 1 H 2 + A λ λs 1 S 2 S 3 + H.C.) + (m 2 SS 1 SS 1 + m 2 SS 2 SS 2 + m 2 S 1 S 2 S 1 S 2 + H.C.) S i m Si /λ large for small λ Breaking along D(U(1) ) 0 Smaller S, H i, dominated by ha h tan β 1, S H i Large doublet-singlet mixing Two sectors nearly decoupled Tree-level CP breaking in S, S i sector in general
Nonstandard Higgs (T. Han, PL, B. McElrath) Complex Higgs, neutralino spectrum and decays, very different from MSSM and NMSSM because of mixing and D terms
6 scalars and 4 pseudoscalars Can have tree level CP breaking mixing May separate into two sectors, one weakly coupled Often light scalars with significant doublet admixture, but reduced coupling due to singlet admixture; often light pseudoscalar Can have lightest Higgs up to 168 GeV with all couplings perturbative to M P because of D terms M 2 h h2 v 2 + (M 2 Z h2 v 2 ) cos 2 2β + 2g 2 Z v 2 (Q H2 cos 2 β + Q H1 sin 2 β) 2 + 3 4 m 4 t v 2 π 2 log m t 1 m t 2 m 2 t. Typically, tan β 1 3
CP-Even MSSM fractions 1 MSSM Fraction ξ MSSM H 1 H 2 H 3 H 4 H 5 H 6 0.8 0.6 0.4 0.2 MSSM Fraction 0 10 100 1000 10000 M H (GeV)
LEP2 (209 GeV) Higgsstrahlung Cross Section σ(e + e - -> ZH) (fb) 400 350 300 250 200 150 100 50 H 1 H 2 Standard Model MSSM NLO (tanβ=5) MSSM NLO (tanβ=10) MSSM NLO (tanβ=20) + - 0 0 10 20 30 40 50 60 70 80 90 100 110 120 M H
LEP2 H A Cross Section σ(e + e - -> H A) (fb) H 1 A 1 H 1 A 2 H 2 A 1 MSSM NLO (tanβ=5) 1000 1 0.001 1e-06 0 25 50 75 100 125 150 M A (GeV)
M H vs. M A by MSSM fraction ξ MSSM > 0 ξ MSSM > 0.001 ξ MSSM > 0.01 ξ MSSM > 0.1 ξ MSSM > 0.9 500 400 M H (GeV) 300 200 100 0 0 100 200 300 400 500 M A (GeV)
χ 0 1 χ0 1 Lightest Higgs Branching Ratios χ 0 1 χ0 i>1 χ 0 i>1 χ0 i>1 A A W + W - Z Z b b τ + τ c c 1 Branching Ratio 0.1 0.01 0 50 100 M H1 (GeV)
Linear Collider (500 GeV)Higgsstrahlung Cross Section 100 σ(e + e - -> ZH)(fb) H 1 H 2 H 3 H 4 Standard Model MSSM h NLO (tanβ=5) MSSM H NLO (tanβ=5) 0 100 200 300 400 M H (GeV) 10 1 0.1 0.01 0.001 + -
Cold Dark Matter (V. Barger, C. Kao, PL, H.-S. Lee) 0.09 < Ω χ 0h 2 < 0.15 MSSM: limited parameter space for sufficient LSP (co)annihilation; mainly bino in most of parameter space. U(1) : additional Z -ino and singlino. ((n)nmssm: additional singlino) may have enhanced annihilation coupling to Z Solutions compatible with observations for most m χ 0 (only examined for large Z -ino mass)
1 0.1 S-model (M 2 > 0) (b) Zχ 0 χ 0 Coupling 0.01 0.001 MSSM (M 2 > 0) Singlino (M 2 < 0) MSSM (M 2 < 0) 0.0001 S-model (M 2 < 0) 1e-05 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 m 0 χ (GeV)
500 Ω χ h 2 < 0.09 500 Ω χ h 2 < 0.09 0.09 < Ω χ h 2 < 0.15 0.09 < Ω χ h 2 < 0.15 400 0.15 < Ω χ h 2 < 1.0 400 0.15 < Ω χ h 2 < 1.0 (P3) (P1) (P1) 300 300 s (GeV) s (GeV) 200 200 100 100 LEP exclusion (m + χ1 < 104 GeV) (b) tanβ = 2.0 0-500 -400-300 -200-100 0 100 200 300 400 500 M 2 (GeV) LEP exclusion (m + χ1 < 104 GeV) (c) tanβ = 2.5 0-500 -400-300 -200-100 0 100 200 300 400 500 M 2 (GeV)
Muon g µ 2 (V. Barger, C. Kao, PL, H.-S. Lee) BNL E821: a µ (exp) = (11659208.0 ± 5.8) 10 10 2.4σ deviation from its Standard Model (SM) prediction a µ a µ (exp) a µ (SM) = 23.9(7.2)(3.5)(6) 10 10, assuming e + e hadrons value for hadronic vacuum polarization MSSM: a µ (SUSY) 13 10 10 tan β sign(µ) (M SUSY /100 GeV) 2, for common superpartner masses M SUSY, favoring large tan β and/or small M SUSY LEP2: m µ > 95 GeV
Z diagrams small for allowed M Z New Z -ino and singlino contributions in U(1), and different parameter range Neutralino mass matrix in { B, W 3, H 0 1, H 0 2, S, Z } basis M 1 0 g 1 v 1 /2 g 1 v 2 /2 0 0 0 M 2 g 2 v 1 /2 g 2 v 2 /2 0 0 g 1 v 1 /2 g 2 v 1 /2 0 h s s/ 2 h s v 2 / 2 g Z Q (H 0 1 )v 1 g 1 v 2 /2 g 2 v 2 /2 h s s/ 2 0 h s v 1 / 2 g Z Q (H 0 2 )v 2 0 0 h s v 2 / 2 h s v 1 / 2 0 g Z Q (S)s 0 0 g Z Q (H 0 1 )v 1 g Z Q (H 0 2 )v 2 g Z Q (S)s M 1
Adequate g µ 2 possible, even with small tan β, consistent with m µ constraints, while also giving observed CDM 80 60 50 aμ 10 10 60 40 20 aμ 10 10 40 30 20 10 0 1 2 3 4 tanβ Maximum a µ Observation: (13.9 33.9) 10 10 100 200 300 400 500 M soft GeV
Electroweak Baryogenesis (J. Kang, PL, T. Li, T. Liu) Baryon asymmetry n B /n γ 6 10 10 Basic ideas worked out by Sakharov in 1967, but no concrete model Possible mechanisms Affleck-Dine baryogenesis GUT baryogenesis (wiped out by sphalerons for B L=0) Leptogenesis Electroweak baryogenesis
The Sakharov conditions 1. Baryon number violation 2. CP violation: to distinguish baryons from antibaryons 3. Nonequilibrium of B-violating processes
Electroweak baryogenesis Utilize the electroweak (B-violating) tunneling to generate the asymmetry at time of electroweak phase transition (Kuzmin, Rubakov, Shaposhnikov) Off the wall scenario (Cohen, Kaplan, Nelson) Strong first order phase transition from electroweak symmetry unbroken (massless W, Z, fermions) to broken phase (massive W, Z, fermions) proceeds by nucleation and 0 expansion of bubbles φ crit φ (Figures: W. Bernreuther, hep-ph/0205279) V eff T = T 2 > T C T = T C T = T 1 < T C
CP violation by asymmetric reflection of quarks and leptons (or charginos/neutralinos) from the wall Electroweak B violation in unbroken phase outside wall Scenario requires strong first order transition, v(t c )/T c > 1 1.3 and adequate CP violation in expanding bubble wall v Wall q q broken phase φ = 0 becomes our world unbroken phase q q CP Sph Γ B + L _~ 0 CP _ q _ q _ q _ q Sph Γ B + L >> H
Implementation of off the wall Standard model: no strong first order for M h violation too small > 114.4 GeV; CP Minimal supersymmetric extension (MSSM): small parameter space for light Higgs and light stop; new sources for CP violation NMSSM (extension to include extra Higgs fields): can have strong first order for large ha h SH 1 H 2 but cosmological domain walls nmssm: strong transition without domain walls (Menon, Morrissey, Wagner)
Secluded sector U(1) : Symmetry breaking driven by large ha h SH 1 H 2 Tree level CP breaking in Higgs sector associated with soft SM singlet terms New contributions to electric dipole moments negligible First phase transition breaks U(1), second breaks SU(2) U(1) Phase transition strongly first order
Potential Value -1310 0 2 4 6 8 10 10-1311 T=114.4 GeV -1312 T=119.5 GeV -1313 T=123.1 GeV -1314 8 T=124.6 GeV -1315-1316 -1317 6-1318 -1319-1320 -1321 4-1322 -1323-1324 2-1325 -1326-1327 -1328 0 0 50 100 150 200 250 v (GeV) Transition at T c = 120 GeV, v(t c )/T c = 1.31
For τ lepton use thin wall approximation (justified) For reasonable parameters, can obtain adequate asymmetry, even for large t mass, from τ alone n B s = 90γ3 w (1 + v w v L )ξ Lm 2 δ θ CP h(δ, T )Γ (2π) 4 v w g T 3 s Larger contributions from neutralinos/charginos if not too heavy
-10 ) n B /s(10 1 0.8 v w =0.01 v w =0.02 v w =0.04 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 γ(π) γ = explicit CP phase. Exp: n B /s (0.8 0.9) 10 10.
FCNC and rare B decays U(1) couplings often family-nonuniversal in string constructions FCNC (Z and Z from Z Z mixing) after family mixing (GIM breaking) (also from exotic mixing) Depends on V ψl and V ψr, ψ = u, d, e, ν, but only V CKM = V ul V d L and V MNS = V νl V e L known from exp K and µ decays first two families are universal (PL, Plümacher) Third family could be nonuniversal A 0b F B (Erler, PL) B s B s mixing and rare B decays, especially in competition with SM (or SUSY) loops, e.g. B φk, η K, πk or B s µ + µ (Leroux, London; Barger, Chiang, Jiang, PL, Lee) s b Z s s
Interaction L Z = g J µ Z µ, where J µ = i,j ψ I i γ µ [(ɛ ψl ) ij P L + (ɛ ψr ) ij P R ] ψ I j Can pick basis with ɛ ψl,r real and diagonal, but non-universal. In mass basis, couplings are B L d V d L ɛ dl V d L, B R d V d R ɛ dr V d R, which is Hermitian but non-diagonal.
x s = M s /Γ s > 20.8 SM box: x SM s = 26.3 ± 5.5 φ SM s Z (tree) B s B s mixing (V. Barger, C.-W. Chiang, J. Jiang,, PL) = 2 arg(v tb V ts ) = 2λ2 η 2 s b Z s b H Z eff = G ( F g2 M 2 Z B 2 g 1 M sb) L O LL (m b ) + LR + RR + RL Z G F 2 ρ 2 L e2iφ L O LL (m b ) + LR + RR + RL
100 x s 50 150 100 φ L (degrees) 50 0 0 0.001 0.002 ρ L 0.003
150 sin2φ s =0.5 50 70 x s =90 φ L (degrees) 100 50 Consistent with SM 1σ range of x s 26.3 Exp. excluded 0-0.5-0.07 0 0.001 0.002 0.003 ρ L
Conclusions Important to explore alternatives to MSSM Top-down string constructions very often contain extra Z and SM singlets S Elegant solution to µ problem (string-motivated extension of NMSSM) Many implications, including nonstandard Higgs spectrum/couplings, CDM, g µ 2, efficient EW baryogenesis, B s B s mixing, rare B decays, neutrino masses But, must observe Z