Higgs, neutralinos and exotics beyond the MSSM

Higgs, neutralinos and exotics beyond the MSSM N 5 (Singlino in χ ).8.6.4. nmssm N 6 in Beyond the MSSM Heavy Z Higgs Neutralinos Exotics 3 (GeV) M χ Fermilab (March, 6)

References V. Barger, PL and H. S. Lee, Lightest neutralino in extensions of the MSSM, Phys. Lett. B 63, 85 (5), hep-ph/587 T. Han, PL and B. McElrath, The Higgs sector in a U() extension of the MSSM, Phys. Rev. D 7, 56 (4), hep-ph/4544 Higgs Sector in Extensions of the MSSM, V. Barger, PL, H.S. Lee and G. Shaughnessy, to appear Quasi-Chiral Exotics, J. Kang, PL and B. Nelson, to appear Fermilab (March, 6)

Abel, Bagger, Barger, Bastero-Gil, Batra, Birkedal, Carena, Choi, Cvetic, Dedes, Delgado, Demir, Dermisek, Dobrescu, Drees, Ellis, Ellwanger, Erler, Espinosa, Everett, Godbole, Gunion, Haber, Han, Hooper, Hugonie, Kaplan, King, Landsberg, Li, Matchev, McElrath, Menon, Miller, Moretti, Morrissey, Nevzorov, Panagiotakopoulos, Perelstein, Pilaftsis, Poppitz, Randall, Rosner, Roy, Sarkar, Sopczak, Tait, Tamvakis, Vempati, Wagner, White, Zerwas, Zhang Fermilab (March, 6)

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: W µ = µĥ u Ĥ d, µ = O(electroweak) 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, extended Higgs/neutralino sectors Important to explore alternatives/extensions to MSSM Fermilab (March, 6)

Z or other gauge Remnants Physics from the Top-Down Extended Higgs/neutralino (doublet, singlet) Quasi-Chiral Exotics Charge / (Confinement?, Stable relic?) Quasi-hidden (Strong coupling? SUSY breaking? Composite family?) Time varying couplings LED (TeV black holes, stringy resonances) LIV, VEP (e.g., maximum speeds, decays, (oscillations) of HE γ, e, gravity waves (ν s)) Fermilab (March, 6)

A TeV-Scale Z Strings, GUTs, DSB, little Higgs, LED often involve extra Z Typically M Z > 6 9 GeV (Tevatron, LEP, WNC); θ Z Z < few 3 (Z-pole) (CDF di-electron: 85 (Z seq ), 74 (Z χ ), 75 (Z ψ ), 745 (Z η )) Discovery to M Z 5 8 TeV at LHC, ILC, (pp e + e, µ + µ, q q) (depends on couplings, exotics, sparticles) Diagnostics to - TeV (asymmetries, y distributions, associated production, rare decays) Implications: µ problem; extended Higgs/neutralino sector (cosmology); exotics; FCNC; decays into sparticles/exotics Fermilab (March, 6)

Higgs singlets S i Standard model singlets extremely common in string constructions Needed to break extra U() gauge symmetries Solution to µ problem (U(),, nmssm) W h s ŜĤ u Ĥ d µ eff = h s S Relaxed upper limits, couplings, parameter ranges (e.g., tan β = v u /v d can be close to ), singlet-doublet mixing Large A term and possible tree-level CP violation electroweak baryogenesis Fermilab (March, 6)

Models with Dynamical µ Model Symmetry Superpotential CP-even CP-odd MSSM µĥ u Ĥ d H, A Z 3 h s ŜĤ u Ĥ d + κ 3 Ŝ3 H,, H 3 A, A nmssm Z R 5, ZR 7 h s ŜĤ u Ĥ d + ξ F M nŝ H,, H 3 A, A U() h s ŜĤ u Ĥ d H,, H 3 A smssm U() h s ŜĤ u Ĥ d + λ s Ŝ Ŝ Ŝ 3 H,, H 3, A, A, A 3, A 4 H 4, H 5, H 6 MSSM: gaugino unification but general µ : may be domain wall problems nmssm: avoids domain walls; tadpoles from high order loops : additional Z (µ eff, M Z generated by single S) smssm: stringy w. decoupled µ eff, M Z (Ĥ u, Ĥ d, Ŝ reduces to nmssm in S i decoupling limit ) Fermilab (March, 6)

A Unified Analysis of Higgs and Neutralino Sectors (B. Barger, PL, H.-S. Lee, G. Shaughnessy, hep-ph/587 (BLL) and to appear) V F = h s H u H d +ξ F M n +κs + h s S ( H d + H u ) V D = G 8 + g ( Hd H u ) g ( + Hd H u H u H d ) ( QHd H d + Q Hu H u + Q S S ) V soft = m d H d + m u H u + m s S + (A s h s SH u H d + κ3 ) A κs 3 +ξ S M 3n S + h.c. black = MSSM (with µ = h s S ); blue= extensions; cyan = ; magenta = ; red= Fermilab (March, 6)

Mass matrices in {H d, H u, S} basis CP-even (tree level) ( H u,d v u,d/, S s/ ) (M + ) dd = (M + ) du = (M + ) ds = (M + ) uu = (M + ) us = " G 4 + Q H g d " G # v d + (h sa s + h sκs # 4 h s Q H d Q H ug h h s + Q H d Q S g i v d s ( h sa s " # G 4 + Q Hu g v u + (h sa s h h s + Q HuQ S g i v u s ( h sa s + h sξ F M n s v d v u ( h sa s + h s κs)v u + h sκs + h sξ F M n s + h s κs)v d ) v us v d + h sκs ) v ds v u + h sξ F M n s ) (M + ) ss = h Q S g + κ i s + ( h sa s ξs M 3 n v d v u ) v dv u s + κa κ s Fermilab (March, 6)

Also CP-odd and charged Higgs (CP breaking ignored) Leading loop corrections (top-stop loops) are common Theoretical upper limits on H MSSM M H relaxed ( smaller tan β allowed) M Z cos β + M () M () = (M () + ) dd cos β + (M () + ) uu sin β + (M () + ) du sin β,, and Peccei-Quinn limits M H M Z cos β + h s v sin β + M () M H M Z cos β+ h s v sin β+g Z v (Q Hd cos β+q H u sin β) + M () Fermilab (March, 6)

with a 95% C. L. Points falling below this curve pass the ZZH i constraint. (b) cos Experimental LEP SM and MSSM bounds may be relaxed by singlet-doublet mixing ξ ZZH.. MSSM LEP limit 95% C.L.. 5 5 M H (GeV) Reduced ZZH i coupling.8 ξ ZZHi = (R i + cos (β α).6.4 mass,. Z Z mixing, cos β+ri + MSSM sin β) Also, Z HA, Z width, χ ± V minimum, RGE 6 8 4 6 M A (GeV) (a) (b) FIG. 3: (a) LEP limit [34] on ξ ZZHi = ( g ZZHi /gzzh SM ) = ΓZ ZHi /Γ SM Z Zh, th coupling in new physics, versus the light Higgs mass. The solid black curve is the Fermilab (March, 6)

Limiting Cases MSSM limit (s with µ eff = h s s/ fixed) two MSSM-like CP-even Higgs and one largely singlet (heavy in, light in, depends on κ in ) PQ and R limits (massless pseudoscalar) Model Limits Symmetry Effects MSSM B U() P Q M A κ, A κ U() P Q M A A s, A κ U() R M A ξ F, ξ S U() P Q M A g U() M Z, M A Fermilab (March, 6)

CP Even CP Odd 5 5 MSSM PQ Limit s = 5 GeV 5 5 MSSM PQ Limit s = 5 GeV tan β tan β (a) (b) CP Even CP Odd 5 5 MSSM PQ Limit tan β = 8 6 4 MSSM PQ Limit tan β = s (GeV) (c) s (GeV) (d) (A s = M n = 5 GeV, A κ = 5 GeV, h s = κ =.5, ξ F,S =.) FIG. : Lightest CP-even and lightest CP-odd Higgs masses vs. tan β and s for the MSSM,,,, and the PQ limits. Only the theoretical constraints are applied Fermilab (March, 6) with s = 5 GeV (for tan β-varying curves), tan β = (for s-varying curves). Input parameters of A s = 5 GeV, A t = TeV, M Q = MŨ = TeV, κ =.5, A κ = 5 GeV, M n = 5 GeV,

ξ MSSM.8.6.4 H H 3 A A ξ MSSM.8.6.4 H H 3 A A.. (a) (b) Lightest Higgs ξ MSSM.8.6.4 H H 3 A ξ MSSM.8.6.4.. (c) 4 6 8 4 (d) (MSSM FIG. fraction 4: Higgs masses ξ H i MSSM vs. = P u ξ MSSM j=d in (Rij the + (a) ), ) (b), (c) and (d) the lightest CP-even Higgs of all extended models. The vertical line is the LEP lower bound on the Fermilab MSSM (March (SM-like), 6) Higgs mass.

CP-Even Higgs Mass Range CP-Odd Higgs Mass Range MSSM Scan Scan LEP M H 9 Th. 35 Th. 64 Th. 7 LEP MSSM 94 Th. Th. Scan 45 Scan 685 Scan 6893 LEP & α ZZ 89 Th. 73 LEP & α ZZ 9 Scan 367 5 5 4 6 FIG. : Mass ranges of the lightest CP-even and CP-odd Higgs boson in each extended-mssm model from the grid and random scans. Explanation of extremal bounds and their values are provided for each model. Explanations are Th. - theoretical bound met, value not sensitive to limits of the scan parameters; Scan - value sensitive to limits of the scan parameters; LEP - experimental constraints from LEP; α ZZ - experimental constraints in the on the ZZ Fermilab (March, 6) mixing angle.

Lightest Higgs Decays Partial Width (MeV).. SM H MSSM H H H W W* Partial Width (MeV).. Z Z*... 4 6 8 4. 4 6 8 4 g g Partial Width (MeV).... 4 6 8 4 FIG. 9: Decay widths for W W, ZZ, and gg in the MSSM and extended-mssm models. Lines Fermilab (March, 6) denote the corresponding SM width. For clarity, not all points generated are shown.

[7, 4]. However, in the most of the kinematic region is disfavored due to a large χ relic density [7]. This is indicated in Fig. a below the red horizontal line Invisible Decays at M χ = 3 GeV. However, this region is not excluded since the relic density calculation includes only the Z pole. In principle, other annihilation channels may decrease the relic density to the preferred range. Lightest Neutralino Mass (GeV) 8 6 4 H MSSM H H H M H = M χ Branching Fraction... χ χ 5 5 Lightest (a). 4 6 8 4 (b) FIG. : (a) M H vs. M χ in all the models considered. Points falling below the blue line allow the decay of the lightest CP-even Higgs to two χ. (b) Branching fraction to χ χ Fermilab (March, 6) The χ χ partial decay width is given by

H, A A M A (GeV) 5 5 M Z =M H +M A H MSSM H H M H =M A Branching Fraction... A A 5 5 M H (GeV) (a). 4 6 8 4 (b) FIG. : (a) M H vs. M A showing the kinematics for decays in extended-mssm models. H A A decays are allowed for regions below the blue-dashed line. Decays of Z H A are allowed to the left of the green dark line. (b) H A A branching fraction Paul versus Langacker Higgs (Penn) mass. The Fermilab (March, 6) parameter ξ S is scanned with a higher density at low ξ S to allow low Higgs masses.

Total Width Total Width (MeV) e+5.... SM H MSSM H H H 5 5 tal decay Fermilab width (Marchfor, 6) each model. Large enhancementspaul with Langacker respect (Penn) to the

Lightest Neutralino Mass matrix (M χ ) in basis { B, W 3, H, H, S, Z }: M g v / g v / M g v / g v / g v / g v / µ eff µ eff v /s g Z Q H v g v / g v / µ eff µ eff v /s g Z Q v µ eff v /s µ eff v /s κs gz Q S s g Z Q H v g Z Q v g Z Q S s M ( S s, H i v i, p v + v v 46 GeV, Q φ = φ U() charge) (black = MSSM; blue= extensions; cyan = ; magenta = ) Fermilab (March, 6)

N 5 (Singlino in χ ).8.6.4 nmssm N 6 in "!! h.. nmssm nmssm WMAP+SDSS (3##.. 3 (GeV) M χ. 3 4 5 6 7 8 M!"! (GeV) (Relic density in nmssm from χ χ Z only; may be χ secluded in smssm) Fermilab (March, 6)

5 4 tanβ = 7.9 < Δa µ < 39.9 Ω χ h <.9.9 < Ω χ h <.5 s = 5 GeV µ (GeV) 3 h s =.75 M χ ± < 4 GeV Γ Z-->χχ >.3 MeV h s =. -4-4 M (GeV) (Relic density and g µ in ) Fermilab (March, 6)

5 Masses of χ + vs χ 5 Masses of χ + vs χ M χ > Μ χ + M Z M χ > Μ χ + M h () M χ+ (GeV) 4 3 M + χ > Μ χ + M + W M χ + = M χ M χ + = M χ M χ+ (GeV) 4 3 M + χ > Μ χ + M + W M χ + = M χ M χ + = M χ M + χ < 4 GeV 3 (GeV) M χ nmssm MSSM M + χ < 4 GeV 3 (GeV) M χ nmssm MSSM Often χ χ 5 are MSSM-like with light singlino-dominated χ MSSM-like cascades with extra χ χ + (l l, q q, Z, h) Often χ χ + (Z, h); χ+ χ + (W +, H + ) are open (e.g., χ + χ W + h + E T l + b b + E T ) Fermilab (March, 6)

Quasi-Chiral Exotics (J. Kang, PL, B. Nelson, in progress) Often find exotic (wrt SU() U()) quarks or leptons at TeV scale Assume non-chiral wrt SM gauge group (strong constraints from precision EW, expecially on extra or mirror families) Can be chiral wrt extra U() s or other extended gauge Usually needed for U() anomaly cancellation Modify gauge unification unless in complete GUT multiplets Can also be more extreme exotics (e.g., adjoints, symmetric, fractional charge, mixed quasi-hidden) Experimental limits relatively weak Fermilab (March, 6)

Examples in 7-plet of E 6 D L + D R (SU() singlets, chiral wrt U() ) ( ) ( ) E E E + E (SU() doublets, chiral wrt U() ) L R Pair produce D + D by QCD processes (smaller rate for exotic leptons) D or D decay by D u i W, D d i Z, D d i H if driven by D d mixing (not in minimal E 6 ; FCNC) m D > GeV (future: TeV) D quark jets if driven by diquark operator ūū D D quark jet + lepton if driven by leptoquark operator lq D May be stable at renormalizable level due to accidental symmetry (e.g., from extended gauge group) hadronizes and escapes or stops in detector (Quasi-stable from HDO τ < / yr) Fermilab (March, 6)

Conclusions Combination of theoretical ideas and new experimental facilities may allow testable theory to Planck scale From the bottom up: there may be more at TeV scale than (minimal SUGRA) MSSM (e.g., Z, extended Higgs/neutralino, quasichiral exotics) From the top down: there may be more at TeV scale than (minimal SUGRA) MSSM Dynamical µ term leads to very rich Higgs/neutralino physics at colliders and for cosmology Fermilab (March, 6)

Implications of a TeV-scale U() Natural Solution to µ problem W hsh u H d µ eff ( stringy version of ) = h S Extended Higgs sector Relaxed upper limits, couplings, parameter ranges (e.g., tan β can be close to ) Higgs singlets needed to break U() Doublet-singlet mixing highly non-standard collider signatures Large A term and possible tree-level CP violation (no new EDM constraints) electroweak baryogenesis Fermilab (March, 6)

Extended neutralino sector Additional neutralinos, non-standard couplings, e.g., light singlino-dominated, extended cascades Enhanced possibilities for cold dark matter, g µ (even small tan β) Exotics (anomaly-cancellation) May decay by mixing; by diquark or leptoquark coupling; or be quasi-stable Constraints on neutrino mass generation Flavor changing neutral currents (for non-universal U() charges) Tree-level effects in B decay competing with SM loops (or with enhanced loops in MSSM with large tan β) Fermilab (March, 6)

Extended Higgs Sector Standard model singlets S i and additional doublet pairs H u,d very common. Additional doublet pairs Richer spectrum, decay possibilities May be needed (or expand possibiities for) quark/lepton masses/mixings (e.g., stringy symmetries may restrict single Higgs couplings to one or two families) Extra neutral Higgs FCNC (suppressed by Yukawas) Significantly modify gauge unification Fermilab (March, 6)

The µ problem Superpotential: W = µ Ĥ u Ĥ d }{{} superfields +h t ˆQĤ u ˆdc }{{} superfields L fermion = µ L W scalar = φ L D = g +g 8 H u H d }{{} Higgsino mass +h t ( QH u d c }{{} top Yukawa + } Q H u d c {{ + Q H u d } c ) Higgsino quark squark δw δφ = µ ( H u + H d ) +h }{{} t terms Higgs masses ( Hu H d ) + charged Higgs, squark, slepton L soft = m u H u + m d H d + (m 3 H uh d + h.c.) + squark/slepton + M 3 g g }{{} gluino + M w w }{{} wino + M b b }{{} bino Fermilab (March, 6)

Soft terms set ew scale, e.g., m soft F /M pl, F GeV, M pl 9 GeV µ problem: µ is supersymmetric could be very large (or exactly zero in string theory), but need µ m soft < TeV Two classes of solutions Generate µ in hidden sector along with m soft Dynamical: µ by symmetry or string, but W = h s }{{} Ŝ Ĥ u Ĥ d µ eff = h s S, SM singlet S m soft (Examples: Z models,, nmssm) Fermilab (March, 6)

H H 3 A A 5 5 s (GeV) (a) H H 3 A A 5 s (GeV) 5 (b) Lightest Higgs H H 3 A 4 8 6 4 5 5 s (GeV) 5 5 s (GeV) (c) (d) Fermilab (March, 6) FIG. 6: Higgs masses vs. s in the (a), (b), (c) and (d) the lightest

Higgs mass (GeV) H H 3 A A Higgs mass (GeV) H H 3 A A tan β (a) tan β (b) 5 Lightest Higgs Higgs mass (GeV) H H 3 A Higgs mass (GeV) 5 tan β tan β Fermilab (March, 6) (c) (d) FIG. 7: Higgs masses vs. tan β in the (a), (b), (c) and (d) the lightest

, M n = 5 GeV -. -.4 ξ SH -.6 -.8 H 3 A A - iggs mass dependence on ξ S in the. When ξ S., and llowing a light CP-even Higgs below the LEP limit. Fermilab (March, 6)

MSSM H A s = 5 GeV s = 5 GeV H H 3 A A s = 5 GeV H H 3 A A tan β tan β tan β All models, PQ limit s = 5 GeV tan β H H 3 A 9 8 7 6 5 4 3 s = 5 GeV H H 3 A 3 4 tan β MSSM H A tan β = Fermilab (March, 6) 5 5 H H 3 A A tan β = 7 6 5 4 3 H H 3 A A tan β = s (GeV) s (GeV) s (GeV)

Higgs Mass tan β Higgs Mass 5 4 3 3 4 tan β MSSM H A tan β = 5 5 H H 3 A A tan β = 7 6 5 4 3 H H 3 A A tan β = s (GeV) s (GeV) s (GeV) All Models, PQ Limit 8 6 4 H H 3 A tan β = 8 7 6 5 4 3 H H 3 A tan β = s (GeV) 4 5 6 7 8 s (GeV) FIG. 5: Higgs masses vs. tan β and s for the,,, and the PQ limit for the extended models. Only the theoretical constraints are applied. Input parameters of A s = 5 GeV, A t = TeV, M Q = MŨ = TeV, κ =.5, A κ = 5 GeV, M n = 5 GeV, ξ F =., Fermilab (March, 6) ξ S =., h s =.5, θ E6 = tan 5, and the renormalization scale Q = 3 GeV are used. 3 Note that the U() P Q symmetry allows only one CP-odd Higgs boson to be massive.

γγ, and Zγ are presented in Fig. for the lightest CP-even Higgs boson in the MSSM, W W* Z Z* Branching Fraction... SM H MSSM H H H Branching Fraction.... 4 6 8 4. 4 6 8 4 τ τ Branching Fraction... b b Branching Fraction.... 4 6 8 4. 4 6 8 4 Branching Fraction... γ γ Branching Fraction... Z γ. 4 6 8 4. 4 6 8 4 FIG. : Branching fractions for various modes in the MSSM and extended-mssm models. Lines Fermilab (March, denote 6) SM branching fractions.

5 4 MSSM nmssm Masses of χ vs χ M χ = M χ + M h (5) + M h () + M Z 5 4 Masses of χ + vs χ + M H + (3) M χ = M χ + M + H () + M + H () + M W (GeV) M χ 3 3 (GeV) M χ M χ = M χ M χ+ (GeV) 3 3 (GeV) M χ M χ + = M χ M + χ < 4 GeV MSSM nmssm Often χ χ + (Z, h); χ+ χ + (W +, H + ) open w. fairly light χ +, χ (e.g., χ + χ W + h + E T l + b b + E T, or χ + χ W + Z + E T l + l l + E T ) Fermilab (March, 6)