Mass Spectrum and Dark Matter in the CSE 6 SSM

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1 Mass Spectrum and Dark Matter in the CSE 6 SSM P. Athron D. Harries R. Nevzorov A. G. Williams March 8, 016 New Directions in Subatomic Physics 1 / 0

2 The MSSM MSSM at tree-level: m h 1 M Z cos β (91 GeV) m h GeV large higher order corrections ( mh 1 MZ cos β 1 3 m ) t 8π v ln m t 1 m t Mt + 3 mt 4 4π v ln m t 1 m t Mt +... also large corrections to prediction for M Z at SUSY scale M S : RGE effects {}}{ MZ = m µ H + d mh u tan β tan +δ 1 loop, β 1 ( ) ( δ 1 loop = 3 mt [m t1 8π v ln m t 1 cos β MS 1 + m t ln m t MS Little Hierarchy Problem µ problem: M Z = µ +... µ soft parameters? 1 )] +... / 0

3 Solving the Little Hierarchy Problem? Additional F-terms from new fields, e.g. NMSSM: W λŝĥd Ĥu Tree Level Upper Bound on m h1 E 6SSM NMSSM MSSM Additional D-terms from extended gauge sector, e.g. U (1) extensions: SU (3) C SU () L U (1) Y SU (3) C SU () L U (1) Y U (1) Care required (anomaly cancellation) 0 mh1 (GeV) NMSSM {}}{ ) m M h1 Z cos β + λ }{{} v sin β + M Z 4 ( cos β MSSM tan β 3 / 0

4 E 6 Inspired Models Can arise from E 8 E 8 heterotic string theory Low-energy models have extra U (1) coming from breakdown E 6 SO(10) U (1) ψ SU (5) U (1) ψ U (1) χ SU (3) C SU () L U (1) Y U (1) ψ U (1) χ SU (3) C SU () L U (1) Y U (1) Resulting U (1) = U (1) χ cos θ E6 + U (1) ψ sin θ E6 Matter content fills complete 7 representations anomaly cancellation guaranteed Exotic states at low-energies (extra scalars + vector-like fermions, anyone?) Break U (1) with singlet dynamically generate µ term, massive Z 4 / 0

5 The E 6 SSM Additional U (1) N under which right-handed neutrinos are uncharged (θ E6 = arctan 15) Extra ˆL 4, ˆL 4 from incomplete 7, 7 for gauge unification Low-energy matter content from 7-plet: ( ˆQ i, û c i, ˆd c i, ˆL i, ê c i ) + ( ˆD i, ˆD i ) + (Ŝi) + (Ĥ u i ) + (Ĥ d i ) Higgs doublets Ĥ 3 d Ĥd, Ĥ 3 u Ĥu and one singlet Ŝ3 Ŝ get VEVs ( EWSB and break U (1) N ) SU (3) C SU () L 5 3 QY i 40Q N i 1 ˆQ i ûi c ˆd i c ˆL i 1 1 êi c Ŝ i Ĥi u 1 1 Ĥi d ˆD D ˆ ˆL L ˆ W E6SSM y τ ˆL3 Ĥdê c 3 + y b ˆQ3 Ĥd ˆd c 3 + y t Ĥ u ˆQ 3 û c 3 + λ i ŜĤ d i Ĥ i u + κ i Ŝ ˆD i ˆDi + µ ˆL4 ˆL 4 5 / 0

6 E 6 SSM: M Z M S σ B [pb] ATLAS s = 8 TeV Z ll Expected limit Expected ± 1σ Expected ± σ Observed limit Z χ Z ψ [GeV] m 1/ MSUGRA/CMSSM: tan(β) = 30, A = m 0, µ > All limits at 95% CL τ LSP ATLAS h (1 GeV) 1 s = 8 TeV, L = 0 fb h (14 GeV) h (16 GeV) Expected (±1 σ exp ) SUSY Observed (±1 σ ) theory Expected (0+1) lepton combination Observed miss Expected 0 lepton jets + E T Observed miss Expected 0/1 lepton + 3 b jets + E T Observed miss Expected Taus + jets + E T Observed miss Expected SS/3L + jets + E T Observed miss Expected 1 lepton (hard) + 7 jets + E T Observed ~ g (1400 GeV) ee: L dt = 0.3 fb -1 µµ: L dt = 0.5 fb M Z [TeV] ~ g (1000 GeV) ~ q (1600 GeV) ~ q (400 GeV) m 0 [GeV] [PRD 90 (014) (arxiv: )] [JHEP 10 (015) 054 (arxiv: )] 6 / 0

7 Issues in the E 6 SSM MZ c (tan β) }{{} λ S + m H d mh u tan β tan + d (tan β) M Z β 1 O(1) Extra D-terms cut both ways.5 TeV another large contribution must cancel M Z Unnatural or fine-tuned? E.g. as measured using traditional measure of fine-tuning Also, dangerous B, L violating interactions need approximate Z H + exact Z L/B DM in simplest versions of model requires another exact Z S [PRD 91 (015) (arxiv: )] 7 / 0

8 The SE 6 SSM Modification of E 6 SSM, arising from 5D or 6D orbifold GUT [1] Low-energy matter content augmented by components of extra 7, 7 -plets, including: doublets Ĥ u, Ĥd (note: now not from 7-plet) singlets Ŝ, Ŝ with opposite U (1) N charges Still potentially dangerous B, L violating interactions But now can forbid using single, exact discrete Z H Stabilise scalar potential pure singlet ˆφ W SE6SSM = λŝ(ĥd Ĥu) σ ˆφŜŜ + κ 3 ˆφ 3 + µ ˆφ + Λ F ˆφ + λαβ Ŝ(Ĥ α d Ĥ β u ) + κ ij Ŝ ˆD i ˆDj + f iα Ŝ i (Ĥu Ĥ α) d + f iα Ŝ i (Ĥ α u Ĥd) + gij D ( ˆQ i ˆL 4 ) ˆD j + hiαê E i c (Ĥ α d ˆL 4 ) + µ L (ˆL 4 ˆL 4 ) + σ ˆφ(ˆL 4 ˆL 4 ) + W MSSM (µ = 0) [1] R. Nevzorov, Phys. Rev. D 87, (013) (arxiv: ) 8 / 0

9 Dark Matter Candidates ˆQ i ûi c ˆd i c ˆL i êi c ˆN i c Ŝ S ˆ Ŝ i Ĥ u Ĥ d Ĥα u Ĥα d ˆD i ˆD ˆL4 ˆL4 Z H Z M Z E Symmetry breaking pattern automatically conserved Z M = ( 1) 3(B L) ( R-parity) Per MSSM, implies stable DM candidate (typically χ 0 1) Write Z H = Z M Z E exotic Z E also conserved Lightest exotic (Z E odd) state is also stable DM candidate Very light inert singlinos form hot DM, but negligible contribution to relic density relic density almost entirely due to ordinary neutralino 9 / 0

10 EWSB in the SE 6 SSM E 6 SSM: EWSB conditions M Z M S (i.e. S M S ) At physical minimum, H 0 d = v 1, H 0 u = v, S = s 1, S = s s, φ = ϕ S, S VEVs develop along nearly D-flat direction S = S with S S M S σ Small σ MZ g 1 QS (s 1 + s) far heavier than M S can have M Z far above limits while keeping sparticles (relatively) light Note: also suppress D-term contribution to EWSB scale, i.e. M Z 10 / 0

11 The CSE 6 SSM General model is complicated O(00) new parameters (assuming no new sources of CP-violation) Many masses and mixings Consider constrained model (CSE 6 SSM) inspired by gravity mediated SUSY breaking Universal soft breaking parameters: M 1/, A 0, B 0, m 0 Want Z mass decoupled from EWSB conditions fix heavy s = s1 + s = 650 TeV Suitable DM candidate small µ eff, i.e. small λ Exotic λ αβ, κ i,... free, but small λ natural for these to be small also FlexibleSUSY mass spectrum at full one-loop level, including full two-loop RGEs In general, want to use automated tools for studying with high precision 11 / 0

12 Semi-analytic Solutions Useful technique for studying constrained models (e.g. CE 6 SSM) RGEs for SUSY parameters independent of soft SUSY breaking parameters (up to effects of threshold corrections) Treat RGEs for SUSY breaking parameters as system of linear ODEs Combine with boundary conditions semi-analytic solutions, M i (Q) = p i (Q)M 1/ + q i (Q)A 0, A i (Q) = e i (Q)A 0 + f i (Q)M 1/, m i (Q) = a i (Q)m 0 + b i (Q)M 1/ + c i(q)a 0 M 1/ + d i (Q)A 0,... Coefficients depend only on SUSY parameters, calculated numerically Relate SUSY scale parameters to high-scale inputs, e.g. trade m 0 for µ eff Contrast with e.g. CMSSM: µ output for given m0 1 / 0

13 Two-scale Algorithm Initial guess Calculate g i (M Z ), y f (M Z ), apply low-scale BCs Run all parameters to M X, apply high-scale BC Run to M S, solve EWSB and apply SUSY-scale BC Converged? Calculate pole masses 13 / 0

14 Semi-analytic Algorithm Initial guess Calculate g i (M Z ), y f (M Z ), apply low-scale SUSY BCs Iterate SUSY parameters Determine semi-analytic solutions at M S Solve EWSB, apply SUSY-scale BC Converged? Calculate pole masses Apply threshold corrections 14 / 0

15 Sparticle Masses Mass / GeV νl, ll, lr D i H Ii 0 ντ, τ1, τ χ 0 1, χ0, χ0 3, χ0 4 qr ql g χ ± 1, χ± t1, b1, t, b Altered RG running gaugino masses at low energies lighter than sfermion masses EWSB conditions physical solutions satisfy m 0 > M 1/, A 0 MSSM sfermions are very heavy, out of reach of LHC run II Conversely, small λ αβ, κ i light exotic fermions are observable Exotic leptoquarks Di, e.g. in p p t t τ + τ + ET miss + X, p p b b + ET miss + X Charged and neutral inert Higgsinos p p Z Z + ET miss + X, p p W Z + ET miss + X, p p W W + ET miss + X 15 / 0

16 CP-even Higgs Mass m 0 [GeV] λ = , κ ij =λ αβ = M 1/ [GeV] m h [GeV] Split spectrum large logarithms contribute to m h Small exotic couplings corresponding logarithms small Mainly due to t s Standard DR calculation is inaccurate Solution: use EFT calculation (using SUSYHD now, cross checked with FlexibleHiggs prototype) m h 15 GeV obtained over large part of parameter space 16 / 0

17 Dark Matter Relic Density: Higgsino LSP λ = , κ ij =λ αβ =3 10 3, 0 <(Ωh ) th. < For Higgsino LSP, ( Ωh (Ωh µeff ) ) obs 1 TeV m 0 [GeV] M 1/ [GeV] (Ωh ) th. /(Ωh ) exp. Mainly co-annihilations χ 0 i χ ± 1 f 1 f, χ 0 1 χ 0 f f Requires m χ TeV Higgsino M 1/ must be large ( 6 TeV) to suppress bino component Universal gaugino masses at M GUT all gauginos are heavy, e.g. m g 5 TeV 17 / 0

18 Dark Matter Relic Density: Mixed Bino-Higgsino LSP m 0 [GeV] λ = , κ 1000 ij =λ αβ =1 10 3, 0 <(Ωh ) th. < M 1/ [GeV] (Ωh ) th. /(Ωh ) exp. Alternative: mixed bino-higgsino LSP, e.g. 300 GeV m χ 0 1 Need M 1 µ eff for large mixing M1 < µ eff pure bino, Universe overclosed M1 > µ eff χ 0 1 light Higgsino LSP, underabundant DM Mainly pair annihilation, e.g. χ 0 1 χ 0 1 f f Much lighter M 1/ can also have g within reach at run II and HL-LHC 18 / 0

19 Direct Detection m 0 [GeV] λ = , κ 1000 ij =λ αβ =1 10 3, 0 <(Ωh ) th. < M 1/ [GeV] σ p SI [ cm ] Strong constraints from LUX limits on σ SI σ SI (product of Higgsino, bino components) highly mixed bino-higgsino LSP large σ SI Very close to LUX limit, would be immediately observed at XENON1T Pure Higgsino LSP small bino component (+ heavy), σ SI is safely below LUX limits But still detectable at XENON1T 19 / 0

20 Summary E 6 inspired models can resolve the Little Hierarchy problem of MSSM Simplest variants, e.g. E 6 SSM, faced with several issues (Z limits, multiple discrete symmetries...) Considered well-motivated extension, SE 6 SSM, with exact custodial symmetry Heavy Z sfermions out of LHC reach, but observable exotic fermions, gauginos DM relic density can be fitted by MSSM-like neutralino Higgsino LSP ( heavy spectrum) Mixed bino-higgsino LSP ( observable gauginos) Direct detection limits strong constraints, easily observable at XENON1T Thank you for listening! 0 / 0