Implication of Higgs at 125 GeV within Stochastic Superspace Framework

Transcription

1 Implication of Higgs at 125 GeV within Stochastic Superspace Framework Department of Theoretical Physics Indian Association for the Cultivation of Science [ With U.Chattopadhyay and R.M.Godbole Phys.Rev. D88 (2013) arxiv: [hep-ph] ] Aug 29, 2013

2 SUSY must be broken Non observation of SUSY particles SUSY must be broken. Minimal Supersymmetric Standard Model has a large no of soft SUSY breaking terms. Choosing a particular model like msugra, GMSB, AMSB etc can be useful to reduce the no of parameters. In this work we study a SUSY breaking scenario by considering a superspace where some unknown but fundamental mechanism of SUSY breaking can be manifested as the stochasticity of Grassmann variables. ref:kobakhidze,pesor,volkas arxiv: [hep-ph] arxiv: [hep-ph] arxiv: [hep-ph]

3 Stochastic superspace formulation θ and θ are stochastic and a probability distribution function P(θ, θ) describes this stochasticity. P(θ, θ) = A + θ α Ψ α + θ α Ξ α + θ α θ α B + θ α θ α C + θ α σ µ α β θ βv µ +θ α θ α θ α Λ α + θ α θ α θ α Σ α + θ α θ α θ α θ α D Here A, B, C, D and V µ are complex numbers. Ψ, Ξ, Λ, and Σ are Grassmann numbers.

4 stochastic superspace formulation contd Now, Normalisation: d 2 θd 2 θ P(θ, θ) = 1. D = 1 Vanishing of fermionic moments due to Lorentz invariance: < θ >=< θ >=< θ θ >=< θ 2 θ >=< θ θ2 >= 0 Σ = Λ = V µ = Ξ = Ψ = 0 Bosonic moments: < θθ >= C, < θ θ >= B Calling B = 1/ξ one has B = C = 1/ξ < θθ θ θ >= A A = 1/ ξ 2 ξ is a quantity of mass dimension. Thus : P(θ, θ) ξ 2 = P(θ, θ) = 1 + ξ (θθ) + ξ( θ θ) + ξ 2 (θθ)( θ θ)

5 application to the simplest case Let s consider a single chiral superfield Φ in the Wess-Zumino model : Φ = φ(x) iθσ µ θ µ φ(x) 1 4 θ2 θ 2 µ µ φ(x) + 2θψ(x) + i 2 θ 2 µ ψ(x)σ µ θ + θ 2 F(x) Kinetic term Φ Φ Superpotential term W = 1 2 mφ hφ3

6 averaging over Grassmannian coordinates L =< L >= d 2 θd 2 θ P(θ, θ)l Where, L = Φ Φ + Wδ (2) ( θ) + W δ (2) (θ) < L kinetic >= [ ] Φ Φ D + SUSY {}}{ ξ 2 φ 2 + ξ φf + ξφ F SUSY { ( }}{ < W + h.c. >= [W + h.c.] F + 1 ξ 2 mφ2 + 1 ) 3 hφ3 + h.c.

7 averaging contd where, and L = < L > SUSY + < L > SUSY < L > SUSY = [ ] Φ Φ + [W + h.c.] F D < L > SUSY = ξ 2 φ 2 + ξ φf + ξφ F + ( 12 [ξ mφ ) ] hφ3 + h.c.

8 emergence of soft terms The eqns of motion of auxiliary field : Substituting for F and F in L : F = (ξ φ + mφ + hφ 2 ) L = L On shell SUSY + L soft, where, L On shell SUSY = µ φ µ φ + i ( ψσ µ µ ψ µ ψσ µ ψ ) 2 m 2 φ 2 h 2 ( φ 2 ) 2 [(mh φ 2 φ + 12 ) ] mψψ + hψψφ + h.c. and L soft is given by, [( 1 L soft = 2 ξ mφ ) ] 3 hξ φ 3 + h.c.

9 MSSM MSSM Superpotential : W MSSM = ūy u QH u dy d QH d ēy e LH d + µh u H d µh u H d ξ µ H u Hd ūy u QH u 2ξ ŷ up QŨ c Hu gaugino mass term ξ 2 Σ iλ (i) λ (i) Fundamental parameters : m 1/2 = 1 2 ξ, B µ = ξ,a 0 = 2ξ All depend on a single parameter ξ the scale of SUSY breaking No SUSY breaking scalar soft mass term. ξ considered to be real for simplicity. scale of input taken to be : M GUT < Λ < M pl

10 SSM : advantages and drawbacks Non zero A parameter can enhance the loop correction to m h : [ mh m t = 2π 2 v 2 sin 2 log M2 S 2 β m + X 2 ( t t 2MS 2 1 X t 2 )] 6MS 2 M S = m t1 m t2, X t = A t µcot β, v = 246 GeV in ref [hep-ph ] the authors used m 0 = 0 at Λ = M GUT tachyonic sleptons. With Λ > M GUT they could reach only upto m h 116 gev. ref [hep-ph ]

11 Our analysis : mod-ssm SSM is naturally favourable for large higgs loop correction. can we reach m h 125 GeV? We consider m 0 0 helps to meet phenomenological demands like FCNC constraints. input scale Λ = M GUT to avoid the issues related to post-gut Physics.

12 mod-ssm contd ξ real,positive number with an additional input sign(ξ). We discuss only the case ξ < 0 because the other sign does not produce a spectra satisfing DM relic density constraint. m 1/2 taken to be independent parameter with A 0 = sign(ξ)4m 1/2 and B 0 = sign(ξ)2m 1/2 Model parameters : m 0,m 1/2,sign(ξ),sign(µ) tanβ is a derived quantity here. Since we are using the code SUSPECT [version 2.41], which takes tanβ as an input, Newton Raphson root finding scheme is used to find out the value of tanβ for a given B(M GUT ).

13 the evolution of a few relavant couplings µ ξ < 0 m 1/2 =600 GeV, m 0 =2 TeV m 2 Couplings (GeV) m 1 B Α τ A t A b Scale Q (GeV) m 1/2 = 600 GeV, m 0 = 2 TeV and µ > 0 B must evolve to a positive value at EW scale.

14 REWSB conditions: µ 2 = 1 2 M2 Z + m2 H D m 2 H U tan 2 β tan 2 β 1 + Σ 1 Σ 2 tan 2 β tan 2 β 1 sin2β = 2Bµ/(m 2 H D + m 2 H U + 2µ 2 + Σ 1 + Σ 2 )

15 Allowed range of tanβ 60 ξ< tanβ m1/2 (GeV) tanβ is constrained to have large values.

16 Scanning the m 0 m 1/2 plane reigion I can not satisfy REWSB. Region III stau becomes LSP. region II chargino coannihilation region: gives underabundant DM. m h is considered to have a theoretical uncertainity of 3 GeV I II 5000 m h = 123 GeV ξ < 0 m h = 127 GeV m 0 (GeV) b --> s+γ B s --> µ + µ III m 1/2 (GeV)

17 Direct detection XENON100 ζσ SI(p-χ) (pb) m 0 χ1 (GeV) The scaling factor ζ = Ω eχ h 2 /(Ω CDM h 2 ) min = ρ χ /ρ 0 ref :Fornengo,Scopel,Bottino [arxiv: [hep-ph]]

18 let s vary m t! The small µ region is very sentitive to REWSB. Sentitivity can be reduced by varying a non-susy parameter like m t. experimental data : m t ±0.9 GeV from pp t t + X crosssection. NNLO QCD prediction of the inclusive pp t t + X cross section and the exp data of the same used to extract m t in the modified ( MS) scheme. This was then used to compute the pole mass m t ±2.8 GeV ref:alekhin,djouadi,moch arxiv: [hep-ph] Relic density satisfied points shown in red for m t = ± 2.8 GeV. The central value of 173.3GeV is clearly disfavoured. Ω χ h ξ<0 (m 1/2 < 2 TeV, m 0 < 7 TeV) m t (GeV)

19 m 0 -mhalf plane with m t scanned I A m top scanned (ξ<0) 5000 m 0 (GeV) C m h =124 GeV 2000 b-->sγ B s -->µ + µ B II m 1/2 (GeV) DM satisfied points of right abundance obtained.

20 10-7 (m top scanned) 10-8 XENON100 σ SI(p-χ) (pb) m 0 χ1 (GeV) effect of varying m t on σ SI p eχ 0 1 Significant amount of hadronic uncertainity in σ SI p eχ 0 1. ref:perelstein and Shakya[arXiv: [hep-ph]] may cause a reduction in σ SI by almost an order of magnitude. p eχ 0 1

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22 conclusion The model has a natural advantage of having a non zero A parameter helps to raise m h in the region m h 125 GeV. This framework can be extended to non minimal models like NMSSM,RPV models etc.

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24 b s γ SM contribution (almost saturates the experimental value) t W ± loop. MSSM contribution: 1. χ ± t loop: BR(b sγ) eχ ± = µa t tanβf (m t1,m t2,m eχ ±) 2. H ± t loop: BR(b sγ) H ± m b v(1+ m b ) = m b(y tcosβ δy tsinβ) vcosβ(1+ m b ) g(m H ±,m t ) where, δy t = y t 2α s 3π µm gtanβ(cos 2 θ t I(m sl,m t2,m g )+sin 2 θ t I(m sl,m t1,m g )) destructive interference for A t µ < 0 prefered. NLO contributions (from squark-gluino loops: due to the corrections of top and bottom yukawa couplings) become important at large µ or large tanβ.

25 B s µ + µ dominant SM contribution from : Z penguin top loop & W box diagram. SM value : BR(B s µ + µ )=3.23 ± LHCb result : (stat.) (syst.) no room for large deviation. BR(B s µ + µ ) SUSY tan6 β m 4 a

26 Relic Density Some diagrams contributing to relic density:

27 Direct Detection The elastic scattering of LSP depends on their scattering off heavy neucli in a detector. effective Lagrangian for SI/SD interaction between a WIMP and a neucleon: L SI = λ N ψχ ψ χ ψn ψ N L SD = ξ N ψχ γ 5 γ µ ψ χ ψn γ 5 γ µ ψ N σ SI 0 = 4µ2 χ π (λ pz + λ n (A Z)) 2 Where µ χ is the WIMP-nucleous reduced mass. There is strong enhancement for large nuclei σ SI 0 A2 for λ p λ n.

28 Diagrams corresponding to SI scattering: Diagrams corresponding to SD scattering: