New Results from GRACE/SUSY at 1-loop

Transcription

1 New Results from GRACE/SUSY at 1-loop J.Fujimoto, T.Ishikawa, M.Jimo, T.Kaneko T.Kon, Y.Kurihara, M.Kuroda Y.Shimizu (Susy Minami-Tateya Collaoration) RADCOR5 Shonan Village, Japan Octoer 6, 5

2 Outline Introduction Renormalization scheme Physical results Summary

3 Introduction Why RC is important? Precise O(1%) measurement at LC Same accuracy of Theoretical predictions RC in MSSM renormalization, mass spectrum, decays, production (Higgs, chargino / neutralino, sfermion) Fritzsche, Hollik / Eerl, Majerotto, Yamada et al. / Denner / Öller, Eerl, Majerotto / Hollik, Rzehak / Arhri, Hollik / Kovarik, Weer, Eerl, Majerotto / Freitas, Miller, von Manteuffel, Zerwas / Guasch, Hollik, Solà etc.

4 Why automatic calculation is needed? SUSY Models Many possile processes for SUSY particle production a large numer of Feynman diagrams FeynArts & FormCalc Küleck, Böhm, Denner / Hahn, Perez-Victoria / Hahn / Hahn, Schappacher CompHEP & LanHEP Moscow group / Boudjema, Bèlanger, Semenov... see Boudjema s talk

5 Tree level GRACE/SUSY "GRACE/SUSY AUTOMATIC GENERATION OF TREE AMPLITUDES IN THE MINIMAL SUPERSYMMETRIC STANDARD MODEL" KEK-CP-19, Aug, hep-ph/836 Comput.Phys.Commun. 153 (3) 16 GRACE/SUSY at 1-loop

6 Renormalization scheme Gauge symmetric & On-shell scheme On-shell conditions Gauge osons, Fermions, Scalar fermions (A,H ) + + ( χ1, χ1, χ ) Renormalization of tanβ 1 δv1 δv δtan β = tan β δz H1 δz H + v v 1 δv1 δv v1 v

7 Renormalization of sfermions δm f = Re Σ f f (m f ) ( ) δmν l = cosθl sin θlδθl m l m l1 + cos θlδm l1 + sin θlδm l ( +δ M W cos β ml δθu = ) δθl Σ (m ) + Σ (m 1 u 1u u u u 1 u 1 ) mu mu 1 ( ) cosθu sin θuδθu (mu mu ) cos θuδmu +δ ( M W cos β + mu md ) δθd sin θuδmu = cosθd sin θdδθd md md 1 + cos θdδmd 1 + sin θdδmd 1 1

8 Mass shifts for h, H+ ( phys ms ) = ms + Σˆ s (ms ) for neutralinos (i=,3,4) q/ m χ i ˆ Σii (q/ ) = example : SPA1a mh mh + mχ m χ3 m χ4 : GeV : GeV : GeV : GeV : GeV

9 Nonlinear gauge (NLG) fixing terms in MSSM FW ± = ( µ ±ieα Aµ ±igcw β Z µ )W ± µ g (v + δ H H + δ h h ±iκ G )G ± gz µ FZ = µ Z + ξ Z (v + ε H H + ε h h )G Fγ = µ A µ ±iξ W (α, β, δ h, δ H, κ, ε h, ε H ) : NLG parameters

10 Physical results -ody decay widths (Higgs & sparticles) Chargino pair production at LC

11 -ody decay widths parameter set : SPA1a Γ (GeV ) H δγ / Γ % H + ντ τ + H + χ 1 χ % +4.% e 1 e χ % χ 1+ ντ τ % χ + Z χ % χ 3 W χ 1+ χ 3 Z χ % %

12 How to Calculate Tree %%%%%%%%%%%% Model= mssm.mdl ; %%%%%%%%%%%% Process; ELWK={1}; Initial={higgs}; Final={ -ar}; Kinem= 11 ; Pend; Feynman diagram generation H 1-loop Tree+photon %%%%%%%%%%%% Model= mssm.mdl ; %%%%%%%%%%%% Process; ELWK={3, 1}; Initial={higgs}; Final={ -ar}; Kinem= 11 ; Pend; %%%%%%%%%%%% Model= mssm.mdl ; %%%%%%%%%%%% Process; ELWK={}; Initial={higgs}; Final={photon -ar}; Kinem= 131 ; Pend; numerical calculation event generation

13 H Graph 1 Graph Graph 3 Graph 4 Graph 5 Graph 6 Graph 7 Graph 8 Graph 9 Graph 1 Graph 11 Graph 1 Graph 13 Graph 14 Graph 15 Graph 16 Graph 17 Graph 18 Graph 19 Graph Graph 1 Graph Graph 3 Graph 4 Graph 5 Graph 6 Graph 7 Graph 8 Graph 9 Graph 3 Graph 31 Graph 3 Graph 33 Graph 34 Graph 35 Graph 36 Graph 37 Graph 38 Graph 39 Graph 4 Graph 41 Graph 4 Graph 43 Graph 44 Graph 45 Graph 46 Graph 47 Graph 48 Graph 49 Graph 5 Graph 51 Graph 5 Graph 53 Graph 54 Graph 55 Graph 56 Graph 57 Graph 58 Graph 59 Graph 6 Graph 61 Graph 6 Graph 63 Graph 64 W+ W+ W+ H+ H+ H+ X+ X+ Ht H+ Ht X+ Ht W+ Ht W+ Ht H+ Ht X+ Ht W+ Ht H+ H H H H H H H H a a a a a a a a X+ Z Z Z A A A X3 H H H H H H H H X+ A X3 Z Z A X3 Z t H H H H H H H H a a a a a a a a X3 X3 t Ht t Ht t H H H H A H X3 H t W+ H+ X+ Z A h H H H H H H H H a a a a a a a a ~t1 ~t1 ~t1 ~t1 ~t HA HX3 H ~t1~w1+ HH H ~t1~w+ H ~t~w1+ H ~t~w+ H ~t~w1+ H H H H H H H H a a a a a a a a ~t ~t ~t ~1 ~1 ~1 ~1 ~1 H H H H H H H H ~t ~t1 ~t1 ~1 ~1 ~1 ~1 ~ ~w+ ~w1+ ~w+ ~sz1 ~sz ~sz3 ~sz4 ~sz1 H H H H H H H H a a a a a a a a ~1 ~1 ~ ~ ~ ~ ~ H~1 H H H H H H H ~ ~ ~ ~ ~ ~ ~ ~1 ~sz ~sz3 ~sz4 ~sz1 ~sz ~sz3 ~sz4 ~sz1 H H H H H H H H a a a a a a a a H~ H~ H~ H~w1+ H~w1+ H~w1+ H~w1+ H~w+ ~1 ~1 ~1 ~w1+ ~w1+ ~w+ ~w+ ~w+ ~sz ~sz3 ~sz4 ~t1 ~t ~t1 ~t ~t1 H H H H H H H H a a a a a a a a ~w+ ~w+ ~w+ ~sz1 ~sz1 ~sz1 ~sz1 ~sz1 ~w+ H~t1 ~w1+ H~t ~w1+ H~1 ~sz1 H~ ~sz1 H~1 ~sz H~ ~sz H~1 ~sz3 H~t H H H H H H H H a a a a a a a a

14 Graph 65 Graph 66 Graph 67 Graph 68 Graph 69 Graph 7 Graph 71 Graph 7 Graph 73 Graph 74 Graph 75 Graph 76 Graph 77 Graph 78 Graph 79 Graph 8 Graph 81 Graph 8 Graph 83 Graph 84 Graph 85 Graph 86 Graph 87 Graph 88 Graph 89 Graph 9 Graph 91 Graph 9 Graph 93 Graph 94 Graph 95 Graph 96 Graph 97 Graph 98 ~sz1 ~sz1 ~sz1 ~sz ~sz ~sz ~sz ~sz ~sz3 H~1 ~sz4 H~ ~sz4 H~1 ~sz H~ ~sz H~1 ~sz1 H~ ~sz1 H~1 ~sz3 H~ H H H H H H H H a a a a a a a a ~sz ~sz ~sz ~sz3 ~sz3 ~sz3 ~sz3 ~sz3 ~sz3 H~1 ~sz4 H~ ~sz4 H~1 ~sz3 H~ ~sz3 H~1 ~sz1 H~ ~sz1 H~1 ~sz H~ H H H H H H H H a a a a a a a a ~sz3 ~sz3 ~sz3 ~sz4 ~sz4 ~sz4 ~sz4 ~sz4 H H H H H H H H ~sz ~sz4 ~sz4 ~sz4 ~sz4 ~sz1 ~sz1 ~sz ~ ~1 ~ ~1 ~ ~1 ~ ~1 H H H H H H H H a a a a a a a a ~sz4 ~sz4 ~sz4 h h H H H ~sz H~1 ~sz3 H~ ~sz3 H h H H H h H H H~ H H H H H H H H a a a a a a a a H H h 1 H H H a a

15 How to check results? UV (Cuv) independence Soft photon mass (λ) independence cut off photon energy (kc) independence Nonlinear gauge parameter independence check for physical finite contriution

16 H Γ = 1.819(GeV ) CUV =, λ = 1 4, kc =.1GeV Γ1loop+soft = (GeV ) CUV = 1 3, λ = 1 4, kc =.1GeV Γ1loop+soft = (GeV ) CUV =, λ = 1 7, kc =.1GeV Γ1loop+soft = (GeV ) CUV =, λ = 1 4, kc =.1GeV (α, β, δ h, δ H, κ, ε h, ε H ) = (,L,) (, 3, 4,5,6, 7,8) Γ1loop+soft = (GeV )

17 CUV =, λ = 1 4, kc =.1GeV Γ1loop+soft = (GeV ) H (γ ) Γhard (kc =.1GeV ) = (GeV ) Γhard (kc =.1GeV ) =.8659(GeV ) Γ1loop+soft+hard (kc =.1GeV ) =.1741(GeV ) = δγ Γ1loop+soft+hard (kc =.1GeV ) =.1741(GeV ) H δγ =9.66% Γ

18 Chargino pair production at LC parameter set : SPA1a e+e χ 1+ χ 1. σ [p].15 Born 1-lp corr W [GeV] 1 14

19 Weak = 1-loop + soft - BORN*QED e+e χ 1+ χ Δσ/σ[%] W [GeV] GRACE Wien group (hep-ph/5419)

20 Summary : developed gauge symmetric & on-shell scheme full automatic calculation various check system useful tools for precise phenomenologies

21 SPA1a msugra values M1/ = 5 GeV M = 7 GeV A = -3 GeV sign(μ) = +1 tanβ = 1 low energy inputs M = GeV M1 = 1.1 GeV mse1 = 13. GeV msτ1 = 11.1 GeV msu1 = 56.5 GeV msd1 = 56.5 GeV mst1 = GeV ms1 = GeV MA = 431. GeV μ = 399. GeV tanβ = 1 mse = GeV θe =.5 msτ = 19.4 GeV θτ =.41 msu = GeV θu =-.5 θd =-.5 mst = GeV θt =-.31 θ =.1