DECOUPLING PROPERTIES OF MSSM PARTICLES IN HIGGS AND TOP DECAYS Mar a J. Herrero Universidad Autónoma de Madrid In collaboration with: H.Haber, H.Loga

Transcription

1 DEOUPLING PROPERTIES OF MSSM PRTILES IN HIGGS ND TOP DEYS Mar a J. Herrero Universidad utónoma de Madrid In collaboration with: H.Haber, H.Logan, S.Pe~naranda, S.Rigolin and D.Temes RDOR/2 armel, alifornia, September -5, 2

2 MOTIVTIONS/GOLS ffl We want to distinguish MSSM from SM even if SUSY spectra and extra Higgses are heavy $ M SUSY ;M fl M Z ffl Use radiative corrections from SUSY particles and extra Higgses in observables with external SM particles as indirect signals of new physics from MSSM (Same spirit of EW precision fits: indirect top signals, indirect SM Higgs searches...) ffl We want to know if Higgs decays, top decays...are significantly affected by radiative corrections from heavy SUSY particles and/or heavy Higgses -Is there decoupling of heavy MSSM particles beyond tree level?. Do the various sectors decouple separately? - In case there is decoupling, how is it? (fast,slow,..?) - re there special choices of the MSSM parameters, where radiative corrections are significant even for a heavy MSSM spectrum?: Delayed decoupling? (large tanfi, size and sign of μ,...?) ffl In this talk I will concentrate on the SUSY-QD corrections to the main h ;H ± ;t decays

3 DEOUPLING LIMIT IN THE HIGGS SETOR (Haber & Nir 99)!Tree level, M fl M Z M Ho ' M H± ' M fl M Z M h o ' M Z jcos2fij Higgs couplings in the MSSM normalized to SM couplings ffi g ffi μtt g ffi μ bb g ffiv V SM H MSSM h o cos ff= sin fi sin ff= cos fi sin(fi ff) H o sin ff= sin fi cos ff= cos fi cos(fi ff) o = tan fi tan fi cos ff ' sin fi +O(M Z 2=M 2 sin ff ) ; ' cos fi +O(M Z 2=M 2) sin(fi ff) ' +O(MZ 4=M 4)!eyond tree level, M fl M Z M Ho ' M H± ' M fl M Z M h o» 3 35 GeV Interested in the decoupling behaviour of heavy SUSY particles and heavy Higgses, at one loop, in h couplings/production/decays

4 DEOUPLING LIMIT IN THE SUSY-QD SETOR -sbottoms: ^M 2~ b = -stops: ^M 2 ~t = M 2~ + Q m2 b MZ 2( + Q 2 bs 2 )cos2fi W m b ( b μ tan fi) M 2~ + Q m2 t + M Z 2( Q 2 ts 2 )cos2fi W m t ( t μ cot fi) m b( b μ tan fi) M 2~ + D m2 b + M Z 2Q bs 2 W cos 2fi m t( t μ cot fi) M 2~ + U m2 t + M Z 2Q ts 2 W cos 2fi We consider the limit: M SUSY ο M ~ Q ο M ~ D ο M ~ U ο M ~g ο μ ο b ο t fl M Z () heavy squarks and heavy gluino and study two extreme cases for: ^M 2 M 2 L m q X q m q X q M 2 R -lose to maximal mixing: ~q ο 45 ffi jm 2 L M 2 R j fi m qx q ) jm 2 ~q M 2 ~q 2 j fi jm 2 ~q + M 2 ~q 2 j -lose to minimal mixing: ~q ο ffi jm 2 L M 2 R j fl m qx q ) jm 2 ~q M 2 ~q 2 j ο OjM 2 ~q + M 2 ~q 2 j

5 Decoupling in low-energy electroweak gauge boson physics It has been shown that all one-loop corrections to low-energy electroweak gauge boson physics involving SUSY particles and extra Higgses decouple in the limit of large sparticle masses and large M (.Dobado, M.H & S.Pe~naranda 999, 2) ffl omputation of eff [; Z; W ± ] by integrating out ~q; l; ~ ~χ ± ; i ~χo j ;H± ;H ; to one loop. e i eff [V ] = Z [d ~ f][d ~ f Λ ][d~χ + ][dμ~χ + ][d~χ ][dh]e i MSSM [V; ~ f;~χ + ; ~χ ;H] ffl Large sparticle masses and large M expansion of eff [; Z; W ± ]. m ~q ; m ~ l ; m ~χ ± i ; m ~χ o j ; M fl EW scale j ~m 2 i ~m 2 j j fi j ~m 2 i + ~m2 j j 8i;j V V 2 3 ^ V 2 ^ V 3 ~ ~ H H -+ f χ! ψ + O p M SUSY m ; MEW M SUSY r ; MSUSY t! M SUSY V V n ^ V g^ ^ V n Decoupling a la ppelquist arazzone

6 SUSY-QD corrections to h o! μ bb (h o! b μ b) to one loop and O(ff S ): ~ b j b ~g a h ~g a μ~ b i b b μ b ~ bi (h o! b μ b) (h o! b μ b)( + 2 QD + 2 SQD ); ffl QD, QD correction gives a ο 5% reduction in (h o! b μ b) decay rate for M h in its MSSM range. QD correction has the same form in MSSM as in SM. (raaten & Leveille 98, Sakai 98, Inami & Kubota 98) ffl SQD, SUSY-QD correction is comparable to QD correction for a wide window of the parameter space. (Dabeltein '95, orasa,jimenez& Sola '96), (arena et al. '99, Eberl et al. '), (Heinemeyer et al. ') We are interested in SQD in the decoupling limit Previous numerical computations seem to reveal decoupling of SUSY-QD corrections in the heavy sparticles limit (orasa,jimenez& Sola 996) We want to explore decoupling behaviour both numerically and analitically

7 SQD in the Decoupling Limit (H.Haber,M.H,H.Logan,S.Pe~naranda,S.Rigolin & D.Temes, 2) We consider the limit: M SUSY ο M Q ο M ~ D ο M ~ ~g ο μ ο b fl M Z ) heavy sbottoms and heavy gluino and expand ; ; sin ~ b...in inverse powers of M SUSY defining: 2 (M 2~ b + M 2~ b 2 ) ; R M ~g ~M S ; f i () = X b b μ tan fi ; Y b b + μ cot ff We get, for ~ b ο ±45ffi, and up to O(M 2 Z;h o=m 2 SUSY ): SQD = ff s 3ß + 2 MZ 2 3 ~M S 2 8 >< >: μm ~g (tan fi + cot ff) f (R) Y bm ~g m 2 h 2 M ~ f S 4 4 (R) cos fi sin(ff + fi) I b 3 sin ff f 5 (R)+ M ~gx b f ~M S 2 2 (R) + O m 2 b 9 >= >; First term agrees with effective coupling result in the zero ext. mom. approx. (arena,mrenna & Wagner 999) No Decoupling with M SUSY if fixed M

8 Recovering decoupling if all MSSM spectra heavy If, in addition, to heavy sbottoms and gluino, we have also heavy extra Higgses, M fl M Z,, then: cot ff = tan fi 2 M 2 Z M 2 and, therefore: SQD = ff s 3ß M 2 Z 8 >< >: tan fi cos 2fi + O 2μM ~g f ~M S 2 (R) tan fi cos 2fi M Z 2 M 2 cos fi sin(ff + fi) I b 3 sin ff M 4 Z M 4 ( b μ tan fi) M ~gm 2 h o 2 M ~ f S 4 4 (R) f 5 (R)+ M ~gx b f ~M S 2 2 (R) + O m 2 b 9 >= >; Decoupling if and only if M SUSY and M! omments: ffl Dominant terms go as SQD ο M 2 Z M M 2 Z;h M 2 SUSY ffl In the limit tan fi fl : j SQD j grows with tan fi: delayed decoupling oth and 2 enhanced by tan fi sign of SQD governed by sign of μ and M ~g ffl Similar results for ~ b ο ffi

9 simple example with ~ b ο 45ffi Take just one scale M S : b = μ = M ~ Q = M ~ D = M ~g = M S M = M S In the limit M S fl M Z we get: SQD = ff s 3ß M 2 S ( 2 tan fi cos 2fiM 2 Z M 2 Z cos 2fiIb 3 (2 tan fi) M h 2 o ( tan fi)+ ) 2 In agreement with numerical behaviour of exact result: M = M S D SQD. tanb = tanb =35 tanb = M S HGeVL Decoupling with M S Typical size for M S 25 GeV : SQD» %

10 Two different scales M 6= M S ) For fixed M S and large M SQD tends to a non vanishing constant: -. M S = 5 GeV M S = 2 GeV -.2 D SQD tanb =8 exact result large M S expansion M HGeVL No independent decoupling with M 2) For fixed M and large M S SQD tends to a non vanishing constant: M = 5 GeV M = 3 GeV D SQD -.3 M = 2 GeV tanb =8 exact result large M S expansion M S HGeVL No independent decoupling with M S

11 Independent decoupling of gluino We expand the correction in the heavy gluino limit M ~g fl ~ M S ο μ ο b fl M Z : SQD = ff ( s 2μ (tan fi + cot ff) log 3ß M ~g + 2X b M ~g M 2 Z cos fi sin(ff + fi) sin ff M 2 ~g I b 3 Y b 3M ~g m 2 h In agreement with exact numerical result: (orasa, Jimenez & Sola 996) + O M 2 ) M 2 ~g : -.25 tanb =8 D SQD tanb =3 tanb=4 M = M S = 2 GeV M g HGeVL Very slow decoupling with M ~g Sizeable correction even for large M ~g : For tan fi = 3 and M ~g = TeV, SQD = 2%

12 Independent decoupling of sbottoms We expand the correction in the heavy sbottoms limit ~M S fl M ~g ο μ ο b fl M Z : SQD = ff s 3ß 8 >< >: 2μM ~g (tan fi +cotff) ~M S 2 cos fi sin(ff + fi) + M 2 Z sin ff I b + O m 2 b 3 ~M S 2 9 >= >;.5 tan β = 8 tan β = 3 SQD -.5 tan β = 5 -. M = M gluino = µ = b = 2 GeV exact formula analytic formula large M S expansion M S [GeV] Fast decoupling with ~ M S

13 No decoupling of heaviest sbottom Expand the correction in the heavy sbottoms limit M ~ D fl M ~ Q ο M ~g ο μ ο b fl M Z, so that M~ b 2 fl M~ b : SQD = ff s 3ß 8 >< >: 2 MZ 2 cos fi sin(ff + fi) (I b 3 M 2~ sin ff Q 3 bs 2 W )f 5(R ) b + 2μM ~g (tan fi + cot ff) M 2~ b 2 + M 2 Z M 2~ b 2 cos fi sin(ff + fi) sin ff +O m 2 b M 2 SUSY 9 >= : >; h (R )+log M 2 ~g M 2~ b (I b 3 Q b s 2 W )2M ~gx b f (R )+Q b s 2 W M 2~ b tan β = 8 tan β = SQD tan β = 5 -. M b = M gluino = µ = b = M = 2 GeV exact formula analytic formula large M b2 expansion M b2 [GeV] No decoupling with M ~ b 2

14 SUSY-QD corrections to H +! tμ b (H +! t μ b) to one loop and O(ff S ): (R. Jimenez and J. Sola,. artl et al., 996) ~t j t ~g a ~g a H + ~g a μ~ bi b b ~ bi t t μ b ~t i Results in the decoupling limit (M.H., S.Pe~naranda and D.Temes in progress) (H +! t μ b) (H +! t μ b)( + 2 QD + 2 SQD ); includ- We have obtained analytical expansions for SQD ing O(MEW 2 =M SUSY 2 ) corrections, for max/min ~ b;~t For ~ b;~t ο 45o and ~ M 2 S 2 (M 2~ b + M 2~ b 2 ) 2 (M 2 ~t + M 2 ~t 2 ) we get: SQD = ff s 3ß 8 >< >: μm ~g (tan fi + cot fi) f (R)+O M 2 EW 9 >= >; The leading term agrees with result from effective lagrangian approach: (Eberl et al. ', arena et al. ') No Decoupling with M SUSY ffl Enhanced by tan fi ffl Proportional to M ~g μ ffl Similar results for ~ b;~t ο o

15 H +! tμ b in the decoupling limit (M.H., S.Pe~naranda and D.Temes in progress) ) One scale M S = M ~ Q = M ~ U = M ~ D = M ~g = b = t = μ.5 M Q é =M D é = M U é =M g é = b = t =m=m S M H = 25 GeV D SQD -.5 tanb =8 tanb =3 - tanb = M S HGeVL No decoupling with M SUSY 2) Independent decoupling of gluino D SQD tanb =8 tanb =3 tanb = M Q é =M D é = M é U = b = t =m= TeV M H = 25 GeV Mé g HGeVL Very slow decoupling with M ~g Large correction even for large M ~g : For tan fi = 3 and M ~g = TeV, SQD = 75%

16 SUSY-QD corrections to t! W + b (Dabelstein et al 995, Guasch et al 995) b ~g a ~g a ~g a t ~ b i t t b b ~t j W + ~t i ~ bi SQD ο 5% to % quite insensitive to tan fi to be compared with SUSY-EW corrections (Garcia et al 994): SEW ο % to % growing with tan fi SUSY-QD corrections in the decoupling limit (M.H,D.Temes, in progress) Simplest choice: M ~ Q = M ~ U = M ~ D = t = b = μ = M ~g = M S fl m EW Expanding SQD in inverse powers of M S we get: SQD = 2ff s 3ß m 2 t M 2 S ( cot fi)2 + ( cot fi) + ::: 6 Fast decoupling with M S ; Not enhanced by tan fi

17 ONLUSIONS The one-loop SUSY-QD corrections to (h o! μ bb) : ffl Do not decouple if internal ~g and ~ b are very heavy!! ffl Decouple if and only if both M SUSY very large and M are ffl Sizeable for large tan fi ) Delayed decoupling ffl Decouple independently and very slowly with M ~g ffl Decouple independently and fast with M ~ b (H +! t μ b) : ffl Do not decouple if internal ~g and ~ b, ~t are very heavy!! ffl Sizeable for large tan fi ) Delayed decoupling ffl Decouple independently and very slowly with M ~g (t! W + b) : ffl Decouple fast with M SUSY Indirect SUSY breaking signals at low energy Higgs physics? Sizeable corrections that can be negative ) Interesting enhacements in R(h! fi + fi ) and R(H +! fi + ν fi )