tgβ sensitivity to λ hhh ee Zhh s = 500 GeV M A [GeV]

Transcription

1 Quanum Effecs o he Higgs boson self-couplings in he SM and in he MSSM. Siannah Pe~naranda Insiu für Theoreische Physik (ITP) Universiä Karlsruhe From works in collaboraion wih: W. Hollik Eur. Phys. J. C23, 63-72, 22, hep-ph/8245 A. Dobado, M.J. Herrero and W. Hollik In preparaion, KA-TP-25-2 SUSY2, DESY Hamburg June 7-23, 22

2 Plan of he alk ffl Inroducion ffl Tree-level Higgs boson self-couplings ffl One-loop conribuions - Analyical sudies - Higgs secor iself - Leading conribuions from ~ secor ffl Numerical analysis for heavy op-squarks secor ffl Conclusions

3 Higgs self-couplings To esablish he Higgs mechanism experimenally in an unambiguous way, he Higgs self-ineracion poenial mus be reconsruced. This ask requires he measuremen of he rilinear and quaric selfcouplings, as prediced in he Sandard Model or in supersymmeric heories. TESLA physics programme a p s = 5 GeV TESLA Technical Design Repor, DESY 2- Double Higgs-srahlung: e + e! ZHH e + Z Z H H e H ffl For a SM-like Higgs boson wih m h = 2 GeV a fb, a precision of ffi hhh = hhh = 23% is possible. D.J.Miller e al., hep-ph/94; C.Casanier e al., hep-ex/28 ffl Regions of accessibiliy in MSSM parameers for MSSM Higgs self-couplings have been deermined: R.Lafaye e al., hep-ph/2238; A.Djouadi, hep-ph/ gβ sensiiviy o λ hhh ee Zhh s = 5 GeV M A [GeV]

4 Radiaive correcions o neural Higgs self-couplings ffl Use radiaive correcions o obain informaion for esablishing he Higgs poenial and hus he Higgs mechanism as he basic mechanism for generaing he masses of he fundamenal paricles ffl Three-poin one-loop radiaive correcions for he neural Higgs sysem in he MSSM have been calculaed wihin he effecive poenial approximaion and in some limiing siuaions V. Barger e al., Phys.Rev. D45 (992) P.Osland and P.N.Pandia, Phys.Rev. D59 (999), hep-ph/98635 ffl Phenomenological sudies have addressed he issue of he measuremens of some of he Higgs self-couplings in he MSSM M. Mühlleiner, hep-ph/827 and references herein ffl Our inenion is o invesigae how far he MSSM Higgs poenial reproduces he SM poenial when he non-sandard paricles are heavy ffl We wan o explore decoupling behaviour, boh numerically and analyically, of he radiaive correcions o self-couplings a he one-loop level ffl We have sared by Leading conribuions from ~ secor (m > m h in he MSSM) Conribuions from he Higgs secor iself.

5 Tree-level Higgs boson self-couplings Trilinear and quaric SM and MSSM Higgs boson self-couplings ffi ffiffiffi ffiffiffiffi SM H 3gM 2 H 2 M W 3g 2 M 2 H 4 M 2 W MSSM h o 3gM Z 2c W cos 2ff sin(fi + ff) 3g 2 4c 2 cos 2 2ff W Decoupling limi in he Higgs secor, Haber & Nill 99 M A fl M Z M Ho ' M H± ' M A fl M Z M h o ' M Z j cos 2fij ff! fi ß 2 ) cos 2ff! cos 2fi sin(fi + ff)! cos 2fi + ffi ffiffiffi ' 3g 2 M W M 2 ree h ; ffiffiffiffi ' 3g2 M 2ree 4 MW 2 Tree-level couplings lead o equal resuls in he MSSM and in he SM in he decoupling limi ) Decoupling a ree-level

6 One-loop conribuions o he Higgs self-couplings ANALYTICAL STUDIES ffl Our inenion is o invesigae he differences beween he correcions o he self-couplings wih respec o he H SM self-couplings ffl We wan o sudy he radiaive correcions from heavy op-squarks and Higgs secor iself o he Higgs self-couplings a one-loop level ffl Analyical resuls for he n poin renormalized verex funcions in he MSSM and in he SM Is here decoupling of heavy paricles beyond ree-level? ffl By using he sandard on-shell renormalizaion procedure A. Dabelsein, Z. Phys. C67 (995) 495; Nucl. Phys. B456 (995) 25; M. Böhm, H. Spiesberger, W. Hollik, Forsch. Phys. 34 (986) 687; W. Hollik, Forsch. Phys. 38 (99) 65. ffl Generic R ο gauge ffl We consider he decoupling limi M H ο M H ± ο M A fl M Z while boh he mass and he momena of he exernal paricles remain a he same low energy scale below M A and in ~ secor: m 2 ~ ;m 2 ~ 2 fl M 2 Z ;M 2 jm 2 ~ m 2 ~ 2 j fi jm 2 ~ + m 2 ~ 2 j

7 Higgs secor conribuions SIMPLIFICATIONS. We have checked ha one-loop conribuions from diagrams ha have a leas one gauge boson paricles are he same in boh models - pure gauge boson diagrams are exacly he same - ( fl;z;w ± ) + ( H ;H ± ;A ) one-loop diagrams are proporional o cos(fi ff)! in he decoupling limi 2. We consider ffi ffi ffi ffi H ;H ± ;A, Heavy Conribuions ffi H ;H ± ;A and G ;G ± ;, Mixed Conribuions ffi G ;G ± ; ( or H SM ), Ligh Conribuions (using pah inegral formulaion, diagrammaic compuaion and FeynArs, FormCalc programs) T.Hahn, hep-ph/226, T.Hahn, M.Pérez-Vicoria, Compu.Phys.Com.8 (999) 53, hep-ph/ hp://

8 MSSM HIGGS SELF-INTERACTIONS IN THE DECOUPLING LIMIT ffl One-loop conribuions: (n) = M 2 Z +M 2 A 2 6 4O 2 6 A + O ffl M 2 EW M 2 Z ;M2 W ;M2 M EW 2 μ A B + M 2 A ffl μ 2 C A + O M 2 A C A + finie erms μ C A + finie erms - All poenial non-decoupling effecs of heavy Higgs MSSM paricles manifes as divergen conribuions in D = 4 and some finie conribuions, one of which is logarihmically dependen on M A and he oher one is quadraically dependen on M A. ffl Renormalized verex: (2) R = M 2 ; (3) R = (4) R = 3g 2M Z c W M 2 + 3g2 4M 2 Zc 2 W g3 64ß 2 c 3 W M 2 + g4 64ß 2 c 4 W M Z Ψ rem MSSM ; Ψ rem MSSM : where: M 2 = M 2 Z Ψ rem MSSM ο O 2 4O ψ! log M 2 EW μ 2 + log M 2 EW μ 2 A + finie erms A + log M 2 A μ 2 A + finie erms finie funcion dependen on fi, and ο-gauge dependen come only from ligh conribuions The quadraic heavy mass erms, M 2 A, disappear in he onshell renormalizaion procedure - The UV-divergence and he logarihmic dependence on M 2 A can be absorbed in he redefiniion of he Higgs boson mass M 2 - All poenial non-decoupling effecs of heavy Higgs bosons disappear, bu Ψ rem MSSM remains

9 SM HIGGS SELF-INTERACTIONS ffl The renormalized Higgs propagaor has a pole a M 2 H SM ffl Renormalized H SM self-couplings (2) R H SM (M 2 H SM ) = (3) R H SM = g3 64ß 2 c 3 W M Z Ψ rem SM ; (4) R H SM = g4 64ß 2 c 4 W Ψ rem SM : where: Ψ rem SM! finie funcion also ο-gauge dependen ffl Commens: - All divergen erms dissappear in he on-shell renormalizaion procedure - Some finie erms, included in Ψ rem SM, remain They are, in principle, differen o Ψ rem MSSM - HOWEVER, by idenifying MH 2 SM $ M ree2 h ' MZC 2 2 2fi decoupling limi, we have obained ha Ψ rem SM! Ψ rem MSSM in he ) The EW-finie erms are common o boh and H SM (in he SM afer renormalizaion of he rilinear and quaric couplings) if and only if M A fl M Z.

10 O(m 4 ) one-loop conribuions ffl We consider he large masses limi: ffl One-loop ~ diagrams m 2 ~ ;m 2 ~ 2 fl M 2 Z ;M2 h ; jm 2 ~ m 2 ~ 2 j fi jm 2 ~ + m 2 ~ 2 j : Green Funcions Counererms: ffi () ;ffi (2) ;ffi (3) ;ffi (4) ) ffiz H;2 ;ffiv;ffig2 ;ffig 2 ;ffim 2 ;ffim2 2 ;ffim2 2

11 ffl MSSM Renormalized verex funcions ^ ; ~ (2) = M 2 ; ^ ; ~ (3) = 3g 2M Z c W M 2 3 8ß 2 g 3 M 3 W ^ ; ~ (4) = 3g2 4M 2 Zc 2 W M 2 3 4ß 2 g 4 M 4 W m 4 ; m 4 : where: M 2 = 3 8ß 2 g 2 M 2 W m 4 log m 2 m ~ m ~ 2 - The UV-divergence cancel ou in he renormalizaion procedure, such ha he mass correcion M 2 is finie - The logarihmic erms in he heavy-squark masses disappear when he verices are expressed in erms of he Higgs-boson mass M ) hey decouple - bu lineal heavy mass erms O(m 4 ) remain - Wihou he non-logarihmic op-mass erm, he rilinear and quaric self couplings a he one-loop level have he same form as he ree level couplings, wih he ree-level Higgs mass replaced by he corresponding one-loop mass M 2 = M 2ree + M 2. ffl SM Renormalized rilinear and quaric self-couplings ^ (3) H = 3g3 8ß 2 M 3 W m 4 ; ^ (4) H = 3g4 4ß 2 M 4 W m 4 : The non-logarihmic op-mass erms are common o boh and H SM (in he SM afer renormalizaion of he rilinear and quaric couplings).

12 SUMMARY ffl Tree-level couplings are equal in he MSSM and in he SM in he decoupling limi ffl Finie erms are he same in boh models in he decoupling limi by idenifying M 2 H SM $ M ree 2 ' M 2 Z C2 2fi ffl Difference beween Renormalized MSSM and SM Higgs self-ineracions (2) R MSSM (2) R H SM SM = M 2 ; (3) R MSSM (3) R H SM SM = 3 v M 2 ; (4) R MSSM (4) R H SM SM = 3 v 2 M 2 : ffl The one-loop MSSM conribuions o he verex funcions in he asympoic limi eiher represen a shif in he mass and in he riple and quaric self-couplings, which can be absorbed in M, or reproduce he SM one-loop correcions The riple and quaric couplings hereby acquire he srucure of he SM Higgs-boson self-couplings. ffl DECOUPLING IF AND ONLY IF M A fl M Z

13 O(m 4 ) conribuions o hhh= hhh M ~Q ο M ~U ο 5 TeV ; μ ο ja j ο :5 TeV ) jm 2 ~ m 2 ~ 2 j fi jm 2 ~ + m 2 ~ 2 j! Large op-quark/squark correcions, even for large M A Exac resul Asympoic resul 3. λ hhh /λ hhh an β = 5 an β = an β = M A [GeV]! The radiaive correcions dissappear when hhh is expressed in erms of M Exac resul for M 2 h o /M 2 ho Exac resul for λ hhh /λ hhh Asympoic resul for λ hhh /λ hhh an β

14 Trilinear self-couplings ffl Exac analyical resuls for ~ conribuions o he rilinear self-couplings. hhh = 3g3 32ß 2 M 3 W m 4 cos 3 ff sin 3 fi 8 >< >: 3logm2 ~ m 2 ~ 2 m 4 + ::: 9 >= >; We agree wih he resuls given in V. Barger, M. S. Berger, A. L. Sange, R. J. Phillips, Phys. Rev. D45 (992) 428; P. Osland, P. N. Pandia, Phys. Rev. D59 (999) 553; hep-ph/99295; hep-ph/99227 ffl Numerical analysis: - The SUSY parameers have been aken o be M ~Q ο TeV ; M ~U ο μ ο ja j ο 5 GeV m m ~ and m ~ 2, are heavy as compared o he o he elecroweak scale, bu heir difference is of O(M ~U ) m 2 ~ ;m 2 ~ 2 fl M 2 Z ;M 2 ; jm 2 ~ m 2 ~ 2 j ' jm 2 ~ + m 2 ~ 2 j : - The radiaive correcion o he ff angle is included.

15 .3.2 M 2 h o /M 2 h o λ hhh /λ hhh an β=5. an β= an β= M A [GeV].3.2 M 2 h o /M 2 h o for M o A = 2 GeV λ hhh /λ for M hhh Ao = 2 GeV M 2 o h /M 2 o o h for M A = TeV λ hhh /λ for M hhh Ao = TeV an β - Large correcion which decrease wih an fi - The relaion hhh = hhh ß M 2 =M 2 ree small difference which remains also for large M A is fulfilled up o a

16 SUMMARY ffl For heavy sop sysem wih large mass spliing, O(M SUSY ), he O(m 4 ) correcions o he rilinear h self-couplings are large, bu heir main par can again be absorbed in he mass M. ffl The genuine loop correcions o he riple couplings, afer re-expressing hem in erms of M, is of he order of a few per cen! They are larges for low an fi and M A, ypically 5%.! For large M A, hey decrease o he level of %. ffl No possible o measure a TESLA ffl Similar resuls have been obained for he quaric selfcoupling.

17 CONCLUSIONS ffl We showed analyically ha Higgs secor and O(m 4 ) oneloop conribuions o he self-couplings : - Decouple when he self-couplings are expressed in erms of he Higgs-boson mass, in he limi of large M A and heavy op squarks, wih masses close o each oher. ) The riple and quaric couplings acquire he srucure of he SM Higgs-boson self-couplings. Decoupling if and only if M A fl M Z. ffl For large mass spliing in he sop secor, he correcions o he riple couplings, afer re-expressing hem in erms of M, is of he order of a few per cen Examples: For low an fi and M A, ypically 5%. For large M A, hey decrease o he level of %. - Similar resuls have been obained also for he quaric self-coupling. The self-ineracions are very close o hose of he SM Higgs boson for he heavy sop secor and would need high-precision experimens for heir experimenal verificaion. No possible a TESLA ffl IN PROGRESS: - Explore boh numerically and analyically complee radiaive correcions o self-couplings and Phenomenological implicaions