Introduction H + decay to t ¯ b Conclusion Precision calculations in the MSSM H + decay to t ¯ b Hana Hluch´ a Institute for High Energy Physics Vienna March 2009 Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
Introduction H + decay to t ¯ b Conclusion Table of contents Introduction 1 MSSM theory plan and motivation work done so far H + decay to t ¯ b 2 review of several works on H + decay to t ¯ b tree-level one-loop level renormalization of the charged Higgs sector linear R ξ gauge running of the couplings resummation of leading tan β terms preliminary results Conclusion 3 Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
Introduction MSSM theory H + decay to t ¯ plan and motivation b Conclusion work done so far Brief Intro to MSSM MSSM: is the minimal supersymmetric extension of the SM supersymmetry: relates bosons and fermions minimal: minimal (=1) set of Susy generators Q , ¯ Q 1 minimal (=2) number of Higgs doublets 2 has the following particle spectrum SM with extended Higgs sector Susy partners fermions, higgses sfermions, higgsinos γ, ˜ W , ˜ gauge bosons ( g , γ, W , Z ) gauginos (˜ g , ˜ Z ) neutral gauginos + neutral higgsinos ⇒ neutralinos charged gauginos + charged higgsinos ⇒ charginos requires many new parameters: m A 0 , t β , µ , M 1 , M 2 , M 3 , A l , A u , A d , M E , M L , M D , M Q , M U (msugra: m 0 , m 1 2 , A 0 , sign( µ ), t β ) Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
Introduction MSSM theory H + decay to t ¯ plan and motivation b Conclusion work done so far plan and motivation plan long term: to create a numerical program for calculating full one-loop total decay widths and branching ratios for Susy and Higgs particles within the SPA convention motivation application to 1 → 3 and 2 → 3 processes with resonant propagators; total 1-loop widths are necessary for these one-loop calculations Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
Introduction MSSM theory H + decay to t ¯ plan and motivation b Conclusion work done so far work done so far our work - brief overview : we use the packages FeynArts, FormCalc, LoopTools, SPheno we have been developing a fully automatized generator for the calculation of decay processes we have been developing an automatic calculation of particle decay widths at one-loop level we have implemented all the 1-loop counterterms in a mathematica .m file calculated processes are UV and IR convergent soft radiation is included, hard radiation is implemented in fortran code for SSS, SFF, SSV, SVV configurations; works generally - also with clashing arrows and one zero fermion mass we have calculated the H + → t ¯ b process in the DR scheme and in the linear R ξ W ,ξ Z gauge ( R ξ γ, g gauge automatization is on the plan) our work is done within the SPA convetion Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level review of several works on H + decay to t ¯ b Bartl, Eberl, Hidaka, Kon, Majeroto, Yamada: QCD corrections to the decay H + → t ¯ b in the Minimal Sypersymmetric Standard Model , (1995) ֒ → complete QCD corrections, Susy-QCD comparable to SM-QCD in a large region of MSSM parameter space Jimenez, Sola: Supersymmetric QCD corrections to the top quark decay of a heavy charged Higgs boson , (1996) ֒ → comparison of Susy-QCD and SM-QCD Coarasa, Garcia, Guasch, Jimenez, Sola: Quantum effects on t → H + b in the MSSM: A window to ”virtual” supersymmetry? , (1996) ֒ → analysis of strong and electroweak one-loop effects on top quark decay, OS scheme, Standard QCD and Susy-QCD corrections have opposite sign → regions where Susy-EW corr. are not negligible Coarasa, Garcia, Guasch, Jimenez, Sola: Heavy charged Higgs boson decaying into top quark in the MSSM , (1997) ֒ → inclusion of leading EW corrections originating from large yukawas, comparable to QCD corrections in relevant portions of MSSM par. space Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level review of several works on H + decay to t ¯ b Eberl, Hidaka, Kraml, Majeroto, Yamada: Improved Susy QCD corrections to Higgs boson decays into quarks and squarks , (2000) ֒ → expansion of the Higgs decay width in terms of m b ( m H + ) → better convergence Carena, Garcia, Nierste, Wagner: Effective lagrangian for the ¯ tbH + interaction in the MSSM and charged Higgs phenomenology , (2000) ֒ → resummation of the dominant supersymmetric corrections proportional to tan β to all orders for large tan β Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level Tree level lagrangian: tb = H −† ¯ t ( y t P L + y b P R ) b = H −† ¯ L H + ¯ t ( h t c β P L + h b s β P R ) b where h t , h b are yukawa couplings. The CKM matrix is assumed to be diagonal. e e y t = √ 2 m W s w m t cot β, y b = √ 2 m W s w m b tan β tree-level width: κ b )( | y t | 2 + | y b | 2 )] b ) + ( m 2 H + − m 2 t − m 2 C F [ − 2 m t m b ( y ∗ t y b + y t y ∗ Γ 0 = 16 π m 3 H + � b ) 2 − 4 m 2 ( m 2 H + − m 2 t − m 2 t m 2 where κ = b note: tan β ∼ 20 → y 2 t ∼ 0 . 01 y 2 b Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level One-loop level corrected width κ C F [ − 2 m t m b ( y ∗ t Y b + Y t y ∗ Γ 1 = b ) 16 π m 3 H + +( m 2 H + − m 2 t − m 2 b )( y ∗ t Y t + y ∗ b Y b )] + Γ rad where y b , t + y ( v ) b , t + y ( w ) b , t + y ( c ) Y b , t = b , t DR scheme: y ( c ) b , t → only UV divergent part y ( w ) b , t → UV part + part due to LSZ formula ( y ( v ) b , t + y ( w ) b , t + y ( c ) b , t ) UV = 0 IR divergence present in: y ( v ) b , t , y ( w ) , LSZ , Γ rad b , t Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level charged Higgs sector The relevant parts of the tree level lagrangian read: ∂ µ G −† ∂ µ G − + ∂ µ H −† ∂ µ H − − ( m 2 H ± + t H ± H ± ) | H − | 2 L = G ± + t G ± G ± ) | G − | 2 − ( t G ± H ± ) G −† H − − t H ± G ± H −† G − ( m 2 − where: m 2 m 2 A 0 + m 2 = H ± W ± m 2 ξ ± W m 2 = G ± W ± �� 1 e � � − s 2 β s α / c β + c 2 � � s 2 β s α / c β + c 2 t H ± H ± = T h 0 β c α / s β + T H 0 β s α / s β 2 m W s w e = 2 m W s w [ T h 0 ( s α s β + c β c α ) + T H 0 ( − s β c α + c β s α )] t G ± H ± ✐ i τ H 0 tree-level: T H 0 = T h 0 = 0 , one-loop level: T H 0 → τ H 0 renormalization conditions: ∆ ∂ ˆ Γ H − H − ( p 2 ) � H ± ) | ∆ = ˆ H ± ) | ∆ = 0 , Γ H − H − ( m 2 ˆ Γ G − H − ( m 2 � = 1 2 � ∂ p 2 � p 2 = m 2 H ± 1 see for example Pierce and Papadopoulos, arXiv:hep-ph/9206257 2 ∆ - parts of t GH , t HH and Π( p 2 ) are taken Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level charged Higgs sector The above RCs lead to: m 2 m 2 A 0 + m 2 W 0 + δ m 2 A 0 + δ m 2 W + t ∆ H ± H ± − Π ∆ H − H − ( m 2 = H ± ) H ± − ˙ Π ∆ H − H − ( m 2 δ Z H − H − = H ± ) 2 (Π ∆ G − H − ( m 2 H ± ) − t ∆ δ Z G − H − = G − H − ) m 2 G ± − m 2 H ± n LSZ formula: S ( p 1 , . . . , p n ) ∼ G tr 3 0 ( p 1 , . . . , p n ) R 2 0 √ after field renormalization f → Zf : n S ( p 1 , . . . , p n ) ∼ G tr R ( p 1 , . . . , p n ) R R , where R R = R 0 / Z 2 in the DR scheme: R R = 1 − ˙ H ± ) ⇒ δ Z H − H − → − ˙ H ± ) − ˙ H − H − ( m 2 Π ∆ H − H − ( m 2 H − H − ( m 2 Π fin Π fin H ± ) 3 written for n fields of the same type Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
review of several works on H + decay to t ¯ Introduction b H + decay to t ¯ tree-level b Conclusion one-loop level linear R ξ gauge By a proper modification of the packages FeynArts and FormCalc, we are now able to get a working numerical code in the general R ξ gauge (except photon/gluon gauge - on the plan). We have checked the gauge independence of the calculated result. notice: α m t ∆ m ξ =1 − ∆ m ξ A 0 ( m 2 Z ) − A 0 ( ξ m 2 Z ) + 2 A 0 ( m 2 W ) − 2 A 0 ( ξ m 2 � � t = W ) t 32 π m 2 w s 2 w ∆ m 1 − 0 0 200 400 600 800 1000 t PDG: m t = 171 . 2 ± 2 . 1 GeV 1.2 1.2 1. 1. SPheno: RGEs in Landau gauge 0.8 0.8 SEs in Feynman gauge 0.6 0.6 0.4 0.4 0.2 0.2 0 0 µ -scale 0 200 400 600 800 1000 Hana Hluch´ a HEPTOOLS meeting, Lisbon, 2009
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