Higgs to tau muon in a MSSM flavor extended model XV Mexican - PowerPoint PPT Presentation

Higgs to tau muon in a MSSM flavor extended model Higgs to tau muon in a MSSM flavor extended model XV Mexican Workshop on Particles and Fields XV Mexican Workshop on Particles and Fields Rafael Espinosa Casta˜ neda Rafael Espinosa Casta˜ neda Thesis Ad- Thesis Advisor:PhD. Melina G´ omez Bock visor:PhD. Melina G´ omez Bock Universidad de las Am´ ericas Puebla Motivation rafael.espinosaca@udlap.mx of the Research Experimental November 3, 2015 Motiva- tion FV Standard Model MSSM Ansatz for FV in

Overview Higgs to tau muon in a MSSM flavor extended Motivation of the Research 1 model Experimental Motivation XV Mexican Workshop on FV Standard Model 2 Particles and Fields Rafael MSSM 3 Espinosa Casta˜ neda Thesis Ad- visor:PhD. Ansatz for FV in MSSM Melina 4 G´ omez Bock Motivation Calculations with the Ansatz 5 of the Research Experimental Motiva- Conclusions tion 6 FV Standard Model MSSM Ansatz for FV in

Reports of Flavour Violation in CMS and ATLAS Higgs to tau muon in a MSSM flavor extended model XV CMS Mexican 2014/07/05 Workshop on Standard desviation of the Branching Ratio BR ( h 0 − > τµ ): 3.0 σ of the Standard Particles Model Prediction and Fields Experimental Branching Ratio: (0 . 89 +0 . 4 − 0 . 37 ) x 10 − 2 Rafael Espinosa 2015/08/21 Casta˜ neda Standard desviation of the Branching Ratio BR ( h 0 − > τµ ): 2.4 σ of the Standard Thesis Ad- visor:PhD. Model Prediction Melina G´ omez Experimental Branching Ratio: (0 . 84 +0 . 39 − 0 . 37 ) x 10 − 2 Bock ATLAS Upper limit BR( h 0 → τµ ) < 1 , 87 x 10 − 2 Motivation of the Research Experimental Motiva- tion FV Standard Model MSSM Ansatz for FV in

The Standard Model Higgs to tau muon in a MSSM flavor extended model XV Mexican The Model explains three of the fundamental forces of Nature (weak, strong and Workshop electromagnetic). It is used in all experimental calculations. on Particles and Fields L = − 1 4 F µν F µν + i ¯ D Ψ + hc . + Ψ i Y ij Ψ j Φ + hc . + | D µ Φ | 2 − V (Φ) Ψ ✚ (1) Rafael Espinosa 4 F µν F µν represents the electromagnetic interaction, i ¯ where − 1 ✚ Casta˜ neda Ψ D Ψ + hc . represents Thesis Ad- the interaction of fermionic fields, Ψ i Y ij Ψ j Φ + hc . represents the interaction of the visor:PhD. bosonic field with the fermionic field, | D µ Φ | 2 represents the interaction of the Higgs Melina G´ omez field with the fermionic field and V (Φ) is the Higgs Potential. Bock Motivation of the Research Experimental Motiva- tion FV Standard Model MSSM Ansatz for FV in

SUSY Transformations from bosonic fields to fermionic fields and viceversa. Higgs to tau muon in a MSSM δφ = ǫψ, δφ ∗ = ǫ † ψ † (2) flavor extended � model d 4 x δ L = 0 δ S = (3) XV Mexican where where ǫ is an infinitesimal, anticommuting, two-component Weyl fermion Workshop on object parameterizing the supersymmetry transformation Particles and Fields Rafael Espinosa Casta˜ neda Thesis Ad- visor:PhD. Melina G´ omez Bock Motivation of the Research Experimental Motiva- tion FV Standard Model MSSM Ansatz for Figure : The super-partner particles FV in

MSSM Higgs to tau muon in a MSSM flavor extended model XV Minimum number of Higgs doblets for Supersymmetrize the Standard Model. Mexican Workshop on 1)It can explain Dark Matter Particles and Fields 2)Radiative Higgs boson mass correction quadratic divergences vanish. m H receives Rafael enormous quantum corrections from the virtual effects of every particle that couples, Espinosa directly or indirectly, to the Higgs field Casta˜ neda Thesis Ad- visor:PhD. 3)It could be considered that it extends the Standard Model naturally.(Requiring the Melina G´ omez SUSY transformation) Bock Motivation 4) It could join gravity (super-gravity) of the Research Experimental Motiva- tion FV Standard Model MSSM Ansatz for FV in

MSSM soft Supersymmetry-Breaking Higgs to tau muon in a MSSM flavor extended model XV Mexican Within the MSSM, this soft Lagrangian includes the following terms Workshop on L soft = L mass sfermion + L mass bino + L mass wino + L mass Particles gluino + L Higgsino + L h 0 ˜ (4) f j ˜ f k and Fields In order to establish the free parameters of the model coming from this Lagrangian, Rafael we write down the form of the slepton masses and the Higgs- slepton-slepton Espinosa Casta˜ neda couplings, the first and last term of eq. 4 , which are given as Thesis Ad- visor:PhD. E k † − m 2 Melina ˜ E j ˜ ˜ L k − ( A e , jk ˜ E j ˜ soft = − m 2 l ¯ ¯ L , j , k ˜ L j † ˜ ¯ L k H 1 + h . c ) G´ omez L (5) ˜ ˜ Ejk Bock Motivation of the Research Experimental Motiva- tion FV Standard Model MSSM Ansatz for FV in

MSSM extended in Flavour Ansatz Higgs to tau muon in a MSSM In principle, any scalar with the same quantum numbers could mix through the soft flavor extended SUSY parameters. This general mixing includes the parity superpartners fermionic model labels, and leads us to a sfermion mass matrix given as a squared 6 × 6 matrix, which XV can be written as a block matrix as Mexican Workshop on Particles and Fields � M 2 M 2 � ˜ M 2 LL LR f = (6) M 2 † ˜ M 2 Rafael LR RR Espinosa where Casta˜ neda Thesis Ad- visor:PhD. + 1 L + M (0)2 M 2 m 2 2 cos 2 β (2 m 2 W − m 2 Melina = Z ) I 3 × 3 , (7) LL ˜ l G´ omez Bock E + M (0)2 − cos 2 β sin 2 θ W m 2 M 2 M 2 = Z I 3 × 3 , (8) ˜ RR l Motivation of the A l v cos β − M (0) M 2 = √ µ tan β. (9) Research LR l 2 Experimental Motiva- tion where M (0) is the lepton mass matrix. FV l Standard Model MSSM Ansatz for FV in

MSSM extended in Flavour Ansatz Higgs to tau muon Current data mainly suppress the Flavour mixing associated with the first two slepton in a families, but allow considerable mixing between the second and third slepton families MSSM flavor Thus, our proposal includes dominant terms that mix the second and third families, as extended model follows XV Mexican   0 0 0 Workshop A LO = A ′  A 0 , l = 0 (10) w z on  Particles 0 y 1 and Fields The dominant terms give a 4 × 4 decoupled block mass matrix, in the basis Rafael e L , ˜ ˜ e R , ˜ µ L , ˜ µ R , ˜ τ L , ˜ τ R , as Espinosa Casta˜ neda Thesis Ad-  m 2  ˜ 0 0 0 0 0 0 visor:PhD. m 2 0 ˜ 0 0 0 0 Melina   0 G´ omez  m 2  0 0 ˜ 0 X τ A z M 2 ˜ Bock   l = 0 , (11) ˜  m 2  0 0 X τ ˜ A y 0   0 Motivation  m 2  0 0 0 A y ˜ X µ   of the 0 m 2 0 0 A z 0 X µ ˜ Research 0 Experimental Motiva- 1 with X 3 = 2 A 0 v cos β − µ m τ tan β and X 2 = A w − µ m µ tan β . Where µ is the √ tion SU (2) − invariant coupling of two different Higgs superfield doublets, A 0 is the FV Standard trilinear coupling scale and tan β = v 2 v 1 is the ratio of the two vacuum expectation Model values coming from the two neutral Higgs fields, these three are MSSM parameters MSSM Ansatz for FV in

Higgs to tau muon in a In order to obtain the physical slepton eigenstates, we diagonalize the 4 × 4 mass MSSM sub-matrix given in (11).For simplicity we consider that z = y , which represent that flavor extended the mixtures ˜ µ L ˜ τ R and ˜ µ R ˜ τ L are of the same order . The rotation will be performed model to this part using an hermitian matrix Z l , such that XV Mexican Z † l M 2 l Z l = ˜ M 2 Workshop Diag , (12) ˜ on Particles where and Fields  m 2  ˜ X τ 0 A y 0 m 2 X τ ˜ A y 0 Rafael M 2   0 l =  . (13) ˜  m 2  Espinosa 0 ˜ A y X µ  0 Casta˜ neda m 2 A y 0 X µ ˜ Thesis Ad- 0 visor:PhD. Melina G´ omez 1 Bock A z = 2 zA 0 v cos β √ Motivation 1 A y = 2 yA 0 v cos β √ of the Research 1 A w = 2 wA 0 v cos β √ Experimental Motiva- tion Table : Explicit terms of the sfermion mass matrix ansatz. FV Standard Model MSSM Ansatz for FV in

Masses to the supersymmetric particles Higgs to tau muon in a MSSM flavor extended model Having new general physical non-degenerate slepton masses XV Mexican Workshop 1 on m 2 m 2 = 2 (2 ˜ 0 + X τ + X µ − R ) ˜ Particles µ 1 and Fields 1 m 2 m 2 = 2 (2 ˜ 0 − X τ − X µ + R ) µ 2 ˜ Rafael Espinosa 1 m 2 m 2 Casta˜ neda = 2 (2 ˜ 0 − X τ − X µ − R ) τ 1 ˜ Thesis Ad- visor:PhD. 1 Melina m 2 m 2 = 2 (2 ˜ 0 + X τ + X µ + R ) (14) G´ omez τ 2 ˜ Bock � Motivation y + ( X τ − X µ ) 2 , X τ = 1 4 A 2 where R = 2 A 0 vcos ( β ) − µ susy m τ , √ of the Research X µ = A 0 vcos ( β ) − µ susy m µ tan ( β ) Experimental Motiva- tion FV Standard Model MSSM Ansatz for FV in