Probing lepton flavour violation in the Higgs sector with hadronic! decays

Transcription

1 Probing lepton flavour violation in the Higgs sector with hadronic! decays Los Alamos National Laboratory LUPM & L2C, Montpellier February 13, 2014 In collaboration with : Alejandro Celis, IFIC Valencia Vincenzo Cirigliano, LANL Phys. Rev. D. 89 (2014) [ArXiv: [hep-ph]]

2 Outline : 1. Introduction and Motivation 2. Framework: 2HDM and beyond 3. CP-even Higgs with LFV 4. CP-odd Higgs with LFV 5. Conclusion and Outlook 2

3 1. Introduction and Motivation

4 1.1 Introduction Discovery of a 125 GeV scalar particle : Standard Higgs? Need to study its properties Consider the possibility of non-standard LFV couplings of the Higgs arise in several models Goudelis, Lebedev,Park 11 Davidson, Grenier 10 Conveniently parametrized by effective interaction! ( )! + h.c L Y =!m k f k L f k! R! Y ij f i j Harnick, Koop, Zupan 12 L f R Blankenburg, Ellis, Isidori 12! McKeen, Pospelov, Ritz 12 Arhrib, Cheng, Kong 12 h m SM i In the SM : Y ij =! ij v In full generality parametrization of the Yukawas!! m i! Yii = yi v real for! " h CP-even Higgs! Assumption: CP conservation Y! ij Imaginary for! " A CP-odd Higgs 4

5 1.1 Introduction! Y EFT L d=6 =!! 'ij! f! 2 L i j ( f R ) H H H ( ) + h.c. +...! Y mediates LFV Higgs and generates at low energy! 4 fermions operators! Dipole (loops) 5

6 1.2 Constraints on LFV Higgs couplings Results : Harnick, Koop, Zupan 12 From LHC : best constraints on h! µ, h!e Bounds from flavour factories : MEG, Belle, Babar and LHCb for! 3µ" Strong constraint from! µ# loop induced process, very sensitive to UV completion Model dependent N.B.: Diagonal couplings set to the SM values 6

7 1.3 Constraints from hadronic! decays (! µ$$) Most of the time not taken into account but important because tree level Higgs exchange less sensitive to UV completion Contribution from tree level Higgs exchange + PDG 12 Complementary analysis between LHC and flavour physics : crossed channel! two different energy scales :! LHC: perturbative QCD! Flavour factories: intermediate energy, use of ChPT + dispersion relations Very interesting processes to look at! 7

8 2. Framework: 2HDM and beyond

9 2.1 Introduction Two Higgs doublet models, specific gauge-invariant framework LFV for both CP-even and CP-odd Higgs bosons at tree level ( )! a, a=1,2 0! T a (x) 0 = 1, % 1 = 0, % = % 1 % 2" 2 v a ei! a,0 & & & " v = v v 2 2 Higgs basis:, tan! = v 2 v 1 "! % ( 1 cos! sin! $ #!! ' = * 2 & )* sin!!cos! + "" % - 1,- $ # e!i! " ' 2 &! 1 = " $ $ # $ G ± ( ) 12 v + S 1 + ig 0 % ' ' &',! 2 = " $ $ # $ 1 H ± ( ) 2 S 2 + is 3 % ' ' &' 9

10 2.2 The Model! 1 = " $ $ # $ G ± ( ) 12 v + S 1 + ig 0 % ' ' &',! 2 = " $ $ # $ 1 H ± ( ) 2 S 2 + is 3 % ' ' &' Goldstones: G +/-, G 0 Mass eigenstates:! i 0 (x) = {h(x), H(x), A(x)} = R ij S j (x) CP conserving scalar potential:! h $ ( # & * # H & = * # " A & * % ) cos! sin! 0 'sin! cos! ! -# -# -#," S 1 S 2 S 3 $ & & & % Gauge couplings: 10

11 2.3 Yukawa Interactions In the Standard Model : one Higgs doublet "! = $ $ #! +! 0 % ' ' & # $!! " i! 2! * % & Q L '! u ' ' ( L,d L ) SSB Diagonalization Yukawa proportional to masses No Flavour-Changing Neutral Currents at tree level CKM unitary GIM mechanism 11

12 2.3 Yukawa Interactions In the 2HDM SSB M f fermion mass matrices and " f arbitrary complex matrices (Yukawa of # 2 ) 12

13 2.3 Yukawa Interactions Diagonalization M f becomes diagonal but " f remain arbitrary complex FCNCs! Suppress FCNCs: e.g., type III : (! f ) =! ij ij m i m j Recover the effective Lagrangian L Y =!m k f k L f k! R! Y ij f i j! ( L f R )! + h.c. +...! with the matching conditions : and 13

14 2.3 Yukawa Interactions Diagonalization M f becomes diagonal but " f remain arbitrary complex FCNCs! Suppress FCNCs: e.g., type III : (! f ) =! ij ij m i m j Recover the effective Lagrangian L Y =!m k f k L f k! R! Y ij f i j! ( L f R )! + h.c. +...! In the following: We will constrain LFV couplings of! h: 125 GeV CP-even Higgs (H is not considered here)! A: CP-odd Higgs 14

15 3. CP-even Higgs with LFV

16 3.1 Constraints from! µ$$" Tree level Higgs exchange h + h! Y Problem : Have the hadronic part under control, ChPT not valid at these energies! Use form factors determined with dispersion relations matched at low energy to CHPT Dreiner, Hanart, Kubis, Meissner 13 16

17 3.1 Constraints from! µ$$ Tree level Higgs exchange h + h with the form factors: h f ( y q ) 17

18 3.1 Constraints from! µ$$ Contribution from dipole diagrams! = cq + cq + hc.. eff L L! R R! with the dim-5 EM penguin operators : e!" Q = m ( µ% P $ ) F 8& L#, R# 2 $ L, R!" with the vector form factor : ( Y ) CLR, = f!µ Diagram only there in the case of! # $ µ # " + " # absent for neutral mode more model independent # # 0 0! $ µ "" 18

19 3.2 Determination of the FFs: dispersion relations Knowing the discontinuity of write a dispersion relation for it Cauchy Theorem and Schwarz reflection principle F(s) = 1 F(s')! ds'! s'! s F 1 2i!! disc! " F(s') # $ " ds' s'! s! i! 4 M! 2 F(s) = 1!! Im! " F(s') # $ " ds' s'! s! i! 4 M! 2 2 sth " 4m! F can be reconstructed everywhere from the knowledge of Im! " F(s) # $ F s!" If doesn t converge fast enought for subtract the DR F(s) = P n!1 (s) + sn! & ' 4 M! 2 ds' Im" # F(s') $ % s 'n s'! s! i! ( ) P n-1 (s) polynomial 19

20 3.2 Determination of the form factors : F V (s) Vector form factor! Precisely known from experimental measurements + " + " ee!! $ 0 $ # and (isospin rotation)! % " " #!! Theoretically: decay very well described by resonances Folllowing properties of analyticity and unitarity of the FF Dispersive parametrization for F V (s) * F V (s) = exp, '!, V + ( ) s m + 1 2! 2! '' '2!! V V! Determined from a fit to the Belle data " $ # s m! 2 % ' & 2 + s3! $ 0 $! % " " #! Guerrero, Pich 98, Pich, Portolés 08 Gomez, Roig 13 - ( ds'! V (s') / ) 2 4m s' 3! ( s'! s! i! )/. Extracted from a model including 3 resonances '(770), ' (1465) and ' (1700) fitted to the data 20

21 3.2 Determination of the form factors : F V (s) Very precise determination of F V (s) thanks to very precise measurements of Belle! 21

22 3.2 Determination of the form factors : ( $ (s), ) $ (s), % $ (s) With one channel, in the energy region $$ $$ unitarity the discontinuity of the form factor is known Phase of the FF is $$ scattering phase Known from experiment 1 2i disc F ( s) = Im F ( s) = F ( s) sn i! s) e I I I I ( I " i! ( s) Watson s theorem Use analyticity to reconstruct the form factor in the entire space: Omnès representation: F ( s) = P ( s)! ( s) I I I polynomial Omnès function 2 sth " 4m! + I % s $ ds' # I ( s') & ( s) = exp '! -sth s' s' ) s i" ( * ), P I (s) not known but determined from a matching to CHPT at low energy 22

23 3.2 Determination of the form factors : ( $ (s), ) $ (s), % $ (s)! µ$$ Two channels contribute $$ and Generalisation of the previous method : Unitarity 2 2 ( ) ( ) 2 4 m! < s< m" # mµ ~ 1.77 GeV KK Donoghue, Gasser, Leutwyler 90 Moussallam 99 Scattering matrix $$ $$, $$ KK KK $$, KK KK Solve the dispersive integral equations iteratively starting with Omnès functions According to Muskhelishvili, 2 sets of solutions {C 1 (s), D 1 (s)}, {C 2 (s), D 2 (s)} FFs linear combinations :! ( s) = P ( s) C ( s) + Q ( s) D ( s) n! n! n Determined from a matching to ChPT + lattice 23

24 3.2 Determination of the form factors : ( $ (s), ) $ (s), % $ (s) Inputs : Several inputs solve the Roy-Steiner equations Ananthanarayan et al 01, Colangelo et al 01 Buettiker, Descotes, Moussallam 02 Inelasticity $$ scattering 24

25 3.2 Determination of the form factors : ( $ (s), ) $ (s), % $ (s) Inputs : $$ KK A large number of theoretical analyses Descotes-Genon et al 01, Kaminsky et al 01, Garcia-Martin et al 09, Colangelo et al. 11 and all agree 3 inputs: * $ (s), * K (s), + from B. Moussallam reconstruct T matrix 25

26 26

27 (s) [GeV 2 ] Moduli: "! " (s) [GeV 2 ] f s [GeV 2 ] s [GeV 2 ] 4 (s) [GeV 2 ] f 0 f s [GeV 2 ] 27

28 3.3 Results Dominated by! '(770) (photon mediated)! f 0 (980) (Higgs mediated)! f0 Belle except for * CLEO 97 28

29 2.4 Comparison with ChPT ChPT, EFT only valid at low energy for It is not valid up to E =! 29

30 3.4 Comparison with ChPT Rigorous treatment of hadronic part bound reduced by one order of magnitude! Very robust bounds! ChPT, EFT only valid at low energy for (! µ ) not valid up to E = m " m! p << " = 4! ~ 1 GeV f! 30

31 4. CP-odd Higgs with LFV

32 4.1 Constraints from! lp Tree level Higgs exchange A + A! Y Mediate only one pseudoscalar meson very characteristic! 32

33 4.1 Constraints from! lp Tree level Higgs exchange! +, + with the decay constants :! $ : 33

34 4.2 Results! µp BaBar 06 10, Belle A 2 A 2 µ!!µ Z = Y + Y (*) : No contribution from effective dipole operator or CP-even Higgs N.B.: Diagonal couplings y A = 1 f 34

35 4.2 Results! ep BaBar 06 10, Belle A 2 A 2 e!! e Z = Y + Y (*) : No contribution from effective dipole operator or CP-even Higgs N.B.: Diagonal couplings y A = 1 f 35

36 4.3 Prospects at LHC see also e.g., Assamagan, Deandrea, Delsart 03 Davidson & Verdier 12 Arana-Catania, Arganda, Herrero 14 Decay width : Assumption : only SM channels ( A " gg, bb, cc,!!... ) are important Large BR for A "!µ can be expected since A does not couple to WW, ZZ at tree level. Results : A N.B.: Diagonal couplings y = 1 36 f

37 5. Conclusion and Outlook

38 5.1 Conclusion We have studied the LFV mode! µ$$ for constraining LFV couplings of the Higgs Very interesting and important :! The more model independent (tree level exchange of Higgs)! Same process can be studied at LHC and at the flavour factories with totally different experimental and theoretical conditions! Very little hadronic uncertainties : using form factors and dispersion relations + ChPT More robust bounds! Phenomenology of CP-odd Higgs, very peculiar pattern decays through! lp, clear signature 38

39 5.2 Oulook The more model independent process is! " µ! " 0 " 0! no loop induced processes! the only experimental bound from CLEO and weak ~10-5 need to be remeasured Dedicated experimental analyses The form factors can be used for EFT analyses of LFV 39

40 5. Back-up

41 1.2 Constraints on LFV Higgs couplings Constraints from! µ# (! e#, µ e#)! Interactions through loop diagrams 5 " m! 2 2 (! µ# ) 4 ( C L C R ) % & = + 64$ ( Y ) CLR, = f!µ + Harnick, Koop, Zupan 12! Strong bounds from flavour factories especially for µ" e# Constraints from! " 3µ! Tree level contribution subdominant, mainly dominated by loops +! m $ m %! µ ( 2 )( CL CR ) ( # ) ( m! ) " &(! ' 3µ ) = 12log log * +! Bounds from flavour factories + LHCb 41

42 Results for the fit of the $$ vector form factor 42

43 Details on the parametrization of the phase Model for the phase: tan! V = Im! F V (s) Re! F V (s) Guerrero, Pich 98, Pich, Portolés 08 Gomez, Roig 13 with and 43

44 Details on the fit The minimized quantity: 2 sum-rules are added such that F V (s)! 1 / s Brodsky & Lepage 44

45 Results for the $$ vector form factor 45

46 Determination of the polynomial General solution Fix the polynomial with requiring + ChPT: Feynman-Hellmann theorem: F P (s)! 1 / s (Brodsky & Lepage) At LO in ChPT: 46

47 Determination of the polynomial General solution Fix the polynomial with requiring + ChPT: Feynman-Hellmann theorem: F P (s)! 1 / s At LO in ChPT: 47

48 Determination of the polynomial General solution At LO in ChPT: Problem: large corrections in the case of the kaons! Use lattice QCD to determine the SU(3) LECs Dreiner, Hanart, Kubis, Meissner 13 Bernard, Descotes-Genon, Toucas 12 48

49 Determination of the polynomial General solution For $ P enforcing the asymptotic constraint is not consistent with ChPT The unsubtracted DR is not saturated by the 2 states Relax the constraints and match to ChPT 49

50 Determination of the polynomial General solution At LO in ChPT: Problem: large corrections in the case of the kaons! Use lattice QCD to determine the SU(3) LECs Dreiner, Hanart, Kubis, Meissner 13 Bernard, Descotes-Genon, Toucas 12 50

51 Determination of the polynomial General solution For $ P enforcing the asymptotic constraint is not consistent with ChPT The unsubtracted DR is not saturated by the 2 states Relax the constraints and match to ChPT 51

52 1.1 Introduction: LFV, probe of new physics Workshop Neutrino oscillations individual lepton family numbers are not conserved L e,µ,! «accidental» symmetries of the SM In the SM with massive neutrinos effective CLFV vertices are tiny due to GIM suppression unobservably small rates! E.g.: µ " e! 3! % m Br ( µ & e" ) = ' U U < M # i = 2,3 2 * µ i ei 1i 2 W 2 $ 54 Petcov 77, Marciano&Sanda 77 Extremely clean probe of beyond SM physics! =! +!! SM SM!" mass dim 4 Dirac or dim 5 Majorana 52

53 1.2 LFV: flavour factories & LHC Workshop E! BSM High energy: "if % FV ~ TeV sensitive to new resonances, direct discovery " if % FV >> TeV EFT approach pp $ R $ " " + X R = Z ', h,!,... pp #!!" +! " # X Low energy: if % LE << % FV EFT approach sensitive to scale + flavour structure of couplings! LE (5) (6) C (5) Ci (6)! =! SM + O + "... 2 O i +!! i Reconstruct the underlying dynamics ( ) ( ) µ " e!, µ " eee, µ A, Z " e A, Z # %! $, # %!!!, # %! Y! " " P, S, V, PP,... 53