Scalar leptoquarks from GUT to accommodate the B-physics anomalies

Transcription

1 Scalar leptoquarks from GUT to accommodate the B-physics anomalies Nejc Košnik Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

2 Lepton universality violation in charged and neutral currents Lepton (flavor) universality violation in V (τ) cb HFLAV SM dev R D 0.06(15) 0.5().6σ R D 0.407(46) 0.00(8).σ R D ( ) 4σ R J/ψ measurement points in the same direction: 0.0 < R J/ψ < Vs. R(J/ψ) LHCb = 0.71(17)(18) R(D*) BaBar, PRL109,10180(01) Belle, PRD9,07014(015) LHCb, PRL115,11180(015) Belle, PRD94,07007(016) Belle, PRL118,11801(017) LHCb, PRL10,17180(018) Average χ = 1.0 contours Average of SM predictions R(D) = 0.99 ± 0.00 R(D*) = 0.58 ± Summer 018 P(χ ) = 74% R(D) σ 4σ HFLAV 1 Cohen et al., 18 Isidori et al. 16 Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

3 Lepton universality violation in charged and neutral currents Lepton (flavor) universality violation in V (τ) cb HFLAV SM dev R D 0.06(15) 0.5().6σ R D 0.407(46) 0.00(8).σ R D ( ) 4σ R J/ψ measurement points in the same direction: 0.0 < R J/ψ < Vs. R(J/ψ) LHCb = 0.71(17)(18) LFUV in b sl + l LHCb SM dev. R K 0.745(97) 1.00(1).6σ R K low 0.660(11) 0.906(8).1σ R K 0.685(1) 1.00(1).6σ 4σ R(D*) BaBar, PRL109,10180(01) Belle, PRD9,07014(015) LHCb, PRL115,11180(015) Belle, PRD94,07007(016) Belle, PRL118,11801(017) LHCb, PRL10,17180(018) Average χ = 1.0 contours Average of SM predictions R(D) = 0.99 ± 0.00 R(D*) = 0.58 ± Summer 018 P(χ ) = 74% R(D) σ 4σ HFLAV 1 Cohen et al., 18 Isidori et al. 16 Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

4 Implications for New Physics R K ( ) 10% modification of the 1-loop GIM-suppressed amplitude R D ( ) 10% effect on the tree-level W exchange V cb. Can the two effects have common NP origin? What are typical mass scales of NP addressing the two LFUV phenomena? (Assume NP contributes to the SM operator with coupling 1) R K ( ) (b sµµ) SM: G F V ts V tb α (4π) ( sγ µ P L b)( µγ µµ) 1-loop NP: 1 (4π) Λ Tree-level NP: C 9 1 Λ Λ TeV Λ 0 TeV R D ( ) (b cτν) SM: G F V cb ( cb) V A ( lν) V A Tree-level NP: Λ TeV 1 Λ How to explain different sizes of the effects? 1 Different scales of NP for R K ( ) and R D ( ) Loop (R K ( )) Vs. tree (R D ( )) Suppression of NP couplings in R K ( ) compared to R D ( ) Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

5 Identifying a viable model Effective theory analysis focused on left-handed current operators C 1 Λ ( Q γ µ Q )( L γ µl ) + C Λ ( Q σγ µ Q ) ( L σγ µl ) [Buttazzo et al 17, Bhattacharya et al 14, Feruglio et al 16] As a single mediator particle, vector leptoquark U 1(, 1, /) is singled out [Buttazzo et al 17] UV complete setting needed (Pati-Salam, 41 model) [Assad et al 17, Bordone et al 17,18, Greljo et al 18, Di Luzio et al 17, Blanke, Crivellin et al 18, Calibbi et al 17] Scalar LQs are not UV sensitive, however single LQ does not work Two scalar LQs can generate left-handed operators and solve the B-anomalies [Crivellin 17] Two scalar LQs can also contribute to alternative Lorentz structures, no UV complete model available Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

6 Two light scalar LQ model SM + leptoquarks at 1 TeV, guided by SU() c SU() L U(1) Y R (,, 7/6) : Y ij R Q i l RjR + Y ij L ū Ri R L j mass basis (V Y R E R )ij ū Li l Rj R 5 + (Y R E R )ij dli l Rj R + (U R Y L ) ij ū Ri ν Lj R (U R Y L ) ij ū Ri l Lj R 5 ( ) ( ) Assumption: Y R E R = 0 0 0, U R Y L = 0 y cµ 0 0 yr bτ L yl cτ S (,, 1/) : Y ij Q C i iτ (τ k S k )L j mass basis (Y ) ij C d Li ν Lj S 1 + (V Y ) ij ūliν C Lj S GUT relation : Y ij d Li C l Lj S 4 (V Y ) ij ūlil C Lj S 1 ( ) ( ) Y = Y L = 0 cos θ sin θ 0 y cµ L yl cτ 0 sin θ cos θ Free parameters: m R, m S, complex y bτ R, y cµ L, y cτ L, θ Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

7 GUT framework for R and S SU(5) unified gauge group fermions 5i = (L, d R ) i, 10 i = (ē R, ū R, Q) i At unification scale M GUT gauge bosons of SU(5) (vector leptoquarks) couple leptons and quarks Scalar representations contain scalar leptoquarks: 4 breaks SU(5), M X,Y g GUT M GUT 45 contains R and S 50 contains R Yukawa couplings a ij 10 i 5 j 45 b ij 10 i 10 j 50 (b = b T, symmetric in flavor space) R and R mix via µ into light R and heavy R H. Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

8 GUT framework for R and S Matching onto effective theory results in the couplings considered in flavor and LHC where Y ij Q R i l RjR + Y ij L ū R Ri L j + Y ij Q i C iτ (τ k S k )L j Y L = a cos φ Y R = b sin φ, Y = a Assume φ = π/ (assumption is not crucial to further analysis) Proton destabilizing diquark interactions Q QS (10 i 10 j 45) can be forbidden.[doršner et al, 017] Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

9 Charged currents τ R ν L,µ,τ τ R τ L, µ L R / R / R 5/ R 5/ b µ, τ c ν Lµ,τ t, c, u ν L,µ,τ c µ, τ S 1/ S 1/ S / S 4/ t, c, u s, b } {{ } R D ( ) t, c, u s, b } {{ } R K ( ) Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

10 Charged currents τ R ν L,µ,τ τ R τ L, µ L R / R / R 5/ R 5/ b µ, τ c ν Lµ,τ t, c, u ν L,µ,τ c µ, τ S 1/ S 1/ S / S 4/ t, c, u s, b } {{ } R D ( ) t, c, u s, b } {{ } R K ( ) R D ( ) Dominant contribution by R via scalar and tensor interactions H = 4G F V cb [ gsl ( c R b L )( τ R ν L ) + g T ( c R σ µνb L )( τ R σ µν ν L ) ] yl cν g SL = 4g T = y R bτ 4 mr (g SL (m b ) 7g T (m b )) G F V cb Scalar and tensor B D form factors from lattice QCD [HPQCD 15, MILC 15] B D FFs extracted from exp. spectra using the heavy quark symm. [Bernlochner et al 18, HFLAV] Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

11 Charged currents constraints b cτν is the only charged-current affected by R B c τν taken into account Leptoquark state S affects many charged currents via charge 1/ component: ν Lµ,τ S 1/ µ, τ s, b t, c, u We consider the most relevant constraints: R µ/e = B(B D ( ) D( ) µ ν)/b(b D ( ) e ν) B τν B(K eν)/b(k µν) B(τ Kν)/B(K eν) Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

12 R K ( ) and neutral currents Explained by the S 4/ charge eigenstate τ R ν L,µ,τ τ R τ L, µ L R / R / R 5/ R 5/ b µ, τ c ν Lµ,τ t, c, u ν L,µ,τ c µ, τ S 1/ S 1/ S / S 4/ t, c, u s, b } {{ } R D ( ) t, c, u s, b } {{ } R K ( ) Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

13 R K ( ) and neutral currents S 4/ couples to left-handed fermions µ, τ S 4/ µ, τ Left-handed current operators with µ and τ Heff b sll = 4G F λ t C i (µ)o i (µ) O 9(10) = b, s i=7,9,10 e ( sl (4π) γ µb L )( lγ µ (γ 5 )l ) δc µµ 9 = δc µµ 10 = πv b, s y bµ ( y sµ ) λ tα em m S = πv sin θ and large mass supresses the S effect in R K ( ) cµ sin θ (yl ) λ tα em ms Use constraint on δc 9 = δc 10 determined from clean observables: R K ( ), B s µ + µ δc µµ 9 ( 0.85, 0.50) 1 1 In agreement with global analyses of b sµµ observables. [Capdevilla et al 17,... ] Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

14 Neutral current constraints B s B s, m s constraint, suppressed by θ [S ] m S s [ sin θ B(τ µγ) < [S and R ] Z ll constraints at LEP [S and R ] g τ V g e V = 0.959(9), ga τ ga e = (15), (y cµ L ) + (y cτ ) ] /m S g µ V g e V L = 0.961(61), g µ A g e A = (1) B(τ µφ) cos 4 θ(y cµ L y L cτ ) /ms 4 < , resolves θ = 0, π degeneracy [S ] Small effect in (g ) µ We predict the S contribution to R νν ( ) compare it with R νν ( ) <.7 [Belle 17] = B(B K ( ) νν)/b(b K ( ) νν) SM and Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

15 Flavor coupling analysis Perform a fit with fixed m R = 0.8 TeV, m S = TeV, variables y cµ cτ L,yL, Re yr bτ, Im yr bτ, mixing angle θ Larger mass m S and small sin θ suppress the effects in neutral currents relative to R D ( ) 0.5 m R = 0.8 TeV, m S =.0 TeV, θ π/ Im[g S τ ] 0.0 R D * R D Degeneracy of minima with θ 0, π/ is broken by τ µφ which selects -0.5 θ π/. S couplings to s-quark are suppressed ( ) ( ) ( ) Re[g τ S ] Y dl y cµ L yl cτ y cµ L yl cτ Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

16 Flavor coupling analysis m R = 0.8 TeV, m S =.0 TeV, θ π/ 0.5 Complex gs τ needed in order to reconcile R D and R D. Imaginary gs τ has strictly positive effect on R D ( ). Im[g S τ ] 0.0 R D * R D SM point is excluded at.8σ (5 degrees of freedom) Both R D ( ) and R K ( ) anomalies are reduced to < 1σ level Re[g τ S ] [Becirevic, Dorsner, Fajfer, Faroughy, NK, Sumensari, ] Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

17 Perturbativity Couplings defined at scale 1 TeV, renormalized with scale 16π d ln yr bτ d ln µ = y cµ L + y cτ L + 9 bτ yr + 1 y t +... Require Yukawa couplings of the two LQs to remain perturbative to the unification scale GeV Calculated with the SARAH package [Staub et al, 1] Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

18 Perturbativity Couplings defined at scale 1 TeV, renormalized with scale 16π d ln yr bτ d ln µ = y cµ L + y cτ L + 9 bτ yr + 1 y t +... Require Yukawa couplings of the two LQs to remain perturbative to the unification scale GeV Calculated with the SARAH package [Staub et al, 1] Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

19 LHC constraints t-channel pp τ + τ. Dominated by R, S only from b-quarks b, c τ+ b /,5/ 4/ R S τ b, c τ b Constrained by searches for heavy τ τ resonance τ+ [ATLAS, JHEP 1801, 055] Leptoquark pair production bounds the R mass mr = 0.8 TeV, ms = TeV, θ π/ LHC 1 TeV, 100 fb -1 - i yrbτ b b, c c τ τ ttττ b b τ τ ccν ν ylcτ Nejc Koˇsnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

20 Future tests LFV and ν modes in reach of future experiments Correlation between LFV observables B(B Kν ν) 1.5 B(B Kν ν) SM. Not included in the fit. To be improved by Belle LFV decays B(τ µγ) > B(B Kµ ± τ ) [1.1, 6.5] Current bound [BaBar 1] B(B K τµ) 1.9 B(B Kµτ) B(B s τµ) 0.9 B(B Kµτ) All LFV limits will be improved by LHCb and Belle Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18

21 Conclusion Presented model with two light leptoquarks, R (,, 7/6) and S (,, 1/) R accommodates R D ( ) via complex Scalar and Tensor couplings S accommodates R K ( ) via real C 9 = C 10 SU(5) GUT framework connects the couplings of R and S Flavor fit Light m R = 0.8 TeV, requires complex coupling yr bτ Heavier S =.0 TeV Complete resolution of R K ( ) and R D ( ) Well-defined GUT completion, perturbative couplings to high scales Model consistent with LHC constraints, preferred region can be probed at HL-LHC Predicted enhanced LFV signals in τµ sector as well as enhanced b sν ν modes Interesting target for future Belle and LHCb searches Nejc Košnik (JSI, Univ. of Ljubljana) Corfu Summer Institute / 18