Flavour physics beyond the Standard Model

Transcription

1 Young Experimentalists and Theorists Institute, IPPP Durham, 15 January 2014 Flavour physics beyond the Standard Model David M. Straub Junior Research Group New Physics Excellence Cluster Universe, Munich

2 Outline 1 Introduction Why physics beyond the SM? Why flavour physics as a probe of BSM? 2 New physics in meson mixing Model-independent discussion Implications for NP models 3 New physics in rare decays B X s γ and dipole operators B s µ + µ and scalar operators B K µ + µ and new physics in b s transitions David Straub (Universe Cluster) 2

3 The Standard Model [Photo: Ph. Tanedo, see David Straub (Universe Cluster) 3

4 Why physics beyond the SM? We know from observations that physics BSM exists dark matter neutrino masses baryogenesis... and we also have strong theoretical reasons to expect it quantization of charges flavour puzzle... David Straub (Universe Cluster) 4

5 Flavour puzzle L Yukawa = q L Y u HuR + q L Y d Hd R + l L Y l He R 10 e ud Μ,s cτ b t 4 V = 13 What is the origin of the peculiar structure of fermion masses and mixings? David Straub (Universe Cluster) 5

6 Why physics beyond the SM? We know from observations that physics BSM exists dark matter neutrino masses baryogenesis... and we also have strong theoretical reasons to expect it quantization of charges flavour puzzle... What is the scale Λ at which new physics shows up? David Straub (Universe Cluster) 6

7 The gauge hierarchy problem The Higgs mass receives contributions from all the heavy particles it couples to Our knowledge of the existence of the Higgs and of new physics leaves 3 options: 1. enormous fine-tuning in the fundamental high-scale parameters 2. Higgs is part of a SUSY multiplet 3. Higgs is not elementary Naturalness requires new physics at the TeV scale! David Straub (Universe Cluster) 7

8 SM as effective theory Any new physics that is too heavy for us to produce directly (yet) can show up as a new local interaction among SM fields = a higher dimensional operator L = L SM + d>4 i c i O(d) Λd 4 i At D = 5: neutrino mass term ( LL ɛh)(h T ɛl L ) Needed anyway to explain neutrino oscillations At D = 6: numerous operators, including flavour-changing ones such as ( Qi L γ µ Q j L )2 David Straub (Universe Cluster) 8

9 } } Introduction Meson mixing Rare decays Flavour physics beyond the SM How to probe higher-dimensional operators? Need to look at observables that can be measured to an extreme precision and/or are suppressed in the SM but not necessarily beyond the SM Examples (g 2) µ Electric dipole moments Charged lepton flavour violation flavour-changing neutral currents b LFVtbf tl W } g,γ,z yfv td F dl V tdfdl b LF Vtbf tlf } } W W d L V tdfu,c,t LfV tb b L David Straub (Universe Cluster) 9

10 FCNCs are strongly suppressed in the SM because they arise only at the loop level because quark mixing is so hierarchical (off-diagonal CKM elements 1) because of the GIM mechanism because only the left-handed chirality participates in flavour-changing interactions Any of these conditions could be violated by physics beyond the SM. That s why FCNCs are so important! David Straub (Universe Cluster) 10

11 Bounds on the scale of new physics [Isidori et al ] L = L SM + i c i O(D) ΛD 4 i Operator Bounds on Λ in TeV (c ij = 1) Observables Re Im ( s L γ µ d L ) m K ; ɛ K ( s R d L )( s L d R ) m K ; ɛ K ( c L γ µ u L ) m D ; q/p, φ D ( c R u L )( c L u R ) m D ; q/p, φ D ( bl γ µ d L ) m Bd ; S ψks ( br d L )( bl d R ) m Bd ; S ψks ( bl γ µ s L ) m Bs ( br s L )( bl s R ) m Bs David Straub (Universe Cluster) 11

12 Bounds on the scale of new physics [Isidori et al ] L = L SM + i c i O(D) ΛD 4 i David Straub (Universe Cluster) 11

13 Bounds on the scale of new physics [Isidori et al ] L = L SM + i c i O(D) ΛD 4 i TeV-scale NP cannot have a generic flavur structure! David Straub (Universe Cluster) 11

14 Collider vs. flavour searches natural Higgs unnatural Higgs Λ [TeV] the collider frontier c If direct searches find new states at scale Λ, flavour physics measures the flavour couplings In the absence of signals in direct searches: for generic flavour violation, flavour physics probes very high scales David Straub (Universe Cluster) 12

15 Collider vs. flavour searches natural Higgs unnatural Higgs Λ [TeV] the collider frontier minimal flavour viol c the flavour frontier generic flavour viol. If direct searches find new states at scale Λ, flavour physics measures the flavour couplings In the absence of signals in direct searches: for generic flavour violation, flavour physics probes very high scales David Straub (Universe Cluster) 12

16 1 Introduction Why physics beyond the SM? Why flavour physics as a probe of BSM? 2 New physics in meson mixing Model-independent discussion Implications for NP models 3 New physics in rare decays B X s γ and dipole operators B s µ + µ and scalar operators B K µ + µ and new physics in b s transitions David Straub (Universe Cluster) 13

17 b b Introduction Meson mixing Rare decays Flavour physics beyond the SM Meson-antimeson mixing in the SM In the SM, M- M mixing proceeds via box diagrams with W exchange d i LFfF d j L f d d j L } } L i and occurs in the four neutral meson systems d i LFgF d j L g d d j L L i K 0 = (d s) B 0 d B 0 = (d b) B 0 s B s = (s b) D 0 = (c ū) Observables: M 12, Γ 12, φ David Straub (Universe Cluster) 14

18 F = 2 observables sensitive to NP CP-violation in the K system, ɛ K Mass difference and CP phase in B d mixing, M d and φ d Mass difference and CP phase in B s mixing, M s and φ s While the remaining F = 2 observables are long-distance dominated and/or poorly sensitive to NP. David Straub (Universe Cluster) 15

19 More on NP in F = 2 To constrain/discover NP, measurements have to be compared with SM predictions SM predictions depend on CKM elements Md = 2 M12 d (V tb Vtd) 2 (Aλ 3 ) 2 [(1 ρ) 2 + η 2 ] 2 Ms = 2 M12 s (V tb Vts) 2 A 2 λ 4 φd = sin 2β ɛ K more complicated dependence... Identification of NP contributions requires the determination of CKM parameters David Straub (Universe Cluster) 16

20 Unitarity triangle: loop vs. Tree Loop observables ( M d,s, sin 2β, ɛ K ) can be affected by NP η excluded area has CL > 0.95 sin 2β m d & m s m d ε K CKM f i t t e r FPCP 13 sol. w/ cos 2β < 0 (excl. at CL > 0.95) ε K α 0.1 γ β ρ David Straub (Universe Cluster) 17

21 Unitarity triangle: loop vs. Tree Loop observables ( M d,s, sin 2β, ɛ K ) can be affected by NP Tree observables (V ub from b ulν, γ from b cūs/u cs) mostly NP-insensitive η excluded area has CL > 0.95 γ(α) CKM f i t t e r FPCP α 0.1 V ub γ β ρ David Straub (Universe Cluster) 17

22 UT fit & new physics NP can show up as disagreement among the F = 2 ( loop ) observables ɛ K, φ d, M d,s NP can show up as disgagreement between loop and tree observables Crucial to improve the experimental determination of CKM parameters from tree only Uncertainties of ɛ K, M d,s dominated by theory: lattice progress required to improve NP sensitivity David Straub (Universe Cluster) 18

23 Special case: φ s The B s mixing phase is tiny in the SM Can be measured at LHC from the mixing-induced CP asymmetry in B s J/ψφ (and B s J/ψππ) φ LHCb s = ± 0.07 φ SM s = 0.04 Still room for a sizable NP contribution. Updated LHCb analysis with 2012 data much anticipated! David Straub (Universe Cluster) 19

24 Allowed room for NP NP effects can modify the mixing amplitudes. E.g., B d,s mixing: M d 12 = (M d 12) SM (1 + h d e 2iσd ) M s 12 = (M s 12) SM (1 + h s e 2iσs ) 3.0 excluded area has CL > 0.95 CKM f i t t e r 2013 p value excluded area has CL > 0.95 CKM f i t t e r 2013 p value σ s σ d h s h d 0.0 Constraints as of today [Charles et al ] David Straub (Universe Cluster) 20

25 Allowed room for NP NP effects can modify the mixing amplitudes. E.g., B d,s mixing: M d 12 = (M d 12) SM (1 + h d e 2iσd ) M s 12 = (M s 12) SM (1 + h s e 2iσs ) 3.0 excluded area has CL > 0.95 CKM f i t t e r Stage II p value excluded area has CL > 0.95 CKM f i t t e r Stage II p value σ s σ d h s h d 0.0 Hypothetical constraints in 10 years, assuming the SM [Charles et al ] David Straub (Universe Cluster) 20

26 Bounds on the scale of new physics [Isidori et al ] L = L SM + i c i O(D) ΛD 4 i Operator Bounds on Λ in TeV (c ij = 1) Observables Re Im ( s L γ µ d L ) m K ; ɛ K ( s R d L )( s L d R ) m K ; ɛ K ( c L γ µ u L ) m D ; q/p, φ D ( c R u L )( c L u R ) m D ; q/p, φ D ( bl γ µ d L ) m Bd ; S ψks ( br d L )( bl d R ) m Bd ; S ψks ( bl γ µ s L ) m Bs ( br s L )( bl s R ) m Bs David Straub (Universe Cluster) 21

27 Implications for NP models How to build a model of TeV-scale NP that can satisfy the strong constraints from the agreement of F = 2 observables with SM expecations? We cannot impose flavour as a conserved symmetry, since it is broken already in the SM (unlike e.g. baryon number) The best we can do is to demand that there be no new sources of flavour breaking apart from the Yukawa couplings: Minimal Flavour Violation (MFV) Formally: flavour symmetry U(3) 3 = U(3) ql U(3) ur U(3) dr in the quark sector broken by the spurions Y u (3, 3, 1), Yd (3, 1, 3) David Straub (Universe Cluster) 22

28 Consequences of MFV for F = 2 A single operator, ( Qi L (Y u Y u ) ij γ µ Q j L )2 ( d i L (y 2 t V ti V tj)γ µ d j L )2 Suppressed by the same CKM factors as the SM contribution NP scale can be as low as 5 TeV (tree) or 0.5 TeV (loop) Universal relative contribution to B d, B s and K mixing No modification of mixing phases David Straub (Universe Cluster) 23

29 Examples of MFV models Gauge mediated SUSY breaking Soft terms mediated by flavour-blind gauge interactions, RG induced flavour effects are governed by the Yukawa couplings Hidden sector (SUSY) Mediators Visible sector (MSSM) Constrained MSSM Flavour-blind soft terms at GUT scale assumed ad hoc. Again, RG induced effects compatible with the MFV assumption. m 2 q = m 0 1 A u,d = A 0 Y u,d NB: MFV assumption is RG invariant and can be imposed on many NP models, SUSY or non-susy. David Straub (Universe Cluster) 24

30 Beyond MFV: the SUSY example MFV is a very strong assumption models addressing the flavour puzzle typically contain new sources of flavour violation In the context of SUSY, it is also at variance with naturalness: LHC bounds on first/second generation squarks exceed 1 TeV Third generation partners should be light MFV requires 3 squark generations to be approximately degenerate David Straub (Universe Cluster) 25

31 A natural SUSY spectrum (in 2014) 10 TeV 1 TeV 100 GeV David Straub (Universe Cluster) 26

32 Split families and flavour symmetry A hierarchy between the 3rd and the 1st/2nd family is also seen in the quark masses and mixings (,, ) (,, ) V CKM Consider a minimally broken U(2) 3 symmetry (under which 3rd generation fields are singlets): natural SUSY spectrum + (partial) explanation of quark mass/mixing hierarchies [Barbieri et al ] David Straub (Universe Cluster) 27

33 Consequences of U(2) 3 for F = 2 Still only 1 operator and universal contribution to B d and B s mixing Universality between K and B d,s is broken Universal, non-zero contribution to the mixing phases in B d and B s mixing [Barbieri et al ] David Straub (Universe Cluster) 28

34 Scan of F = 2 effects in MSSM with U(2) 3 Direct LHC constraints on sparticle masses taken into account Direct constraints limit the size of the effects to within the alowed regions, but visible effects in near-future measurement of φ s possible [Barbieri, Buttazzo, Sala, DS (to appear)] David Straub (Universe Cluster) 29

35 Forgetting about flavour symmetries and naturalness For generic flavour violation, F = 2 observables probe very high squark mass scales (here, m g = 3 TeV) [Altmannshofer et al ] ΦK 3 2 sd sd Φd 3 2 bd bd David Straub (Universe Cluster) 30

36 1 Introduction Why physics beyond the SM? Why flavour physics as a probe of BSM? 2 New physics in meson mixing Model-independent discussion Implications for NP models 3 New physics in rare decays B X s γ and dipole operators B s µ + µ and scalar operators B K µ + µ and new physics in b s transitions David Straub (Universe Cluster) 31

37 Rare B (and K ) decays Rare decays = FCNC decays with F = 1 particularly interesting: leptonic, semi-leptonic and radiative decays David Straub (Universe Cluster) 32

38 Rare decays An incomplete list of rare inclusive and exclusive decays that are sensitive to the existence of physics beyond the SM b s ( λ 2 ) b d ( λ 3 ) s d ( λ 5 ) γ B X s γ B X d γ B K γ B ργ l + l B K l + l B ρl + l B Kl + l B πl + l K L πl + l ν ν B X s l + l B X d l + l B s µ + µ B µ + µ K L µ + µ B X s ν ν B X d ν ν K + π + ν ν B Kν ν K L π 0 ν ν B K ν ν David Straub (Universe Cluster) 33

39 Dipole operators O 7 = m b e ( s Lσ µν b R )F µν O 8 = g sm b ( s e 2 L σ µν T a b R )G µν a Contribute to d i d j γ and d i d j l + l transitions Involve a helicity flip and are therefore suppressed by m di /m W in the SM Measurement can lead to stringent constraints in models that can lift the helicity suppression, even for Minimal Flavor Violation SUSY, 2HDM: chirality flip by VEV of H u instead of H d tan β enhancement Models with heavy fermions: chirality flip by heavy fermion mass David Straub (Universe Cluster) 34

40 Magnitude of C 7 In MFV models, the strongest constraint on C 7 comes from the measurement of B X s γ BR(B X s γ) exp = (3.43 ± 0.22) 10 4 BR(B X s γ) NP (3.14 ± 0.22) = CNP 7 (m b ) C SM,eff 7 (m b ) 7 [ 0.05, 0.14] [ 2.14, 1.95] (at 2σ) David Straub (Universe Cluster) 35

41 B K µ + µ 4-body decay: angular distribution with many observables sensitive to NP self-tagging : sensitive to CP violation David Straub (Universe Cluster) 36

42 Forward-backward asymmetry [ 1 0 ] / A FB (B K µ + µ d 2 (Γ Γ) d(γ + Γ) ) = d cos θ l 0 1 dq 2 d cos θ l dq [( ) ] 2 Re C eff 9 + 2m bm B C eff 7 C 10 q 2 Sensitive to the sign of C 7! LHCb 2013 [Aaij et al ] David Straub (Universe Cluster) 37

43 Bounds on C 7 0 Re C 9 NP Re C 7 NP Constraints from B X s γ, B X s µµ [Altmannshofer and DS ] David Straub (Universe Cluster) 38

44 Bounds on C 7 0 Re C 9 NP Re C 7 NP Constraints from B X s γ, B X s µµ, B K µµ [Altmannshofer and DS ] David Straub (Universe Cluster) 38

45 B X s γ in the two Higgs doublet model M H ± 300 GeV [Misiak et al. hep-ph/ ] David Straub (Universe Cluster) 39

46 B X s γ in the MFV MSSM f ( ) m 2 t M 2 H ± m2 t m 2 t A t µ tan β m 2 t ( m2 t M 3 µ m 2 t m 2 c m 2 b m 2 b tan β m 2 t ) cancellation between various contributions makes bound more model-dependent David Straub (Universe Cluster) 40

47 1 Introduction Why physics beyond the SM? Why flavour physics as a probe of BSM? 2 New physics in meson mixing Model-independent discussion Implications for NP models 3 New physics in rare decays B X s γ and dipole operators B s µ + µ and scalar operators B K µ + µ and new physics in b s transitions David Straub (Universe Cluster) 41

48 B s µ + µ Strongly helicity suppressed in the SM: one of the rarest B decays BR SM = (3.65 ± 0.23) 10 9 BR exp = (2.9 ± 0.7) 10 9 [Bobeth et al ], [LHCb+CMS 2013] David Straub (Universe Cluster) 42

49 Operators probed by B s µ + µ O ( ) 10 = ( sγ µp L(R) b)( lγ µ γ 5 l) O ( ) S = ( sp L(R)b)( ll) O ( ) P = ( sp L(R)b)( lγ 5 l) In the SM, only C 10 non-zero C S,P can be generated in models with extended Higgs sector (e.g. SUSY) C i require RH flavour violation and are absent in MFV models BR(B s µ + µ ) [ S 2 ( 1 4m2 µ m 2 B s ) + P 2 ] S = m B s 2 C S P = m B s 2 C P + m µ C 10 David Straub (Universe Cluster) 43

50 B s µµ in the MSSM with MFV Contributions to C S,P are generated by H 0 and A 0 exchange. In the decoupling limit (M H0,A 0 m h) one has C S C P Dominant contribution: chargino-stop loop C S C P µa t m 2 t Potentially huge enhancement for large tan β m Bs m µ tan 3 β m 2 A David Straub (Universe Cluster) 44

51 B s µµ constrains tan β/m A 60 b a d 50 tanβ M A GeV MFV; (a,b) µa t > 0; (c,d) µa t < 0 gray: A, H τ + τ [Altmannshofer et al ] c Large tan β + light Higgs spectrum disfavoured Direct Higgs searches more constraining for tan β 25 Milder bounds for µa t > 0 (destructive interference with SM) NB: in CMSSM, A t 0.8A 0 2.2m 1/2 David Straub (Universe Cluster) 45

52 B s µ + µ beyond SUSY Even in the absence of scalar/pseudoscalar operators, visible new physics effects can be generated in B s µ + µ and B d µ + µ Example: models with partial compositeness e.g. models with a composite Higgs or warped extra dimensions fermion masses generated by linear mixing with composite states Tree-level resonance exchange generates contributions to Q 10 = ( s L γ µ b L )( µγ µ γ 5 µ) Q 10 = ( s R γ µ b R )( µγ µ γ 5 µ) David Straub (Universe Cluster) 46

53 B s,d µ + µ from partial compositeness 3 models with different electroweak and flavour structures (blue: model with a U(2) 3 symmetry) [DS ] David Straub (Universe Cluster) 47

54 1 Introduction Why physics beyond the SM? Why flavour physics as a probe of BSM? 2 New physics in meson mixing Model-independent discussion Implications for NP models 3 New physics in rare decays B X s γ and dipole operators B s µ + µ and scalar operators B K µ + µ and new physics in b s transitions David Straub (Universe Cluster) 48

55 Global analysis of b s transitions O ( ) 7 = mb e ( sσµνp R(L)b)F µν O ( ) 9 = ( sγ µp L(R) b)( lγ µ l) O ( ) 10 = ( sγ µp L(R) b)( lγ µ γ 5l) b s operators contribute to many observables measured by B factories and/or at LHC global analysis necessary Decay C ( ) 7 C ( ) 9 C ( ) 10 B X s γ X B K γ B X s µ + µ X X X B Kµ + µ X X X B K µ + µ X X X B s µ + µ X X David Straub (Universe Cluster) 49

56 B K µ + µ exclusive semi-leptonic decay probing the b s transition 4-body decay: angular distribution with many observables sensitive to NP self-tagging : sensitive to CP violation David Straub (Universe Cluster) 50

57 [ highlights by myself] David Straub (Universe Cluster) 51

58 B K ( Kπ)µ + µ angular decay distribution d 4 Γ dq 2 d cos θ l d cos θ K dφ = 9 32π { I s 1 sin2 θ K + I c 1 cos2 θ K + (I s 2 sin2 θ K + I c 2 cos2 θ K ) cos 2θ l + I 3 sin 2 θ K sin 2 θ l cos 2φ + I 4 sin 2θ K sin 2θ l cos φ + I 5 sin 2θ K sin θ l cos φ + ( I s 6 sin2 θ K + I c 6 cos2 θ K ) cos θl } + I 7 sin 2θ K sin θ l sin φ + I 8 sin 2θ K sin 2θ l sin φ + I 9 sin 2 θ K sin 2 θ l sin 2φ Full set of observables: 12 angular coefficient functions I i (q 2 ) David Straub (Universe Cluster) 52

59 B K ( Kπ)µ + µ angular decay distribution d 4 Γ dq 2 d cos θ l d cos θ K dφ = 9 32π { + I s 2 sin2 θ K (3 + cos 2θ l ) I c 2 2 cos2 θ K sin 2 θ l + I 3 sin 2 θ K sin 2 θ l cos 2φ + I 4 sin 2θ K sin 2θ l cos φ + I 5 sin 2θ K sin θ l cos φ + I 6 sin 2 θ K cos θ l } + I 7 sin 2θ K sin θ l sin φ + I 8 sin 2θ K sin 2θ l sin φ + I 9 sin 2 θ K sin 2 θ l sin 2φ Full set of observables: 12 angular coefficient functions I i (q 2 ) Neglecting lepton mass, scalar/tensor operators: 9 independent I i (q 2 ) David Straub (Universe Cluster) 52

60 B K ( Kπ)µ + µ angular decay distribution d 4 Γ dq 2 d cos θ l d cos θ K dφ = 9 32π { + Ī s 2 sin2 θ K (3 + cos 2θ l ) Ī c 2 2 cos2 θ K sin 2 θ l + Ī 3 sin 2 θ K sin 2 θ l cos 2φ + Ī 4 sin 2θ K sin 2θ l cos φ Ī 5 sin 2θ K sin θ l cos φ Ī 6 sin 2 θ K cos θ l } + Ī 7 sin 2θ K sin θ l sin φ Ī 8 sin 2θ K sin 2θ l sin φ Ī 9 sin 2 θ K sin 2 θ l sin 2φ Full set of observables: 12 angular coefficient functions I i (q 2 ) Neglecting lepton mass, scalar/tensor operators: 9 independent I i (q 2 ) CP-conjugate decay: another 9 independent functions Ī i (q 2 ) David Straub (Universe Cluster) 52

61 Basis of observables consider sums and differences of I i, Ī i to separate CP violating and CP conserving NP effects normalize to CP-averaged decay rate to reduce th. & exp. uncertainties CP-averaged angular coefficients CP asymmetries ( S (a) i (q 2 ) = ( A (a) i (q 2 ) = I (a) i I (a) i ) / (q 2 ) + Ī (a) d(γ + Γ) i (q 2 ) dq 2 ) / (q 2 ) Ī (a) d(γ + Γ) i (q 2 ) dq 2 [Kruger et al. hep-ph/ , Bobeth et al , Altmannshofer et al ] David Straub (Universe Cluster) 53

62 Experimental status of angular observables Observable NP-sensitive? measured dbr/dq 2 yes Belle, BaBar, CDF, LHCb, CMS F L = S2 c yes Belle, BaBar, CDF, LHCb, ATLAS, CMS S 3 yes CDF, LHCb S 4 yes LHCb S 5 yes LHCb A FB = 3 4 S 6 yes Belle, BaBar, CDF, LHCb, ATLAS, CMS S 7 no LHCb S 8 no LHCb S 9 no LHCb A CP no CDF, LHCb A , 8 A 9 yes CDF, LHCb orange = updated in 2013 David Straub (Universe Cluster) 54

63 Kinematical regions low q 2 6 GeV 2 : expansion in m K /E K intermediate q 2 [6, 15] GeV 2 : c c resonances, B K ψ( µ + µ ) high q 2 15 GeV 2 : expansion in E K / q 2 David Straub (Universe Cluster) 55

64 SM vs. data: F L [Altmannshofer and DS ] C 7 NP 0.1, C 7 ' C 9 NP 1.5, C 9 ' 1.5 C NP ' 9 2, C FL σ tension at low q 2 David Straub (Universe Cluster) 56

65 SM vs. data: S 4 [Altmannshofer and DS ] S C 7 NP 0.1, C 7 ' 0.2 C 9 NP 1.5, C 9 ' 1.5 C NP ' 9 2, C σ tension at high q 2 David Straub (Universe Cluster) 57

66 SM vs. data: S 5 [Altmannshofer and DS ] C 7 NP 0.1, C 7 ' 0.2 C 9 NP 1.5, C 9 ' 1.5 C NP ' 9 2, C 10 1 S σ tension at low q 2 David Straub (Universe Cluster) 58

67 Fitting C 7 and C A FB B XsΓ Re C 9 NP S 5 B K ΜΜ 3 F L Although the S 5 and F L tensions could be solved with NP in C 7 or C 9 only, this is strongly disfavoured by the bounds from BR(B X s γ) and BR(B Kµ + µ ), respectively David Straub (Universe Cluster) 59

68 Fitting C 9 and C 9,10 3 S 4 ' B K ΜΜ 1 A FB 1 Re C 9 ' 0 S 5 Re C A FB 2 F L B K ΜΜ 2 S F L David Straub (Universe Cluster) 60

69 Fit results and χ 2 Scenario C NP 7 C 7 C NP 9 C 9 C 10 χ 2 (SM) (7) 0.07± (9) 0.8± (77 ) 0.06± ± (97) 0.05± ± (97 ) 0.1± ± (99 ) 1.0± ± (910 ) 1.0± ± Real David Straub (Universe Cluster) 61

70 The B K µ + µ anomaly There is a tension in some angular observables B K µ + µ that could be due to new physics (or statistical fluctuation, or underestimated theory errors) If due to NP, it requires a simultaneous contribution to the Wilson coefficients C 9 and C 9 in order not to violate constraints from other processes Which actual NP model could explain such an effect? David Straub (Universe Cluster) 62

71 1st try: MSSM b Z 0 l H ± bl sl bl tr sl s l + tr γ µ µ H ± γ µ µ (a) (b) bl,r bl,r sl,r sl,r bl tl cl sl bl bl sl sl g γ µ µ W ± γ µ µ W W µ l µ (c) (d) (e) By systematically studying all relevant contributions, one can show that the effect in C 9 and C 9 is negligible throughout the MSSM parameter space, in particular once LHC direct bounds and other flavour constraints (B s mixing) taken into account David Straub (Universe Cluster) 63

72 2nd try: partial compositeness b Z µ + b ρ µ + b ρ µ + s (a) µ s C ( ) 9 are generated at tree level from vector resonance exchange also here, contributions numerically negligible (b) µ s (c) µ David Straub (Universe Cluster) 64

73 Solving the anomaly with a Z boson L g [ ] 2 sγ µ (g L bs 2c P L + g R bs P R)b + µγ µ (gµ V + γ 5 gµ)µ A Z µ, W { } { } C NP 9, C 9 m2 Z m 2 (gbs)(g L µ V ), (gbs)(g R µ V ) Z [Descotes-Genon et al , Altmannshofer and DS , Gauld et al , Buras and Girrbach , Gauld et al , Buras et al ] David Straub (Universe Cluster) 65

74 Simultaneous contribution to B s mixing M s M SM s [ ] 1 m2 Z m 2 (gbs) L 2 + (gbs) R 2 9.7(gbs)(g L bs) R Z The requirement to solve the B K µµ anomaly + the M s constraint lead to an upper bound on M Z : C NP 9 = 1, C 9 = 1 M Z < g V µ 0.9 TeV C NP 9 = 1.5 M Z < g V µ 2.0 TeV David Straub (Universe Cluster) 66

75 Summary Flavour-changing neutral currents probe physics beyond the SM in a way complementary to the LHC direct searches Finding new physics in meson mixing requires disentangling tree-level and loop-induced observables in the determination of CKM parameters The B s mixing phase φ s is a promising place to look for BSM effects B s µ + µ and B K µ + µ are being measured to an unprecedented precision and are sensitive to many kinds of NP, even with MFV The potential anomaly in B K µ + µ, if due to NP, requires a Z with peculiar couplings. More data to be analyzed by LHCb very soon David Straub (Universe Cluster) 67