Constraints on new physics from rare (semi-)leptonic B decays

Rencontres de Moriond, QCD and High Energy Interactions, 12 March 2013 Constraints on new physics from rare (semi-)leptonic B decays David M. Straub Johannes Gutenberg University Mainz

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays What s new? O O exp /O SM (σ O /O) exp (σ O /O) th BR(B s µ + µ ) 0.9 40% 9% BR(B Kµ + µ ) lo 1.0 10% 25% F L (B K µ + µ ) lo 0.8 10% 5% F L (B K µ + µ ) lo 0.9 20% 50% A FB (B K µ + µ ) 0 1.2 25% 5% A FB (B K µ + µ ) hi 0.8 15% 35%... Also: B πµµ, hadr. decays (LHCb), B Kν ν, B D ( ) τν (BaBar), B τν (Belle),... David Straub (JGU Mainz) 2

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Implications No sign of new physics, but flavour experiments extremely valuable to constrain BSM, especially given inconclusive direct searches SM provides dominant contribution to flavour observables, but plenty of room for natural O(50%) effects Clean observables (B s,d µµ,...) Null tests (CP asymmetries,... ) Theory progress (lattice... ) David Straub (JGU Mainz) 3

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays 3 types of new physics in b s transitions Magnetic dipole operators Flavour-changing Z couplings Scalar operators David Straub (JGU Mainz) 4

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Pattern of effects allows to distuinguish models model variant C 7 C 7 C Z C Z C S,P SUSY MFV generic Composite Higgs triplet bidoublet David Straub (JGU Mainz) 5

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Magnetic dipole operators David Straub (JGU Mainz) 6

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Constraints on magnetic penguins 0.5 0.5 Im C 7 0.0 Im C 7 ' 0.0 0.5 0.5 0.5 0.0 0.5 Re C 7 NP 0.5 0.0 0.5 Re C 7 ' Constraints from B X s γ, B (K, X s )µµ, B K γ, combined (0, 0) =SM [Altmannshofer et al. 1111.1257, Altmannshofer and DS 1206.0273] see also [Bobeth et al., Matias et al., Descotes-Genon et al.] David Straub (JGU Mainz) 7

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Scalar operators David Straub (JGU Mainz) 8

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Scalar penguins & B s µµ Can lift the helicity-suppression present in the SM potentially huge effects Prime example: MSSM with large tan β mbs mµ m 2 A µa t m 2 t tan β 3 BR exp = (3.2 +1.5 1.2 ) 10 9 BR SM = (3.5 ± 0.3) 10 9 [LHCb-CONF-2012-17], [De Bruyn et al. 1204.1735, Buras et al. 1208.0934] David Straub (JGU Mainz) 9

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays B s µ + µ vs. SUSY 2.0 1.5 1.0 SM4 MSSM-LL MSSM-RVV2 MFV LHCb 95% C.L. 0.5 0.0 MSSM-AKM MSSM-AC SM 0 10 20 30 40 50 Moriond 2012 [DS 1205.6094] David Straub (JGU Mainz) 10

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays David Straub (JGU Mainz) 11

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays What the measurement actually tells us about SUSY: Large tan β with light pseudoscalar Higgs is disfavoured. 60 b a d tanβ 50 40 30 20 10 c m f = 2 TeV (a) µ = 1 TeV, A t > 0 (b) µ = 4 TeV, A t > 0 (c) µ = 1.5 TeV, A t > 0 (d) µ = 1 TeV, A t < 0 gray: A, H τ + τ [Altmannshofer et al. 1211.1976] 200 400 600 800 1000 1200 M A GeV David Straub (JGU Mainz) 12

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Flavour-changing Z couplings Scalar operators David Straub (JGU Mainz) 13

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Constraints on Z penguins 6 6 4 4 2 2 Im C Z 0 Im C Z ' 0 2 2 4 4 6 6 4 2 0 2 4 6 Re C Z NP 6 6 4 2 0 2 4 6 Re C Z ' Constraints from B (K, K, X s )µµ and B s µµ, combined (0, 0) =SM [Altmannshofer et al. 1111.1257, Altmannshofer and DS 1206.0273] David Straub (JGU Mainz) 14

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Concrete example: partial compositeness Solving the hierarchy problem without SUSY: the Higgs is composite Successful theory of flavour requires quarks to be partially composite L λ L ψ L O R + λ R ψ R O L David Straub (JGU Mainz) 15

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Z penguins from partial compositeness After EWSB, composite-elementary mixing leads to correlated tree-level contributions to flavour-changing Z couplings...... and Z b b David Straub (JGU Mainz) 16

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Numerical analysis of Z penguins in 3 models Two choices for the fermion content (irreps of SU(2) L SU(2) R U(1) X ) (2, 2) 2/3 + (2, 2) 1/3 + (1, 1) 2/3 + (1, 1) 1/3 ( bidoublet model ) (2, 2)2/3 + (1, 3) 2/3 + (3, 1) 2/3 ( triplet model ) Two choices for the flavour structure flavour anarchy U(2) 3 flavour symmetry see [Barbieri et al. 1203.4218, Barbieri et al. 1211.5085, DS 1302.4651] and ref. therein David Straub (JGU Mainz) 17

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays B s µµ vs. B d µµ Partial compositeness: triplet + anarchy bidoublet + anarchy bidoublet + U(2) 3 [DS 1302.4651] David Straub (JGU Mainz) 18

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays B s µµ vs. B K µµ Partial compositeness: triplet + anarchy bidoublet + anarchy bidoublet + U(2) 3 [DS 1302.4651] David Straub (JGU Mainz) 19

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays K + π + ν ν vs. K L π 0 ν ν Partial compositeness: triplet + anarchy bidoublet + anarchy bidoublet + U(2) 3 [DS 1302.4651] David Straub (JGU Mainz) 20

Introduction Magnetic penguins Scalar penguins Z penguins Constraints on NP from B decays Conclusions 1. No spectacular deviations from the SM have been found, but O(50%) modifications of the SM only start to be probed 2. B s µ + µ measurement rules out MSSM at large tan β with light pseudoscalar Higgs 3. Flavour-changing Z penguins are typical for models with partial compositeness (composite Higgs, RS... ). Rare decays now start to probe these effects and allow to distinguish between different models. David Straub (JGU Mainz) 21

Backup David Straub (JGU Mainz) 22

The b sγ operators H eff = 4 G F V tb V ts 2 8 (C i O i + C i O i ) + h.c.. i=7 O ( ) 7 = em b 16π 2 ( sσ µνp R(L) b)f µν O ( ) 8 = g sm b 16π 2 ( sσ µνt a P R(L) b)g µν a O ( ) 7,8 mix under renormalization C ( )NP 7 (µ b ) = 0.623 C ( )NP 7 (µ h ) + 0.101 C ( )NP 8 (µ h ) SM: C 7 = O(m s /m b ), C 7 R David Straub (JGU Mainz) 23

Z penguins L eff = g c w sγ µ [δg L P L δg R P R ] b Z µ C ( ) Z = 8π2 e 2 V tb V δg L,R ts They contribute to the usual Wilson coeffcients as C ( ) 9 = (1 4sw)C 2 ( ) Z C ( ) = 10 C( ) Z David Straub (JGU Mainz) 24

Properly defining FC Z couplings L Z eff = g c W Z µd i γ µ [ (g ij L + δg ij L)P L + (g ij R + δg ij R)P R ] d j. (g ii L) tree = 1 2 + 1 3 s2 W (g ii R) tree = 1 3 s2 W (g i j L,R) tree = 0 (g ij L) (g=0) 1-loop = m2 t 16π 2 v 2 V ti V tj L NP eff = 1 2 n,a ( ) O ij 1L = i Q i Lγ µ Q j L H D µh ( ) O ij 2L = i Q i Lτ a γ µ Q j L i,j H τ a D µh ( ) δg ij L = v 2 c ij 4Λ 2 1L + 1 4 cij 2L (g ij R) (g=0) 1-loop = 0 c ij na Λ 2 Oij na ( ) O ij 1R = i D i Rγ µ D j R H D µh δg ij R = v 2 4Λ 2 cij 1R [Guadagnoli and Isidori 1302.3909] David Straub (JGU Mainz) 25

Scalar and pseudoscalar operators H eff = 4 G F V tb V ts 2 (C i O i + C i O i ) + h.c.. i=s,p O ( ) S = e2 16π 2 m b m Bs ( sp R(L) b)( ll), O ( ) P = e2 16π 2 m b m Bs ( sp R(L) b)( lγ 5 l), O ( ) S,P are RG invariant SM: C ( ) S,P = 0 David Straub (JGU Mainz) 26

Can BR(B s µ + µ ) be suppressed in the MSSM? BR B s Μ Μ BR B s Μ Μ SM 1.5 1.0 0.5 0.0 0.05 0.00 0.05 0.10 0.15 C P C S Yes. By up to 50%. David Straub (JGU Mainz) 27

B s µ + µ : theoretical progress Dramatic increase in experimental precision need to reevaluate TH errors BR(B s µ + µ ) SM τ Bs f 2 B s V tb V ts 2 Y 2 (m 2 t /m 2 W ) = (3.23 ± 0.27) 10 9 NLO M t ΤB s V ts State of the art: [Buras et al. 1208.0934] Using f Bs = (227 ± 8) MeV Missing NLO corrections estimated by analogy to K πν ν, but might be larger. Full NLO calculation desirable. f Bs David Straub (JGU Mainz) 28

B s µ + µ : theoretical progress To relate the theoretical BR to experiment, two correction factors have to be taken into account (by the experimentalists) Emission of soft photons, depending on the experimental cut on E γ : O( 10%) shift [Buras et al. 1208.0934] Γ s leads to difference between flavour-averaged time-integrated rate and the unmixed one (t = 0): O(+10%) shift [De Bruyn et al. 1204.1735] David Straub (JGU Mainz) 29

B s µ + µ beyond the SM Two types of contributions: (pseudo)vector and (pseudo)scalar H eff C i O i + C i O i i ( ) ] BR(B s µ + µ ) [ S 2 1 4m2 µ + P 2 mb 2 s S = m B s 2 (C S C S) P = m B s 2 (C P C P) + m µ (C 10 C 10) David Straub (JGU Mainz) 30

B K µ + µ : a gold mine for new physics searches Angular distribution gives access to many observables d 4 Γ dq 2 d cos θ l d cos θ K dφ = i,a I (a) i (q 2 ) }{{} angular coefficient f(θ l, θ K, φ) }{{} dependence on angles Self-tagging decay: straightforward to extract CP asymmetries David Straub (JGU Mainz) 31

B K µ + µ observables Separate CP-violating and -conserving effects, normalize to reduce form factor uncertainties CP asymmetries ( A (a) i (q 2 ) = I (a) i ) / (q 2 ) Ī (a) d(γ + Γ) i (q 2 ) dq 2 CP-averaged angular coefficients ( S (a) i (q 2 ) = I (a) i ) / (q 2 ) + Ī (a) d(γ + Γ) i (q 2 ) dq 2 David Straub (JGU Mainz) 32

B K µ + µ observables: status Measured by LHCb (also Belle, BaBar, CDF) BR, S s 6( A FB ), S c 2( F L ), S 3 Not measured (or with poor precision), but sensitive to NP S 4, S 5, A 7, A 8, A 9 David Straub (JGU Mainz) 33

B K µ + µ : low vs. high q 2 Different theoretical tools required in the two kinematical limits. 0.2 0.0 A FB 0.2 0.4 0.6 5 10 15 q 2 GeV 2 Low q 2 Non-factorizable corrections not proportional to form factors can be calculated by means of QCD factorization [Beneke et al. hep-ph/0106067,... ] Form factors can be calculated by means of QCD sum rules on the light cone [Ball and Zwicky hep-ph/0412079] David Straub (JGU Mainz) 34

B K µ + µ : low vs. high q 2 Different theoretical tools required in the two kinematical limits. 0.2 0.0 A FB 0.2 0.4 0.6 5 10 15 q 2 GeV 2 High q 2 Non-perturbative corrections beyond form factors are negligible [Beylich et al. 1101.5118] Form factors are poorly known. Lattice! David Straub (JGU Mainz) 34

B K µ + µ : theory vs. experiment CDF CDF CDF Belle Belle Belle B B 0 BaBar BaBar BaBar LHCb LHCb LHCb 0.8 0.6 0.4 0.2 0.0 0.2 0.8 0.6 0.4 0.2 0.0 0.2 0.8 0.6 0.4 0.2 0.0 0.2 A FB 16 Everything consistent with the SM up to now. At high q 2, theory precision already saturated... [Altmannshofer and DS 1206.0273] David Straub (JGU Mainz) 35

B K µ + µ : theory vs. experiment CDF CDF CDF Belle Belle Belle B B 0 BaBar BaBar BaBar LHCb LHCb LHCb 0.4 0.2 0.0 0.2 0.4 0.6 0.8 0.4 0.2 0.0 0.2 0.4 0.6 0.8 0.4 0.2 0.0 0.2 0.4 0.6 0.8 F L 1,6 F L 14.18,16 F L 16 Everything consistent with the SM up to now. At high q 2, theory precision already saturated... [Altmannshofer and DS 1206.0273] David Straub (JGU Mainz) 35

B K µ + µ : theory vs. experiment CDF CDF CDF Belle Belle Belle BaBar BaBar BaBar LHCb LHCb LHCb 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 BR B K Μ Μ 1,6 10 7 BR B K Μ Μ 14.18,16 10 7 BR B K Μ Μ 16 10 7 Everything consistent with the SM up to now. At high q 2, theory precision already saturated... [Altmannshofer and DS 1206.0273] David Straub (JGU Mainz) 35

The two-site picture Consider 1 set of resonances (4D) composite sector elementary sector Captures the most relevant phenomenology (in particular for tree-level effects) Spin-1 resonances of mass m ρ = g ρ f Spin- 1 2 resonances of mass m ψ = Yf David Straub (JGU Mainz) 36

Setup composite sector elementary sector L s = Qi m i Q Qi Ū i m i R Ui Di m i R ( ) Di + Y ij Q i U LHU j + R Y ij Q i D LHD j + R h.c L mix = m j Q λij L qi L Qj R + mi Rλ ij RuŪi L uj R + mi Rλ ij Rd D i L d j R David Straub (JGU Mainz) 37

Setup: the triplet model L triplet mix = m j L λij L qi L Qj R + mi Rλ ij RuŪi L uj R + mi Rλ ij Rd D i L d j R ( ) L = (Q Q T T 5 3 ) = B T 2 3 (2, 2) 2 3 R = U 5 3 U D (1, 3) 2 3 b L mixes with B which is an eigenstate of P LR which exchanges SU(2) L SU(2) R David Straub (JGU Mainz) 38

Setup: the bidoublet model SU(3) c SU(2) L SU(2) R U(1) X L U = (Q u Q u) 3 2 2 L D = (Q d Q d) 3 2 2 1 3 U 3 1 1 D 3 1 1 1 3 2 3 2 3 ( ) L bidoublet s = tr[ LiU mi Q u L i U] Ū i m i U Ui + Y ij U tr[ Li UH] L U j ] + R h.c +(U, u D, d) L bidoublet mix = m Qu λ ij Lu qi L Qj + Ru m Uλ ij RuŪi L uj R + (U, u D, d), David Straub (JGU Mainz) 39

K + π + ν ν vs. K L µ + µ Partial compositeness: triplet + anarchy bidoublet + anarchy bidoublet + U(2) 3 [DS 1302.4651] David Straub (JGU Mainz) 40

Anarchic bidoublet model: Z couplings [DS 1302.4651] David Straub (JGU Mainz) 41

Anarchic triplet model: Z couplings [DS 1302.4651] David Straub (JGU Mainz) 42

U(2) 3 bidoublet model: Z couplings [DS 1302.4651] David Straub (JGU Mainz) 43

Constraints on vector and axial vector Z couplings 6 6 4 4 2 2 Im C ZV 0 Im C ZA 0 2 2 4 4 6 6 4 2 0 2 4 6 Re C ZV 6 6 4 2 0 2 4 6 NP Re C ZA Constraints from B (K, K, X s )µµ and B s µµ, combined (0, 0) =SM [Altmannshofer et al. 1111.1257, Altmannshofer and DS 1206.0273] David Straub (JGU Mainz) 44