Long distance weak annihilation contribution to

Transcription

1 Long distance weak annihilation contribution to B ± (π/k) ± l + l Sergio Tostado In collaboration with: A. Guevara, G. López-Castro and P. Roig. Published in Phys. Rev. D 92, (2015). Physics Department, CINVESTAV-IPN November 5, 2015 XV Mexican Workshop on Particles and Fields Mazatlán, México S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

2 1 Motivation 2 Weak Efective Hamiltonian for FCNC 3 Long Distance Weak Annihilation... 4 Matching to SD 5 Results 6 Conclusions S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

3 Introduction In the SM mixings between quarks occur in the CC L CC g 2 W + µ ŪLV CKM γ µ D L + h.c. (1) which are well described by the CKM matrix 1 where 2 V us λ , and 1 M. Kobayashi and T. Maskawa, PTP 49, 652 (1973). 2 Wolfenstein, S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

4 Current status excluded at CL > 0.95 excluded area has CL > γ & m s m d sin 2β 0.5 ε K α m d η α V ub γ β α 1.0 γ ε K sol. w/ cos 2β < 0 (excl. at CL > 0.95) Experiments expect to reach the % level in the near future. 3 K.A. Olive et al. (Particle Data Group), Chin. Phys. C, 38, (2014). S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38 ρ

5 Flavor Changing Neutral Current In the SM FCNC are supressed at the tree level. The CMS and LHCb collaboration, Nature 522, 6892 (2015). They are induced by loops and are sensitive to new physics (NP) effects. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

6 FCNC experimental results Branching Ratios LHCb and CMS: Br(B 0 s µ + µ ) = ( ) 10 9 Br(B 0 µ + µ ) = ( ) Agree with SM at 1.2σ and 2.2σ, respectively. SM a Br(B 0 s µ+ µ ) = (3.66 ± 0.23) 10 9 Br(B 0 µ + µ ) = (1.06 ± 0.09) a Bobeth et.al. PRL 112 (2014) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

7 Angular Observables 4 in B K l + l 4 LHCb coll., PRL 111 (2013) Straub et. al., Eur.Phys.J. C75 (2015) 8, 382. Mathias et.al., JHEP 1412 (2014) 125 and 1305 (2013) 137. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

8 Tests of lepton universality Ratios 5 R D = Br(B0 D + τ ν τ ) Br(B 0 D + l ν l ) (2) 5 Kamenik, talk given at Jozef Stefan Institute. LHCb, PRL 115 (2015) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

9 S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

10 We are interested in the ratio 6 : where 6 LHCb, PRL 113 (2014) Babar, PRD 86 (2012) Belle, PRL 103 (2009) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

11 If tensions are due to NP... Neutrinos: See Prof. Valle talk. 7 7 D. Straub, talk given at Rencontres de Moriond (2015). S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

12 This talk Could this anomaly be caused by a missing process? S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

13 Weak efective hamiltonian for FCNC For B + (K, π) + l + l : S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

14 Weak efective hamiltonian for FCNC S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

15 Four quark operators S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

16 Weak efective hamiltonian for FCNC with the matrix elements similar for B π. All of them related to a single form factor f + (q 2 ) ξ P (q 2 ) in the limit m b (Isgur-Wise). S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

17 the leading contributions comes from with F V = C 9 + 2m b M B T P (q 2 ) ξ(q 2 ), F A = C 10 (3) [ T P (q 2 ) = ξ(q 2 ) C eff (0) 7 + M B ] Y (0) (q 2 ) m b C 9 = and C 10 = have been computed at NNLL 8 and C eff 7 at NLO 9. WA included in Y (0). (4) 8 Beneke et.al. NPB 612 (2001)25. 9 Buras et. al., Rev. Mod. Phys. 68, 1125 (1996) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

18 Form Factors The form factors are taken in the form ξ π (q 2 ) = ξ K (q 2 ) = where P P (q 2 ) is a polynomial q 2 /(5.32 GeV) q 2 /(6.18 GeV) 2 + P π(q 2 ), q 2 /(5.41 GeV) [1 q 2 /(5.41 GeV) 2 ] 2 + P K (q 2 ), 10 Ball, Zwicky, PRD 71 (2005) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

19 SM prediction with: for (q 2 min, q 2 max) = (1, 6)(2, 6)(1, 7)(2, 7)GeV 2, from top to bottom Bobeth et.al., JHEP 12 (2007) 040. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

20 An interesting observable (LHCb) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

21 Long distance WA contribution to B ± (π/k) ± l + l S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

22 LD WA contribution to K ± π ± l + l has been previously considered by Ecker, Pich and Rafael Ecker, Pich and Rafael, Nucl. Phys. B. 291 (1987) 692. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

23 The decay amplitude corresponding to WA M WA LD = e2 q 2 lγ µ l M WA µ (5) where M WA µ denotes the effective hadronic electromagnetic current coupled to the leptonic current. Conservation of the electromagnetic current demands M WA µ = [ (p B + p P ) µ m2 B m2 P q 2 q µ ] F (q 2 ), (6) where only the first term within square brackets gives a non-vanishing contribution. q µ lγ µ l = 0, we can also replace (p B + p P ) µ 2p Bµ S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

24 S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

25 The leading order one-photon exchange (WA) amplitude corresponding to the diagrams (i) and (j) can be computed taking into account that 0 ūγ µ (1 γ 5 )b B = i f B p µ B, P Dγ µ (1 γ 5 )u 0 = i f P p P µ, (7) and is given by M LD,WA = 2G F (4πα)V ub VuDf 1 B f P q 2 (mb 2 m2 P ) [ mb 2 ( FP (q 2 ) 1 ) mp 2 ( FB (q 2 ) 1 )] p µ lγ B µ l, (8) where f X denotes the decay constant of the pseudoscalar meson X according to the PDG 13 conventions for f K,π,B and F X (q 2 ) is the electromagnetic form factor of the corresponding meson. 13 PDG 2014 S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

26 Long distance WA contribution to C 9 Due to the vector nature of the one-photon exchange contribution, its amplitude can be absorbed into the contribution of the O 9 operator in the SM amplitude under the replacement [ ξ P (q 2 )F V ξ P (q 2 )F V + κ P mb 2 FP (q 2 ] ) 1, (9) where κ P = 8π 2 V ubv ud V tb V td q 2 f B f P mb 2. (10) m2 P Note that κ P O(10 2 ) V ubv ud V tb V so that its influence is governed by the ratio of td CKM factors which is O(λ 0 ) for P = π and O(λ 2 ) for P = K. This suggests a larger effect for B π l + l transitions but a detailed analysis of the electromagnetic meson form factors is needed to confirm these expectations. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

27 Form Factors They are important in the 1GeV region, where theory is better controlled Two different approaches are used Resonance Chiral Theory (Ecker et.al. Nucl. Phys. B. 321 (1989) 311) Gounaris- Sakurai parametrizations (PRL 21 (1968) 244) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

28 π electromagnetic form factor F π (m ll 2 ) 2 1 BaBar data RχT BaBar fit m ll (GeV) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

29 K electromagnetic form factor BaBar data RχT BaBar fit F K (m ll 2 ) m ll (GeV) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

30 (1/Γ)(dΓ/dm ll 2 ) (GeV -2 ) (1/Γ)(dΓ/dm ll 2 ) (GeV -2 ) 1e-06 1e-12 µ e 1e m ll (GeV ) 1e-06 µ e There is a huge breaking of lepton universality. It is important only for q 2 0.3GeV 2. Its effect is always smaller than the SD contribution RK SM = 1 + (3 ± 1) 10 4 Rπ SM = 1 + (6 ± 1) 10 4 RP LD 1 = O(10 5 ) (P = K, π) 1e-12 1e m ll (GeV ) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

31 Matching of the RχT and SD descriptions of the WA contributions For q 2 q 2 match P = (K, π) while for q 2 q 2 match S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

32 Smooth matching between the LD and SD WA contributions S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

33 Smooth matching between the LD and SD WA contributions S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

34 Results B π l + l B K l + l 0.05 q 2 8 GeV 2 1 q 2 8 GeV 2 1 q 2 6 GeV 2 LD (9.06 ± 0.15) 10 9 (4.74 ± 0.05) (1.70 ± 0.21) 10 9 interf. ( 2.57 ± 0.13) 10 9 ( ) ( 6 ± 2) SD ( ) 10 9 ( ) 10 9 ( ) 10 7 Total ( ) 10 8 ( ) 10 9 ( ) 10 7 S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

35 Results B π l + l B K l + l 0.05 q 2 8 GeV 2 1 q 2 8 GeV 2 1 q 2 6 GeV 2 LD (9.06 ± 0.15) 10 9 (4.74 ± 0.05) (1.70 ± 0.21) 10 9 interf. ( 2.57 ± 0.13) 10 9 ( ) ( 6 ± 2) SD ( ) 10 9 ( ) 10 9 ( ) 10 7 Total ( ) 10 8 ( ) 10 9 ( ) % 3% 1% Current accuracy is sensitive to it! Still ideal place to look for NP. It can be controlled, so it is a good place to search for NP! Very large hadronic contamination. It is better to take q 2 1GeV 2. For the fully integrated rate, the LHCb measurements Br(B π l + l ) = (2.3 ± 0.6 ± 0.1) 10 8 Br(B π l + l ) = (1.83 ± 0.24 ± 0.05) Ali et.al., JHEP12(2012) arxiv: Br SM SD+LD (B π l + l ) = ( ) 10 8 (11) S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

36 CP violation A direct CP assymetry can be generated A CP (P) = Γ(B+ P + l + l ) Γ(B P l + l ) Γ(B + P + l + l ) + Γ(B P l + l ), (12) from the interference of the SD and LD diagrams, such that CP = Γ(B + P + l + l ) Γ(B P l + l ) = 32α 2 GF 2 f P f B Im {V tb VtDV ubv ud } ] dq 2 1 ds 12 [2(P q 2 (MB 2 m2 P ) B P + )(P B P ) M2 B q2 (13) 2 Im { ξ P (q 2 )F V (q 2 ) [ MB 2 ( FP (q 2 ) 1 ) mp 2 ( FB (q 2 ) 1 )]}, where s 12 = (p K + p + ) 2. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

37 (16.1 ± 1.9)%, for P = π, 0.05 q 2 8 GeV 2, A CP (P) = (7.8 ± 2.9)%, for P = π, 1 q 2 8 GeV 2, ( 1.0 ± 0.3)%, for P = K, 1 q 2 6 GeV 2. (14) (qmin 2, q2 max) Hou 16 [%] Our results 17 [%] Khodjamiriam 18 [%] (1, 8) GeV 2 13 ± ± (1, 6) GeV 2 16 ± ± 1.7 ( ) (2, 6) GeV ± Recently, for P = π (LHCb 19 ) A CP = 0.11 ± 0.12 ± 0.01, (1, 6)GeV 2 (15) 16 Hout et.al. PRD (2014) 17 A. Guevara, G. López-Castro, P. Roig and ST, PRD 92 (2015) Khodjamiriam et.al R. Aaij et.al. arxiv: S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38

38 Conclusions One-photon exchange contribution to the rare B ± P ± l + l decays, with P = π or K. Its effects in BR of the P = K case 1% with respect to the (top quark loop dominated) SD contribution for 1 q 2 6 GeV 2. The corresponding effect in P = π turns out to be significant in integrated observables starting close to the threshold. We suggest to take the range 1 q 2 8 GeV 2 for precision measurements. More refined measurements of the fully integrated branching fraction for this decay could be sensitive to our contribution. CP asymmetry is large in the case of a pion in the final state for 0.05 q 2 8 GeV 2, but also sizable and worth measuring in the 1 q 2 8 GeV 2 interval. Our CP violation results are smaller than those obtained from SD because of the different description (origin) of the WA amplitudes at low energies. S. L. Tostado (CINVESTAV-IPN) B ± (π/k) ± l + l November 5, / 38