A new long-distance contribution to B K/π l + l decays

Transcription

1 A new long-distance contribution to B K/π l + l decays Adolfo Guevara 1 Departamento de Física Centro de Investigación y de Estudios Avanzados del IPN (), México D.F. 1 in collaboration with G. López Castro, P. Roig and S. Tostado Rencontres de Moriond QCD 15 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 1 / 19

2 Outline 1 Motivation Short Distance contribution 3 Long Distance contribution 4 Conclusions Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 / 19

3 LHCb measurement vs SM prediction R P, where P = K, π, is defined as R P = BR(B P µ µ + )/BR(B P e e + ) LHCb measurement for P = K between the 1 q 6 GeV is 1 R LHCb K = ± 0.036, which is.6σ below SM prediction (R SM K = 1 + ( ) 10 4 ). Some processes, such as τ πl + l ν τ, have different BR for different lepton pairs l = e, µ, specially near threshold. 3 This is why we decided to reconsider the LD contribution to the B P l + l process. 1 LHCb collaboration, R. Aaij et al., Phys. Rev. Lett. 113(014) C. Bobeth, G. Hiller and G. Piranishvili JHEP 071 (007) P. Roig, A. Guevara and G. López Castro, Phys.Rev. D88 (013) Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 3 / 19

4 Short-distance (SD) contribution ū ū ū ū b s, d b s, d l l Fig. 1 Short distance at leading order, penguin (left) and W-box (right) contributions. Using the weak effective Hamiltonian, with q = d, s and q = c, t H eff = G F α V q π bvq q C q i (µ s )O q i (µ s). The B P l + l matrix element can be written as M[B P l + l ] = G F α V q π bvq q ξ P(q )p µ ( B FV lγµ l + F A lγµ γ 5 l ). i l l Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 4 / 19

5 Short-distance contribution The leading contribution comes from the O 9 and O 10, O q 9 = [ qγ µb L ][ lγ µ l], O q 10 = [ qγ µb L ][ lγ µ γ 5 l] The q dependence of the form factors ξ P, F V, and F A may be computed using HQET, QCDF and LCSM 4 ξ π (q ) = ξ K (q ) = q /(5.3 GeV) q /(6.18 GeV) + P π(q ) q /(5.41 GeV) [1 q /(5.41 GeV) ] + P K (q ) F A = C 10 = 4.31 F V C 9 = 4.14 Where P P (q ) is a q polynomial; C 9 and C 10 are taken at NNLL 5. 4 C. Bobeth et al. JHEP 071 (007) 040 A. Khodjamiriam et al. JHEP 130(013) 010 P. Ball and R. Zwicky Phys.Rev.D71 (005) M. Beneke et al. Nucl.Phys.B 61(001)5 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 5 / 19

6 New long-distance contribution l l γ l + W B B P B l + W γ P P Fig. Feynman diagrams of the new long-distance contribution. The square is for structure dependent one photon exchange contribution. We are considering the region below 8 GeV, therefore the J/ψ resonance will not contribute. The diagram on the left hand side is suppresed by a factor m P /m B with respect to the one on the right hand side. Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 6 / 19

7 New long-distance contribution Using Resonance Chiral Theory (RχT) 6 we computed the amplitude M(B P l + l ) for this new long-distance part. M LD = G F V ub Vuqf e mb B f P q mb (F P (q ) 1)p µ lγ m B µ l 7 P This amplitude has the same structure as the F V part of the SD amplitude, so this effect can be included to the SD contribution as a correction to the F V as where F eff V = F V + κ PmB F P (q ) 1 q ξ P (q ) κ P = 8π V ubv uq V tb V tq f B f P (m B m P ) 6 G. Ecker, J. Gasser, A. Pich and E. de Rafael, Nucl.Phys.B 31(1989)311, G. Amoros et al. Eur. Phys. J. C7 43(003). 7 This amplitude corresponds to the dominant part of the LD calculation. Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 7 / 19

8 F π For P = π, in Wolfenstein s parametrization κ π [O(λ 0 )]. BaBar data RχT BaBar fit F π (m ll ) m ll (GeV) Fig. 3. RχT form factor 8 and BaBar fitted form factor. 9 8 O. Shekhovtsova et al. Phys. Rev. D86(01) J. P. Lees et al. BaBar Collaboration Phys.Rev. D88 (013) Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 8 / 19

9 F K For P = K, κ K O(λ ). F K so large around m φ, it surpasses CKM suppresion BaBar data RχT BaBar fit F K (m ll ) m ll (GeV) Fig. 4. RχT form factor 10 and BaBar fitted form factor E. Arganda, et al. JHEP0806(008) J. P. Lees et al. BaBar Collaboration Phys.Rev. D86 (01) Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 9 / 19

10 LD invariant mass spectrum for P = π. (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-09 RχT BaBar fit m ll (GeV ) Fig. 5. Invariant mass spectrum for P = π, using RχT and BaBar fitted form factor. Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

11 LD invariant mass spectrum for P = K. (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-09 RχT BaBar fit 1e m ll (GeV ) Fig. 6. Invariant mass spectrum for P = K, using RχT and BaBar fitted form factor. Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

12 LD normalized decay width from threshold (P = π) (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-06 µ e 1e-1 1e m ll (GeV ) Fig. 7. B πl + l width for l = e and l = µ Difference becomes important below q 0.3 GeV Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 1 / 19

13 LD normalized decay width from threshold (P = K) (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-06 µ e 1e-1 1e m ll (GeV ) Fig. 8. B Kl + l differential width for l = e and l = µ Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

14 Our long-distance contribution B πl + l 0.05 q 8 GeV 1 q 8 GeV LD (9.16 ± 0.15) 10 9 (5.47 ± 0.05) Interf (.6 ± 0.13) 10 9 ( + 1 ) SD ( ) 10 9 ( ) 10 9 Total ( ) 10 8 ( ) 10 9 Table 1. LD, SD and their interference contributions to the BR. [1,8] GeV range is a clean region for the search of new physics. The LHCb measurement in the whole q spectrum is 1 BR LHCb = (.3 ± 0.6(stat.) ± 0.1(syst.)) The SM prediction for the range [0.05, (m B m π ) ] changes from 13 BR SM (SD) = ( ) 10 8, to BR SM (LD + SD) = ( ) R. Aaij et al. JHEP1 (01)15 13 A. Ali et al. Phys. Rev. D (014),W. Jian-Jun et al. Phys Rev D77(008)014017, Wen-Fei et al. Phys Rev D86(01)11405 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

15 Our long-distance contribution B Kl + l 1 q 6 GeV LD (1.70 ± 0.1) 10 9 Interf ( 6 ± ) SD ( ) 10 7 LHCb 14 (l = e) ( ) 10 7 Table. LD, SD and their interference contributions to the BR. The interference is suppressed due to the fact that F K (q ) does not surpass the CKM suppression factor, contrary to the LD contribution where the F K (q ) does overcome this suppression. With this, the SM Branching Ratio is BR SM (LD + SD) [1,6] GeV = ( ) 10 7 We find that R P R P (SD) where the LD contribution adds up to R P (LD) 1 = O(10 5 ) for P = K or π. 14 R. Aaij et al., Phys. Rev. Lett. 113(014) Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

16 CP Asymmetry We also computed the CP asymetry for both P = K and B = π A P [q min,q max ] = Γ [q min,q max ] (B+ P + l + l ) Γ [q min,q max ] (B P l + l ) Γ [q min,q max ] (B+ P + l + l ) + Γ [q min,q max ] (B P l + l ) with q max = 6, 8 for π, K respectively; and obtained the following values q min = 1 GeV q min = 4m µ P = π (.5 ± 1.5) 10 (14 ± ) 10 P = K (1.3 ± 0.5) 10 (0.5 ± 0.5) 10 Table 3. CP Asymmetry for the diferent energy ranges for π and K. Thus we get a measurable CP asymetry for π and K. We encourage experimentalists to search for this effect. Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

17 Conclusions B πl + l Our analysis shows that new physics studies should be restricted to the [1,8] GeV range. The new contribution is important to understand the current LHCb measurement. LHCb could be able to measure this LD effect on the next run in the [1,8] GeV range. B Kl + l LHCb might be sensitive to our contribution, but not in the next run. This Long Distance contribution will not affect the search for new physics in the [1, 6] GeV region. There is a significant CP asymmetry for π and K that has to be taken into account in the search for new physics. Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

18 K πl + l γ γ V 0 K + π + K + V 0 π + We also analyzed the K + π + l + l process, where we compare our values with those given in the Particle Data Group (PDG) 15 obtaining BR(K πµ + µ ) = (1.64 ± 0.04) Where the PDG value adds up to BR(K πµ + µ ) = (9.4 ± 0.6) K.A. Olive et al. (PDG) Chinese Physics C38(014) Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19

19 Normalized invariant mass spectrum Nevertheless we obtain a very similar spectrum for the invariant mass to that of Ecker et al e e-07 K-->πµ + µ - 8.0e-07 (dγ/dq )/(1Γ) 7.0e e e e e-07.0e e e Ecker et al. Nucl. Phys B91(1987)69 Z=q /M K Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD / 19