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
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
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 = 0.745 +0.090 0.074 ± 0.036, which is.6σ below SM prediction (R SM K = 1 + (3.0+1.0 0.7 ) 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)151601 C. Bobeth, G. Hiller and G. Piranishvili JHEP 071 (007) 040 3 P. Roig, A. Guevara and G. López Castro, Phys.Rev. D88 (013) 033007 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 3 / 19
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
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 ) = 0.918 1 q /(5.3 GeV) 0.675 1 q /(6.18 GeV) + P π(q ) 0.0541 1 q /(5.41 GeV) + 0.166 [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) 014015 5 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
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
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
F π For P = π, in Wolfenstein s parametrization κ π [O(λ 0 )]. BaBar data RχT BaBar fit F π (m ll ) 1 0.01 0.5 1 1.5.5 3 m ll (GeV) Fig. 3. RχT form factor 8 and BaBar fitted form factor. 9 8 O. Shekhovtsova et al. Phys. Rev. D86(01)113008 9 J. P. Lees et al. BaBar Collaboration Phys.Rev. D88 (013) 03013 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 8 / 19
F K For P = K, κ K O(λ ). F K so large around m φ, it surpasses CKM suppresion. 10000 100 BaBar data RχT BaBar fit F K (m ll ) 1 0.01 1 1. 1.4 1.6 1.8..4 m ll (GeV) Fig. 4. RχT form factor 10 and BaBar fitted form factor. 11 10 E. Arganda, et al. JHEP0806(008)079 11 J. P. Lees et al. BaBar Collaboration Phys.Rev. D86 (01) 03013 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 9 / 19
LD invariant mass spectrum for P = π. (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-09 RχT BaBar fit 0 4 6 8 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 15 10 / 19
LD invariant mass spectrum for P = K. (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-09 RχT BaBar fit 1e-1 1 3 4 5 6 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 15 11 / 19
LD normalized decay width from threshold (P = π) (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-06 µ e 1e-1 1e-06 0.0001 0.01 1 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
LD normalized decay width from threshold (P = K) (1/Γ)(dΓ/dm ll ) (GeV - ) 1e-06 µ e 1e-1 1e-06 0.0001 0.01 1 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 15 13 / 19
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) 10 10 Interf (.6 ± 0.13) 10 9 ( + 1 ) 10 10 SD (9.83 +1.49 1.04 ) 10 9 (8.71 +1.35 0.90 ) 10 9 Total (1.64 +0.15 0.11 ) 10 8 (9.06 +1.36 0.90 ) 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.)) 10 8. The SM prediction for the range [0.05, (m B m π ) ] changes from 13 BR SM (SD) = (1.88 +0.3 0.1 ) 10 8, to BR SM (LD + SD) = (.6 +0.4 0.3 ) 10 8. 1 R. Aaij et al. JHEP1 (01)15 13 A. Ali et al. Phys. Rev. D89 09401(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 15 14 / 19
Our long-distance contribution B Kl + l 1 q 6 GeV LD (1.70 ± 0.1) 10 9 Interf ( 6 ± ) 10 11 SD (1.90 +0.69 0.41 ) 10 7 LHCb 14 (l = e) (1.56 +0.0 0.16 ) 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 = (1.9 +0.69 0.41 ) 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)151601 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 15 / 19
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 15 16 / 19
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 15 17 / 19
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) 10 7. Where the PDG value adds up to BR(K πµ + µ ) = (9.4 ± 0.6) 10 8. 15 K.A. Olive et al. (PDG) Chinese Physics C38(014)090001 Adolfo Guevara 1 () A new long-distance contribution to B K/π l + l decays QCD 15 18 / 19
Normalized invariant mass spectrum Nevertheless we obtain a very similar spectrum for the invariant mass to that of Ecker et al. 16. 1.0e-06 9.0e-07 K-->πµ + µ - 8.0e-07 (dγ/dq )/(1Γ) 7.0e-07 6.0e-07 5.0e-07 4.0e-07 3.0e-07.0e-07 1.0e-07 0.0e+00 0 0.1 0. 0.3 0.4 0.5 16 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 15 19 / 19