B Kl + l at Low Hadronic Recoil

Transcription

1 B Kl + l at Low Hadronic Recoil Gudrun Hiller Danny van Dyk Christian Wacker TU Dortmund - Theoretische Physik III DPG-Frühjahrstagung Karlsruhe March 11 Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 1 / 1

2 Introduction to B Kl + l b s transitions mediated by Flavor Changing Neutral Currents (FCNCs) FCNCs forbidden at tree level in SM, but not through loops New Physics contributions can enter via extended particle content s l s l W χ c, t W γ, Z c, t χ γ, Z b l b l Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 / 1

3 Branching Fraction db/dq of B Kl + l q = dilepton invariant mass db/dq [1 7 /GeV ] SM prediction with form factors from Khodjamirian et al. (1) experimental data from BaBar (6), Belle (9) and CDF (11) J/Ψ Ψ q [GeV ] large recoil q m b c c-veto low recoil q m b Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 3 / 1

4 Low Recoil Framework by Grinstein, Pirjol (4) Form Factors K s γ µ b B f +, f K s σ µν b B f T Results improved Isgur-Wise form factor relation: f T (q ) = (m B + m K )m B q κ f + (q ) + O κ = 1 + O ( α s ) for µ = mb ( α s, reduction of independent form factors: 3 better control of non-perturbative matrix elements of operators ( s b)( q q) Derivation express QCD matrix elements through an Operator Product Expansion (OPE) in 1/Q, Q {m b, q } using Heavy Quark Eective Theory (HQET) elds relate HQET currents to quark currents Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 4 / 1 Λ m b )

5 Performance of Improved Isgur-Wise Relation at Low Recoil 1 R T (q ) q f T (q ) for LCSRmand f B +(q Lattice ) κ LCSR Lattice q [GeV ] Form Factors Light Cone Sum Rules (LCSR): Khodjamirian et al. (1) Lattice (preliminary): Liu et al. (11) Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 5 / 1

6 Eective Framework eective Hamiltonian for b s l + l H e = 4 G F V tb V ts renormalization scale µ = m b most relevant operators 1 i=1 C i (µ) O i (µ) + O(V ub V us) O 7 [ s σ µν P R b ] F µν O 9(1) [ s γ µ P L b][ l γ µ (γ 5 ) l] Wilson coecients C i eective coecients C e 7 = C 7 + O C e 9 = C 9 + ( C 3...6, α s C 1,,8, m c ( 4 3 C 1 + C ) q ) h ( q ) + O ( ) C 3...6, α s C 1,,8, m c q Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 6 / 1

7 Universal Short Distance Couplings if lepton masses negligible (l = e, µ) amplitude for B Kl + l depends only on ρ 1 ρ 1 : bilinear combination of Wilson coecients ρ 1 = κ m b m B q 7 + C e 9 C e + C 1 ρ 1 known from B K l + l, Bobeth et al. (1) same sensitivity on ρ 1 in both decays reduced uncertainties due to possibility of global t (in preparation) Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 7 / 1

8 Constraining Wilson Coecients C C 9 vs C 1 from B Kµµ low recoil C 9 95% CL 68% CL Parameter-Scan vary C 7,9,1 C 1...6,8 xed on SM goodness-of-t for every scan-point based on low recoil data from Belle and CDF numerical analysis with EOS green mark represents SM prediction results compatible with B K l + l EOS: Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 8 / 1

9 Current Situation for B Kµ + µ combined Belle and CDF data: 5 events LHCb: 35 events at 37 pb 1 (talk by A. Golutvin, La Thuile, 11).6 db/dq [1 7 /GeV ] J/Ψ Ψ q [GeV ] Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 9 / 1

10 Estimation for LHCb Run in B Kµ + µ events at 1- fb 1 (talk by A. Golutvin, La Thuile, 11) hypothetical error reduction.6 db/dq [1 7 /GeV ] J/Ψ Ψ q [GeV ] Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 9 / 1

11 Summary and Outlook Summary analysis of B Kl + l at low recoil with heavy quark OPE by Grinstein and Pirjol same short distance coupling for B Kl + l as in B K l + l present B Kl + l data already probes New Physics Outlook global B {K, K, X s }l + l scan allowing for CP violation via complex-valued Wilson coecients LHCb prediction for 11: 9-18 B Kµ + µ events Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 1 / 1

12 Backup Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March / 1

13 Constraining Wilson Coecients π 3π C 9 vs φ 9 from B Kµµ low recoil 95% CL 68% CL π 3π C 1 vs φ 1 from B Kµµ low recoil 95% CL 68% CL φ9 π φ1 π π π C 9 C 1 no sensitivity on φ 1 no correlation between φ 9 and φ 1 Christian Wacker (TU Dortmund) B Kl + l at Low Hadronic Recoil 31. March 11 1 / 1