Search for CP Violation in D K S π+ π Michael Feindt, Michal Kreps, Thomas Kuhr, Felix Wick Institut für Experimentelle Kernphysik October 6, 11 CDF Felix Wick (KIT) CPV in D K S π+ π October 6, 11 1 / 15
Overview and Motivation considered decay: D K S π+ π study of resonant substructure (Dalitz plot) production flavor tagged: D (1) + D π + respective D (1) D π search for time-integrated CPV (very small in SM) no hints for CPV in charm sector up to now further applications of D K S π+ π : D - D mixing (time-dependent Dalitz analysis) CKM angle γ from B D K (problem: K-π separation) Felix Wick (KIT) CPV in D K S π+ π October 6, 11 / 15
Signal Selection hadronic trigger requires two displaced tracks with p T > GeV (selection of secondary vertex decays) use integrated luminosity of 6. fb 1 NeuroBayes training based on real data only by means of s Plot weights (improved sideband subtraction) no need for simulated events Candidates per 1. MeV 16 S 353 B 37 1 1 1 8 6 1.8 1.8 1.8 1.86 1.88 1.9 1.9 1.9 1.96 1.98 Mass(K π + π ) [GeV ] s Candidates per.1 MeV S 35 B 38 18 16 1 1 1 8 6 1 1 1 16 18 15 15 15 156 Mass(K π + π π + ) Mass(K π + π ) [MeV ] s s Felix Wick (KIT) CPV in D K S π+ π October 6, 11 3 / 15
+ Resonant Substructure (Dalitz Plot) m D + m K S + m π + + m π + = M K S π+ + M K S π + M π + π K S π : K (89), K (13) K (13), K (11) π + π : ρ(77), ω, f (98) f (17), f (137), ρ(15), f (6), σ K S π+ (DCS): K (89) + K (13) +, K (13) + nonresonant Candidates per.1 GeV 18 16 1 1 1 8 6 K*(89) K *(13) Candidates per.1 GeV 7 6 5 3 1 ρ(77)/ω(78) f (98).5 1 1.5.5 3.5 1 1.5.5 3.5 1 1.5.5 3 M [GeV ] K s π M π π [GeV ] M [GeV ] K π + s Felix Wick (KIT) CPV in D KS π+ π October 6, 11 / 15 Candidates per.1 GeV 6 5 3 1 + K*(89)
+ Relative Reconstruction Efficiency Events per bin 3 5 15 1 5 1.5 M π + π [GeV ] 1.5.5 1 1.5 M K s π.5 3 [GeV ] phase space flat over Dalitz plot efficiency varies strongly (hadronic trigger) determined with simulated events (generated nonresonantly) CDF Run II Simulation CDF Run II Simulation CDF Run II Simulation Candidates per.3 GeV 5 15 1 5 Candidates per.3 GeV 5 15 1 5 Candidates per.3 GeV 5 15 1 5 K s.5 1 1.5.5 3 M [GeV ] π.5 1 1.5.5 3 [GeV ] M π π s.5 1 1.5.5 3 M [GeV ] K π + Felix Wick (KIT) CPV in D K S π+ π October 6, 11 5 / 15
Applied Dalitz Model decay rate of D A B C depends on complex matrix element M Isobar model dγ = M dmabdm 56π 3 MD 3 BC M = a e iδ + a j e iδj A j j a j, δ j : relative amplitudes and phases (fit parameters) fixed reference resonance a ρ(77) = 1, δ ρ(77) = a e iδ : nonresonant contribution A j : individual complex matrix elements (Breit-Wigner with spin-dependent angular factor) Felix Wick (KIT) CPV in D K S π+ π October 6, 11 6 / 15
Likelihood Function binned maximum likelihood method J J J ln L( a) = n j ln µ j + µ j + ln(n j!) j=1 a: free parameters n j : number of entries in bin j µ i : expected number of entries in bin i fit function µ(m K S π, M π + π ) = T ɛ(m K S π, M π + π ) M(M K S π, M π + π ) j=1 j=1 + (1 T ) ɛ(m K S π, M π + π ) M(M K S π+, M π + π ) + B(M K S π, M π + π ) (1 T ): mistag fraction (free fit parameter) ɛ(m K S π, M π + π ): relative efficiency over Dalitz plot B(M K S π, M π + π ): background distribution Felix Wick (KIT) CPV in D K S π+ π October 6, 11 7 / 15
Fit Results Candidates per.1 GeV 18 16 1 1 1 8 6 Data Fit Function Background.5 1 1.5.5 3 M [GeV ] π K s Candidates per.1 GeV 7 6 5 3 1 Data Fit Function Background.5 1 1.5.5 3 M π + π [GeV ] Candidates per.1 GeV 6 5 3 1 Data Fit Function Background.5 1 1.5.5 3 M [GeV ] K π + s ] [GeV M π + π 1.8 1.6 1. 1. 1.8.6...5 1 1.5.5 3 M [GeV ] π K s 5 3 1 1 3 5 Felix Wick (KIT) CPV in D K S π+ π October 6, 11 8 / 15
Fit Fractions correspond to individual resonance contributions to total decay rate calculated from fitted amplitudes and phases FF r = ar e iδr A r dm K S π dm π + π j a je iδ ja j dm K S π dm π + π F F K (89) = (59. ±.9)% F F ρ(77) = (1.8 ±.)% F F f (98) = (5. ±.3)%... Felix Wick (KIT) CPV in D K S π+ π October 6, 11 9 / 15
Search for CPV in Dalitz Fit separate D and D samples (from D + and D ) D - D differences and fit projections: per.1 GeV #D #D 6 6.5 1 1.5.5 3 M [GeV ] K s π per.1 GeV #D #D 5 3 1 1 3 5.5 1 1.5.5 3 M π+π [GeV ] per.1 GeV #D #D 5 3 1 1 3 s 5.5 1 1.5.5 3 M [GeV ] K π + calculate fit fraction asymmetries: A FF = FF D FF D FF D + FF D Felix Wick (KIT) CPV in D K S π+ π October 6, 11 1 / 15
Results for A FF Resonance A FF [%] K (89).5 ±.39 ±.1 K (13).8 ±.89 ± 3.5 K (13).8 ±.93 ±.5 K (11) 13.66 ± 5.95 ± 7.83 ρ(77).9 ±.17 ±.13 ω 11.76 ± 5.77 ± 1.58 f (98). ± 1.8 ± 1.6 f (17).1 ±. ±.35 f (137) 5.63 ± 15.7 ± 1.77 ρ(15) 1.96 ± 9.87 ± 5.1 f (6).7 ±.31 ± 3.6 σ.65 ± 7.67 ±.66 K (89) + 1. ±.5 ±.75 K (13) +.3 ± 8.33 ± 1.59 K (13) + 13.56 ± 13.59 ± 15.88 Felix Wick (KIT) CPV in D K S π+ π October 6, 11 11 / 15
Overall integrated CP Asymmetry A CP = M M M + M dm K S π dm π + π dm K S π dm π + π statistical uncertainty determined by random parameter sets generated according to full covariance matrix of Dalitz fit Entries per.1 8 7 6 5 3 1 3 µ =.5 x 1 3 σ = 5.6 x 1.5..15.1.5.5.1.15. A CP =. ±.6 ±.5 value from CLEO for comparison: A CP =.9 ±.1 +.1.3 +.13.37 A CP Felix Wick (KIT) CPV in D K S π+ π October 6, 11 1 / 15
Direct vs. Indirect CPV slow D mixing allows approximation: A CP = a dir CP + t τ aind CP Candidates per.1 1 1 1 8 Data Prompt Nonprompt <t>/τ(d ) =. A CP measured assuming a dir CP = 6 a ind CP =.18 ±.6 ±. 1 3 5 6 7 8 9 1 t/τ (D ) Felix Wick (KIT) CPV in D K S π+ π October 6, 11 13 / 15
Model-independent Approach binning of D and D Dalitz plots consider significance asymmetry per bin N D N D ND +N D sum of squares of significance asymmetries per bin corresponds to χ, NDF = Dalitz plot bins minus 1 (normalization), p-value ] [GeV M π + π 1.8 1.6 1. 1. 1.8.6...5 1 1.5.5 3 M [GeV ] π χ = 917.6 NDF = 59 prob =.96 K s 5 3 1 1 3 5 Dalitz plot bins 3 1 1 1 1 =.3 ±.1 Significance µ σ =.987 ±.9 Felix Wick (KIT) CPV in D K S π+ π October 6, 11 1 / 15
Conclusion D KS π+ π, first full Dalitz fit at hadron collider results compatible and comparable in precision to B-factories production flavor tagged by D (1) + D π + search for time-integrated CPV in Dalitz fit most precise determinations of CP violating quantities no hints for CPV complementary verification by model-independent approach Felix Wick (KIT) CPV in D K S π+ π October 6, 11 15 / 15
Backup
Individual Matrix Elements A j A j consist of Breit-Wigner part and spin-dependent angular factor for spin- resonances for spin-1 resonances 1 A r(abc ) = F D F r Mr MAB imrγab A r(abc 1) = F D F r M AC MBC + (M D M C )(M B M A ) Mr Mr MAB imrγab spin-... mass-dependent width Γ AB Γ AB = Γ r ( pab p r ) J+1 ( ) Mr Fr M AB F D, F r : spin-dependent Blatt-Weisskopf penetration factors for D respective the different intermediate resonances Felix Wick (KIT) CPV in D K S π+ π October 6, 11 17 / 15
Dalitz Fit Results Resonance a δ [ ] FF [%] K (89) 1.77 ±.1 13. ±.7 59. ±.9 K (13) 1.677 ±.38 17. ± 1..1 ±.17 K (13) 1.19 ±.7 35.9 ± 1.5.17 ±.9 K (11).877 ±. 131. ±.6.7 ±.7 ρ(77) 1 1.8 ±. ω(78).38 ±. 11.9 ± 1.7.5 ±.5 f (98).53 ±.1 5.5 ±.1 5. ±.3 f (17) 1.8 ±.33 3.1 ±.5.8 ±.5 f (137).77 ±.67 8.5 ± 6.6.3 ±.6 ρ(15).98 ±.151 36.9 ± 3.8.5 ±.6 f (6) 1.5 ±.51 193.8 ± 1.8 1.38 ±.1 σ.1 ±. 165.7 ± 8..56 ±. K (89) +.18 ±.8 318.5 ± 1.8.63 ±.5 K (13)+.61 ±.36 11.7 ± 3.5.55 ±.6 K (13)+.8 ±.3 3. ± 5.7.1 ±. Nonresonant 3.37 ±.13 11.7 ±.3 6.71 ±.7 Sum 113.7 Felix Wick (KIT) CPV in D K S π+ π October 6, 11 18 / 15
Efficiency Discrepancies between D and D differences between D and D efficiencies over the Dalitz plot can fake CPV can originate from p T (π D +)-dependent π D + charge asymmetry A = N π N π + N π + N π + Asymmetry.1.8.6.....6.8.1..6.8 1 1. 1. 1.6 1.8 p (π D* +) [GeV] T reweighting of D Dalitz plot according to deviations between p T (π D +) and p T (π D ) distributions Felix Wick (KIT) CPV in D K S π+ π October 6, 11 19 / 15
Systematic Uncertainties experimental sources efficiency asymmetries varying over Dalitz plot repeat fits without reweighting D Dalitz plot asymmetries of D and D background repeat fits with separate D and D background samples modeling uncertainties included resonances repeat fits when excluding K (11), f (137), σ, K (13) +, or nonresonant contribution discrepancies between fit and data repeat fits when excluding Dalitz plot regions with largest discrepancies Felix Wick (KIT) CPV in D K S π+ π October 6, 11 / 15
+ Fit Discrepancies exclude regions with largest discrepancies ] [GeV M π + π 1.8 1.6 1. 1. 1.8.6...5 1 1.5.5 3 M [GeV ] π K s 5 3 1 1 3 5 Candidates per.1 GeV 1 8 6 Data Fit Function Background K s.5 1 1.5.5 3 M [GeV ] π Candidates per.1 GeV 6 Data 5 3 1 Fit Function Background.5 1 1.5.5 3 [GeV ] M π π Candidates per.1 GeV 5 35 3 5 15 1 5 Data Fit Function Background s.5 1 1.5.5 3 M [GeV ] K π + Felix Wick (KIT) CPV in D K S π+ π October 6, 11 1 / 15