γ/φ3 measurements at LHCb CKM2014, Vienna Till Moritz Karbach (on behalf of the LHCb collaboration) CERN 11.09.2014 Introduction Introduction I LHCb is a forward spectrometer operated in collider mode. I precision measurements of band c-hadron decays I rare decays, CP violation, γ I very good K ± /π ± separation: two RICH detectors I very good time resolution (Bs0 oscillation): VELO I Dataset: 2011: 1 fb−1 2012: 2 fb−1 total: 3 fb−1 T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 1 / 21 Introduction Introduction 0.7 0.6 it can be measured entirely from tree decays I 0.5 0.4 excluded area has CL > 0.95 γ is the least well known angle of the unitarity triangle I md see Brod on Tuesday! Brod, Zupan 2013 [1] I I K CKM fitter Winter 14 sin 2 0.3 the residual uncertainty is negligible: δγ/γ ≈ 10−7 I md & ms sol. w/ cos 2 < 0 (excl. at CL > 0.95) K 0.2 Vub 0.1 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 however: the branching ratios are small, typically at the 10−7 level measure γ in different “methods” GLW ADS GGSZ GLS time-dep. CP eigenstates, e.g. D → KK flavored states, e.g. D → Kπ self-conjugate 3-body decays, e.g. D → KS0 ππ singly Cabibbo suppressed states, e.g. D → KS0 Kπ e.g. Bs0 → Ds∓ K ± T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 2 / 21 Introduction Introduction Figure: Example interference diagram. Coherence factors appear with multibody states. Example observable: DK,K3π R+ = DK,K3π R+ = Γ(B + → [πKππ]D K + ) , Γ(B + → [Kπππ]D K + ) DK 2 K3π 2 K3π DK K3π DK K3π (rB ) + (rD ) + 2κD rB rD cos(δB + δD + γ) DK 2 K3π 2 K3π DK K3π DK K3π 1 + (rB ) (rD ) + 2κD rB rD cos(δB − δD + γ) T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 3 / 21 Introduction Introduction Our new results, LHCb-CONF-2014-004, supersede the previous LHCb combinations. Table: Summary of results for γ from the B factories BaBar and Belle, and from LHCb, and combiners. Errors correspond to 68% confidence or credibility. experiment BaBar [2] Belle [3] LHCb 3 fb−1 preliminary [4] LHCb 1 fb−1 [5] UTfit CKMfitter CKMfitter T.M. Karbach (CERN) result ◦ (69+17 −16 ) ◦ (68+15 −14 ) (67 ± 12)◦ ◦ (72.6+9.7 −17.2 ) (68.3 ± 7.5)◦ ◦ (70.0+7.7 −9.0 ) +6.3 ◦ (73.2−7.0 ) CKM2014 γ from LHCb date Jan 2013 Jan 2013 Apr 2013 (superseded!) Aug 2013 (superseded!) post Moriond 2014 Moriond / Jun 2014 CKM2014 11.09.2014 4 / 21 LHCb Inputs Inputs new LHCb results and changes Two combinations: robust full B → DK-like B → DK-like and B → Dπ I updated: Update the auxiliary inputs I B + → Dh+ , D → hh, GLW/ADS, 1 fb−1 LHCb [6] I I I I I B + → Dh+ , D → Kπππ, ADS, 1 fb−1 LHCb [7] updated: B + → DK + , D → KS0 hh, model-ind. GGSZ, 3 fb−1 LHCb [8] new: B + → DK + , D → KS0 Kπ, GLS, 3 fb−1 LHCb [9] new: B 0 → D0 K ∗0 , D → hh, GLW/ADS, 3 fb−1 LHCb [10] new: Bs0 → Ds∓ K ± , 1 fb−1 LHCb [11] T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 5 / 21 new: B + → DK + , D → KS0 Kπ, GLS, 3 fb−1m([K K π ] 0 5200 5400 first GLS measurement! LHCb [9] I no significant CP violation was observed 1 LHCb 1 1.5 2 2.5 K ) [MeV/c2] 3 m2 (K0K) [GeV2/ c4] S es selected in (a) the B ± ! [KS0 K⇡]D K ± and (b) he data in the SS and OS modes, and the two KS0 T.M. Karbach (CERN) ed are required to have a refitted B ± mass in a Entries / (15 MeV/ c2) LHCb − B+ → [K 0SK π +]D K + (e) Sum, incl. combinatorics Signal 20 Mis-ID Partially reconstructed 10 5200 5400 5600 3 2 1 5800 − m([K 0SK π+]D K +) [MeV/c2] (b) 1.5 30 0 2 0.5 5800 − D we restrict the phase space to the more sensitive D → K ∗+ K − region 30 LHCb − B → [K 0SK +π −]D K − (g) Sum, incl. combinatorics Signal 20 Mis-ID Partially reconstructed 10 0 5200 5400 5600 − 5800 m([K 0SK +π−]D K ) [MeV/c2] Phys. Lett. B733 (2014) 36 [9] Entries / (15 MeV/ c2) I S m2 (K0π) [GeV2/ c4] use singly Cabibbo suppressed D decays to non-CP eigenstates Entries / (15 MeV/ c2) Grossman, Ligeti, Soffer 2002 [12] I 1 OS candidat GLS method Entries / (15 MeV/ c2) I 5600 − + 0 S Entri 0 new: B + → DK10+ , D → KS Kπ, GLS, 3 fb−1 Entri LHCb Inputs 3 2 1 FigureFigure: 1: Distributions of B ± invariant mass of th “opposite-sign” decays B ± ! DK ± and (b, d, f, h) B ± ! D⇡ ± candidates i for (a, b, e, f) B + and (c, d, g, h) B candidates. Fi CKM2014 γ from LHCb 11.09.2014 66 / 21 LHCb Inputs new: B 0 → D 0 K ∗0 , D → hh, GLW/ADS, 3 fb−1 D ! K0 K and one ⇡ ); the fractions of longitudinal polarisation new: B → D0 Kfor∗0D, !D⇡ → hh, GLW/ADS, 3 fb−1 in the B ! D K and B ! D K backgrounds and the yields for each fit component within + ⇤ 0 + ⇤0 ⇤ 0 s ⇤0 LHCb 250 B0®D K *0 Bs0® D K *0 Combinatorial 200 B0®D ρ 0 150 Bs0® D* K *0 B 0® D* K *0 100 50 LHCb 250 B0®D K *0 Bs0® D K *0 Combinatorial 200 B0®D ρ 0 150 Bs0® D* K *0 B 0® D* K *0 100 50 5200 140 T.M. Karbach (CERN) 5400 5600 5800 5000 M(D(p K )K * ) [MeV/c ] – + 0 2 LHCb eV/c2 eV/c2 5000 300 140 CKM2014 γ from LHCb 5200 5400 5600 5800 M(D(p K )K * ) [MeV/c ] + – 0 LHCb 2 11.09.2014 Phys. Lett. B712 (2012) 203 [10] 300 Candidates per 10 MeV/c2 Candidates per 10 MeV/c2 in B 0 ! D⇤ K ⇤0 decays is allowed by floating the yields of Ieach thiscategory. mode CP hasviolation great potential exploiting the full D0 Kπ phase space this background in the DK ⇤0 and DK ⇤0 categories separately. The di↵erence between the Gershon 2009 [13] central value of the Bs0 and B 0 mass is fixed to its known value from Ref. [10] and the between the signal Gaussian resolutions is fixed from the simulation. Iratio the K ∗0 decay tags the B flavour at decay—no time dependent The non-parametric functions used to model all the specific backgrounds are smeared measurement to take into account the di↵erent mass resolutions observed in data and simulation. The 0 →D 0 K ∗0from −K + : 2.9σ mass distributions together with the B function resulting shown in Iinvariant significance for suppressed decay , D0the→fitπare Figs. 3 and 4. The numbers of signal events in each category are summarised in Table 1. 7 / 21 0 ∓ ± new: Bs → Ds K , 1 fb−1 LHCb-PAPER-2014-038, 1407.6127, sub. to JHEP Candidates / ( 0.1 ps) LHCb 2 10 data ± B0s → Ds K B0s → D*s − π+ ± B0d → D K + − 0 Λb → Λc K − 0 Λb → Ds p ± B0d → Ds K 10 ± This new technique gains sensitivity to γ through Bs0 mixing. ± I ± new: Bs0 → Ds∓ K ± , time-dep., 1 fb−1 total − B0s → Ds π+ − B0s → Ds ρ+ B0d → D π± + 0 Λb → Λc π− 0 Λb → D*s − p Combinatorial ± LHCb Inputs 1 B tagging power of eff = 5.07% I Lots of hadronic backgrounds: use multidemsional fit to identify the signal I 1770 ± 50 signal events 8 2 4 6 8 10 12 14 τ(Bs→ DsK) (ps) 10 12 14 τ (B0s → Ds K± ) [ps] + 6 LHCb 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 0 See also talk by Vava Gligorov! T.M. Karbach (CERN) 4 CKM2014 γ from LHCb 0.1 0.2 0.3 τ modulo (2π/∆ms) [ps] 11.09.2014 LHCb-PAPER-2014-038 [11] I − first measurement! Different set of systematics, pure “LHCb only” A(Ds K ) I 2 ± 2 0 -2 8 / 21 D 0 –D 0 mixing correction i 0 γ1 2 3 4 D0 –D0 mixing correction I D0 –D0 mixing has an effect on Meca, Silva, Atwood, Grossman [14, 15, 16, 12, 17] ti [ps] 0.05 0.135 0.35 1.2 3.5 I see also Matteo Rama on Tuesday! I O(1◦ ) on γ for B → DK I The effect can be larger for B → Dπ [18, Rama 2013]: q 2 /r Dπ ≈ O(1) x2D + yD B h_D0_TAU ai 0.0 0.014 0.018 0.0165 0.002 Acceptance function (binned) Acceptance function (binned) h_D0_TAU Entries 0.07 91279 Mean 0.488 RMS 0.3737 0.018 0.018 0.016 0.016 0.014 0.014 0.012 0.012 0.06 0.05 0.04 0.01 0.01 0.008 0.03 0.008 0.006 0.006 0.02 0.004 I 0.01 0.002 0 0 I 0.004 The topic was revisited following FPCP2013 Rama; Bondar et al. [19, 18]. 0.002 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0 0.5 1 1.5 2 2.5 0 3 3.5 4 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 We correct for the effect of D –D mixing Figure: LHCb D decay time Figure 34: Left: D decay time distribution of the two-body GLW/ADS analysis, taken + 0 ± ⌥ acceptance B +decaying → DKexpo, from the B ± order ! D⇡ ± in redfor is the I in leading in, DxD! , yKD ⇡ 2011 data. Overlayed nential with PDG lifetime, ⌧ = 410 fs, convolved with a single Gaussian of 60 fs width. D → hh. 0 I taking into account individual D Middle: Resulting binned acceptance, and a stepwise approximation using straight lines. decay acceptances The red time lines illustrate the nominal acceptance, blue corresponds to systematic variation (see text). Right: Zoom in of the middle plot. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 9 / 21 Auxiliary input Auxiliary input for D0 → K ± π ∓ π + π − 300charm system. 1σ I amplitude 250 200 I eff. ratio: 2 σ K3π rD strong phase diff.: 3 σ 150 I coherence factor: 250 150 κK3π D 100 50 D 0CLEO legacy. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 RKππ0 I We use a CLEO [20] and a Belle measurement [21] on 0 − + − + → Konline] π π Scans π ) and ure 5: Γ(D [Colour of the 0 − + − + K3⇡ Γ(D → π K π π ) to , ) parameter space. K3⇡ D K3π constrain rD . T.M. Karbach (CERN) 300 200 K3π δD 100 fit I We useBest the histogrammed 50likelihood for δ K3π , κK3π from D 350 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 RK3π 2 Phys. Lett. B731 (2014) 197 [22] I The D 0 → K ± π ∓ π + π − ADS 350measurement needs input on the π δK3 (deg.) D δD K ππ0 (deg.) updated: K3π Figure: CLEO legacy likelihood for δD K⇡⇡ 0 in the ) and (righ K3π(left) (RK⇡⇡ 0 , D and κD (labeled “RK3π ”) D → K3π. Histogram is used in the combination. CKM2014 γ from LHCb 11.09.2014 10 / 21 Auxiliary input Other auxiliary input updated: The GLW/ADS measurements need inputs on the charm system: I Kπ Kπ for the D0 → K − π + and D0 → π − K + decays: rD , δD I for charm mixing: xD , yD I dir for direct CP violation in D0 → h+ h− decays: Adir CP (KK), ACP (ππ) I We use the recent HFAG charm fit (FPCP 2014). new: Input for D → KS0 Kπ GLS I KS Kπ KS Kπ S Kπ We use a CLEO measurement for rD , δD , κK CLEO [23]. D new: Input for B 0 → D 0 K ∗0 GLW/ADS I We use a MC-based estimate for κDK B ∗0 = 0.95 ± 0.03 LHCb [10]. new: Input for Bs0 → Ds∓ K ± time-dep. to interpret γ − 2βs I We use the LHCb measurement of −2βs ≈ φs = 0.01 ± 0.07 ± 0.01 rad LHCb [24]. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 11 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 old preliminary 1 LHCb 0.8 Preliminary 67+12 −12 0.6 0.4 68.3% 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 old preliminary ...new auxiliariy input 1 LHCb 0.8 Preliminary 0.6 0.4 68.3% 67+12 −12 64+14 −15 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 ...new GGSZ ...new auxiliariy input 1 LHCb 0.8 Preliminary 0.6 0.4 68.3% 69+11 −11 64+14 −15 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 ...new GGSZ ...adding D→KSKπ GLS 1 LHCb 0.8 Preliminary 0.6 0.4 68.3% 69+11 −11 67+11 −11 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 ...adding DK*0 GLWADS ...adding D→KSKπ GLS 1 LHCb 0.8 Preliminary 0.6 0.4 68.3% 71.0+9.4 −10.1 67+11 −11 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 ...adding DsK time-dependent ...adding DK*0 GLWADS 1 LHCb 0.8 Preliminary 71.0+9.4 −10.1 72.9+9.2 −9.9 0.6 0.4 68.3% 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Evolution Evolution from the previous preliminary result LHCb preliminary [4] 2. Update the auxiliary inputs 3. Add new B + → DK + , D → KS0 hh GGSZ measurement 4. Add new B + → DK + , D → KS0 Kπ GLS measurement 5. Add new B 0 → D0 K ∗0 , D → hh GLW/ADS measurement 1-CL 1. previous result 1.2 ...adding DsK time-dependent 1 LHCb 0.8 Preliminary 72.9+9.2 −9.9 0.6 0.4 68.3% 0.2 95.5% 0 6. Add new Bs0 → Ds∓ K ± time-dependent measurement 50 60 70 80 90 100 110 γ [°] Figure: Making one change at a time. Robust combination. 7. robust nominal T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 12 / 21 Statistical procedure Statistical procedure The method is unchanged from previous combinations. I We assume (almost) all observables to be Gaussian distributed. I We assume Gaussian systematic fluctuations. I We don’t allow non-physical parameter values. I Use the plugin method for nominal results (Feldman-Cousins based frequentist method nuisances at their best-fit values). I Use the profile likelihood method for 2D illustration. I Estimate the frequentist coverage. I Additional Bayesian interpretation with uniform priors. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 13 / 21 Results robust combination Result of the robust combination LHCb-CONF-2014-004 Table: Credibility regions and most probable values for the hadronic parameters extracted from the robust combination. The second part of the table repeats the frequentist results for comparison. Observable Frequentist γ[◦ ] DK ◦ δB [ ] DK rB Bayesian γ[◦ ] DK ◦ δB [ ] DK rB Central value 72.9 126.8 0.0914 71.9 127.4 0.091 Intervals 68% 95% [63.0, 82.1] [52.0, 90.5] [115.3, 136.7] [101.6, 145.2] [0.0826, 0.0997] [0.0728, 0.1078] 68% 95% [61.9, 81.8] [50.9, 91] [115.6, 137.3] [100.3, 147.1] [0.0826, 0.0984] [0.0740, 0.106] The agreement of frequentist and Bayesian results is quite good. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 14 / 21 Results robust combination 1-CL Result of the robust combination LHCb-CONF-2014-004 1 LHCb Preliminary 0.8 72.9+9.2 −9.9 0.6 0.4 68.3% 0.2 95.5% 0 50 60 70 80 90 100 110 γ [°] Figure: Graphs for the robust combination (left: frequentist 1 − CL curves, right: Bayesian posterior). T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 15 / 21 Results robust combination 1-CL Result of the robust combination LHCb-CONF-2014-004 1 LHCb Preliminary 0.8 126.8+9.9 −11.5 0.6 0.4 68.3% 0.2 95.5% 1-CL 0 80 100 120 140 160 δDK B [°] 1 LHCb Preliminary 0.8 0.0914+0.0083 −0.0088 0.6 0.4 68.3% 0.2 95.5% 0 0.06 0.08 0.1 0.12 rDK B T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 16 / 21 Results full combination Lets add B + → Dπ + information LHCb-CONF-2014-004 Table: Confidence intervals and central values for the full combination. quantity γ (◦ ) 68% CL (◦ ) 95% CL (◦ ) DK rB 68% CL 95% CL DK ◦ δB ( ) 68% CL (◦ ) 95% CL (◦ ) Dπ rB 68% CL 95% CL Dπ ◦ δB ( ) 68% CL (◦ ) 95% CL (◦ ) T.M. Karbach (CERN) full 78.9 72.8 [71.5, 84.7] [54.6, 91.4] 0.0928 [0.0845, 0.1008] [0.0732, 0.1085] 128.9 [118.9, 137.9] [102.0, 145.9] 0.027 0.006 [0.016, 0.034] [0.005, 0.007] [0.001, 0.040] 341.8 215.6 [328.7, 351.4] [210.2, 231.5] no constraint CKM2014 γ from LHCb 11.09.2014 17 / 21 Results full combination LHCb-CONF-2014-004 1-CL Lets add B + → Dπ + information 1.2 robust full 1 LHCb 0.8 Preliminary 0.6 0.4 68.3% 0.2 95.5% 0 50 60 70 80 90 100 110 γ [°] Figure: 1 − CL curve for the robust and full combinations. I I I A second minimum appears. The 1σ errors are misleadingly small: highly non-Gaussian! At 2σ, the agreement with the robust combination is very good. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 18 / 21 Results full combination LHCb-CONF-2014-004 1 1-CL 1-CL Result of the full combination LHCb Preliminary 0.8 0.0928+0.0080 −0.0083 0.6 0.4 1 LHCb Preliminary 0.8 128.9+9.0 −10.0 0.6 0.4 68.3% 0.2 68.3% 0.2 95.5% 0 0.06 95.5% 0.08 0.1 0 0.12 80 100 1 1-CL 1-CL rDK B LHCb Preliminary 0.8 0.6 0.4 140 160 δDK B [°] 1 LHCb Preliminary 0.8 0.6 0.4 68.3% 0.2 68.3% 0.2 95.5% 0 0 120 0.01 0.02 0.03 0.04 0.05 0.06 rDBπ 95.5% 0 180 200 220 240 260 280 300 320 340 360 δDBπ [°] Dπ is compatible with 0. At 2σ, rB T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 19 / 21 Results full combination LHCb-CONF-2014-004 0.05 LHCb Preliminary 0.04 rDBπ rDBπ Result of the full combination 0.05 LHCb 0.03 0.03 0.02 0.02 0.01 0.01 contours hold 68%, 95% CL 0 Preliminary 0.04 50 60 contours hold 68%, 95% CL 70 80 90 100 0 γ [°] 200 250 300 350 Dπ δB [°] Figure: Profile likelihood contours, full combination. The contours are the two-dimensional 1σ and 2σ contours. Dπ also pulls up γ. The high observed value of rB T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 20 / 21 Coverage test LHCb-CONF-2014-004 toys Coverage test We test the frequentist coverage at the minima of the combinations. I We find that the profile likelihood construction undercovers quite a bit. I α (prof. LH.) 0.6158 0.5593 0.5454 α (plugin) 0.6494 0.6154 0.6120 120 full (1) Prob Plugin 80 60 The coverage of the full combination is worse than of the robust. Expected due to Dπ . the low value of rB η = 0.683 robust Dπ full (1), rB = 0.027 Dπ full (2), rB = 0.006 140 100 40 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p-value toys I The robust plugin method has good coverage. robust p-value toys I 140 Prob 120 Plugin 100 80 60 40 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 180 Prob 160 Plugin 140 120 100 80 60 40 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 full (2) p-value T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21 Conclusion Conclusion I We updated the LHCb γ combination of tree-level measurements. I The effect of D0 –D0 mixing is taken into account, the frequentist coverage was tested. I robust Bayesian results are available and agree. I We explore B + → Dπ + channels: they show up early all obstacles on the way to high precision. I The robust coverage is good. I Robust frequentist combination: ◦ γ = (72.9+9.2 −9.9 ) @ 68% CL , ◦ @ 68% CL , ◦ @ 95% CL . γ ∈ [63.0, 82.1] γ ∈ [52.0, 90.5] I More precise than the B factory legacy. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 22 / 21 Backup L 0 Backup Auxiliary input for D → KS Kπ 0 Tag KK ππ KS0 π 0 π 0 KS0 π 0 KS0 ω KS0 η(γγ) KS0 η(πππ ) KS0 η ′ Kπ SS 0 S(KS Kπ|G) 6.0±14.2 2.0±11.1 43.7±37.8 233.1±57.9 199.9±68.7 47.8±28.2 10.1±18.1 83.0±87.5 288.9±48.7 Auxiliary input for D → KS0 Kπ TABLE XXIII. Efficiency–corrected signal yields in the re0 L. stricted region for the CP tags with a K new: Tag KL0 π 0 KL0 ω KL0 η KL0 π 0 π 0 0 IS(KSimilar input 25.9±38.9 is needed as186.4±194.0 in the −4.7±8.5 S Kπ|G) 116.2±37.1 case of D → Kπππ. KS Kπ I rate RinD tainty if theratio: migration both directions is equal, but the presence of the resonance means that a larger fracS Kπ tion of events will migrate out diff.: of the restricted region I eff. strong phase δ isKdetermined than migrate in. The net migration factor D from the simulated data. It is different different types Kπ Sfor I coherence factor: κK of tags due to the quantum correlations D which alter the 0 distribution of the KS Kπ decay on the Dalitz plot. The I usefactor a single net We migration is treatedCLEO in the same way as a systematic uncertainty on the efficiency in the analysis. The net migration factor, that is the net loss of events inside the region, varies between tag categories and is of order 1% of the yield within the region. K S Kπ Tables XXVI–XXIX give the results for the observable D its uncertainties for the K ∗ (892)± bin. The average FIG. 10. The best–fit point for R ∗ and δK∗ K which are κ and K K D S Kπ K values are κ+ = 0.44 ± 0.30 and κ− = 3.18 ± 1.08 with a Figure: KS Kπ and CLEO likelihood fortheδregions measured over the restricted region, and enclosing D χ2D /dof of 6.5/10. The uncertainties due to non–uniform 1, 2, and 3 standard deviations from that point. KS Kπ (labeled “RK ∗ K ”) [23]. efficiency are 0.002 and 0.001 for p and q, respectively. κD KS are Kπreduced in comparison to the full Dalitz plot They Histogram is not used in the D measurement as the efficiency is more uniform over the restricted region. combination. ues for γ, δB , and rB are consistent with current knowlThe fitted values of p and q are p = 0.893 ± 0.089 and edge [4]. The data samples are fit with only the parameq = 0.446 ± 0.304, with χ2 /dof given by 48.7/40. ∗This ter γ free. The width of the best–fit γ distribution is 10◦ . K K γ from LHCb T.M. (CERN) CKM2014 11.09.201460% of24the / 21 leads to aKarbach measurement of RK ∗ K = 1.00±0.16 and δD = The restricted region will have approximately measurement [23]. R δ κ = 0.356 ± 0.034 ± 0.007 , = 0.46 ± 0.28 , = 1.00 ± 0.16 . Backup Auxiliary input from HFAG Auxiliary input from HFAG taking a step back Comparing the old auxiliary inputs to the new ones: old: I I we needed input on the D → Kπππ system from CLEO that measurement had some influence on the charm mixing parameters xD , yD I it was obtained using the HFAG status as of 2009 as input I . . . so we took the 2009 CLEO input and added the new LHCb D0 wrong sign mixing measurement I we also added “∆ACP ” T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 25 / 21 Backup Auxiliary input from HFAG Auxiliary input from HFAG taking a step back Comparing the old auxiliary inputs to the new ones: new: I the input for D → Kπππ was updated using more CLEO-c data I the new measurement no longer impacts xD , yD , as the world average is much stronger now I it was obtained using the HFAG status as of 2014 as input I . . . so now we can use HFAG directly, including up-to-date charm mixing, and “∆ACP ” T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 25 / 21 Backup Auxiliary input from HFAG Auxiliary input from HFAG comparing old and new yD rKπ 0.015 0.064 old old new 0.062 new 0.01 0.06 0.058 0.005 0.056 0.054 contours hold 68%, 95% CL (etc.) 160 180 200 contours hold 68%, 95% CL (etc.) 220 240 δKπ [°] 0 0 0.005 0.01 0.015 xD Figure: Profile likelihood contours: The “old” contour corresponds to what was used in the previous (2013) combination (the 2009 CLEO input [25] together with the 2013 LHCb charm mixing measurement [26]). The “new” contour is what is used in this combination (HFAG 2014). The contours are two-dimensional 1–4σ contours. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 26 / 21 Backup Auxiliary input from HFAG Auxiliary input from HFAG RD Kπ The parameter RD is the squared ratio of the doubly-Cabibbo-suppressed 0 amplitude D → π − K + to the favored one D0 → K − π + . It is not the ratio of branching ratios. It gets often measured in time-dependent wrong-sign D0 mixing measurements: 2 q 2 t x2D + yD t Kπ Kπ Kπ Kπ RW S = RD + RD x cos(δD ) ± y sin(δD ) + τ 4 τ 0.0037 0.00365 nominal errors 0.0036 diff.-in-squares to previous 0.00355 0.0035 0.00345 0.0034 0.00335 0.0033 0.00325 0.0032 EPS 09 FPCP 10 CHARM 10 LP 11 Mar 12 Apr 13 CHARM 13 FPCP 14 Kπ Figure: Evolution of HFAG results on RD . T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 27 / 21 Backup Auxiliary input for D 0 → K ± π ∓ π + π − Auxiliary input for D0 → K ± π ∓ π + π − K3π updated: We use an updated CLEO-c measurement of κK3π and δD D (histogrammed likelihood). For the amplitude ratio K3π rD = A(D0 → π − K + π − π + )/A(D0 → K − π + π − π + ) (1) we use I a CLEO measurement [20] of Γ(D0 → K − π + π − π + ), Γ(D0 → K − π + π − π + ) = 0.08290 ± 0.00043 ± 0.00200 , I a Belle measurement [21] of Γ(D0 → π − K + π − π + ), Γ(D0 → π − K + π − π + ) = 0.00026 ± 0.00001 ± 0.00001 . I (2) (3) K3π These are related to rD through the equation RW S (D → Kπππ) = (4) 1 2 K3π 2 K3π K3π K3π (rD ) − κK3π − xD sin δD ) + (x2D + yD ). D rD (yD cos δD 2 T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 (5) 28 / 21 Backup Goodness of fit Goodness of fit Table: Fit probabilities of the best fit values of the two combinations. Combination robust full T.M. Karbach (CERN) P (Prob) 89.7% 97.2% CKM2014 γ from LHCb P (toy-based) (89.4 ± 0.5)% (96.8 ± 0.3)% 11.09.2014 29 / 21 Backup robust combination: Frequentist 2D 0.14 LHCb Preliminary 0.12 0.1 δDK B [°] rDK B Result of the robust combination 180 LHCb Preliminary 160 140 0.08 120 0.06 100 contours hold 68%, 95% CL 50 60 70 80 90 100 γ [°] rDK B 0.04 40 40 contours hold 68%, 95% CL 50 60 70 80 90 100 γ [°] LHCb Preliminary 0.1 0.05 contours hold 68%, 95% CL 90 100 110 120 130 140 150 160 170 180 δDK B [°] Figure: Profile likelihood contours, robust combination. The contours are the two-dimensional 1σ and 2σ contours. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 30 / 21 Backup full combination: Frequentist 2D 0.14 LHCb Preliminary 0.12 rDBπ rDK B Result of the full combination 0.05 LHCb 0.1 0.03 0.08 0.02 0.06 0.01 contours hold 68%, 95% CL 0.04 Preliminary 0.04 50 60 contours hold 68%, 95% CL 70 80 90 100 γ [°] 0 50 60 70 80 90 100 γ [°] Figure: Profile likelihood contours, full combination. The contours are the two-dimensional 1σ and 2σ contours. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 31 / 21 Backup full combination: Frequentist 2D δB [°] LHCb Dπ δDK B [°] Result of the full combination Preliminary 160 140 LHCb 300 Preliminary 200 120 100 100 contours hold 68%, 95% CL 60 0 70 80 90 100 γ [°] 0.14 LHCb Preliminary 0.12 100 200 300 LHCb Preliminary 0.04 0.03 0.08 0.02 0.06 γ [°] 0.05 0.1 0.01 contours hold 68%, 95% CL 0.04 contours hold 68%, 95% CL 0 rDBπ rDK B 50 100 T.M. Karbach (CERN) 120 contours hold 68%, 95% CL 140 160 δDK B 0 [°] CKM2014 γ from LHCb 200 250 300 350 Dπ δB [°] 11.09.2014 32 / 21 Backup Coverage test Coverage test Table: Measured coverage α of the confidence intervals for γ. The expected coverage is denoted as η. robust η = 0.6827 η = 0.9545 η = 0.9973 Dπ full, rB = 0.027 η = 0.6827 η = 0.9545 η = 0.9973 Dπ full, rB = 0.006 η = 0.6827 η = 0.9545 η = 0.9973 T.M. Karbach (CERN) α (profile likelihood) 0.6158 ± 0.0089 0.9200 ± 0.0050 0.9923 ± 0.0016 α (profile likelihood) 0.5593 ± 0.0091 0.9160 ± 0.0051 0.9929 ± 0.0015 α (profile likelihood) 0.5454 ± 0.0091 0.9026 ± 0.0054 0.9906 ± 0.0018 (α − η) −0.0669 −0.0345 −0.0050 (α − η) −0.1234 −0.0385 −0.0044 (α − η) −0.1373 −0.0519 −0.0067 CKM2014 γ from LHCb α (Plugin) 0.6494 ± 0.0087 0.9358 ± 0.0045 0.9919 ± 0.0016 α (Plugin) 0.6154 ± 0.0089 0.9402 ± 0.0043 0.9929 ± 0.0015 α (Plugin) 0.6120 ± 0.0089 0.9314 ± 0.0046 0.9933 ± 0.0015 (α − η) −0.0333 −0.0187 −0.0054 (α − η) −0.0673 −0.0143 −0.0044 (α − η) −0.0707 −0.0231 −0.0040 11.09.2014 33 / 21 References [1] J. Brod and J. Zupan, The ultimate theoretical error on γ from B → DK decays, JHEP 1401 (2014) 051, arXiv:1308.5663. [2] Babar collaboration, J. P. Lees et al., Observation of direct CP violation in the measurement of the Cabibbo-Kobayashi-Maskawa angle γ with B ± → D(∗) K (∗)± decays, Phys. Rev. D87 (2013) 052015, arXiv:1301.1029. [3] K. Trabelsi, Study of direct CP in charmed B decays and measurement of the CKM angle γ at Belle, arXiv:1301.2033. [4] LHCb collaboration, A measurement of γ from a combination of B ± → DK ± analyses including first results using 2 fb−1 of 2012 data, LHCb-CONF-2013-006. [5] LHCb collaboration, R. Aaij et al., Measurement of the CKM angle γ from a combination of B ± → Dh± analyses, Phys. Lett. B726 (2013) 151, arXiv:1305.2050. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21 References [6] LHCb collaboration, R. Aaij et al., Observation of CP violation in B + → DK + decays, Phys. Lett. B712 (2012) 203, arXiv:1203.3662. [7] LHCb collaboration, R. Aaij et al., Observation of the suppressed ADS modes B ± → [π ± K ∓ π + π − ]D K ± and B ± → [π ± K ∓ π + π − ]D π ± , Physics Letters B723 (2013) 44, arXiv:1303.4646. [8] LHCb collaboration, Measurement of the CKM angle γ with a model-independent Dalitz plot analysis of B ± → DK ± , D → KS0 π + π − and D → KS0 K + K − decays, LHCb-PAPER-2014-041. [9] LHCb collaboration, R. Aaij et al., A study of CP violation in B ± → DK ± and B ± → Dπ ± decays with D → KS0 K ± π ∓ final states, Phys. Lett. B733 (2014) 36, arXiv:1402.2982. [10] LHCb collaboration, Measurement of CP violation parameters in B 0 → DK ∗0 decays, LHCb-PAPER-2014-028. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21 References [11] LHCb collaboration, Measurement of CP asymmetry in Bs0 → Ds∓ K ± decays, LHCb-PAPER-2014-038. [12] Y. Grossman, Z. Ligeti, and A. Soffer, Measuring gamma in B ± → K ± (KK∗)(D) decays, Phys. Rev. D67 (2003) 071301, arXiv:hep-ph/0210433. [13] T. Gershon and A. Poluektov, Double Dalitz Plot Analysis of the Decay B 0 → DK + π − , D → KS0 π + π − , Phys. Rev. D81 (2010) 014025, arXiv:0910.5437. [14] C. C. Meca and J. P. Silva, Detecting new physics contributions to the D0 - anti-D0 mixing through their effects on B decays, Phys. Rev. Lett. 81 (1998) 1377, arXiv:hep-ph/9807320. 0 [15] J. P. Silva and A. Soffer, Impact of D0 –D mixing on the experimental determination of γ, Phys. Rev. D61 (2000) 112001, arXiv:hep-ph/9912242. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21 References [16] D. Atwood, I. Dunietz, and A. Soni, Improved methods for observing CP violation in B ± → KD and measuring the CKM phase γ, Phys. Rev. D63 (2001) 036005, arXiv:hep-ph/0008090. [17] Y. Grossman, A. Soffer, and J. Zupan, The Effect of D–D mixing on the measurement of γ in B → DK decays, Phys. Rev. D72 (2005) 031501, arXiv:hep-ph/0505270. [18] M. Rama, Effect of D–D mixing in the extraction of γ with B − → D0 K − and B − → D0 π − decays, Phys. Rev. D89 (2014) 014021, arXiv:1307.4384. [19] A. Bondar, A. Dolgov, A. Poluektov, and V. Vorobiev, Effect of direct CP violation in charm on γ extraction from B → DK ± , D → KS0 π + π − Dalitz plot analysis, Eur. Phys. J. C73 (2013) 2476, arXiv:1303.6305. [20] CLEO Collaboration, G. Bonvicini et al., Updated measurements of absolute D+ and D0 hadronic branching fractions and T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21 References σ(e+ e− → DD) at Ecm = 3774 MeV, Phys. Rev. D89 (2014) 072002, arXiv:1312.6775. [21] Belle Collaboration, E. White et al., Measurement of the wrong-sign decay D0 → K + π − π + π − , Phys. Rev. D88 (2013), no. 5 051101, arXiv:1307.5935. [22] J. Libby et al., New determination of the D0 → K − π + π 0 and D0 → K − π + π + π − coherence factors and average strong-phase differences, Phys. Lett. B731 (2014) 197, arXiv:1401.1904. [23] CLEO collaboration, J. Insler et al., Studies of the decays D0 → KS0 K − π + and D0 → KS0 K + π − , Phys. Rev. D85 (2012) 092016, arXiv:1203.3804. [24] LHCb collaboration, R. Aaij et al., Measurement of CP violation and the Bs0 meson decay width difference with Bs0 → J/ψK + K − and Bs0 → J/ψπ + π − decays, Phys. Rev. D87 (2013) 112010, arXiv:1304.2600. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21 References [25] CLEO collaboration, N. Lowrey et al., Determination of the D0 → K − π + π 0 and D0 → K − π + π + π − Coherence Factors and Average Strong-Phase Differences Using Quantum-Correlated Measurements, Phys. Rev. D80 (2009) 031105, arXiv:0903.4853. [26] LHCb collaboration, R. Aaij et al., Measurement of D0 –D0 mixing parameters and search for CP violation using D0 → K + pi− decays, arXiv:1309.6534. T.M. Karbach (CERN) CKM2014 γ from LHCb 11.09.2014 21 / 21