7th February Determination of γ from B ± →DK ± : Input from CLEOc Jim Libby (University of Oxford)

7th February Outline Measuring γ with B ± →DK ± Measuring γ with B ± →DK ± Complementary measurements of D decay at CLEO-c Complementary measurements of D decay at CLEO-c –K 0 ππ –K ± X (X=π,ππ or πππ) Other modes will be discussed later today Other modes will be discussed later today

7th February Searching for new physics Non Standard Model particles contribute within the virtual loops Non Standard Model particles contribute within the virtual loops Differences between tree-level and loop-level triangles Differences between tree-level and loop-level triangles –Signature of new physics Complements direct searches Complements direct searches TREE LOOP

7th February B→DK decays involve b → c and b → u transitions B→DK decays involve b → c and b → u transitions Access  via interference if D 0 and D 0 decay to the same final state Access  via interference if D 0 and D 0 decay to the same final state These measurements are theoretically clean These measurements are theoretically clean –No penguin  CKM standard candle –largest correction is sub-degree from D-mixing LHCb looking at a number of strategies to study such decays LHCb looking at a number of strategies to study such decays –B + : Atwood-Dunietz-Soni ('ADS'), 3 and 4 body Dalitz Plot Anal. Introduction B ± →DK ± Ratio of absolute amplitudes of colour/CKM suppressed to favoured (~0.1) Strong phase difference

7th February For B + →D(K 0 π + π − )K + For B + →D(K 0 π + π − )K + Assume isobar model (sum of Breit-Wigners) Assume isobar model (sum of Breit-Wigners) Fit D -Dalitz plots from B -decay to extract γ, r B and δ B Fit D -Dalitz plots from B -decay to extract γ, r B and δ B B ± →D(K 0 S π + π − )K ± K*(892)  (770) Number of resonances Amplitude and phase extracted from D *+ →D 0 π + sample at B-factories Rel. BW Non-resonant

7th February B ± →D(K 0 S π + π − )K ± B+B+ B−B− Simulated LHCb data Absence of CP violation: distributions would be identical

7th February Current e + e − results Current best direct constraints on γ : Current best direct constraints on γ : Based on ~300 events each (~1/3 of final data set) Based on ~300 events each (~1/3 of final data set) However, large error from isobar model assumptions However, large error from isobar model assumptions BABAR and Belle use large samples of flavour tagged D* +  D 0 π + events to find parameters of the isobar model BABAR and Belle use large samples of flavour tagged D* +  D 0 π + events to find parameters of the isobar model –Excellent knowledge of |f| 2 but phases less well known Model uncertainties from assumptions about the resonance structures in the model Model uncertainties from assumptions about the resonance structures in the model PRD 73, (2006) hep-ex/

7th February K * 0 (1430) Isobar model uncertainty Most challenging aspects of the model uncertainty come from K π and ππ S- wave Most challenging aspects of the model uncertainty come from K π and ππ S- wave BABAR (PRL ,2005) Fit to flavour tag sample

7th February Model uncertainty impact at LHCb The model-dependent likelihood fit yields an uncertainty on γ between 7-12° for an r B =0.1 The model-dependent likelihood fit yields an uncertainty on γ between 7-12° for an r B =0.1 –One year of data –Range represents differing assumptions about the background However, the current model uncertainty is 10-15° with an r B =0.1 However, the current model uncertainty is 10-15° with an r B =0.1 –Uncertainties  1/ r B Without improvements LHCb sensitivity (and e + e − )will be dominated by model assumptions within 1 year of data taking Without improvements LHCb sensitivity (and e + e − )will be dominated by model assumptions within 1 year of data taking Motivates a model-independent method that relies on a binned analysis of the Dalitz plot Motivates a model-independent method that relies on a binned analysis of the Dalitz plot –Disadvantage is that information is lost via binning

7th February Average cosine and sine of strong phase difference between D 0 and D 0 decay amplitudes ( Δδ D ) in this bin Binned method Proposed in the original paper by Giri, Grossman, Soffer and Zupan and since been extended significantly by Bondar and Poluektov Proposed in the original paper by Giri, Grossman, Soffer and Zupan and since been extended significantly by Bondar and Poluektov –GGSZ, PRD 68, (2003) –BP, most recently arXiv: v1 [hep-ph] Bin the Dalitz plot symmetrically about m − 2 = m + 2 then number of entries in B − decay given by: Bin the Dalitz plot symmetrically about m − 2 = m + 2 then number of entries in B − decay given by:  # events in bin of flavour tagged D 0 decays

7th February CLEO-c measurement status Studies not complete but projected uncertainties on c and s will lead to 3-5 degree uncertainty on γ 1/3 of total data (<1/2 the CP tags)

7th February Inkblot test Bondar and Poluektov show that the rectangular binning is far from optimal for both CLEOc and γ analyses Bondar and Poluektov show that the rectangular binning is far from optimal for both CLEOc and γ analyses –16 uniform bins has only 60% of the B statistical sensitivity –c and s errors would be 3 times larger from the ψ″ Best B-data sensitivity when cos( Δδ D ) and sin( Δδ D ) are as uniform as possible within a bin Best B-data sensitivity when cos( Δδ D ) and sin( Δδ D ) are as uniform as possible within a bin Absolute value of strong phase diff. (BABAR model used in LHCb ) Good approximation and the binning that yields smallest s and c errors is equal Δδ D bins-80% of the unbinned precision

7th February Implementation at LHCb Generate samples of B ± →D(K 0 S ππ)K ± with a mean of 5000 events split between the charges Generate samples of B ± →D(K 0 S ππ)K ± with a mean of 5000 events split between the charges Bin according to strong phase difference, Δδ D  Bin according to strong phase difference, Δδ D  Minimise χ 2 Minimise χ 2 ( γ=60°, r B =0.1 and δ B =130°) K i, c i and s i amplitudes calculated from model In reality from flavour tagged samples and CLEO-c

7th February γ uncertainties with 5000 toy experiments Scenario 2 fb -1 Mod. Indep. 10 fb -1 Mod. Indep. 2 fb -1 Mod. Dep. (LHCb ) No background 7.9° 3.5° 5.9° Acceptance 8.1° 3.5° 5.5° Dπ (B/S = 0.24) (Best case scenario) 8.8° 4.0° 7.3° DK comb (B/S=0.7) (Worst case scenario) 12.8° 5.7° 11.7°

7th February B ± →D(K 0 S π + π − )K ± at LHCb Model independent fit with binning that yields smallest error from exploiting CLEO-c data Model independent fit with binning that yields smallest error from exploiting CLEO-c data –Binning depends on model - only consequence of incorrect model is non-optimal binning and a loss of sensitivity Measurement has no troublesome and hard-to-quantify systematic and outperforms model-dependent approach with full LHCb dataset with currently assigned model error Measurement has no troublesome and hard-to-quantify systematic and outperforms model-dependent approach with full LHCb dataset with currently assigned model error –10 fb -1 statistical uncertainty 4-6° depending on background CLEO-c measurements essential to validation of assumptions in model dependent measurement CLEO-c measurements essential to validation of assumptions in model dependent measurement LHCb – Available via CERN document server LHCb – Available via CERN document server Model independent Model dependent σ(model)=10° σ(model)=5°

7th February ADS

17 Look at DCS and CF decays of D to obtain rates that have enhanced interference terms Look at DCS and CF decays of D to obtain rates that have enhanced interference terms Unknowns : r B ~0.1,  B,  D K , , N K , N hh (r D =0.06 well measured) Unknowns : r B ~0.1,  B,  D K , , N K , N hh (r D =0.06 well measured) With knowledge of the relevant efficiencies and BRs, the normalisation constants (N K , N hh ) can be related to one another With knowledge of the relevant efficiencies and BRs, the normalisation constants (N K , N hh ) can be related to one another Important constraint from CLEOc σ(cos  D K   Important constraint from CLEOc σ(cos  D K   Overconstrained: 6 observables and 5 unknowns Overconstrained: 6 observables and 5 unknowns ADS method h=π or K

7th February Four-body ADS B→D(K πππ)K can also be used for ADS style analysis B→D(K πππ)K can also be used for ADS style analysis –Also K ππ 0 However, need to account for the resonant substructure in D→Kπππ However, need to account for the resonant substructure in D→Kπππ –made up of D→K*ρ, K − a 1 (1260) +,.,… –in principle each point in the phase space has a different strong phase associated with it - 3 and 4 body Dalitz plot analyses exploit this very fact to extract γ from amplitude fits Atwood and Soni (hep-ph/ ) show how to modify the usual ADS equations for this case Atwood and Soni (hep-ph/ ) show how to modify the usual ADS equations for this case –Introduce coherence parameter R K3π which dilutes interference term sensitive to γ R K3π ranges from R K3π ranges from 1=coherent (dominated by a single mode) to 1=coherent (dominated by a single mode) to 0=incoherent (several significant components) 0=incoherent (several significant components) Integrating over phase space

7th February Measurements of the rate of K3 π versus different tags at CLEO-c allows direct access to R K3π and δ K3π Measurements of the rate of K3 π versus different tags at CLEO-c allows direct access to R K3π and δ K3π 1. Normalisation from CF K − π + π + π − vs. K + π − π − π + and K − π + π + π − vs. K + π − 2. CP eigenstates: 3. K − π + π + π − vs. K − π + π + π − : 4. K − π + π + π − vs. K − π + : Determining the coherence factor

7th February Amplitude models To fully exploit D →K3π in B-decay an unbinned fit to the data maybe optimal To fully exploit D →K3π in B-decay an unbinned fit to the data maybe optimal However, need model of DCS decays However, need model of DCS decays –Accessible from CP-tagged data at CLEO-c Furthermore, model can guide division of phase space into coherent regions for binned R K3π analysis Furthermore, model can guide division of phase space into coherent regions for binned R K3π analysis

7th February Conclusion Focussed on the things that are being done and how they impact γ Focussed on the things that are being done and how they impact γ –Apology 1: examples drawn from LHCb because that is what I know best Rest of the meeting in three parts: Rest of the meeting in three parts: –status of the UK work on the ADS and four body fits –extensions to the current work –beer Apology 2: to those on the phone Apology 2: to those on the phone