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Mixing and CPV in the D System Mixing in the D system Time-integrated CPV and new physics Mixing in neutral D system Time-dependent Time-integrated Summary Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Mixing Parameters Mixing in the D system arises from the existence of two mass eigenstates D1 and D2 with eigenvalues It is usually defined by four parameters: where M = (m1+m2) / 2 and = (1+2) / 2 Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Decay Rates and CPV Decay amplitudes and evolve at time t to be where With no CPV in either mixing or decay we expect that and where is the strong phase difference between decays and With CPV in direct decay or in mixing we expect that where Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CPV and Mixing in Charm Meson Decays Time-integrated CPV and new physics Mixing in neutral D system Time-dependent Time-integrated Summary Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Time-integrated CPV results Recent results: D0 → K+K−, π+π− D0 → K+K−π0, π+π−π0 Older result (not covered here): D0 → K+K−π+ -- PRD 71, 091101 (2005) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CPV in D0 → K+K−/π+π− CP asymmetry: Experimentally tricky to measure with per-mille systematics: Tagging efficiency asymmetry for soft pion in D*+ → D0 π+ studied with control sample of D0 → K−π+ events. •Crucial to get this from data, not MC! •Control sample corrected for K+/K− and π+/π− efficiency asymmetry as function of polar angle and momentum. MC simulation Forward-backward production asymmetry •From Z/γ interference & higher-order QED diagrams •These effects are odd in cos(θ*) •CP asymmetry is even in cos(θ*) •... so measure aCP in bins of |cos(θ*)| & odd terms vanish 385/fb, PRL 100,061803 (2008) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CPV in D0 → K+K−/π+π− Plotting CP asymmetry in bins of |cos(θ*)|: Systematics Last bin excluded (due to acceptance) Results are consistent with zero CP asymmetry: 385/fb, PRL 100,061803 (2008) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CPV in D0 → K+K−π0/π+π−π0 •Move to three-body mode -- we now have more tools: •Look for rate asymmetry in bins of |cos(θ*)| as before •Look for asymmetry in distribution. •Second point is crucial -- CP asymmetry may pop up in one corner of phase space or in one intermediate resonance. •Remember: Direct CPV is not universal. •Localized asymmetry may be washed out -- or even cancelled -- when looking at integral over whole phase space. •Several ways used to check for distribution asymmetry: •Bin-by-bin difference in normalized Dalitz plot (model- independent) •Difference in angular moments (model-independent) •Differences in amplitudes & phases of components in Dalitz plot fit Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CPV in D0 → K+K−π0/π+π−π0 Look for distribution Angular distribution asymmetry (first three Legendre polynomial moments only asymmetry in normalized shown here): Dalitz plots: Efficiency-corrected Dalitz plots P(χ2) = 32.8% P(χ2) = 16.6% 385/fb, arXiv:0802.4035 Normalized residuals accepted by PRD-RC No evidence of CP violation found Charm 2007, Ithaca, NY, 8/06/2007 No evidence of CP violation fo Brian Meadows, U. Cincinnati CPV in D0 → K+K−π0/π+π−π0 Asymmetries in Dalitz plot 385/fb, arXiv:0802.4035 Asymmetries in phase- fits? 0 + − 0 accepted by PRD-RC space-integrated rates? D →π π π D0 → K+K−π0 No evidence of CP violation found c.f. Belle: [arXiv:0801.2439, 532/fb] Thus, no evidence for CP violation found in any of the No evidence of CP violation found four tests. U. Cincinnati Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, Low MassS-wave K and Systems Brian Meadows University of Cincinnati S- waves in heavy flavour physics ? What is known about S- wave -+ and K -+ scattering and how this should apply to D decays Measurements of S- wave component D K -++ Other modes Summary Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati S-waves in Heavy Flavour physics ? Low mass K and S- wave systems are of intrinsic interest and important for understanding the spectroscopy of scalar mesons – existence of low mass or states in particular This is not covered in this talk, though a review of recent theoretical and experimental efforts focussing on pole parameters for (476–628)− i (226–346) and of (694- 841)-i(300-400) MeV/c2 cites many of the relevant references: D. V. Bugg, J. Phys. G 34, 151 (2007). The S- wave is also both ubiquitous and “useful” Interference in hadronic final states through Dalitz plot analyses plays a major role in studying much that is new in flavour physics: CKM D0-D0 mixing Sign of cos2, etc…. General belief is that P- and D- waves are well described by resonance contributions, but that better ways to parameterize the S- wave systems are required as our targets become more precise. This talk focusses on recent attempts to improve on this situation. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati What is Known about K Scattering ? SLAC/LASS experiment E135: K -p K -+n (11 GeV/c) NPB 296, 493 (1988) +++ Total S-wave +++ I = 1/2 L=0 L=0 Phase degrees +++ I = 3/2 Phase 0 |T | I =3/2 Phase 0 |T | K +p K ++n M (K -+) (GeV/c2) M (K -+) (GeV/c2) K -p K –-D++ I- spins are separated using I=3/2 phases from K +p K ++n and K -p K –-D++ (13 GeV/c) M (K§ §) (GeV/c2) No evidence for (800) – yet ~no data below 825 MeV/c2 either. Estabrooks, et al, NP B133, 490 (1978) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Effective Range Parametrization (LASS) NPB 296, 493 (1988) Scattering amplitude is unitary (elastic) up to K’ threshold (for even L): where: S-wave (I = 1/2): S-wave (I = 3/2): No resonances: One resonance: a “scattering lengths” M0 ~1435 ; 0 ~275 MeV/c2 b “effective ranges” Strictly, only valid below ~1460 MeV/c2. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati S-wave Scattering (I = 0) Excellent Data from - p - + n G. Greyer, et al, NP B75, 189-245 (1975) (several analyses - including other reactions) B. Hyams, et al, NP B64, 134 (1973) I=0 Im T 00 (degrees) Au, Morgan, Pennington, PR D35, 1633-1664 (1987) PT KK Re T Threshold KK Threshold M() (MeV/c2 No evidence for (500) – essentially no data below 500 MeV/c2 either. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati S-wave Scattering (I = 2) from N. Achasov and G. Shestakov, PRD 67, 243 (2005) Data included in fit: + p + + n (12.5 GeV/c) 02 W. Hoogland, et al, NP B69, (degrees) 266-278 (1974) + d - - ppspec 0 2 (9 GeV/c) N. Durusoy, et al, PL B45, 517- 520 (1973) NOTE - 02 is negative. Fit assumes amplitude to be unitary: Reasonable assumption up to §§ threshold Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati How This Should Apply to 3-body D Decays Decays have amplitudes F(s) related to scattering amplitude T(s) by: Ff (s) = Tfk (s) Qk (s) Intermediate states Weak decay/fragmentation: D+ + • I-spin not conserved Q k T • k scattering on +during Scattering: f kf fragmentation can impart an overall phase K- + Watson theorem: Up to elastic limit (for each L and I ) K -+ phase has same dependence on s as elastic scattering but there can be an from overall phase shift. Behaviour of Q(s) is unknown. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Conventional Approach – Breit-Wigner Model “BWM” The “isobar model” ignores all this, and problems of double-counting: “NR” {12} {13} {23} 2 1 1 1 2 2 3 2 3 3 3 2 1 Amplitude for channel {i j} with angular momentum L: NR - constant R form D form spin (L=0) factor factor factor In the BWM each resonance “R” (mass mR, width R) described as: Lots of problems with this theoretically – especially in S- wave Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Study D Decay Channels with Large S-wave Component D + K -++ (shown to right) E791 Asymmetry Prominent feature: Strong asymmetry in K*(892) bands F-B asymmetry vs. K*(892) Breit- M 2(K -+) Wigner phase (inset) is zero at 560. BW (Differs from LASS where this is zero at 135.50 Interference with large S– wave component. Shift in S–P relative phase wrt elastic scattering by -79.50 M 2(K -+) 0 Another channel with similar features w.r.t. the (770) is D+ -++ Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati (800) in BWM Fit to D+ K-++ E791: E. Aitala, et al, PRL 89 121801 (2002) Without (800): Fraction % Phase 0 NR ~ 90% Sum of fractions 130% Very Poor fit (10-5 %) BUT S~89 % Inclusion of makes K0*(1430) parameters M1430 = 1459 § 7 § 12 MeV/c2 differ greatly from PDG 1430 = 175 § 12 § 12 MeV/c2 or LASS values. M = 797 § 19 § 42 MeV/c2 Similarly, (500) is required in D+ -++ = 410 § 43 § 85 MeV/c2 E791: E. Aitala, et al, PRL 86:770-774 (2001) 2/d.o.f. = 0.73 (95 %) Can no longer describe S- wave by a single BW resonance and constant NR term for either K -+ or for -+ systems. Search for more sophisticated ways to describe S- waves Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati New BWM Fits Agree NEW RESULTS from both FOCUS and CLEO c support similar conclusions: • required (destructively interferes with NR) to obtain acceptable fit. • K0*(1430) parameters significantly different from LASS. These BW parameters are not physically meaningful ways to describe true poles in the T- matrix. FOCUS - arXiv:0705.2248v1 [hep-ex] 2007 CLEO c - arXiv:0707.3060v1 [hep-ex] 2007 Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati E791 Quasi-Model-Independent Partial Wave Analysis (QMIPWA) E791 Phys.Rev. D 73, 032004 (2006) Partial Wave expansion in angular momentum L of K -+ channels from D+ K-++ decays Decay amplitude : S- wave (L = 0): Replace BWM by discrete points cne in P- or D- wave: Define as in BWM Parameters (cn, n) provide quasi-model independent estimate of total S- wave (sum of both I- spins). (S- wave values do depend on P- and D- wave models). Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Compare QMIPWA with LASS for S-wave arg{F0(s)} |F0 (s) | E791 LASS S-wave phase for E791 is shifted by –750 wrt LASS. Energy dependence compatible above ~1100 MeV/c2. Parameters for K*0(1430) are very similar – unlike the BWM Complex form-factor for the D+ 1.0 at ~1100 MeV/c2 ? Not obvious if Watson theorem is broken in these decays ? Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Watson Theorem Breaking vs. I = 3/2 ? FOCUS / Pennington: D K-++ arXiv:0705.2248v1 [hep-ex] 2007 K-matrix fit using LASS Data For I=1/2 production vector: S- wave phase (deg.) LASS I=1/2 phase Includes separate I=3/2 wave Big improvement in 2. Total K-+ I =1/2 K-+ S- wave S- wave Large Data sample: 52,460 § 245 events (96.4% purity) s 1/2 (GeV/c2) Observations: I=½ phase does agree well with LASS as required by Watson theorem except near S- wave fractions (%): I=1/2: 207.25 § 24.45 § 1.81 § 12.23 pole (1.408 GeV/c2) I=3/2: 40.50 § 9.63 § 0.55 § 3.15 This possibility is built in to the fit model stat. syst. Model Huge fractions of each I- spin interfere P- and D- wave fractions & phases ~same as BWM fit. destructively. What about P- wave ? Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CLEO c: D K-++ arXiv:0707.3060v1 [hep-ex] Jul 20, 2007 Very clean sample from (3770) data: 67,086 events with 98.9 % purity. BWM fit similar to E791 (800) in S- wave is required (as a Breit-Wigner) with NR. K* (1410) in P- wave not required Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CLEO c: D K-++ arXiv:0707.3060v1 [hep-ex] Jul 20, 2007 BWM fit is also significantly improved by adding I=2 ++ amplitude – repairs poor fit to ++ inv. mass spectrum. Best fit uses a modification of E791 QMIPWA method … BWM fit QIMPWA fit Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Total S- wave from D+ K-++ Decays • General agreement is good • All differ from LASS (blue curves, 2nd row) CLEO c (Solid line) arXiv:0707.3060v1, 2007 E791 (Error bars) Phys.Rev.D73:032004, 2006 FOCUS (Range) arXiv:0705.2248v1, 2007 M(K- +) (GeV/c2) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CLEO c: D K-++ arXiv:0707.3060v1 [hep-ex] Jul 20, 2007 QMIPWA (E791 method applied to all waves and channels!) Define wave in each channel as: F(s) = C(s) + ae i R(s) Breit-Wigner type Interpolation table of propagator: (26 complex values) K-+ S- wave – K0*(1430) K-+ P- wave – K*(890) D- wave – K2*(1420) ++ S- wave – R = 0 Total of ~ 170 parameters: • Is final fit converged. (Errors?) • Is solution unique? BUT – only float C(s) for one wave at a time. • Is I=2 wave over-constraint? Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati New Data from CLEO c: D -++ arXiv:0704.3965v2 [hep-ex] Jul 20, 2007 BWM fits Use 281 pb-1 sample (3770): • ~4,086 events including background. Had to remove large slice in m+- invariant mass corresponding to FOCUS: Phys.Lett.B585:200-212,2004 D+ Ks+ E. Aitala, et al, PRL 89 121801 (2002) General morpholgy similar to E791 and FOCUS Standard BWM fit requires a amplitude much the same Introduced several variations in CLEO c S- wave parametrization: ………………….. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Complex Pole for : J. Oller: PRD 71, 054030 (2005) Replace S- wave Breit-Wigner for by complex pole: arXiv:0704.3965v2 [hep-ex] Jul 20, 2007 Best fit: Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Linear Model inspired Production Model Black, et al. PRD 64, 014031 (2001), J. Schecter et al., Int.J.Mod.Phys. A20, 6149 (2005) arXiv:0704.3965v2, 2007 Replace S- wave and f0 (980) by weakly mixed complex poles: Weakly mixed Unitary Poles and f0(980) . . . + usual BW terms for f0 (1350) and f0 (1500) % % Full recipe includes both weak and strong mixing between and f0(980) % – 7 parameters in all Excellent fit: Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati CLEO c: D -++ arXiv:0704.3965v2 [hep-ex] Jul 20, 2007 A fourth, “custom model” for S- wave (Achasov, et. Al., priv. comm.) also gave excellent fit All models tried (including BWM): Give essentially the same non S- wave parameters Provide excellent descriptions of the data Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Moments Analysis in D+ K-K++ Focus: hep-ex/0612032v1 (2007) K++ channel has no resonances 6400 Events before cut. Remove meson in K+K+ channel Allows Legendre polynomial moments analysis in K-+ channel free from cross-channel: |S| similar to LASS where (in K – + CMS) Phase was not computed, but appears to be shifted ~900 wrt LASS. |S|2 S*P |P|2 Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati S- Wave in B J/ K+- Similar analysis (more complex due to vector nature of J/) on K- + system Mass dependence of S- and P-wave relative phase in K-+ system was used to determine sign: cos 2 > 0 A clear choice agrees with the LASS data with overall shift + radians. Clearly an interesting way to probe the K- + S- wave 89 fb-1 PRD 71: 032005 (2005) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati + S- Wave in D+ K+- FB asymmetry in K- + system in these decays observed by FOCUS to follow closely the LASS behaviour. Phys.Lett.B621:72-80,2005 Clearly an interesting way to probe the K- + S- wave Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Some K S-wave Measurements Compared to LASS Amplitude S – P | Amplitude | | Amplitude | Decay Process Meas. – LASS m(K ) < 1 GeV m(K ) > 1 GeV Use of LASS S- wave ( deg. ) Unknown; parametrization or B+ K+ - + ~0 (M/p) | ALASS | Similar to LASS determination of used in fit relative S-P phase in Poorly defined ; B0 J/ K+ - ~ + 180 Similar to LASS to be updated various Dalitz plot B+ K+ - + ~ ± 180 Unknown Unknown analyses leads to a confusing picture. D0 K- K+ 0 ~ - 90 Similar to LASS Similar to LASS Very different ; Similar to LASS get ~ same D+ K- + + ~ - 75 significant rise K0*(1430) More channels are toward threshold mass and width needed to understand D+ K- K+ + ~ - 90 Similar to LASS Similar to LASS any pattern. D+ K- + l ~0 Similar to LASS Similar to LASS Adapted from W.M. Dunwoodie, Workshop on 3-Body Charmless B Decays, LPHNE, Paris, Feb. 1-3, 2006 Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Conclusions The most reliable data on S- wave scattering are still from LASS or CERN-Munich data. More information on very low mass data may be accessible through study of semi-leptonic D decays larger samples of B J/ K-(-)+ decays New techniques seem to yield information on the S- wave in various decay modes, BUT it is not yet obvious how to carry that over information from one decay to another. Understanding this will require a systematic study of many more D and B decays This should remain a goal before it becomes a limiting systematic uncertainty in other heavy flavour analyses. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Back Up Slides Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Charged (800) ? Babar: D0 K-K+0 ? 11,278 § 110 events (98% purity) Tried three recipes for K§0 S-wave: 1. LASS parametrization 2. E791 fit * 3. NR and BW’s for and K0 (1430) ? Best fit from #1 rotated by ~-900. No need for + nor -, though not excluded: Fitted with: M = (870§ 30) MeV/c2, Not consistent = (150§ 20) MeV/c2 With “” 385 fb-1: PRC-RC 76, 011102 (2007) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Partial Wave Analysis in D0 K-K+0 Region under meson is ~free p- s from cross channel signals: allows Legendre polynomial moments analysis in K-K+ channel: (Cannot do this is K channels) |S| |P| where (in K –K + CMS) |S| consistent with either a0(980) or f0(980) lineshapes. Babar: 385 fb-1: PRC-RC 76, 011102 (2007) Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati Compare QMIPWA with BWM Fit arg{F(s)} Red curves are §1 bounds on BWM fit. S Black curves are §1 bounds on QMIPWA fit. P Completely flexible S- wave changes P- & D- waves. D E791 Phys.Rev. D 73, 032004 (2006) (S- wave values do depend on P- and D- wave models). Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati E791 Require (500) in D+ -++ E. Aitala, et al, PRL 86:770-774 (2001) Fraction % Phase 0 Without (500): With NR ~ 40% dominates (1400) > (770) !! Very Poor fit (10-5 %) S~116 % Observations: NR and phases differ by ~ 1800 No Inclusion of makes K0*(1430) parameters differ greatly from PDG or LASS 2/d.o.f. = 0.90 (76 %) values. This caught the attention of our theorist friends ! Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati FOCUS / Pennington: D K-++ arXiv:0705.2248v1 [hep-ex] May 15, 2007 Use K-matrix formalism to separate I- spins in S-wave. The K-matrix comes from their fit to scattering data T(s) from LASS and Estabrooks, et al: Extend T(s) to K threshold using PT I= 1/2: 2-channels (K and K’ ) one pole (K * 1430) I= 3/2: 1-channel (K only) no poles This defines the D+ decay amplitudes for each I- spin: where T- pole is at: 1.408 – i 0.011 GeV/c2 Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati FOCUS / Pennington: D K-++ arXiv:0705.2248v1 [hep-ex] May 15, 2007 Amplitude used in fit: I- spin 1/2 and 3/2 Usual BWM model for K-+ S-wave P- and D- waves P- vectors are of form: k=1 K ; k=2 K’ Same as pole in K-matrix that can have s-dependent phase except far from pole. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati … Is Watson Theorem Broken ? E791 concludes: “If the data are mostly I= 1/2 , this observation indicates that the Watson theorem, which requires these phases to have the same dependence on invariant mass, may not apply to these decays without allowing for some interaction with the other pion.” Point out that their measurement can include an I =3/2 contribution that may influence any conclusion. Note: They also make a perfectly satisfactory fit (2 / = 0.99) in which the S-wave phase variation is constrained to follow the LASS shape up to K’ threshold. Charm 2007, Ithaca, NY, 8/06/2007 Brian Meadows, U. Cincinnati

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