Evidence for D 0 - D 0 mixing. Marko Starič. J. Stefan Institute, Ljubljana, Slovenia. March XLII Rencontres de Moriond, La Thuile, Italy

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1 Evidence for D - D mixing - D mixing (page 1)

2 Introduction Mixing observed in K, Bd and B s (26), not yet in D system D mixing in the SM governed by box diagrams Effective GIM suppression mixing in D system rare process Non-perturbative effects difficult to predict Mixing: flavor eigenstates not mass eigenstates: D 1,2 = p D ± q D with masses m 1, m 2 and widths Γ 1, Γ 2. Mixing governed by x = m Γ Time integrated mixing rate R M = x2 + y 2 2 y = Γ 2Γ c d, s, b u D D W W u d, s, b c Mixing Amplitude ( x, y, etc.) D -D Mixing Predictions Reference Index Mixing Rate (1/2 Amplitude 2 ) - D mixing (page 2)

3 Experimental method D + π + D tag the flavor of D / D at production background suppression D proper decay time t measurement: to disentangle DCS decays to increase sensitivity t = l dec cβγ, βγ = p D M D π s π D ldec fit D decay vtx e - D * Beamspot e + extrapolate production vtx Measurements performed in e + e collisions at s 1 GeV (B-factories) to reject D + from B decays: K p CMS D + > 2.5 GeV/c - D mixing (page 3)

4 Measurements at Belle Measurements to be presented in this talk D K + π D Ks π+ π Dalitz (preliminary) D K + K, π + π (preliminary) - D mixing (page 4)

5 D Kπ (Belle, 4 fb 1 ) PRL 96, (26) Wrong sign (WS) final state: via doubly Cabibbo suppressed decay (DCS) or via mixing D MIX DCSD D CF K + π Proper decay time distribution of WS events (assuming negligible CPV) dn dt [R D + y R D (Γt) + x 2 + y 2 (Γt) 2 ]e Γt 4 DCS interference mixing R D ratio of DCS/CF decay rates x = x cosδ + y sinδ y = y cosδ x sinδ δ strong phase between DCS and CF Events/.125MeV Events/.125MeV RS events Signal Random π D 3body Combin Q (MeV) WS events Signal Random π D 3body D s, D + Combin Q (MeV) - D mixing (page 5)

6 D Kπ (Belle, 4 fb 1 ) Unbinned fit to time distribution Assuming CP conservation R D = (.364 ±.17)% x 2 = ( ) 1 3 y = ( ) 1 3 No assumption on CP conservation, fit separately D and D no evidence for CPV A D = R+ D R D : 95% C.L. R + D +R D A M = R+ M R M : (.995, 95% C.L. R + M +R M x 2 < % C.L. y : ( 28, 21) 1 95% C.L. R M < % C.L. - D mixing (page 6)

7 D Kπ, contours, comparison no CPV (stat. only) no CPV CPV Belle: 95% C.L. contours in x 2, y : frequentist approach (toy MC exp.) (x 2 =, y = ) point: 3.6% C.L. For CPV case: large increase of 95% C.L. area (full curve) near x 2 =. y [1 3] 2 1 y σ BaBar x % C.L. CPV allowed Belle Rough comparison: Belle, PRL96, (26) BaBar, hep-ex/ D errors BaBar/Belle 95% C.L. Belle x [1 3 ] - D mixing (page 7)

8 D K s π + π Dalitz (Belle, 54 fb 1 ) 3-body decay modes: amplitudes A(D f) and Ā( D f) depend on Dalitz variables. Dalitz space dependent matrix element is for negligible CPV M(m 2, m2 +, t) = A(m2, m2 + )e 1(t) + e 2 (t) 2 where m ± is defined with the D tag + A(m 2 +, m2 )e 1(t) e 2 (t) 2 { m(ks, π m ± = ± ) D + D π + m(k s, π ) D D π and time dependent functions with e 1,2 (t) = e i(m 1,2 iγ 1,2 /2)t M(m 2, m2 +, t) 2 thus includes x and y The only measurement sensitive directly to x - D mixing (page 8)

9 D K s π + π Dalitz (Belle, 54 fb 1 ) Event Selection Reconstruction K s reconstruction and π selection D decay vertex from π +, π D mass kinematic constraint for m(k s, π +, π ) p (D + ) > 2.5 GeV/c Signal yields and purity signal purity % Events/5MeV 1 5 Events/.125MeV Mass (GeV) Q (MeV) - D mixing (page 9)

10 D K s π + π Dalitz (Belle, 54 fb 1 ) Dalitz fit XIII: The results for Dalitz plot part. The total fraction Resonance Amplitude Phase (deg) Fit fraction K (892) ± ± K (143) 2.12 ±.2.9 ± K2 (143).87 ± ± K (141).65 ± ± 2.48 K (168).6 ± ± 5.2 K (892) ± ± K (143)+.541 ± ± K2 (143)+.276 ±.1 16 ± 3.13 K (141) ± ± 2.13 K (168) +.73 ±.1 13 ± 6.4 ρ(77) 1 (fixed) (fixed).2111 ω(782).38 ± ±.9.63 f (98).38 ± ± f (137) 1.46 ± ± f 2 (127) 1.43 ± ± ρ(145).72 ± ± σ ± ± σ ± ± 3.88 NR 2.36 ± ± Dalitz model: 13 different (BW) resonances and a non-resonant contribution Results with this refined model consistent with the analysis performed for the Belle φ 3 measurement, PRD73, 1129 (26) To test the scalar ππ contributions, K-matrix formalism is also used - D mixing (page 1)

11 D K s π + π Dalitz (Belle, 54 fb 1 ) Time fit (in projection) Systematics Largest contributions ( 1 4 ) x y Total ( 1 4 ) x y Model dependence Time fit Results (preliminary) y.2.15 Belle preliminary Ksππ x =.8 ±.29 ±.17 % y =.33 ±.24 ±.15 % most stringent limits on x up to now Cleo, PRD 72, 121 (25): x = 1.8 ± 3.4 ±.6% y = 1.4 ± 2.5 ±.9% % C.L. inner: stat. only x (x=,y=) point: 2 lnl = 7.3 (2.6% C.L.) - D mixing (page 11)

12 D K + K, π + π (Belle, 54 fb 1 ) Measurement of lifetime difference between D K π + and K + K, π + π mixing parameter: y CP = τ(k π + ) τ(k + K ) 1 in CP conservation limit: y CP = y = Γ/2Γ If CP not conserved, difference in lifetimes of D / D K + K, π + π CP violating parameter: A Γ = ˆΓ(D KK) ˆΓ( D KK) ˆΓ(D KK)+ˆΓ( D KK) Existing measurements: E.M.Aitala et al., PRL 83, 32 (1999); E791 J.M.Link et al., PLB 485, 62 (2); Focus S.E.Csorna et al., PRD 65, 921 (22); Cleo K.Abe et al., hep-ex/3834 (23); Belle (preprint) B.Aubert et al., PRL 91, (23); (BaBar) average y CP = (1.9 ±.46)% - D mixing (page 12)

13 D K + K, π + π (Belle, 54 fb 1 ) Event Selection Reconstruction K and π selection vertex fits p (D + ) > 2.5 GeV/c Analysis cuts m, q, σ t optimized on tuned Monte Carlo figure of merit: statistical error on y CP σ t /τ PDG m/σ m q (MeV) Background estimated from sidebands in m side band position optimized Signal yields (purities) entering the measurement channel KK Kπ ππ signal 11K 1.2M 5K purity 98% 99% 92% events/bin events/bin events/bin x D K + K - side band side band D K - π + m (GeV) D π + π - m (GeV) m (GeV) - D mixing (page 13)

14 D K + K, π + π (Belle, 54 fb 1 ) Lifetime fit Parameterization of proper decay time distribution dn dt = N τ e t/τ R(t) + B(t) Resolution function constructed from normalized distribution of event proper time uncertainty σ t ideally, σ t of event represents uncertainty with Gaussian p.d.f examining pulls p.d.f.=sum of 3 Gauss σ t distribution f i R(t) = n f i i=1 k=1 3 w k G(t; σ ik, t ), σ ik = s k σ pull k σ i σ i σ t /τ PDG R(t) studied in details with D Kπ and special MC samples - also in changing running conditions (two different SVD, small misalignments) - D mixing (page 14)

15 D K + K, π + π (Belle, 54 fb 1 ) Simultaneous KK/ππ/Kπ binned likelihood fit quality of fit: χ 2 = 1.84 (289) events/bin KK χ 2 (ndf).97 (97) Kπ χ 2 (ndf) 1.14 (95) ππ χ 2 (ndf) 1.14 (97) t/τ PDG t/τ PDG t/τ PDG D Kπ lifetime very stable in slightly different running periods τ Kπ (fs) W.A. 48.7±.6 fs 45 4 Belle preliminary run period - D mixing (page 15)

16 D K + K, π + π (Belle, 54 fb 1 ) Cross-checks MC: y CP (out) - y CP (input) <.4% for large range of input values y CP independent of resolution function parameterization: R(t) = single Gaussian: τ = 3.5%, y CP =.1% Exchanging data side band with signal window background from tuned MC: y CP = -.4% Systematics source y CP A Γ acceptance.12%.7% equal t assumption.14%.8% mass window position.4%.3% difference btw. background and side bands.9%.6% difference btw. final states in opening angle.2% background parameterization.7%.7% resolution function.1%.1% analysis cuts.11%.5% binning.1%.1% total.25%.15% - D mixing (page 16)

17 D K + K, π + π (Belle, 54 fb 1 ) Results (preliminary) y CP (%) A Γ (%) KK 1.25±.39±.28.15±.34±.16 ππ 1.44±.57± ±.52±.3 KK + ππ 1.31±.32±.25.1±.3±.15 entries/ D K + D + K, π π K + π Belle preliminary (54 fb 1 ) y CP = 1.31±.32±.25 % > 3σ above zero (4.1σ stat. only) first evidence for D D mixing A Γ =.1±.3±.15 % no evidence for CP violation entries/ D K K, π π D decay time ratio Belle preliminary / t/ τ K + π t/ τ PDG PDG - D mixing (page 17)

18 Conclusions Several measurements of D mixing parameters presented Best sensitivity on x from t-dependent Dalitz analysis: x =.8 ±.29 ±.17 % (2.4σ) First evidence of non-zero y CP : y CP = 1.31 ±.32 ±.25 % (3.2σ including syst.) y σ 3 σ Belle preliminary x - D mixing (page 18)

19 Backup slide: X-checks for y CP Background A comparison of timing distributions signal region background - side bands entries/bin 1 2 KK χ 2 /ndf=.9 entries/bin Kπ χ 2 /ndf=4.21 entries/bin 1 2 ππ χ 2 /ndf= t/τ PDG t/τ PDG t/τ PDG side bands DATA - side bands tuned MC entries/bin 1 2 KK χ 2 /ndf=.85 entries/bin Kπ χ 2 /ndf=.83 entries/bin 1 2 ππ χ 2 /ndf= t/τ PDG 1 t/τ PDG 1 t/τ PDG Difference to result, if using background from tuned MC KK ππ KK + ππ y CP.1% +.9%.4% - D mixing (page 19)

20 Backup slide: X-checks for y CP Run periods P(t) = 1 τ e t/τ R(t) < t >= τ + t <t>/τ PDG -1 mean of Kπ timing distr..6.4 By inspecting < t > of Kπ, four run periods with different resolution function offsets (t ) found Attributed to small SVD misalignments τ Kπ (fs) W.A. fitted Kπ lifetimes 48.7±.6 fs t (fs) Kπ expno fitted r.f. offsets 45 4 Belle preliminary run period run period - D mixing (page 2)

21 Backup slide: X-checks for y CP Test for equal t assumption t /τ PDG (%) / 2 P t /τ PDG (%) / 2 P e e KK Kπ ππ -1 KK Kπ ππ t /τ PDG (%) / 2 P t /τ PDG (%) / 2 P e e KK Kπ ππ -1 KK Kπ ππ t is final state independent - D mixing (page 21)

22 Backup slide: X-checks for y CP Measured y CP versus run periods y CP (%) / 3 P y CP (%) / 3 P y CP (%) / 3 P KK -1-2 ππ -1-2 KK+ππ run period run period run period y CP consistent between run periods - D mixing (page 22)

23 Backup slide: X-checks for y CP Fitted lifetimes of KK, Kπ, ππ Results for t being free for each of the final states τ (fs) / 3 P τ (fs) / 3 P τ (fs) / 3 P KK 39 Kπ 39 ππ run period run period run period lifetimes consistent between run periods KK Kπ ππ τ (fs) 44.± ± ±3.3 χ 2 /ndf lifetimes of KK and ππ consistent (and smaller than Kπ) y CP = 1.25 ±.48 % (central value similar, error 5% larger) - D mixing (page 23)

24 Backup slide: X-checks for y CP Statistical method y CP and A Γ can be determined from mean of the timing distributions (e.g. without fitting the data), and the error from r.m.s Assumptions: timing distribution is a convolution of exponential with some resolution function + some background resolution function offsets of final states are the same and small P(t) = p 1 τ e t/τ R s (t) + (1 p)b(t) < t >= p(τ + t ) + (1 p) < t > b τ + t = < t > (1 p) < t > b p In lifetime difference t cancels, thus if t τ =< t > s y CP = < t > KK < t > Kπ < t > Kπ Result from this method y CP = 1.35 ±.33 stat % - D mixing (page 24)

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