Introduction: general formalism of oscillations Nice review: hep-ph/ (Dec 2007): “Topics in Hadronic B decays”, J.Virto QM perturbation theory Effective Hamiltonian

General formalism of oscillations not Hermitian! Dispersive off-shell part Absorptive on-shell part CPT! by def.

General formalism of oscillations Diagonalize! Eigenvalues Eigenvectors But CPV if ! PDG notation: r = p/q CP =eiei arbitrary! PDG notation: L,H↔1,2 CP!

General formalism of oscillations CP! For D 0 CPV is expected to be very small (see later). Sometimes by def.  m < 0. But we define: D 1 – (almost) CP even, D 2 – CP odd (thus  m ~ x > 0 is possible) If CPV=0 we may choose arbitrary phase  =0 in : CP =eiei (like K 1, K 2 )

Contributes only to М 12 (х) Contributes both to М 12 and to Г 12 (y), very difficult to estimate Can contain New Physics in loops! (Interesting: down-quarks in  C=2 loops) Known resonances dominate, no NP Long distance effects obscure possible short-distance NP in x. Sign of NP could be either or (better) observation of large CPV. Box and long distances

GIM mechanism Take d ’, s ’ basis instead of d, s : Due to different masses in propagators → not exact 0, but small b contribution is suppressed in comp. with d,s by  → negligible. In the absence of 3 rd generation CPV≈0. Box diagram(s)

Box diagrams c u u c d, s, b W+W+ W-W- D0D0 D0D0 c u u c W+W+ W-W- D0D0 D0D0 V cj * V uj V cj * V uj V ci * V ui V ci * SM: x box ≤10 -5, negligible CPV

Boxes for K,D,B,B s c u u c d, s, b W+W+ W-W- D0D0 D0D0 c u u c W+W+ W-W- D0D0 D0D0 V cj * V uj V cj * V uj V ci * V ui V ci * u, c, t d s s d W+W+ W-W- K0K0 K0K0 d s s d W+W+ W-W- K0K0 K0K0 VidVid V jd Vis*Vis* VidVid V is * VjdVjd V js * d b b d u, c, t W+W+ W-W- B0B0 B0B0 d b b d W+W+ W-W- B0B0 B0B0 V id V jd V jb * V ib * V id Vib*Vib* V jd Vjb*Vjb* s b b s u, c, t W+W+ W-W- B0sB0s B0sB0s s b b s W+W+ W-W- B0sB0s B0sB0s VisVis VjsVjs V jb * V ib * VisVis Vib*Vib* VjsVjs Vjb*Vjb* c dominates, sin 2  C s dominates, sin 2  C t dominates, |V td V * tb | 2 t dominates, |V ts V * tb | 2 K0K0 D0D0 B0B0 B0sB0s

Recent paper with the largest x,y A.F.Falk et el., hep-ph/ , Long distance contribution SU(3) breaking in D 0 decays – only due to phase space differences within SU(3) multiplets (e.g., decay to 4  allowed, to 4К – not) x ≤ y ~ Δ – y ■ – x ● – x beyond SM Old predictions H.Nelson, hep-ex/

Comparison of K,D,B,B s c dominates, sin 2  C s dominates, sin 2  C t dominates, |V td V * tb | 2 t dominates, |V ts V * tb | 2 K0K0 D0D0 B0B0 B0sB0s Boxes Box:long dist.≈ 80%:20%  S,L are determined by available decays (long dist.) Long dist. dominateBox:long dist.≈ 80%:20%  S,L are determined by available decays (long dist.) Long dist. dominate Box dominates It contributes through V CKM to  12 as well,  12 /M 12 ≈0.05, y≤1%. CPV is important Box dominates  12 /M 12 ≈0.05, both higher than for B 0, y~10%. CPV is important Spring 2006, CDF, D0:

xy1/Г, psec K0K0 1/Г S =89.53±0.05 1/Г L =51140±210 (3.24±0.04)E-3 B0B ±0.008SM: ~0.2% 1.530± ± SM: B0sB0s 1/Г L =1.21±0.09 1/Г H = 1/Г= 1.40±0.05 SM: D0D0 ~10 -3 … ≤0.01 SM: ~ ±0.0015≈ 0 Comparison of K,D,B,B s

Time evolution of D system Evolution of eigenvectors according to effective Hamiltonian is simple: for simplicity, r=p=q=1, CPV=0 t=0

Now experimental part …

Lepton charge tags D 0 flavor! PDG’ 2006 Semileptonic D 0 decays Probability to have Wrong Sign (WS) lepton = prob. of oscillation = Time integrated ratio of WS and RS, R M

visually unobservable deviation from pure exponential ~ B s 0 probab. X 0 → X 0 or X 0 → X 0 after time t (no assumption x,y<<1) Examples of oscillations

 c c hadron(s)  (4s) B (bu, bd)  =0.42  (bb)  1.1 nb (~800·10 6 bb pairs) → numerous measurements of CPV in B system  (cc)  1.3 nb (~900·10 6 cc- pairs) + light qq production (uds) Perfect for charm physics continuum production BB pair production Main experiments: two B-factories Additional help from: charm-factories, Tevatron hadron(s)

~1 km in diameter Mt. Tsukuba KEKB Belle Continuous injection, peak luminosity: L = 16.5 nb -1 s -1 n.b.: dN/dt = L  Integrated luminosity:  Ldt > 700 fb -1  L dt fb GeV e + 8 GeV e - Belle

Belle detector 3(4) layer Si det. Central Drift Chamber Aerogel Cherenkov (n= ) 1.5T SC solenoid e - 8 GeV e GeV EM calorimeter CsI (16X 0 )  and K L Counter (14/15 layers RPC+Fe) tracking  (p t )/p t = 0.2% √(p t ) PID  (K ± ) ~ 85%  (  ± →K ± )  10% for p < 3.5 GeV/c

detector Collected at PEP-II at SLAC on- and off- the  (4S) resonance NIM A479, 1 (2002) Dataset: 384 fb -1

 s [GeV] e + e - →  (3770) → D 0 D 0, D + D - (coherent 1 -- state); analogous to e + e - →  (4S); symmetric; also higher energy, above DD* or D s + D s - threshold; ~572 pb -1 of data available at  (3770), 2.0x10 6 D 0 D 0, 1.6x10 6 D + D - charm-factory; also upgraded BES at BEPCII CLEO-c detector at CESR Had. ID e - ID tracking Cleo-c, hep-ex/

e Back to semileptonic D 0 decays, latest analyses General method: study D 0 ’s produced from D *+ 1.  + provides a tag of initial D 0 flavor 2. Phase space in D* + decay is very small chances to have random background pion there are also small 2a) background is significantly suppressed. Why? What to measure: compare signs of  + and lepton and find R M = #wrong sign (WS) / #right sign (RS) 2b) Loss of statistics is acceptable since about 50% of D 0 come from D *+ (it has more polarization states, B(D* + →D 0  + )≈2/3).

Interesting difference: initial D 0 flavor at production is tagged twice: by sign of  s ± from D *± and by flavor of the second D meson in the event which is fully reconstructed in the opposite hemisphere. Efficiency of full reconstruction is ~10%, but sensitivity is about the same. N WS = 3ev., expected background = 2.85 ev. e Semileptonic D 0 decays Belle ( PRD72, (2005), 253 fb -1 ) : R M <1.0·10 90% CL N RS = ( ± 0.69) ·10 3 ev. Recent BaBar analysis (hep-ex/ , 344fb -1 ) -1.3·10 -3 <R M <1.2·10 90% CL

Another approaches R M ~ x 2, y 2. Are there any effects linearly dependent on x or y?

Straitforward way: measure y=  /2  directly By measuring difference between Г 1 and Г one can find y CP which coincides with y if CP is conserved. First order in y! CP can be checked by comparing  D &  D in К + К -,  +  - : A  =(  D -  D )/(  D +  D ) К + К - and  +  - can come only from CP-even D 1. К + К - and  +  - verticies should be distributed according to Г 1. In flavor specific decay, e.g. D 0 →K -  +, both D 1 and D 2 contribute equally if CP is conserved CPV case:

Here Belle finds evidence of oscillations … PDG’2006 average y CP =(0.90±0.42)% Previous results on y CP from К + К - and  +  - Problem: Br(D 0 →  +  - )/Br(K -  + ) = 3.6% Br(D 0 →K + K - )/Br(K -  + ) = 10.1 %

The same trick with D *+ is used t = l dec /  = l dec M D /P D, l dec error translates into  t ~  /2 y CP from D 0 → K + K -,  +  - at Belle D from cc-bar continuum are hard. p CMS (D* + )>2.5 GeV: improves error on t, reduces backgrounds, removes D*’s from B→D*X.

Belle D* + … Events from D* + and D 0 signal boxes (|  q|<0.8 MeV, |  M D |<2.3  ) are used in lifetime measurements and D 0 signals (540 fb -1 )

КК КК    Time distributions of selected candidates Where left tail comes from? Time resolution function Background from sidebands Binned LH Fit

Correction for non- one-Gaussian shape of errors Fit parameter, correction for MC/data diff. i/i/ y CP from K + K -,  +  - Resolution function  = 408.7±0.6 fs Lifetime in different run periods is about the same Good agreement with  PDG = 410.1±1.5 fs Check K -  + lifetime from fit: Distribution of errors error from vertex fit

Results K + K - /  +  - and K -  + ratio difference of lifetimes visually observable evidence for D 0 mixing (y CP 6*10 -4 ) 3.2  from zero  2 /ndf=1.084 (ndf=289) + PRL 98, (2007), 540fb -1 y CP =  K  /  KK – 1 = (1.31 ±0.32 ±0.25)% A  =(  D -  D )/(  D +  D )=0.01±0.30 ±0.15 % CPV check: y CP from K + K -,  +  -

D 0  K +  - from BaBar From Jonathon Coleman presentation at 19 July 2007 Manchester, England Interference of a) Double Cabibbo Suppressed (DCS) and b) Cabibbo Favored (CF) decay with mixing (PRL 98, (2007))

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar We use two decay modes: 1. Reference Cabibbo-favored (CF), “right-sign” (RS) decay 2. “Wrong-sign” (WS) decay Two amplitudes contribute: a) Doubly Cabibbo-suppressed (DCS) decay Rate without b): tan 4  C ~ 0.3% b) Mixing followed by CF decay Rate without a): or less, but interference with DCS can enhance Interference term linear in x, y! B A B AR D 0  K  Mixing Analysis

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Time-dependent decay rate Use time dependence to separate DCS and mixing contributions (approximate; for x, y ¿ 1) DCS decayInterference between DCS and mixingMixing Compare with semileptonic decay with only mixing amplitude: and with DCS alone: RDRD

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Time-dependent decay rate x 2 +y 2 =x ’ 2 +y ’ 2  K  is a strong uknown (see later) phase between CF and DCS This phase may differ between decay modes. And may vary over phase space for multi-body decays. DCS decayInterference between DCS and mixingMixing What is y ’ ? It is some linear cobination of x,y:

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar D 0  K ±  Ŧ Analysis Method Identify the D 0 charge conjugation state at prod. & decay using vertices fit to Determines m K ,  m, proper-time t and error  t Vertices fit with beamspot constraint is important Improves the decay-time error resolution Improves the  m resolution Right-sign (RS) decay Beam spot:  x ~ 7  m,  y ~ 100  m D 0 decay vertex D 0 production vertex

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar RS & WS m K ,  m distributions All fits are over the full range shown in the plots 1.81 GeV/c2 < m K  < 1.92 GeV/c 2 and 0.14 GeV/c 2 <  m < 0.16 GeV/c 2 Define a signal region GeV/c 2 < m K  < GeV/c 2 and GeV/c 2 <  m < GeV/c 2

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar RS & WS m K ,  m projections counts/0.1 MeV/c 2 counts/1 MeV/c 2 1,229,000 RS candidates Signal:background ~ 100:1 64,000 WS candidates Signal:background ~ 1:1 RS m K  WS m K  RS  m WS  m

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Fitting strategy Fitting is performed in stages to reduce demand on computing resources All stages are unbinned, extended maximum-likelihood fits. 1.RS & WS m K ,  m fit. Yields PDF shape parameters m K ,  m categories. 2.RS lifetime fit. m K ,  m category shape parameters held constant. Yields D 0 lifetime  D and proper-time resolution parameters. Constrained by the large statistics of the RS sample. 3.WS lifetime fit. Yields parameters describing the WS time dependence. Small correlation between fitted parameters in the different stages justifies the staged approach. The WS fit is performed under three different assumptions. Mixing and CP violation (CPV); mixing but no CPV; and no mixing or CPV. Monte Carlo (MC) simulations are not used directly in the data fits. MC simulations used only to motivate the fit PDFs WS mis-reconstructed D 0 category studied in swapped K↔  data.

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Right-sign m K ,  m fit Shown are the fits to right-sign data for m K  (left) and  m (right). The mis-reconstructed D 0 category is not included in the RS fit. This background is too small to be reliably determined. 1,141,500 ± 1,200 RS signal events

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Wrong-sign m K ,  m fit The m K ,  m fit determines the WS b.r. R WS = N WS /N RS B A B AR (384 fb -1 ): R WS = (0.353 ± ± 0.004)% (PRL 98, (2007)) BELLE (400 fb -1 ): R WS = (0.377 ± ± 0.005)% (PRL 96, (2006)) 4,030 ± 90 WS signal events Check (time integrated, DCS enhanced by CF with mixing)

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar RS  proper decay-time fit The parameters fitted are D 0 lifetime  D Resolution parameters Including a 3.6 fsec offset Signal, background category yields Consistency check Fitted  D = (410.3 ± 0.6) fsec (statistical error only) (PDG 2006: ± 1.5 fsec) RS fit projection in the signal region GeV/c 2 < m < GeV/c GeV/c 2 <  m < GeV/c 2

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar No-mixing WS  decay time fit The parameters fitted are WS category yields WS combinatoric shape parameter As can be seen in the residual plot, there are large residuals. Residuals = data − fit WS no-mixing fit projection in signal region GeV/c 2 < m < GeV/c GeV/c 2 <  m < GeV/c 2

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Mixing WS  decay time fit The fit is significantly improved by allowing for mixing. dotted line --- no-mixing fit. solid line --- mixing fit. DCS Interference Mixing

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar R WS vs. decay-time slices If mixing is present, it should be evident in an R WS rate that increases with decay-time. Perform the R WS fit in five time bins with similar RS statistics. Cross-over occurs at t ~ 0.5 psec Simiar to residuals plot. Dashed line: standard R WS fit (  2 =24). Solid, red line: independent R WS fits to each time bin (  2 = 1.5). No-mixing fit R WS fits

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Mixing fit likelihood contours Contours in y’, x’ 2 computed from −2  ln L Best-fit point is in the non-physical region x’ 2 < 0 1  contour extends into physical region Correlation: −0.95 Contours include systematic errors The no-mixing point is at the 3.9  contour Best fit Best fit, x’ 2 ≥ 0 + No mixing: (0,0) 1 – CL = 3.17 x (1  ) 4.55 x (2  ) 2.70 x (3  ) 6.33 x (4  ) 5.73 x (5  ) R D : (3.03  0.16  0.10) x x’ 2 : (-0.22  0.30  0.21) x y’: (9.7  4.4  3.1) x Contours at 1  intervals

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Fits allowing for CP violation Fit D 0 and D 0 decay-time dependence separately. x' 2+ = (−0.24 ± 0.43 ± 0.30) x y' + = (9.8 ± 6.4 ± 4.5) x x' 2- = (−0.20 ± 0.41 ± 0.29) x y' - = (9.6 ± 6.1 ± 4.3) x D0D0 D0D0 No evidence seen for CP violation

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar List of systematics, validations Systematics: variations in Functional forms of PDFs Fit parameters Event selection Computed using full difference with original value Results are expressed in units of the statistical error Validations and cross-checks Alternate fit (R WS in time bins) Fit RS data for mixing x’ 2 = (−0.01±0.01)x10 -3 y’ = (0.26±0.24)x10 -3 Fit generic MC for mixing x’ 2 = (−0.02±0.18)x10 -3 y’ = (2.2±3.0)x10 -3 Fit toy MCs generated with various values of mixing Reproduces generated values Validation of proper frequentist coverage in contour construction Uses 100,000 MC toy simulations Systematic source RDRD y’y’x’2x’2 PDF: 0.59  0.45  0.40  Selection criteria: 0.24  0.55  0.57  Quadrature total: 0.63  0.71  0.70 

EPS HEP 07, 19 July 2007 Manchester, England Jonathon Coleman D 0 Mixing at BaBar Comparison with BELLE D 0  K  result PRL 96,151801, 400 fb -1 Results consistent within 2  B A B AR 2  B A B AR 3  B A B AR 1  stat. only BELLE 2  (no-mix excl. at 2  ) No mixing excluded > 4  11 22 33 44  x' 2 y' R D : (3.30 ) x x’ 2 : (-0.01±0.20) x y’ : (5.5 ) x May 2007 HFAG Averages

Time dependent Dalitz analysis of D 0 → K S  +  - at Belle PRL 99, (2007), 540 fb -1

Time dependent Dalitz analysis of D 0 → K S  +  - different decays identified through (m + 2 VS m - 2 ) plot CF: D 0 → K* -  + DCS: D 0 → K* +  - CP: D 0 →  0 K S their relative phases determined (unlike D 0 → K +  - ); m ± 2 = m 2 (K S  ± ) if CP conserved and : and decay as Dor anti-D propagate … Dalitz plot can change in time! Selection is similar to K , N sig =(534.4±0.8)x10 3, purity  95%

Time dependent Dalitz analysis of D 0 → K S  +  - K*(892) + K* X (1400) + K*(892) -  Amplitudes and phases in agreement with previous measurement (for  3 ) PRD73, (2006) sum over 18 resonances!

t t [fs]  = 409.9±0.9 fs  PDG =410.1 ± 1.5 fs comb. bkg. Time evolution of D 0 → K S  +  - Number of decays VS time Lifetime agrees with PDG Dalitz plot VS time

most sensitive meas. of x (2.4  ) Cleo, PRD72, (2005) x = 1.8 ± 3.4 ± 0.6% y = -1.4 ± 2.5 ± 0.9 % PRD72, (2005), 253 fb -1 D 0 → K ( * ) l PRL96, (2006), 400 fb -1 D 0 → K +  - 2-d 68% C.L. region B. Golob, BelleLepton Photon ‘07, Daegu 2-d 68% C.L. region D 0 → K + K - /  +  - PRL 98, (2007), 540fb -1 D 0 → K S  +  - : results

CPV in decay: CPV in mixing, if : CPV in interf. mix./decay: D 0 → K S  +  - : CPV search include |q/p| and  as additional free param. 95% C.L.

First attempt to measure strong phase  K  in D 0  K +  - using quantum correlations of D 0 -D 0 pairs produced from  (3770) by Cleo-c hep-ex/ , 281 pb -1

Strong phase  K  in D 0  K +  - CLEO-c: D 0 D 0 are in a J PC = state D mesons can not be simultaneously in the same CP state (e.g. D 1 -D 1 – Bose particles + antisymmetry) and can not decay to CP eigenstates with the same eigenvalue. Such quantum correlations result in e  e    *   (3770)  D 0 D 0

where is the probability of f 2 with the condition that f 1 is chosen. E.g. if f 1 = CP even state = S +, f 2 = e - X: Strong phase  K  in D 0  K +  - All three probabilities are accessible experimentally by counting events N dbl with reconstructed f 1 and f 2 (efficiencies are known) 2. - by counting events N sng with reconstructed f 1 and regardless of f 2 (or vice versa).

Now, if f 1 = CP even state = S +, f 2 = K -  + : Strong phase  K  in D 0  K +  -

Consider different pairs of f 1, f 2 (K , S +, S -, eX). Formulas with and without correlations differ! sensitivity to various parameters, e.g. cos 

Hadronic Single Tags Identify the final state with  E  E beam -E D, Cut on  E, fit M BC distribution to signal and background shapes. Efficiencies from (uncorrelated) DD Monte Carlo simulations. Peaking backgrounds for: – K  from K/  particle ID swap. – Modes with K 0 S from non- resonant     M BC for K 0 S  0 (CP-) M BC for     (CP+) M BC for K    (f) Note log scale DATA (GeV)

Data clearly favors quantum correlations showing constructive and destructive interference and no effect as predicted K -  + vs K -  + K -  + vs K +  - CP+ vs CP+ CP- vs CP- K  vs CP+ K  vs CP- CP+ vs CP- Quantum correlations are visible!

Strong phase  K  in D 0  K +  - Not enough statistics to compete with Belle / BaBar results on x, y, y ’, but: First measurement cos(  )=1.03±0.19 ±0.08 or 0.93 ±0.32 ±0.04 (depending on external measurements used in fit) Main contribution from K  /S ±

Summary 1.First evidence of D 0 mixing in several modes: a) K + K -,  +  - b) DCS+CF with mixing K +  - c) Dalitz plot evolution in K 0 S  +  - 2. First information on strong phase  K  from CLEO-c (more data will be added, x2-3). 3. Theory: The SM box is tiny. D 0 mixing is the only down-quark-mediated transition with  F=2. In principle ideal room for New Physics to show up (extended Higgs, 4 th generation, SUSY, leptoquarks). But big long distance effects, hard to calculate since m c ~hadronic scale, obscure possible short-distance NP in x. Estimates: x box ≤10 -5, x long dist. ≤O(10 -3 ). Since in data x,y ~0.5% - interpretation is difficult (NP or not NP?) 4. The only clear sign - large CPV (immune to hadronic uncertainties)