# Presentation: 285954

## D0D0 Quantum Correlations, Mixing, and Strong Phases Werner Sun, Cornell Universityfor the CLEO-c CollaborationParticles and Nuclei International Conference24-28 October 2005, Santa Fe, NM

- Introduction and motivation
- Experimental technique
- Preliminary results and future plans

## Effect of Quantum Correlations

- |*D*1,2> = *p*|*D*0> ± *q*|*D*0>
- Because of quantum correlation between *D*0 and *D*0, not all final states allowed.  This affects:
- total rate
- apparent branching fractions
- Two entangled causes:
- Interf. between CF and DCSD.
*D* mixing: single tag rates depend on *y* = B(*CP*+)B(*CP*-).
- Semileptonic decays tag flavor unambiguously (if no mixing)  If one *D* is SL, the other *D* decays as if isolated/incoherent.
- Exploit coherence to probe DCSD and mixing—shows up in *time-integrated* rates.

*e**e*  *  *D*0*D*0

- C = 1

| K | K |
| --- | --- |
| K | K |
| K | K |
| K | Kl |
| CP+ | Kl |
| CP- | Kl |
| Kl | Kl |
| CP+ | CP- |
| CP+ | CP+ |
| CP- | CP- |

- interference

- forbidden by
*CP* conservation

- forbidden in
- absence of mixing

- maximal
- constructive
- interference

## Introduction

- In the Standard Model,* D* mixing strongly suppressed (CKM and GIM).
- Previous searches:
- Double semileptonic rates give *R**M*.
- Time-dependent *K*: *x* and *y* rotated by 
- Current analysis:
- Uses *time-independent* yields.
- Sensitive to *y* at *first order*.
- No sensitivity to *p*/*q*≠1; neglect *CPV* in decay.
- References:
- Goldhaber, Rosner:**PRD 15, 1254 (1977).**
- Xing:** PRD 55, 196 (1997).**
- Gronau, Grossman, Rosner:**hep-ph/0103110**.
- Atwood, Petrov: **PRD 71, 054032 (2005)**.
- Asner, Sun: **hep-ph/0507238.**

|  | Definition | Current knowledge |
| --- | --- | --- |
| y | (2-1)/2= 
B(CP+)B(CP-) | 0.008 ± 0.005 |
| x | (M2-M1)/
sensitive to NP | x’ < 0.018 |
| RM | (x2+y2)/2 | < ~1 x 10-3 |
| r | K DCS-to-CF
rel. amplitude | 0.061 ± 0.001 |
|  | K DCS-to-CF
relative phase | (weak) +
? (strong) |
| z | 2cos | None |
| w | 2sin | None |
| A |  Bf rf zf | ~-0.01 w/ SU(3) |

## Single and Double Tag Rates

- Hadronic rates (flavored and *CP* eigenstates) depend on mixing/DCSD.
- Semileptonic modes (*r *= = 0) resolve mixing and DCSD.
- Rate enhancement factors, to leading order in *x*, *y* and *r*2:
- A comes from sum over recoil states.
- With C=+1 *D*0*D*0 at higher energy,
- Can separate A and *y*.
- Sensitivity to *wx* at first order.  Not much info if *w* is small.

|  | f | l+ | CP+ | CP- |
| --- | --- | --- | --- | --- |
| f | ~RM |  |  |  |
| f | 1+r2(2-z2) |  |  |  |
| l- | 1 | 1 |  |  |
| CP+ | 1+rz | 1 | 0 |  |
| CP- | 1-rz | 1 | 2 | 0 |
| X | 1-rz(A-y) | 1 | 1+(A-y) | 1-(A-y) |

- With *C*=-1, cannot
- separate y* *and A

## Experimental Technique

- Use fitter from CLEO-c *D* absolute hadronic branching fraction analysis [**physics/0503050**].
- Based on MARK III double tag technique using:
- single tags ( *n**i* ~ *N**DD**B**i**i* ) and double tags ( *n**ij* ~ *N**DD*B*i*B*j**ij* )
- 281 pb-1 = 1.0 x 106 *C*=-1 *D*0*D*0 pairs.
- Limiting statistics: *CP* tags—our focus is not on Bs.
- Kinematics analogous to (4S)*BB*: identify *D* with
- (*M**BC*) ~ 1.3 MeV, x2 with 0
-                                    (*E*) ~ 7—10 MeV, x2 with 0
- Procedure tested with *CP*-correlated MC.

| Modes |  |
| --- | --- |
| f | K |
|  | K |
| CP+ | KK |
|  |  |
|  | K0S00 |
| CP- | K0S0 |
| l | Xe |
|  | Xe |

- ~ *n*/

## Hadronic Single Tags

- Standard *D* reconstruction.
- 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*0S from non-resonant 

*CP*+

*CP*-

*f*

| Mode |  (%) | % bkg | Signal Yield (103) |
| --- | --- | --- | --- |
| K | 65.7 ± 0.1 | 0.13 | 26.0 ± 0.2 |
| K | 66.7 ± 0.1 | 0.14 | 26.3 ± 0.2 |
| KK | 58.9 ± 0.2 | 0.00 | 4.70 ± 0.08 |
|  | 73.5 ± 0.3 | 0.00 | 2.13 ± 0.12 |
| K0S00 | 14.6 ± 0.1 | 13.8 | 3.58 ± 0.17 |
| K0S0 | 31.4 ± 0.1 | 2.2 | 8.06 ± 0.11 |

*M**BC* for *K*0S0 (*CP*-)

*M**BC* for  (*CP*+)

*M**BC* for *K* (*f*)

- Note log scale

- DATA

- (GeV)

## Hadronic Double Tags

- Cut and count in *M**BC*1 vs. *M**BC*2 plane, define four sidebands.
- Uncorrelated background: one *D* misreconstructed (sometimes both).
- Signal/sideband scale factor: integrate background function from ST fits.
- Mispartition background: particles mis-assigned between *D*0 and *D*0.

- Data

| K | K | KK |  | K0S00 | K0S0 | Yields |
| --- | --- | --- | --- | --- | --- | --- |
| 2.5 ± 0.4
2.0 ± 0.4 | 622 ± 7
599 ± 25 | 62.3 ± 2.1
70.6 ± 8.4 | 25.3 ± 1.3
24.0 ± 4.9 | 31.2 ± 1.4
38.7 ± 6.2 | 78.3 ± 2.3
90.4 ± 9.5 | K |
|  | 2.7 ± 0.4
2.0 ± 1.4 | 64.7 ± 2.1
53.0 ± 7.3 | 30.6 ± 1.4
24.3 ± 5.0 | 32.3 ± 1.5
37.6 ± 6.2 | 85.0 ± 2.4
77.0 ± 8.8 | K |
|  |  | 5.2 ± 0.4
-2.2 ± 1.9 | 4.5 ± 0.3
0.1 ± 0.9 | 5.7 ± 0.4
1.6 ±1.3 | 16.0 ± 0.6
39.6 ± 6.3 | KK |
|  |  |  | 1.1 ± 0.2
0.2 ± 1.4 | 2.2 ± 0.2
1.6 ± 1.3 | 5.8 ± 0.4
14.0 ± 3.7 |  |
|  |  |  |  | 1.2 ± 0.2
1.0 ± 1.0 | 7.3 ± 0.4
19.0 ± 4.4 | K0S00 |
|  |  |  |  |  | 9.7 ± 0.5
3.0 ± 1.7 | K0S0 |

- No-QC expectation
- Observed in data

*M**BC**(K**K* vs. *M**BC**(K*0S0)

- DATA

- (GeV)

- (GeV)

## Inclusive Semileptonic Double Tags

- Tag one side with *K* or *CP* eigenstate, search for electron in remainder of event:
- Fit electron spectrum for signal and background.
-  conversion, 0 Dalitz decay: charge symmetric.
- Mis-ID: hadrons faking electrons.
- Mis-tag: estimate from tag-side *M**BC*-*E* sideband.
- Require right-sign electron charge for *K* tag.
- Efficiency correction in bins of *p**e*.

| Tag | e | e(%) | % bkg | Signal Yield |
| --- | --- | --- | --- | --- |
| K |  | 72.9 | 5.2 | 1206 ± 35 |
| K |  | 71.9 | 2.8 | 1291 ± 36 |
| KK |  | 69.1 | 23.2 | 145 ± 12 |
| KK |  | 69.0 | 34.8 | 136 ± 12 |
|  |  | 70.0 | 28.2 | 78 ± 9 |
|  |  | 70.2 | 29.0 | 55 ± 7 |
| K0S00 |  | 69.2 | 43.8 | 146 ± 12 |
| K0S00 |  | 69.1 | 65.9 | 140 ± 12 |
| K0S0 |  | 69.2 | 8.2 | 231 ± 15 |
| K0S0 |  | 75.1 | 19.1 | 221 ± 15 |

*e* vs. *K*

*e* vs. *K*0S0

- *e* vs. *p**e*

*p**e* (GeV) in DATA

## Systematic Uncertainties

- Mixing/DCS parameters determined from ST/DT double ratios:
- Correlated systematics cancel (tracking/0/*K*0S efficiencies).
- Different systematics from branching fraction measurements.
- Uncorrelated systematic uncertainties included in the fit:
- Yield fit variation.
- Possible contribution from* C*=+1 initial state.
- Can limit with *CP*+/*CP*+, *CP*-/*CP*- double tags—forbidden for C=-1.
- Data provides self-calibration of initial state.
- Signal yields have peaking backgrounds of opposite *CP* or flavor  bias in estimates from uncorrelated MC.
- Possible bias from *CP*-correlated MC test.
- Full systematic error analysis in progress.
- Currently, syst ~ stat.

## Results

- Fit inputs: 6 ST, 14 hadronic DT, 10 semileptonic DT, efficiencies, crossfeeds, background branching fractions and efficiencies.
- 2 = 17.0 for 19 d.o.f. (C.L. = 59%).

| Parameter | Value | PDG or CLEO-c |
| --- | --- | --- |
| NDD | (1.09 ± 0.04 ± ?)x106 | (1.01 ± 0.02)x106 |
| A-y | 0.057 ± 0.066 ± ? |  |
| r2 | -0.028 ± 0.069 ± ? | (3.74 ± 0.18)x10-3
PDG + Belle + FOCUS |
| rz | 0.130 ± 0.082 ± ? |  |
| RM | (1.74 ± 1.47 ± ?)x10-3 | < ~1x10-3 |
| B(K) | (3.80 ± 0.29 ± ?)% | (3.91 ± 0.12)% |
| B(KK) | (0.357 ± 0.029 ± ?)% | (0.389 ± 0.012)% |
| B() | (0.125 ± 0.011 ± ?)% | (0.138 ± 0.005)% |
| B(K0S00) | (0.932 ± 0.087 ± ?)% | (0.89 ± 0.41)% |
| B(K0S0) | (1.27 ± 0.09 ± ?)% | (1.55 ± 0.12)% |
| B(Xe) | (6.21 ± 0.42 ± ?)% | (6.87 ± 0.28)% |

- PRELIMINARY

- Fitted *r*2 unphysical.  If constrain to WA, cos = 1.08 ± 0.66 ± ?.
- Limit on *C*=+1 contamination:
- Fit each yield to sum of *C*=-1 & *C*=+1 contribs.
- Include *CP*+/*CP*+ and *CP*-/*CP*- DTs in fit.
- No significant shifts in fit parameters.
*C*=+1 fraction = 0.06 ± 0.05 ± ?.
- Some branching fracs competitive with PDG.

- Uncertainties are statistical *only*

## Summary and Future Directions

- With correlated *D*0*D*0 system, can probe mixing and DCSD in time-integrated yields with double tagging technique.
- Simultaneous fit for:
- Hadronic/semileptonic/*CP* eigenstate branching fractions
- Mixing and DCSD parameters.
- Different systematics from previous measurements.
- Method unique to threshold production—unavailable at Tevatron and *B* factories.
- Add *D*0  *K*0S with Dalitz fits to increase *CP* eigenstate statistics.
- Add wrong-sign *e* vs. *K*** double tags to separate *r* and *z*.
- Add *C*=+1 pairs from *D*0*D*0 in √s ~4 GeV running to
- separate A and *y.*
- probe *x*.
*Preliminary* first measurements of (*K*) and A-*y*.
- Systematic uncertainties being studied.
- Results affect other CLEO-c analyses.