1. Discussion of B s oscillations and the recent  m s result from D0 LPHE meeting April 3, 2006 Olivier Schneider (EPFL) Presentation given at the LHCb Tuesday meeting, March 21, 2006 + a few additional slides (introduction on mixing, at the beginning)

2. O. SchneiderLPHE meeting, Apr 3, 20062 B s oscillations oNeutral B meson system (B d or B s ): —B 0 and B 0 are quantum superposition of two mass eigenstates B H and B L : —Produce B 0 and observe its decay in a flavour-specific final state at proper time t (assume CP conserved): oSlow B d oscillations: —very well measured:  m d =0.5 ps –1 oFast B s oscillations: —not measured yet:  m s > 15 ps –1 —experimentally very challenging —NB: we know effect is there since  s has been measured to be ~1/2 Example:  m = 15 ps –1  = 0  =1.5 ps

3. O. SchneiderLPHE meeting, Apr 3, 20063 B mixing in Standard Model Extraction of |V td | and |V ts | from B mixing dominated by hadronic uncertainties o2nd-order weak process, box diagrams dominated by virtual top quark exchange oTheory uncertainty (Lattice QCD): oExperimental accuracy:  0.9% as soon as measured  0.5%  ~4%  ~11% [M. Okamoto, hep-lat/0510113]

4. O. SchneiderLPHE meeting, Apr 3, 20064 Constraining CKM unitarity triangle with B mixing  m d  |V td V tb * | 2 = |V td | 2  m s  |V ts V tb * | 2 = |V ts | 2 = |V cb | 2  |V td |/|V cb | ratio  length of right side Global CKM fit without measurements of angles , ,  (CKM fitter, Summer 2005)

5. O. SchneiderLPHE meeting, Apr 3, 20065 Standard Model prediction of  m s oFrom fits of unitarity triangle, assuming Standard Model and using all available information (except from  m s analyses):  m s = 21.2 ± 3.2 ps –1  m s  [15.4, 27.8] ps –1 at 95% CL  m s  [13.8, 30.0] ps –1 at 99% CL M. Bona et al (Utfit collaboration), hep-ph/0501199, Feb 2005 Standard Model  m s SM  |V ts 2 |  s SM = –arg(V ts 2 ) New Physics ? ?? ? ? ms s ms s  Not valid if new physics in B mixing

6. O. SchneiderLPHE meeting, Apr 3, 20066 Statistical significance of B s oscillation signal oExperimental effects dilute statistical significance of B s oscillations: —Flavour tagging effective efficiency  eff : —Proper time resolution  t : —Signal purity (before tagging): oSomewhat naïve but extremely useful formula: —Because  m s is large, very strong dependence on the resolution need to be able to resolve the fast oscillations —If significance too low, set lower limit on  m s need to have a good knowledge of  t and  eff For example, must have significance >5 for a 5  observation of B s oscillations

7. O. SchneiderLPHE meeting, Apr 3, 20067 B s oscillation amplitude Amplitude A oAmplitude method: —Replace “cos(  m s t)” with “A cos(  m s t)” in mixing expressions —Fit tagged rates for A, at many different test values of  m s —Plot A±  A versus  m s (similar to Fourier transform of mixing asymmetry) —A=1 (within error) at true  m s, otherwise A consistent with 0 —Significance = 1/  A —If no significant signal, exclude values of  m s for which A=1 is excluded oExample: D0 result Summer 2005: —No signal, exclude all values of  m s in this range at 95% CL July 2005

8. O. SchneiderLPHE meeting, Apr 3, 20068 DsDs D+D+ New D0 result on  m s V.M. Abazov et al. (D0 collaboration), “First Direct Two-Sided Bound on the B s Oscillation Frequency” hep-ex/0603029, March 15, 2006, submitted to PRL – 1 fb –1 of data (April 2002–October 2005) – B s  D s –(*)  + X, D s –   (K + K – )  – 26.7 k signal events – proper decay length measured in transverse plane – use MC “K factor” to correct p T (D s  ) to p T (B s ) – opposite-side tagging,  D 2 = (2.48 ± 0.21 ±0.07)% A=2.75 ± 1.12 at 19 ps –1 2.5  deviation from A=0 1.6  deviation from A=1 “A true value of  m s above the sensitive region (i.e. > 22 ps –1 ) has a 5% probability to produce a likelihood similar to the one observed in the interval 16 <  m s < 22 ps –1 ” Preferred value:  m s = 19 ps –1 17 <  m s < 21 ps –1 at 90%CL Claim: “This is the first 2-sided bound”

9. O. SchneiderLPHE meeting, Apr 3, 20069 Sensitivity of new D0 analysis From: tschieti@mail.cern.chtschieti@mail.cern.ch Subject: delta ms measurement by D0 Date: 12 mars 2006 22:26:59 GMT+01:00 To: lhcb@cern.chlhcb@cern.ch oAlthough D0 do not claim a measurement, their result is perceived as such by several people ! oNo sensitivity yet to observe a signal above 10 ps –1 oNeed 10 times more data (or equivalent analysis improvements) for a 3  observation at 19 ps –1 oCurrent D0 data display a “lucky” fluctuation at 19 ps –1 —Bump in amplitude spectrum is either a 2.5  fluctuation on top of nothing, or a 1.6  fluctuation on top of a signal at  m s = 19 ps –1 oWith more data, I expect the significance of this effect to first go down —My guess it that it will be a while until D0 submits a second paper on  m s ! D0 sensitivity Now at 1 fb –1 Extrapolated to 10 fb–1 5  observation of  m s up to 5.6 ps –1 14.4 ps –1 3  observation of  m s up to 9.3 ps –1 18.6 ps –1 95% CL exclusion up to14.1 ps –1 24.1 ps –1 D0 “claimed sensitivity” up to~22 ps –1 ? You may believe one or the other, but it’s a fluctuation in any case !

10. O. SchneiderLPHE meeting, Apr 3, 200610  (ln likelihood) curve oThe measured negative log-likelihood difference (with respect to  m s =  ) can be retrieved from the measured amplitude spectrum: oThe “lucky” fluctuation reflects in the  (lnL) curve with a minimum deeper than expected: —Expected depth is0.40 for a signal at 19 ps –1 —Observed depth is1.80 ± 0.89 (stat.+syst.) Expected depth for a signal at 19 ps –1 1.8 ± 0.9 0.4

11. O. SchneiderLPHE meeting, Apr 3, 200611 Effect of new D0 result on world average End 2005 Now Sensitivity of world averageEnd 2005Now 5  observation of  m s up to 10.5 ps –1 11.0 ps –1 3  observation of  m s up to 14.0 ps –1 15.5 ps – 1  tot (A) at  m s = 19 ps –1 World average end 2005± 0.54 New D0 result alone± 1.12 World average now± 0.49

12. O. SchneiderLPHE meeting, Apr 3, 200612 Comparisons —D0 now similar to ALEPH ! —Tevatron finally breaks even with LEP ! Sensitivity for 95%CL exclusion: ALEPH 14.4 ps – 1 LEP 16.9 ps – 1 World 20.1 ps – 1 DELPHI11.9 ps –1 OPAL 7.9 ps –1 SLD11.5 ps –1 SLC11.5 ps –1 CDF1 5.1 ps – 1 Tevatron 16.9 ps – 1 CDF2 13.0 ps – 1 D0 14.1 ps – 1 NEW Weight in world average at 19 ps–1: ALEPH22% LEP32% World100% DELPHI9% OPAL 1% SLD22%SLC22% CDF1 2% Tevatron46% CDF225% D019% —CDF is experiment with largest weight at 19 ps –1 because of fully reconstructed B s sample (but CDF used only 0.355 fb –1 so far) —Can D0 also use fully reconstructed B s ?

13. O. SchneiderLPHE meeting, Apr 3, 200613 Combined amplitude spectrum oCombined amplitude displays a signal-like bump in SM region oCould still be a fluctuation at ~2  level … or the hint of a signal oBut this feature has been around for years ! Now 2.1  End ‘05 1.6  Summer ‘05 2.3  Summer ‘04 1.9  Summer ‘03 2.2  Summer ‘02 2.3  Summer ‘01 2.7  Summer ‘00 2.7  Summer ‘99 1.9  Summer ‘98 1.9  Summer ‘97 1.9  Max. deviation from A=0 in range 17–21 ps–1: Now Summer 2000

14. O. SchneiderLPHE meeting, Apr 3, 200614 Combined  (ln likelihood) curve oThe combined negative log-likelihood difference (with respect to  m s =  ) can be retrieved from the combined amplitude spectrum: —At 19 ps –1 (D0’s preferred value) Expected depth is 2.0 for a signal at 19 ps –1 Observed depth is 1.8 ± 2.0 —At 19.5 ps –1 (world’s preferred value) Expected depth is 1.7 for a signal at 19.5 ps –1 Observed depth is 2.1 ± 1.8 Now Expected depth for a signal at 19 ps –1 1.8 ± 2.02.0

15. O. SchneiderLPHE meeting, Apr 3, 200615 What to expect in the near future oSimple extrapolation based on current Run II results from CDF and D0: —assume 1/sqrt(N) dependence on total amplitude error —possible analysis improvements not taken into account oBottom line: —With 5 fb –1, CDF will definitely have the sensitivity to observe  m s, if  m s < 20 ps –1

16. O. SchneiderLPHE meeting, Apr 3, 200616 Conclusion oFor the world: —New D0 result welcome, weighs ~20% in the new world average (at 19 ps –1 ) —  m s not yet measured ! don’t be intimidated by “first upper bound”, etc … This is just noise ! —Available data consistent with SM prediction —If you believe SM is wrong … … you must also believe a 2  fluctuation (but that’s not much additional faith) oFor LHCb: —CDF+D0 will measure  m s “soon”, unless  m s is large how soon depends on how much luminosity they get + analysis improvements —LHCb’s readiness to measure  m s as early as possible in 2008 is important —Ask LHC to deliver sufficient luminosity at IP8 with high priority 0.25 fb –1 in principle enough for 5  measurement up to 40 ps –1 (beyond Tevatron’s reach) should we foresee a safety factor (to cover possible worse performance at startup) ?