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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)
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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
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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]
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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)
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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
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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
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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
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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”
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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 !
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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
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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
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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 ?
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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
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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
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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
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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) ?
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