Discussion of Bs oscillations and the recent ms result from D0

LPHE meetingApril 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)

O. Schneider LPHE meeting, Apr 3, 2006 2

Bs oscillations Neutral B meson system (Bd or Bs):

— B0 and B0 are quantum superposition of two mass eigenstates BH and BL:

— Produce B0 and observe its decay in a flavour-specific final state at proper time t(assume CP conserved):

Slow Bd oscillations:— very well measured: md=0.5 ps–1

Fast Bs oscillations:— not measured yet: ms > 15 ps–1

— experimentally very challenging— NB: we know effect is there since

s has been measured to be ~1/2

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BL,H = p B0 ± q B 0

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Prob B0 → B0( ) = e−t/τ

2τcosh ΔΓ

2t( ) + cosΔmt( )[ ]

Prob B0 → B 0( ) = e−t/τ

2τcosh ΔΓ

2t( ) − cosΔmt( )[ ]

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m = mH − mL

ΔΓ = ΓL − ΓH

Γ =ΓL + ΓH

2=1 τ

Example:m = 15 ps–1

= 0=1.5 ps

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s = Prob Bs0 → B s

0( )dt∫

O. Schneider LPHE meeting, Apr 3, 2006 3

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⇒ Δms

Δmd

=mBs

mBd

ξ 2 Vts2

Vtd2 where ξ =

fBsBBs

fBdBBd€

mq =GF

2mW2 η BS(mt

2 /mW2 )

6π 2 mBqfBq2 BBq VtqVtb

* 2

B mixing in Standard Model

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σ ξ( )ξ ~ 10 ×

σ Δms Δmd( )Δms Δmd

Extraction of |Vtd| and |Vts| from B mixing dominated by hadronic uncertainties

2nd-order weak process, box diagrams dominated by virtual top quark exchange

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W

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W

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b

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Bd,s0

⎧ ⎨ ⎪

⎩ ⎪

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d,s

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b€

d ,s

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⎫ ⎬ ⎪

⎭ ⎪ B d,s

0

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t

€

t

€

Vtd ,Vts

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Vtb*€

Vtd ,Vts

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Vtb*

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W

€

W

€

b

€

Bd,s0

⎧ ⎨ ⎪

⎩ ⎪

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d,s

€

b€

d ,s

€

⎫ ⎬ ⎪

⎭ ⎪ B d,s

0

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t

€

Vtd ,Vts

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Vtb*€

Vtd ,Vts

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Vtb*

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t

Theory uncertainty (Lattice QCD):

Experimental accuracy:

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md = 0.507 ± 0.004 ps−1 0.9%

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σ(Δms) will be < 0.1 ps−1

as soon as measured 0.5%

~4%

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fBdBBd

= 244 ± 26 MeV

ξ =1.210 + 0.047 − 0.035 ~11%

[M. Okamoto, hep-lat/0510113]

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Constraining CKM unitarity triangle with B mixing

md |VtdVtb*|2 = |Vtd|2

ms |VtsVtb*|2 = |Vts|2 = |Vcb|2

|Vtd|/|Vcb| ratio length of right side

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ρ

€

η

Global CKM fit without measurements of angles , ,

(CKM fitter, Summer 2005)

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Standard Model prediction of ms From fits of unitarity triangle,

assuming Standard Model and using all available information (except from ms analyses):

ms = 21.2 ± 3.2 ps–1

ms [15.4, 27.8] ps–1 at 95% CL

ms [13.8, 30.0] ps–1 at 99% CLM. Bona et al (Utfit collaboration), hep-ph/0501199, Feb 2005

Standard Model

msSM |Vts

2|s

SM = –arg(Vts2)

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b

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Bs0

⎧ ⎨ ⎪

⎩ ⎪

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s

€

b€

s

€

⎫ ⎬ ⎪

⎭ ⎪ B s

0

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W

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W

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t

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t

New Physics ?

? ??

?

ms s

Not valid if new physics in B mixing

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Statistical significance of Bs oscillation signal

Experimental effects dilute statistical significance of Bs oscillations:— Flavour tagging

effective efficiency eff:

— Proper time resolution σt:

— Signal purity (before tagging):

Somewhat naïve but extremely useful formula:

— Because ms 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 ms• need to have a good knowledge of σt and eff

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eff = εD2 = ε 1− 2w( )2

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=tagging efficiencyD = dilutionw = wrong tag probability

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t = l mp

⇒ σ t = mp

σ l ⊕ tσ p

p

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significance =Sεeff

2 exp −

Δmsσ t( )2

2

⎛

⎝ ⎜

⎞

⎠ ⎟ S

S +B

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l =Bs decay lengthp = Bs momentum

m = Bs mass

For example, must have significance >5 for a 5σ observation of Bs oscillations

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SS + B

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S = number of Bs signal eventsB = number of background events

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Bs oscillation amplitude

Am

plit

ude

A Amplitude method:—Replace “cos(mst)” with

“A cos(mst)” in mixing expressions—Fit tagged rates for A, at many

different test values of ms

—Plot A± σA versus ms (similar to Fourier transform of mixing asymmetry)

—A=1 (within error) at true ms,otherwise A consistent with 0

—Significance = 1/σA

—If no significant signal, exclude values of ms for which A=1 is excluded

Example: D0 result Summer 2005:—No signal, exclude all values of ms in this range

at 95% CL

July 2005

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Ds

D+

New D0 result on msV.M. Abazov et al. (D0 collaboration),“First Direct Two-Sided Bound on the Bs Oscillation Frequency”hep-ex/0603029, March 15, 2006, submitted to PRL

– 1 fb–1 of data (April 2002–October 2005)– Bs Ds

–(*)+X, Ds– (K+K–)

– 26.7 k signal events– proper decay length measured in transverse plane– use MC “K factor” to correct pT(Ds) to pT(Bs)– opposite-side tagging, D2 = (2.48 ± 0.21 ±0.07)%

A=2.75 ± 1.12 at 19 ps–1

2.5σ deviation from A=01.6σ deviation from A=1

“A true value of ms 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 < ms < 22 ps–1”

Preferred value: ms = 19 ps–1

17 < ms < 21 ps–1 at 90%CLClaim: “This is the first 2-sided bound”

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Sensitivity of new D0 analysis

From: tschieti@mail.cern.chSubject: delta ms measurement by D0Date: 12 mars 2006 22:26:59 GMT+01:00To: lhcb@cern.ch

Although D0 do not claim a measurement, their result is perceived as such by several people !

No sensitivity yet to observe a signal above 10 ps–1

Need 10 times more data (or equivalent analysis improvements) for a 3σ observation at 19 ps–1

Current D0 data display a “lucky” fluctuation at 19 ps–1 — Bump in amplitude spectrum is either a 2.5σ fluctuation on top of nothing,

or a 1.6σ fluctuation on top of a signal at ms = 19 ps–1

With 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 ms !

D0 sensitivity Now at 1 fb–1

Extrapolated to 10 fb–1

5σ observation of ms up to 5.6 ps–1 14.4 ps–1

3σ observation of ms up to 9.3 ps–1 18.6 ps–1

95% CL exclusion up to 14.1 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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(ln likelihood) curve The measured negative log-likelihood difference (with respect to ms = )

can be retrieved from the measured amplitude spectrum:

The “lucky” fluctuation reflects in the (lnL) curve with a minimum deeper than expected:

— Expected depth is 0.40 for a signal at 19 ps–1 — Observed depth is 1.80 ± 0.89 (stat.+syst.)

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(lnL) = −ln(L(Δms) − −ln(L(∞)( ) = 0.5 − Aσ A

2 ± 1σ A

Expected depth for a signal at 19 ps–1

1.8 ± 0.9

0.4

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Effect of new D0 result on world averageEnd 2005 Now

Sensitivity of world average End 2005 Now5σ observation of ms up to 10.5 ps–1 11.0 ps–1

3σ observation of ms up to 14.0 ps–1 15.5 ps–1

σtot(A) at ms = 19 ps–1

World average end 2005 ± 0.54New D0 result alone ± 1.12World average now ± 0.49

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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

DELPHI 11.9 ps–1

OPAL 7.9 ps–1

SLD 11.5 ps–1 SLC 11.5 ps–1

CDF1 5.1 ps–1

Tevatron 16.9 ps–1CDF2 13.0 ps–1

D0 14.1 ps–1

NEWWeight in world average at 19 ps–1:ALEPH 22%

LEP 32%

World 100%

DELPHI 9%OPAL 1%SLD 22% SLC 22%CDF1 2%

Tevatron 46%CDF2 25%

D0 19%

— CDF is experiment with largest weight at 19 ps–1 because of fully reconstructed Bs sample (but CDF used only 0.355 fb–1 so far)

— Can D0 also use fully reconstructed Bs ?

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Combined amplitude spectrum Combined amplitude displays a signal-like bump in SM region Could still be a fluctuation at ~2σ level … or the hint of a signal But this feature has been around for years !

Now 2.1σEnd ‘05 1.6σSummer ‘05 2.3σ

Summer ‘04 1.9σ

Summer ‘03 2.2σ

Summer ‘02 2.3σ

Summer ‘01 2.7σ

Summer ‘00 2.7σ

Summer ‘99 1.9σ

Summer ‘98 1.9σ

Summer ‘97 1.9σ

Max. deviation from A=0 inrange 17–21 ps–1:

NowSummer 2000

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Combined (ln likelihood) curve The combined negative log-likelihood difference (with respect to ms = )

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 ± 2.0 2.0

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What to expect in the near future Simple 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 Bottom line:

— With 5 fb–1, CDF will definitely have the sensitivity to observe ms, if ms < 20 ps–1

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Conclusion For the world:

—New D0 result welcome, weighs ~20% in the new world average (at 19 ps–1) ms 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 2σ fluctuation (but that’s not much additional faith)

For LHCb:—CDF+D0 will measure ms “soon”, unless ms is large

• how soon depends on how much luminosity they get + analysis improvements

—LHCb’s readiness to measure ms 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 5σ measurement up to 40 ps–1 (beyond Tevatron’s reach)

• should we foresee a safety factor (to cover possible worse performance at startup) ?