Peter Krian

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CP violation and related issues Part 10 Mixing

• Peter Krian
• University of Ljubljana and J. Stefan Institute

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Contents
Motivation Bd mixing Bs mixing D0 mixing
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B oscillations

• mmixed, uunmixed
• (neglecting CP, CPT violation, DG/G0)
• Motivation proceeds through loop diagrams, could
  be a tool to discover new physical phenomena.

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Mixing estimates
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Bd,s oscillations refined theoretical
predictions
B decay constant 19329 MeV (LQCD) 20827
MeV (QCD sum rules)
ren. group inv. param. 1.340.12 (LQCD) 1.100.15
(QCD sum rules)
NLO QCD corr. 0.550.01
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B oscillations
Experimental methods time dependent time
integrated lots of tagging and
reconstructionmethods
(neglecting CP, CPT violation, DG/G0),
mmixed, uunmixed need proper time
measurement st/tBsL/L (t/tB)(sp/p) flavor
tagging _at_decay and _at_production
high energy U(4s)
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Bd oscillations
backup slide
Examples of analyses exclusive method,
BaBar B0?Dln, reconstruct D flavor tagging
other side NN asymmetry(Pu-Pm)/(PuPm) Dmd0.49
20.0180.013 ps-1 (20fb-1) semi inclusive,
Belle two fast leptons flavor tagging lepton
charge Dmd0.5030.0080.010 ps-1 (29fb-1) large
amplitude ? good tagging e large statistics
(BaBar,hep-ex/0212017(02))
(Belle,PRD67,052004(03))
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Bd oscillations
Oscillation probability including DG
no assumption of CPT invariance
CP violated if Im(f)?0 dileptons difference in
ll and l-l- rates CPT violated if
q?p/2 expressions for Pu,m changed by
dependence on q,f
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How to measure Bs mixing?

• Measure probability that a Bs (at t0) turns
  into an anti-Bs at time t.
• Need
• a well defined final state with precisely
  measured vertex, momentum
• a tag to determine the initial Bs flavour (Bs or
  anti-Bs at t0)
• Final states
• m Ds nu, Ds -gt f p, KKS, KK
• J/y K -gt m m K p
• Ds() p ( p p p-)
• Tagging
• charge of kaon and lepton from the
  associated B decay (opposite side tagging)
• charge of kaon from the same side

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Bs oscillations
Cannot be measured at a B factory no Bs
mesons! First measurements were done at LEP (at
Ecms of Z0). tagging opposite side Neural net
(NN) to separate tracks from primary and
secondary vertex NN to compute charge
estimators (jet charge, lepton charge, K charge,
etc.) same side wide b-jet (all Bs decay
products fragmentation products
close in phase space) using large ycut (JADE) NN
to compute charge estimator (from K, jet charge,)
(Aleph,CERN-EP-2002-16)
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Bs oscillations
mmixed, uunmixed Fit the data in a different
way fix Dms and fit the oscillation amplitude A
If A consistent with 0 -gt no mixing. Mixing
established if A1, and A0 excluded with high
significance.
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Bs oscillations
data consistent with oscillations Dms17.5ps-1 _at_2.
2s
(HFAG,winter03)
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Bs mixing dilution effects for xs15
Dilution Tagging
Ideal
Dilution Tagging, Vertex
Dilution Tagging, Vertex
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Bs mixing dilution effects for xs25
Dilution Tagging
Ideal
Dilution Tagging, Vertex
Dilution Tagging, Vertex
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Bs mixing dilution effects due to vertexing
Full curve dilution tagging only Dilution due
to finite vertex resolution events move in the
region - st off the node Simple estimate
linear approx around the node, fraction of events
that move from the up part of the wave to the
down part (Dms st)2/2 Amplitude reduced by a
factor (1-(Dms st)2/2)
Full calculation convolution, exp(-(Dms
st)2/2) Simple estimate the first term in
expansion.
H. G. Moser, A. Roussarie, NIM A384 (1997)
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Bs mixing dilution effects due to vertexing
No dilution Dilution, tagging only Dilution
due to finite proper time resolution st (vertex
and momentum resolution
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Bs mixing sensitivity in Dms
Simple estimate of the statistics required for a
significant measurement fix Dms, and divide the
events in two classes, those from the 'up' part
of the wave, and those from the 'down' part. The
measured oscillation amplitude for a given Dms
differs from zero if the two classes are found to
be differently populated. The distribution over
the two classes is binomial, with probability for
the 'up' part equal to p1/2cD', where c is a
constant of order 1.

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Bs mixing sensitivity in Dms
Error on p for a measurement with N reconstructed
and tagged events s(p) ?(p(1-p)/N). For p
1/2 s(p) ½ 1/?N Error on the amplitude D
s(D) 1/(2c ?(N)) and the significance of the
measurement equals to D'/s(D) 2c ?N D
exp(-(Dms st)2/2) For a given required
significance, the number of events needed is
proportional to exp((Dms st)2). -gt a very steep
function of the proper time resolution and the
mixing parameter above Dms st1 -gt If Dms20/ps,
need st lt 50 fs to stay below this limit.

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Bs mixing sensitivity in Dms
Increase in the number of events needed for a
given significance vs resolution.
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D0 mixing
Dm very small, (Dm t)ltlt1 -gt Time
evolution Almost nothing happens before the D
meson decays. The method search for D mixing in
the decay sequence D? D0p, D0?flavour
specific final state.
D ? D0 p
K- e n
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D0 mixing in D0?Kp and Kln decays

• The method search for D mixing in the decay
  sequence D? D0p, D0?flavour specific final
  state.
• Semileptonic decay
• K- e n no mixing (RS, Right Sign)
• K e- n mixing (WS, Wrong Sign)
• measure WS rate
• Hadronic decay
• K- p no mixing
• K p- mixing or doubly Cabbibo suppressed
  (DCSD)
• measure WS time evolution

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D0 mixing in D0?Kp decays
D0?Kp time evolution
dN/dt a RD RD1/2 y t (x2 y2) t2/4
e-t
interference mixing

• x x cos d y sin d
• y y cos d - x sin d
• x DM/G y DG/2G
• strong phase difference
• SM x lt10-3, ylt10-3 (long dist. effects)
  new physics xgtgty, CPV

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D0 mixing in D0?Kp decays
Signal extraction
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D0 mixing in D0?Kp decays
Free fit RD(0.287 ? 0.037), y(2.541.11-1.02
), x2-(0.1530.08-0.10) Physical region
R(0.3430.027-0.026), y(0.60 ? 0.33), x20
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D0 mixing in D0?Kp decays
Results 95 contour in x2 and y plane (with 90
fb-1)
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D0 mixing in D0?Kp decays
Results 95 contour in x2 and y plane (with
57.1 fb-1)
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D0 mixing in D0?Ken decays

• Selection criteria
• c.m.s. momentum of the Ke system gt 2 GeV (bb,
  combinatorial background)
• Invariant mass of e-e (e?p) gt 0.15GeV (g
  conversions)
• Cut on decay time (backgrounds d(t) e-t, signal
  t2 e-t)
• Neutrino reconstruction hermiticity of the
  spectrometer, kinematic constraints.
• Main observable Dm m(psKen) - m(Ken)

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D0 mixing in D0?Ken decays
?
?
NRS 40198?329 NWS
19?67
rD (NWS/ NRS) (eRS/eWS) (0.20 ? 0.70)
10-3 rD lt 1.4 10-3 (90 conf. level)
rD (x2 y2)/2
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D0 mixing in D0?Ken decays
BaBar employs neural net techniques to
reconstruct the D0 momentum vector (including
again the neutrino), and to reject background
events. Yield fit to Dm, t distributions.
NRS 49620?265 NWS
114?61
rD (2.3 ? 1.2(stat)) 10-3 rD lt 4.2 10-3 (90
conf. level)
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D0 mixing in D0?Ken decays
BaBar rD lt 4.2 10-3 (90 conf. level) Belle rD
lt 1.4 10-3 (90 conf. level)
Theoretical predictions for rD (right scale)
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Backup slides
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Bd oscillations
How about assumptions on CP, CPT violation,
DG/G0? Belle, dilepton analysis
CP violated if Im(f)?0 CPT violated if q ?
p/2 CP violation and DG/G small Re(cosq)0.000.
12 Im(cosq)0.030.03
BaBar fully reconstructed B in flavor or CP
eigenstate different tagging categories multipa
rameter fit including q/p, DG/G, lCP, z
(BaBar,hep-ex/0303043(03))
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Bd oscillations
BaBar general time dependent decay rates of
B0B0 CPT violation in mixing
fully reconstructed B in flavor or CP
eigenstate different tagging categories multipar
ameter fit including q/p, DG/G, lCP, z
(BaBar,hep-ex/0303043(03))