Bs properties: ?Ms, ??s

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Bs properties ?Ms, ??s ?s

• Avdhesh Chandra

for the CDF and DØ collaborations
Lattice QCD Workshop 2007, Fermilab
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Unitary Triangle for Bs
In SM quark mixing (Q2/3? Q-1/3) is given by CKM
matrix

Unitarity triangle equation for b-quark
A squashed unitary triangle ? small CP
violation in Bs
Measurement of Bs properties helps in
constraining unitary triangle and hence new
physics.
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Bs Mixing
b
?b
Schrödinger Equation
?s
s

• M12 stems from the real part of the box
  diagram, dominated by top
• G12 stems from the imaginary part, dominated by
  charm

Diagonalization gives two physically observed
Light and Heavy mass eigenstates
CP even
i.e. no CP violation
CP odd
squashed triangle ? flat triangle
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Physical Quantities
Three physical quantities M12 , ?12 and
arg(-M12/?12)

• In terms of mass eigenstates
• ?s arg(-M12/?12) CP violation phase
• ?Ms MH - ML 2M12 frequency of Bs-?Bs
  oscillations
• ??s ?L - ?H 2?12cos?s decay width
  difference

• Other useful quantities
• afs Im(?12/M12) (?12/M12)sin?s
  (??s/?Ms)tan?s semileptonic CP asymmetry
• AmixCP(Bs?(J/??)CP?) ? sin(-2?s) mixing
  induced CP asymmetries
• A0 A A? Linear polarization amplitudes in
  Bs?J/? ?
• ?0 ? ?? CP-conserving strong phases , ?i ?
  arg(Ai)

In recent years there is a big improvement in
theory prediction of ?Ms , ??s ?s
We can extract all the elements of mixing matrix,
and other physical quantities, describe Bs system
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For New Physics
Theory Predictions
hep-ph/0612167v2
afs (2.06 ? 0.57).10-5 ??s/?Ms (49.7 ?
9.4).10-4
??s (0.096 ? 0.039) ps-1 ?Ms (19.30 ? 6.74)
ps-1 ?s (4.2 ? 1.4).10-3
Note, angle ? of the unitary triangle in Bs
system ?s(2.0 ? 0.5).10-2
New Physics in the Bs system can be parameterized
by a complex number ?s , defined as
where
For SM ?s 1 while ?s? is a physical CP phase
??s/?Ms
?Ms
?Ms ?MsSM ?s (19.30 ? 6.74)ps-1.?s ??s
2?12cos(?sSM ?s?) (0.096 ?
0.039)ps-1. cos( (4.2 ?
1.4).10-3 ?s?) . and others
Im ?s
afs
Re ?s
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The CDF DØ Detector

• Excellent tracking mass resolution
• Silicon ? lt 2 , 90 cm long
• 96 layer drift chamber 44 to 132 cm

• Triggered Muon coverage
• pT gt 1.5 GeV, ? lt 1

• Low pT Muon identification
• pT gt 1.5 GeV, ? lt 2

• High tracking efficiency
• 95 ? lt 3 (Silicon disks)

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Mixing frequency Measurement
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Overview
For ?? 0
The probability of mixing is given by
Tagging efficiency
Proper decay length resolution
Signal
Dilution
Background

• One needs three ingredients
• Bs flavor at decay
• Bs flavor at production
• Good proper decay length resolution

Transverse decay length
Proper decay length
lepton
K
jet
?
PV
frag
frag
SV
b
?b
Bs
B hadron
Lxy
Ds
K
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DØ Bs candidates
Fully reconstructed hadronic and partially
reconstructed hadronic and semileptonic Bs decays
from 2.4 fb-1
semileptonic mode
Nsig
Decay Channels
44777 1663 249 18098
Ds invariant mass
hadronic mode
Ds invariant mass
Bs0 invariant mass
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CDF Bs candidates
From 5600 fully reconstructed hadronic, 3100
partially reconstructed hadronic, and 61500
partially reconstructed semileptonic Bs decays of
1.0 fb-1
semileptonic mode
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Proper decay length resolution

• ?ct event by event, with scale factor
• For partially reconstructed decays

K from MC, for each decay channel
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Initial state flavor tagging
On reconstructed Bs side (due to correlation
between Bs flavor and the charge of fragmentation
K)
Opposite to reconstructed Bs side (due to b ,?b
produciton)
CDF
DØ

• Using both opposite side and same side
• NN combination of the opposite side jet charge ,
  kaon and lepton tags ?D2 1.8
• NN kinematic and identification variables of the
  kaon candidate, for same side tag ?D2 3.7
  (had.) , 4.8 (semilep.)

• Combine OST and SST if both present
• Assume both independent
• Combine SST and Event charge if both present
• Sqi of all tracks on opposite side
• Total ?D2 4.5

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DØ ?Ms result
Combined amplitude scan
DMs (ps-1)

• A parabolic fit to likelihood scan for DMs
  returns
• DMs 18.5 0.9 ps-1
• 3.1s statistical significance

Sensitivity 27.3 ps-1
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CDF ?Ms result

• ?Ms 17.77 ? 0.10 (stat) ? 0.07 (syst) ps-1
• 5.4? statistical significance

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??s ?s from J/? ?
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Angular Distribution

• Bs ? V1 V2 (J/? ?) i.e. Spin
  0 ? 11 L 0,1,2
• L 0 and 2 corresponds to CP even L1 CP
  odd
• Angular distribution can be written in helicity
  basis , BUT generally Transversity basis is
  used to write angular distribution , where polar
  coordinates are defined in J/? rest frame and
  ? rest frame

Polarization Amplitudes
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Polarization Amplitudes
hep-ph/9804253 hep-ph/0012219
Upper sign corresponds to Time evolution of pure
Bs0 ? J/? ? at t0 Lower sign corresponds to
Time evolution of pure?Bs0 ? J/? ? at t0

• ?? ? average decay width of two physical
  eigenstates
• ?1 ?2 ? CP-conserving strong phase ? and 0
• A0(0) , A(0) ?CP-even linear polarization
  amplitude at t0
• A?(0) ?CP-odd linear polarization amplitude at t0

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For untagged
Adding up for all Bs0 and ?Bs0

• Assuming equal production rate of Bs0 and?Bs0 in
  p ?p collisions
• All opposite terms go away Insensitive to
  ?Ms , but sensitive to ?s

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Results (no CP violation)
?s?0
c?s (in ?m)
456 ? 13 (stat) ? 7 (syst)
454 ? 21 (stat) (syst)
??s (in ps-1)
0.076 (stat) ? 0.006 (syst)
0.12 ? 0.09 (stat) ? 0.02 (syst)
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Results (?s free)
??s 0.17 ? 0.09 (stat) ? 0.02 (syst) ps-1 ?s
-0.79 ? 0.56 (stat) (syst)

• no numerical values are given
• 90 95 confidence curves are shown

• above are close to SM values
• results have 4-fold ambiguities

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Angular fit projections
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Semileptonic charge asymmetry

• afss is measured in two independent way at DØ
• Indirectly from time-integrated di-muon charge
  asymmetry
• 0.0064 ? 0.0101
• Directly from time-integrated charge asymmetry
  from Bs ? ??Ds
• 0.0245 ?
  0.0193 ? 0.0035
• Combining above two measurement
• 0.0001 ?
  0.0090

For measured value of ?Ms ??s tan?s 0.002 ?
0.160 ps-1
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Constrained DØ results
??s 0.13 ? 0.09 ps-1 ?s -0.70
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Summary of numbers
DØ
CDF
?Ms (in ps-1)
17.77 ? 0.10 ? 0.07
18.56 ? 0.89
??s (in ps-1)
0.13 ? 0.09
0.076 ? 0.006
?s
-0.70
Results are consistent with SM
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Room for new physics
Using measured values of ?Ms , ?s, ??s/?Ms and
asfs
Theoretical
??s/?Ms
?Ms
Im ?s
afs
Re ?s
Still room for new physics, updated results will
be important for existence of any deviation from
SM stay tuned!
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Coming Soon

• Updated measurement with 2 times data
• Flavour tagging to Bs?J/??
• Relatively small error on physics parameters
  (specially ?s)
• Helpful in resolving ambiguities
• Required
• Better understanding of similar physics
  parameters from other source so Bs?J/?? can be
  benefited for example by Bd?J/?K
• Fixing strong phases from Bd?J/?K

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Additional Slides
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Amplitude Scan
Scan ?Ms, for each value find
If sample frequency is ?Ms amplitude
otherwise
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From QCD
Weak decay constant
Bag parameter
Large uncertainty cancels out
un