Fermilab Wine & Cheese Seminar, 14 May 2010
Evidence for an anomalous like-sign
dimuon charge asymmetry
G.Borissov
G
Borissov
Lancaster University, UK
Matter – Antimatter Asymmetry
• One of major challenges of particle physics – explain the
dominance of matter in our Universe
• Number of particles and antiparticles produced
in the Big Bang is expected to be equal
t0
• For some reason matter becomes more
antimatter
abundant in the early stages of Universe
• Antimatter completely annihilated
• Hence we're left only with matter today
One of conditions (A. Sakharov) required
to explain this process – properties of particles
and antiparticles must be different
(CP violation)
matter
t  t1
antimatter
matter
t  today
antimatter
matter
2
CP violation in SM
• CP violation is naturally included in the standard model
through the quark mixing (CKM) matrix
• Many different measurements of CP violation phenomena
are in excellent agreement
g
with the SM:
– All measurements are consistent with a single apex of this
unitarity triangle plot
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3
CP violation in SM
• The SM disagrees with one experimental fact – our existence
– The SM source of CP violation is not sufficient to explain
p
the
imbalance between matter and antimatter
– See e.g. P. Suet, E. Sather, Phys.Rev.D51, 379-394 (1995)
– Some
S
theoretical
h
i l studies
di claim
l i up to 10 orders
d off magnitude
i d deficit
d fi i off
the CP violation provided by the SM
• New sources of CP violation are required to explain the
matter dominance
Search for new sources of CP violation –
an important task of current and future experiments
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CP violation in mixing
• Main goal of our measurement is to study CP violation in
mixing in the Bd and Bs systems
• Magnitude of this CP violation predicted by SM is negligible
comparing
p
g to ppresent experimental
p
sensitivity
y
• Contribution of new physics can result in a significant
modification of the SM pprediction, which can be tested
experimentally
– Small SM value simplifies detection of possible deviation
A measurement of CP violation significantly different from
zero would be unambiguous evidence of new physics
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Dimuon charge asymmetry
X
B
B
0
B0
X
• We measure CP violation in mixingg usingg
the dimuon charge asymmetry of semileptonic B decays:
N
A 
N
b
sl

b

b
N
N

b

b
– Nb++, Nb−− − number of events with two b hadrons decaying
semileptonically and producing two muons of the same charge
– One
O muon comes ffrom di
directt semileptonic
il t i decay
d
b → μ−X
– Second muon comes from direct semileptonic decay after neutral B
meson mixing:
g B0  B 0    X
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Dimuon and semileptonic
charge asymmetry
• Absl is equal to the charge asymmetry of "wrong sign"
semileptonic
il
i B decays:
d



(
B


X
)


(
B


X)
b
a slb 

A
sl
 (B    X )   (B    X )
– S
See Y. G
Grossman, Y. Nir,
i G
G. Raz, PRL 997, 1151801
1801 (2006)
– "Right sign" decay is B→μ+X
– "Wrong
Wrong sign
sign" decays can happen only due to flavour oscillation in
Bd and Bs
– Semileptonic charge asymmetry can also be defined separately
f Bd andd Bs :
for
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0

0


(
B


X
)


(
B


X)
q
q
q
a sl 
; q  d, s
0

0

 ( B   X )   ( Bq  Wine
 X&)Cheese seminar
Dimuonq charge asymmetry - Fermilab
7
Absl at the Tevatron
• Since both Bd and Bs are produced at the Tevatron, Absl is a
linear combination of adsll and assll :
– Need to know production fractions of Bd and Bs mesons at the
Tevatron
– Measured by the CDF experiment
Aslb  (0.506  0.043)a sld  (0.494  0.043)a sls
Unlike the experiments at B factories, the Tevatron
gives a unique possibility to measure the charge
asymmetry of both Bd and Bs
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Absl and CP violation
• Non-zero value of Absl means that the semileptonic decays
of Bq0 and Bq0 are different
• It implies CP violation in mixing
– it occurs only due to the mixing in the Bd and Bs systems
• It is quantitatively described by the CP violating phase q
of the B0q (q = d,s)) mass matrix:
 q
a 
tan(q )
M q
q
sl
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Absl and the standard model
• Standard model predicts a very small value of Absl:
Aslb  ( 2.3 00..56 )  10 4
– using prediction of adsl and assl from
A. Lenz, U. Nierste, hep-ph/0612167
– New physics contribution can significantly change this value by
changing the CP violating phases d and s
Our goal is to measure Absl and compare it
with the standard model prediction
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Measurement Method
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Experimental observables
• Experimentally, we measure two quantities:
• Like-sign
Like sign dimuon charge asymmetry:
N   N 
A  
N  N 
• Inclusive muon charge
g asymmetry:
y
y
n  n
a 
n  n
– N++, N−− – the number of events with two like-sign dimuons
– n+, n− – the number of muons with given charge
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Experimental observables and Absl
• Semileptonic B decays contribute to both A and a;
• Both A and a linearly depend on the charge asymmetry Absl
a  k Aslb  abkg
A  K Aslb  Abkg
– recall that Absl = absl
• In addition, there are detector related background
contributions
t ib ti
Abkg andd abkg
Our task is:
• Determine the background contributions Abkg and abkg
• Find the coefficients K and k
b
•
Extract
the
asymmetry
A
sl - Fermilab Wine & Cheese seminar
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Dimuon charge asymmetry
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Background contribution
a  k Aslb  abkg
A  K Aslb  Abkg
• Sources of background muons:
–
–
–
–
Kaon and
K
d pion
i decays
d
K+→μ+ν, π+→μ+ν or punch-through
h th
h
proton punch-through
False track associated with muon track
Asymmetry of muon reconstruction
We measure all background contributions directly in
data, with a reduced input from simulation
Wi h this
With
hi approachh we expect to controll andd decrease
d
the systematic uncertainties
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Correlated background
uncertainties
t i ti
• The same background processes contribute to both Abkg and abkg
• Therefore, the uncertainties of Abkg
bk and abkg
bk are correlated
• We take advantage of the correlated background contributions,
and obtain Absl from the linear combination:
A  A   a
– Coefficient α is selected such that the total uncertainty of Absl is minimized
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Measurement Details
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Data in this analysis: 6.1 fb-1
This measurement
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Reversal of Magnet Polarities
• Polarities of DØ solenoid
and toroid are reversed
regularly
• Trajectory
j
y of the negative
g
particle becomes exactly
the same as the trajectory
of the positive particle with the reversed magnet polarity
• by analyzing 4 samples with different polarities (++, −−, +−, −+)
• the difference in the reconstruction efficiency between positive and
negative particles is minimized
Changing polarities is an important feature of
DØ detector, which reduces significantly
systematics in charge asymmetry measurements
18
Event selection
• Inclusive muon sample:
–
–
–
–
–
Charged particle identified as a muon
1.5 < pT < 25 GeV
muon with pT < 4.2 GeV must have |pZ| > 6.4 GeV
|η| < 2.2
Distance to primary vertex: <3 mm in axial plane; < 5 mm along
the beam
• Like-sign dimuon sample:
–
–
–
–
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Two muons of the same charge
Both muons satisfy all above conditions
Primary vertex is common for both muons
M(μμ) > 2.8 GeV to suppress events with two muons from the
same B decay
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Blinded analysis
The central value of Absll was extracted from the full data
set only after the analysis method and all statistical and
systematic uncertainties had been finalized
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Raw asymmetries
a  k Aslb  abkg
A  K Aslb  Abkg
• We select:
– 1.495×109 muon in the inclusive muon sample
– 3.731×106 events in the like-sign dimuon sample
• Raw
R asymmetries:
ti
a  ( 0.955  0.003))%
A  ( 0.564  0.053)%
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n  n
a 
n  n
N   N 
A  
N  N 
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Detailed description of background
a  k Aslb  abkg
A  K Aslb  Abkg
• Background contribution abkgg to inclusive muon sample:
abkg  f k a k  f a  f p a p  (1  f bkg )
– fK , fπ , and fp are the fractions of kaons, pions and protons
identified as a muon in the inclusive muon sample
– aK , aπ , and ap are the charge as
asymmetries
mmetries of kaon,
kaon pion,
pion and
proton tracks
– δ is the charge asymmetry of muon reconstruction
– fbkg = fK + fπ + fp
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Detailed description of background
a  k Aslb  abkg
A  K Aslb  Abkg
• Background
g
contribution Abkg to like-sign
g dimuon sample:
p
Abkg  Fk Ak  F A  F p A p  ( 2  Fbkg )
– FK , Fπ , and Fp are the fractions of kaons, pions and protons
identified as a muon in the like-sign dimuon sample
– AK , Aπ , and Ap are the charge asymmetries of kaon, pion, and proton
tracks
– Δ is the charge asymmetry of muon reconstruction
– Fbkg = FK + Fπ + Fp ;
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Kaon detection asymmetry
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkgg  Fk Ak  F A  F p Ap  ( 2  Fbkgg )
• The largest background asymmetry, and the largest background
contribution comes from the charge asymmetry of kaon track
identified as a muon (aK, AK)
• Interaction cross section of K+ and K− with the detector material
is different, especially for kaons with low momentum
– e.g.,
g , for p(
p(K)) = 1 GeV:
 ( K  d )  80 mb
 ( K  d )  33 mb
b
• It happens
pp
because the reaction K−N→Yπ has no K+N analogue
g
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Kaon detection asymmetry
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkgg  Fk Ak  F A  F p Ap  ( 2  Fbkgg )
• K+ meson travels further than K− in the material, and has more
chance
h
off decaying
d
i to a muon
• It also has more chance to punch-through and produce a muon
signal
i l
• Therefore, the asymmetries aK, AK should be positive
• All other
th background
b k
d asymmetries
t i are found
f
d to
t be
b about
b t ten
t
times less
This asymmetry is difficult to model, and
measuring it directly in data significantly reduces
the related systematic uncertainties
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Measurement of kaon asymmetry
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkg  Fk Ak  F A  F p A p  ( 2  Fbkg )
 → K+ K− decay
• Define sources of kaons:
K *0  K  
 (1020)  K  K 
• Require that the kaon is
identified as a muon
• Build the mass distribution
separately for positive and
negative kaons
• Compute asymmetry in the
number of observed events
N(K+→μ+) + N(K−→μ−)
N(K+→μ+) − N(K−→μ−)
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Measurement of kaon asymmetry
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkgg  Fk Ak  F A  F p Ap  ( 2  Fbkgg )
• Results from K*0→K+π− and (1020)→K+K− agree well
– For
F th
the diff
difference between
b t
two
t channels:
h
l χ2/dof
/d f =5.4
54/5
• We combine the two channels together:
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Measurement of aπ, ap
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkg  Fk Ak  F A  F p Ap  ( 2  Fbkg )
• The asymmetries aπ , ap are measured using the decays
KS →π+ π− and Λ→p π− respectively
• Similar measurement technique
q is used
Data
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aK
aπ
ap
(+5.51 ± 0.11)%
+(0.25 ± 0.10)%
(+2.3 ± 2.8)%
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Measurement of fK , FK
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkgg  Fk Ak  F A  F p Ap  ( 2  Fbkgg )
• Fractions fK , FK are measured
using the decays K*0 →K+π−
• We measure fK*0 , FK*0
• We find fK*0/fK using the similar
decay K*+ →K
KSπ−
– In this decay we measure fK*+/fKs
and convert it into fK*0/fK
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Measurement of fπ , fp , Fπ , Fp
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkg  Fk Ak  F A  F p Ap  ( 2  Fbkg )
• Fractions fπ , fp , Fπ , Fp are obtained using fK , FK with an
additional input from simulation on the ratio of
multiplicities nπ / nK and np / nK
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Summary of background composition
f bkg  f k  f  f p
• We get the following background fractions in the inclusive
muon events:
(1−fbkg)
fK
fπ
fp
MC
(59 0±0 3)%
(59.0±0.3)%
(14 5±0 2)% (25.7±0.3)%
(14.5±0.2)%
(25 7±0 3)%
(0 8±0 1)%
(0.8±0.1)%
Data
(58.1±1.4)%
(15.5±0.2)% (25.9±1.4)%
(0.7±0.2)%
– Uncertainties for both data and simulation are statistical
– Simulation fractions are given as a cross-check only, and
are not used in the analysis
– Good agreement between data and simulation within the
systematic
y
uncertainties assigned
g
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Muon reconstruction asymmetry
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkg  Fk Ak  F A  F p A p  ( 2  Fbkg )
• Reversal of toroid and solenoid polarities cancel the first-order
detector effects
• Quadratic terms in detector asymmetries still can contribute into
tthee muon
uo reconstruction
eco st uct o asymmetry
asy
et y
• Detector asymmetries for a given magnet polarity adet ≈ O(1%)
• We can expect the residual reconstruction asymmetry :
    O(0.01%)
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Muon reconstruction asymmetry
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkg  Fk Ak  F A  F p A p  ( 2  Fbkg )
• We measure the muon
reconstruction asymmetry
y
y
using J/ψ→μμ events
• Average asymmetries
δ and Δ are:
  ( 0.076  0.028)%
  ( 0.068  0.023)%
• To be compared with:
a  ( 0.955  0.003)%
A  ( 0.564  0.053)%
Such small values of reconstruction asymmetries are a
direct consequence of the regular reversal of magnet
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polarities
during data taking
33
Summary of background contribution
abkg  f k a k  f a  f p a p  (1  f bkg )
Abkgg  Fk Ak  F A  F p A p  ( 2  Fbkgg )
• We obtain:
fKaK (%)
or FKAK (%)
fπaπ (%)
or FπAπ (%)
fpap (%)
or FpAp (%)
(1-fbkg)δ (%)
or (2-Fbkg)Δ (%)
abkg
or Abkg
Inclusive
0 854±0 018
0.854±0.018
0 095±0 027
0.095±0.027
0 012±0 022
0.012±0.022
−0 044±0 016
−0.044±0.016
0 917±0 045
0.917±0.045
Dimuon
0.828±0.035
0.095±0.025
0.000±0.021
−0.108±0.037
0.815±0.070
• All uncertainties are statistical
• Notice
N i that
h background
b k
d contribution
ib i is
i similar
i il for
f inclusive
i l i
muon and dimuon sample: Abkg ≈ abkg
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Signal contribution
k Aslb  a  abkg
K Aslb  A  Abkg
n  n
a 
n  n
N   N 
A  
N  N 
• After subtracting the background contribution from the "raw"
asymmetries a and A,
A the remaining residual asymmetries are
proportional to Absl
• In add
addition
t o to the
t e oscillation
osc at o process
p ocess Bq0  Bq0    X ,
several other decays of b- and c-quark contribute to inclusive
muon and like-sign dimuon sample

0
0
• All processes except Bq  Bq   X don't produce any
charge asymmetry, but rather dilute the values of a and A by
contributing
ib i in
i the
h denominator
d
i
off these
h
asymmetries
i
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Coefficients k and K
k Aslb  a  abkg
K Aslb  A  Abkg
• Coefficients k and K take into account this dilution of
"
"raw"
" asymmetries
i a andd A
• They are determined using the simulation of b- and c-quark
decays
– These decays are currently measured with a good precision, and
this input
p from simulation pproduces a small systematic
y
uncertainty
y
• Coefficient k is found to be much smaller than K, because
many more non-oscillating b- and c-quark decays
contribute to the asymmetry a:
k  0.041  0.003
K  0.342  0.023
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k
 0.12  0.01
K
36
Bringing everything together
• Using all results on background and signal contribution we get
two separate measurements of Absl from inclusive and like-sign
dimuon samples:
Aslb  ( 0.94  1.12 ((stat))  2.14 ((syst)
y ) ))% ((from inclusive )
Aslb  ( 0.736  0.266 (stat)  0.305 (syst) )% (from dimuon )
– Uncertainties of the first result
are much larger, because of a
ssmall
a coe
coefficient
c e t k = 0.0
0.041±0.003
0.003
– Dominant contribution into the
systematic uncertainty comes
f
from
the
th measurementt
of fK and FK fractions
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Closure test
• Th
The contribution
t ib ti off Absl in
i
the inclusive muon asymmetry
a is suppressed by k = 0.041±0.003
• The value of a is mainly determined
by the background asymmetry abkg
• We measure abkg in data,
data and we
can verify how well does it describe
the observed asymmetry a
• We compare a and abkg
as a function of muon pT
• We g
get χ2/dof = 2.4/5 for the
difference between these
two distributions
Excellent agreement between the expected and observed
values of a , including a pT dependence
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Combination of measurements
• Many uncertainties in these two measurements are
correlated
• Obtain the final result using the linear combination:
A  A   a  ( K   k ) Aslb  ( Abkg   abkg )
– The parameter α is selected such that the total uncertainty of Absll is
minimized
• Since Abkgg ≈ abkgg and the uncertainties of these quantities
are correlated, we can expect the cancellation of
background uncertainties in A' for α≈1
• The signal asymmetry Absl does not cancel in A' for α ≈ 1
because: k  K
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Combination of measurements
• Optimal value of α is obtained by the scan of the total
uncertainty of Absll obtained from A
A'
• • The value α=0.959 is selected:
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Final result
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Final result
• From A' = A −α a we obtain a value of Absl :
Aslb  ( 0.957  0.251 (stat)  0.146 (syst) )%
• To be compared with
ith the SM prediction:
Aslb ( SM )  ( 0.023 00..005
006 )%
• This result differs from the SM prediction by ~3.2 σ
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Statistical and systematic
uncertainties
Absl
dimuon
Absl
combined
Dominan
nt uncertaainties
Absl inclusive
muon
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Consistency tests
• We modify selection criteria, or
use a part of sample to test the
stability of result
• 16 tests in
i totall are performed
f
d
• Very big variation of raw
asymmetry
t A (up
( to
t 140%) due
d
to variation of background, but
Absll remains stable
Developed method is stable and gives consistent result
after
ft modifying
dif i selection
l ti criteria
it i in
i a wide
id range
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Dependence on dimuon mass
• We compare the expected and
observed dimuon charge
asymmetry for different masses
of μμ pair
• The expected and observed
asymmetries agree well for
Absl = −0.00957
• No singularity in the M(μμ)
shape
h
supports
t B physics
h i as the
th
source of anomalous asymmetry
Dependence on the dimuon mass is well
described by the analysis method
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Comparison with other measurements
• In this analysis we measure
a linear combination of
adsl and assl:
Aslb  0.506 a sld  0.494 a sls
• Obtained result agrees
g
well
with other measurements of
adsl and assl
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preliminary combination
• Our (preliminary) combination of all measurements of
semileptonic charge asymmetry shows a similar deviation
f
from
th SM.
the
SM
SM
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Value of assl
• Obtained Absl value can be translated to the semileptonic
charge asymmetry of Bs meson
• We need additional input of adsl = −0.0047±0.0046
measured at B factories
• We obtain:
a sls  ( 1.46  0.75)%
• To be compared with the SM prediction:
a slb ( SM )  ( 0.0021  0.0006)%
• Disagreement with the SM is reduced because of
additional experimental input of adsl
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Comparison with other measurements
• Obtained value of assl can be translated into the measurement of
the CP violating phase s and ΔΓs
• This constraint is in excellent agreement with an independent
measurement of s and ΔΓs in Bs→J/ψ decay
• This result is also consistent with the CDF measurement in this
channel
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Combination of results
• This measurement and the result of DØ analysis in Bs→J/ψ
can be combined together
• This combination excludes the SM value of s at more than
% C.L.
95%
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This result at a glance
• Evidence of an anomalous charge asymmetry in the number of
muons produced in the initially CP symmetric pp interaction
• This asymmetry is not consistent with the SM prediction at a
3.2σ level
• This new result is consistent with other measurements
• We observe that the number of produced particles of matter
(negative muons) is larger than the number of produced
particles of antimatter
• Therefore,
Th f
the
h sign
i off observed
b
d asymmetry is
i consistent
i
with
ih
the sign of CP violation required to explain the abundance of
matter in our Universe
This result may provide an important input for
explaining the matter dominance in our Universe
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Conclusions
• New measurement of Absl is performed
Aslb  ( 0.957  0.251 (stat)  0.146 (syst) )%
• Almost all relevant
rele ant quantities
q antities are obtained from data with
ith minimal
input from simulation
• Closure test shows good agreement
between expected and observed
asymmetries
y
in the inclusive muon sample;
p ;
• Result differs from the SM prediction by 3.2σ
• Result is consistent with other measurements of CP violation in
mixing
• Dominant uncertainty is statistical – precision can be improved with
more luminosity
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Backup slides
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Absl and CP violation
• Non-zero value of Absl means that the semileptonic decays
of Bq0 and Bq0 are different;
• It implies CP violation in mixing;
– it occurs only due to the mixing in Bd and Bs ;
• Quantity describing CP violation in mixing is the complex
phase q of the B0q (q = d,s)) mass matrix:
p
 Mq
M q   12 *
( M q )
M q12  i   q
   12 *
M q  2 ( q )
 q12 

 q 
M q  M H  M L  2 M q12
 q   L   H  2  q12 cos q
 M q12 
q  arg  12 
 q 
• aqsl is related with the CP violating phase q as:
 q
a 
tan(q )
M q
q
sl
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Measurement of fK , FK
• Fractions fK , FK are measured using the decays K*0 →K+π−
selected in the inclusive muon and like-sign dimuon samples
respectively;
i l
• Kaon is required to be identified as a muon;
• We measure fractions fK*0 , FK*0;
Inclusive muon sample
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like-sign dimuon sample
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Peaking background contribution
• Decay ρ0→π+π− produces a peaking background in the (Kπ)
mass
• The mass distribution from ρ0→π+π− is taken from simulation
ρ0→π+π−
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Measurement of fK , FK
• To convert these fractions to fK , FK we need to know the
fraction R(K*0) of charged kaons from K*0 →K+π− and the
efficiency to reconstruct an additional pion ε0 :
f K *0  f K R( K ) 0 ; FK *0  FK R( K ) 0
*0
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*0
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Measurement of fK , FK
• We also select decay K*+ →KSπ+;
• We have:
N K *  N K S R( K * ) c
– R(K*+) is the fraction of KS mesons
from K*+ →KSπ+ decay;
– εc is the efficiency to reconstruct
an additional pion;
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Measurement of fK, FK
• R(K*+) = R(K*0) due to
isospin invariance:
– verified with the available data
on production of K*+ and K*0 in
jets at different energies (PDG);
– Also confirmed by simulation;
– Related systematic uncertainty 7.5%
• ε0 = εc because the same criteria are used to select the pion in
K*+→KSπ+ and K*0 →K+π−
– Verified in simulation;
– Related systematic uncertainty 3%;
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Measurement of fK, FK
• With these conditions applied, we obtain fK , FK as:
N ((K
KS )
fK 
f K *0
*
N (K )
N (KS )
FK 
FK *0
*
N (K )
– The same values N(KS ),
) N(K*++) are used to measure fK , FK ;
• • We assume that the fraction R(K*0) of charged kaons
coming from K*0 →K+π− decay is the same in the inclusive
muon and like-sign dimuon sample;
– We verified this assumption in simulation;
• We assign the systematic uncertainty 3% due to this
assumption;
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Measurement of fπ, Fπ
• We use as an input:
– Measured fractions fK , FK;
– Ratio of multiplicities of pion and kaon nπ /nK in QCD events taken
from simulation;
– Ratio of multiplicities of pion and kaon Nπ /NK in QCD events with
one additional muon taken from simulation;
– Ratio of probabilities for charged pion and kaon to be identified as
a muon: P(π→μ)/ P(K→μ) ;
– Systematic uncertainty due to multiplicities: 4%
• • We obtain fπ , Fπ as:
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f  f K
P (   ) n
P ( K   ) nK
F  FK
P (   ) N 
P( K   ) N K
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Measurement of P(π→μ)/ P(K→μ)
• The ratio of these probabilities is measured using decays
KS →π+ π− and (1020)→K+K− ;
• We obtain:
P (   ) / P ( K   )  0.540  0.029
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Measurement of fp, Fp
• Similar method is used to measure the fractions fp , Fp ;
• The decay Λ→pπ− is used to identify a proton and measure
P(p→μ)/ P(K→μ);
• We obtain: P ( p   ) / P ( K   )  0.076  0.021
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Muon reconstruction asymmetry
• We measure the asymmetry of
muon reconstruction usingg
decays J/ψ→μ+μ−;
– Select events with only one
id ifi d muon andd one
identified
additional track;
– Build J/ψ
ψ meson in these events;;
– Extract muon reconstruction
asymmetry from the asymmetry
in the number of events with
positive and negative muon;
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n(μ+) + n(μ−)
n(μ
(μ+) − n(μ
(μ−)
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Track reconstruction asymmetry
• We measure track reconstruction
asymmetry using events with one
muon and 1 additional track;
• We compute the expected track
asymmetry using the same method
as in the main analysis, and we
compare it with the observed
asymmetry;
• The difference δ = atrk
t k− aexp
corresponds to a possible residual
track reconstruction asymmetry;
• We find the residual track reconstruction asymmetry consistent
with zero:
  ( 0.011  0.035)%
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Processes contributing to a and A
c Aslb  a  abkg
C Aslb  A  Abkg


n n
a 
n  n
Process
N   N 
A  

N N
a
A
Bq0  Bq0    X
Yes
Yes
b  c   X
Yes
Yes
Yes
No
Yes
No
B    X (without oscillation)
c   X
• All processes except Bq0  Bq0    X don't produce any charge
asymmetry,
y
y but rather dilute the values of a and A by
y
contributing in the denominator of these asymmetries;
66
Processes contributing to a and A
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Consistency tests
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Consistency tests (cont.)
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Consistency tests (cont.)
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Consistency tests (cont.)
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Consistency tests (cont.)
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