Transcript Document

D0-D0 Mixing
Michael D. Sokoloff
University of Cincinnati
The oscillation in time of neutral D mesons into their antiparticles, and
vice versa, commonly called D0-D0 mixing, has been observed by several
experiments in a variety of channels during the past year. While K0-K0
mixing and B0-B0 mixing are (relatively) well understood in the Standard
Model of particle physics, observations of D0-D0 mixing indicate that the
physical eigenstates have decay rate differences and/or mass differences
greater than expected most naively. In this talk I will discuss recent
experimental results and the extent to which mixing measurements can
probe non-perturbative QCD and physics beyond the Standard Model.
1
Strong Nuclear Interactions of Quarks and Gluons
Each quark carries one of three strong charges, and
each antiquark carries an anticharge. For
convenience, we call these colors:
Quarks are never observed as free particles.
Mesons consist of quark-antiquark pairs with
canceling color-anticolor charges
2
Weak Charged Current Interactions
neutrino scattering
charm decay
f
~
f
As a first approximation, the weak charged
current interaction couples fermions of the same
generation. The Standard Model explains
couplings between quark generations in terms of
the Cabibbo-Kobayashi-Maskawa (CKM) matirx.
3
Weak Phases in the Standard Model
b = f1; a = f2; g = f3
4
Charm Meson Mixing
Why is observing charm mixing interesting?
It completes the picture of quark mixing already seen in the
K, Bd, and Bs systems.
K — PR 103, 1901 (1956); PR 103, 1904 (1956).
Bd — PL B186, 247 (1987); PL B192, 245 (1987).
Bs — PRL 97, 021802 (2006); PRL 97, 242003 (2006).
In the Standard Model, it relates to processes with downtype quarks in the mixing loop diagram.
Mixing, itself, could indicate new physics.
It is a significant step toward observation of CP violation in
the charm sector, a clear indication of new physics
5
Mixing Phenomenology
Neutral D mesons are produced
as flavor eigenstates D0 and D0
and decay via
D1, D2 have masses M1, M2 and
widths 1, 2
Mixing occurs when there is a
non-zero mass
or lifetime difference
as mass, lifetime eigenstates D1,
D2
where
and
For convenience define, x and y
where
and define the mixing rate
( < 5 x 10-4 )
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How Mixing is Calculated
7
Standard Model Mixing Predictions
Box diagram SM charm mixing
rate naively expected to be
very low (RM~10-10) (Datta &
Kumbhakar)
Z.Phys. C27, 515 (1985)
CKM suppression → |VubV*cb|2
GIM suppression → (m2s-m2d)/m2W
Di-penguin mixing, RM~10-10
Phys. Rev. D 56, 1685 (1997)
Enhanced rate SM calculations
generally due to long-distance
contributions:
first discussion, L. Wolfenstein
Phys. Lett. B 164, 170 (1985)
8
Standard Model Mixing Predictions
Box diagram SM charm mixing
rate naively expected to be
very low (RM~10-10) (Datta &
Kumbhakar)
Z.Phys. C27, 515 (1985)
CKM suppression → |VubV*cb|2
GIM suppression → (m2s-m2d)/m2W
Di-penguin mixing, RM~10-10
Phys. Rev. D 56, 1685 (1997)
Enhanced rate SM calculations
generally due to long-distance
contributions:
first discussion, L. Wolfenstein
Phys. Lett. B 164, 170 (1985)
Partial History of LongDistance Calculations
• Early SM calculations indicated
long distance contributions
produce x<<10-2:
– x~10-3 (dispersive sector)
• PRD 33, 179 (1986)
– x~10-5 (HQET)
• Phys. Lett. B 297, 353 (1992)
• Nucl. Phys. B403, 605 (1993)
• More recent SM predictions
can accommodate x, y ~1% [of
opposite sign] (Falk et al.)
– x,y ≈ sin2 qC x [SU(3) breaking]2
• Phys.Rev. D 65, 054034 (2002)
• Phys.Rev. D 69, 114021 (2004)
9
New Physics Mixing Predictions
Possible enhancements to mixing due to • Large possible SM contributions to
new particles and interactions in new
mixing require observation of either a
physics models
CP-violating signal or | x | >> | y | to
Most new physics predictions for x
establish presence of NP
Extended Higgs, tree-level FCNC
• A recent survey (Phys. Rev. D76,
Fourth generation down-type quarks
095009 (2007), arXiv:0705.3650)
Supersymmetry: gluinos, squarks
summarizes models and constraints:
Lepto-quarks
Fourth generation
Vector leptoquarks
Q = -1/3 singlet
quark
Flavor-conserving
Two-Higgs
Q = +2/3 singlet
quark
Flavor-changing
neutral Higgs
Little Higgs
Scalar leptoquarks
Generic Z’
MSSM
Left-right
symmetric
Heavy weak iso-singlet quarks
Supersymmetric
alignment
and more
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Time-Evolution of D0K Decays
RS = CF
DCS and mixing amplitudes
interfere to give a “quadratic”
WS decay rate (x, y << 1):
WS = DCS
DCS
K+-
D0
D0
where
and  is the phase difference between DCS and CF decays.
11
D0

K Reconstruction
384 fb-1 e+e-  c,c
Slow pion charge tags neutral
D production flavor
Beam spot:
x ≈ 100 m
y ≈
7 m
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Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
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Simplified Fit Strategy & Validation
Fit m(K) and Dm in bins of time:
 If no mixing, ratio of WS to RS
signal should be constant
 No assumptions made on time
evolution of background
 Each time bin is fit independently
WS (0.75<t<2.5 ps)
m(K+–)
Time bins:
WS (0.75<t<2.5 ps)
Dm
14
Simplified Fit Strategy & Validation
Rate of WS events clearly increases with time:
WS/RS (%)
(stat. only)
15
Simplified Fit Strategy & Validation
Rate of WS events clearly increases with time:
WS/RS (%)
(stat. only)
Inconsistent
with no-mixing
hypothesis:
2=24
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Simplified Fit Strategy & Validation
Rate of WS events clearly increases with time:
WS/RS (%)
(stat. only)
Consistent with
prediction from
full likelihood fit
2=1.5
Inconsistent
with no-mixing
hypothesis:
2=24
17
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
18
m(K)-Dm Fit Results
Signal = 1 141 500 ± 1 200
Signal = 4 030 ± 90
19
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
20
Decay Time Resolution
Average D0 flight length is twice average resolution
Resolution function described by sum of 3 Gaussians
Resolution widths scales with t
Mean of core Gaussian allowed to be non-zero
Observed core Gaussian shifted 3.6±0.6fs
=
For combinatorial background, use Gaussians and
power-law “tail” for small long-lived component
21
RS Decay Time Fit
RS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
D0 lifetime and resolution function
fitted in RS sample:
 = 410.3±0.6 (stat.) fs
Consistent with PDG (410.1±1.5 fs)
NB: Shifted core Gaussian dominates systematic uncertainties
22
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
23
WS Fit with no Mixing
WS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
data - no mix PDF
Fit result assuming no mixing:
RD: (3.53±0.08±0.04)x10-3
24
WS Fit with no Mixing
WS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
data - no mix PDF
Fit result assuming no mixing:
poor fit
RD: (3.53±0.08±0.04)x10-3
25
WS Fit with Mixing
WS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
Fit results allowing mixing:
RD: (3.03±0.16±0.10)x10-3
x’2: (-0.22±0.30±0.21)x10-3
y’: (9.7±4.4±3.1)x10-3
data - no mix PDF
fine fit
26
Signal Significance
Significance calculated from change in log likelihood:
(stat. only)
Best fit
1
2
3
4
No mixing
5
27
Signal Significance
Significance calculated from change in log likelihood:
(stat. only)
Best fit
1
Corresponds to 4.5
(with 2 parameters)
2
3
4
No mixing
5
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Signal Significance
Best fit is in unphysical region (x'2<0)
(stat. only)
Best fit
Physical solution
(y'=6.4x10-3)
1
Corresponds to 4.5
(with 2 parameters)
2
3
4
No mixing
5
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Signal Significance with Systematics
Including systematics (~ 0.7 x stat)
decreases signal significance
[ PRL. 98, 211802 (2007) ]
Best fit
1
2
3
Fit is inconsistent
with no-mixing at 3.9 No mixing
4
5
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K Analysis from Belle
Last year Belle published
analysis of K decays:
PRL 96,151801
Results consistent within 2:
400 fb-1
stat. only
BaBar 1
BaBar 2
BaBar 3
no-mixing
excluded at 2
(0,0)
Belle 2 statistical
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Average K Mixing Results
Heavy flavor averaging group (HFAG)
provides “official” averages
Combine BaBar and Belle likelihoods in 3 dimensions (RD, x'2,y')
May 2007 Averages:
+0.14
RD: (3.30 -0.12 )
x 10-3
x’2: (-0.01±0.20) x 10-3
y’ :
+2.8
(5.5 -3.7
)x
10-3
y'
1
2
No mixing
excluded > 4
x'2
3
4
5
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Preliminary Kπ Mixing Results from CDF
[arXiv:0712.1567]
Best fit for mixing parameters
(uncertainties are combined
stat. and systematic)
• Fit 2 = 19.2 for 17 dof
• 3.8  from Null Hypothesis
RD: (3.04 ± 0.55 ) x 10-3
x’2: (-0.12 ± 0.35) x 10-3
y’ : (8.5 ± 7.6 ) x 10-3
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D in D0 → h+h[ PRL. 91, 121801 (2003) ]
34
BaBar’s Early D in D0 → h+h[ PRL. 91, 121801 (2003) ]
91 fb-1
35
Belle’s Recent D in D0 → h+h[ PRL. 98, 211803 (2007) ]
540 fb-1
Ave
(1.12 ± 0.32)%
36
BaBar’s Preliminary D D0 → h+h-
37
D0 → h+h- : Results
Babar’s preliminary 384 fb-1 results
Combining KK and  results gives
yCP = (1.24 ± 0.39 ± 0.13)%
CP violation consistent with zero.
BaBar
Tagged
(preliminary)
(1.24 ± 0.39 ±0.13)%
BaBar
Untagged (91 fb-1)
(0.2 ± 0.4 ± 0.5)%
BaBar
Combined
(0.94 ± 0.35)%
Belle
Tagged
(1.31 ± 0.32 ± 0.25)%
BaBar + Belle
Combined
(1.10 ± 0.27)%
38
Mixing in D0 → KSπ+π-
39
Mixing in D0 → KSπ+πX : (0.80 ± 0.35 ± 0.15)%
y : (0.33 ± 0.24 ± 0.14)%
(assuming no CP violation)
95% CL
contours
40
Time-Dependence in D0 → KSπ+π-
box size is “capped” linear
box size is logarithmic
plots illustrate the average decay time as a function of
position in the Dalitz plot for (x,y) = (0.8%, 0.3%). The sizes
of the boxes reflect the number of entries, and the colors
reflect the average decay time.
41
Mixing in D0 → K+-0
1483 ± 56 signal events
“Wrong-sign” decay rate varies
across the Dalitz plot:
DCS term
Resonance phase
Interference term
CF (mixed) term
Phase between
RS and WS
Subscript D indicates dependence
on position in the Dalitz plot.
Yields from 384 fb-1
Bad charm
Combinatorics
42
D0 → K+-0 : Results
No mixing is excluded at
the 99% confidence level.
Stat+syst
x’’: (2.39 ± 0.61 ± 0.32) %
Y’’ : (-0.14 ± 0.60 ± 0.40 )%
RM: (2.9 ± 1.6) x 10-4
68.3%
95.0%
99.0%
99.9%
43
44
45
46
20 Years Ago
47
10 Years Ago
RM < 0.92% , no int.
RM < 3.6%, int allowed
RM < 0.50% , semi-lep
RM < 0.85%, CPV allowed in int.
RDCSD = (0.68 ± 0.34 ±0.07) %
RDCSD = (0.77 ± 0.25 ±0.25) %
y = (0.5 ± 1.5 ± syst.) %
results on the way
48
Today
HFAG
D0 → Kπ
RD: (3.30
+0.14
-0.12
) x 10-3
x’2: (-0.01±0.20) x 10-3
+2.8
y’ : (5.5
) x 10-3
-3.7
y'
No mixing
excluded > 4
x'2
CDF
D 0 → K Sπ+ π-
D 0 → K + π- π0
Belle
Stat+syst
D in D0 → h+hBaBar + Belle
(1.10 ± 0.27)%
95% CL contours
68.3%
95.0%
99.0%
99.9%
49
10 Years From Now ??
My guesstimates of measurement precision, assuming 100 fb-1
from LHCb and 50 ab-1 from SuperB, in units of 10-4
x
y
YCP
Kπ
h+hKSπ+π-
(x’)2
y’
0.2
5
x’’
y’’
8
8
5
5
5
K+π-π0
π-π+π0
7
7
KSK+π- + KSK-π+
7
7
BES III should be able to measure cos  ± 3
SuperB and BES III will measure relevant branching fractions with 5%
fractional precision, constraining Standard Model contributions to x & y.
Altogether, D0-D0 mixing measurements, and measurements of CPviolation in mixing, will provide insights into physics beyond the SM
that will complement direct observations made at the LHC.
50