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 )
6
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
10
Time-Evolution of D0K 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
12
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)
13
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
16
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
28
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
29
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
30
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
31
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
32
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
33
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