Alexey Petrov (Wayne State Univ.) FPCP 2002 May 16-18 Theory of D 0 - D 0 mixing Alexey A Petrov Wayne State University Table of Contents: • Introduction • Experimental constraints • Theoretical expectations • Conclusions and outlook Based on works with S. Bergmann, A.F. Falk, Y. Grossman, Z. Ligeti, Y
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FPCP 2002 May 16-18 Alexey Petrov (Wayne State Univ.) Theory of D 0 - D 0 mixing Alexey A Petrov Wayne State University Table of Contents: Introduction.
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Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theory of D0 - D0 mixing
Alexey A Petrov
Wayne State University
Table of Contents:
• Introduction• Experimental constraints• Theoretical expectations• Conclusions and outlook
Based on works with S. Bergmann, A.F. Falk, Y. Grossman, Z. Ligeti, Y. Nir
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Introduction: why do we care?
B-mixing: Q=2: only at one loop in the Standard Model GIM mechanism: sensitive to ultra-heavy particles in the loop
22
21 mmrate
Expectation: rate is “large” in B system
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Introduction: why do we care?
B-mixing: Q=2: only at one loop in the Standard Model GIM mechanism: sensitive to ultra-heavy particles in the loop
22
21 mmrate
00 )()()(
)()( BtbBta
tb
tatB
)()(2
)(2
2
tBAq
pAtB
iMtB
ti
Time-dependence: coupled Schrödinger equations
002,1 BqBpB
Diagonalize: mass eigenstates flavor eigenstates
2
, 1212 yMM
x
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Introduction: why do we care?
D-mixing: Q=2: only at one loop in the Standard Model GIM mechanism: sensitive to ultra-heavy particles in the loop
22
21 mmrate
00 )()()(
)()( DtbDta
tb
tatD
)()(2
)(2
2
tDAq
pAtD
iMtD
ti
Time-dependence: coupled Schrodinger equations
002,1 DqDpD
Diagonalize: mass eigenstates flavor eigenstates
2
, 1212 yMM
x
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Introduction: why do we care?
B-mixing: Q=2: only at one loop in the Standard Model GIM mechanism: sensitive to ultra-heavy particles in the loop
22
21 mmrate
D-mixing: the only probe of down-type quark dynamics GIM mechanism: no ultra-heavy quarks in the loop b-quark contribution can be neglected
(SU(3)F limit)
very sensitive to long-distance QCD, as
Clean probe of New Physics?
0)()( ds mfmfrate
2bub mV
GeVmc 1~
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
How would new physics affect mixing?
D-D mass matrix:
I ID
jC
WC
Wi
D
jC
WiD
ijDij
imm
DHIIHD
m
DHDm
mi
M
22
0110
020)0(
2
1
2
1
2
Real intermediate states, affect both x and y Standard Model
Local operator possible New Physics!
1. : signal for New Physics? : Standard Model?
2. CP violation in mixing/decay
yx yx
With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Experimental constraints
2222
20
4sin'cos'
)(
txyR
txyRRR
AeKtD
mm
K
t
2
sincos1 mCP
Axy
KKD
KDy
1. Time-dependent analysis KtD )(0
p
qeR i
m 2
K
K
A
AR
2. Lifetime difference analysis
3. Semileptonic analysis
22 yxrate
''
:1
00
xx
RR
DDif
mm
Picture courtesy of S. McGeeQuadratic in x,y: not so sensitive
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Experimental constraints
Several groups have measured yCP
Experiment Value
FOCUS (2000) (3.42±1.39±0.74)%
E791(2001) (0.8±2.9±1.0)%
CLEO (2002) (-1.2±2.5±1.4)%
Belle (2002) (-0.5±1.0 )%
BaBar (2002) (1.4±1.0 )%
7.08.0
6.07.0
World average: (1.0±0.7)%G. Raz
What are the expectations for x and y?
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical estimates
• Theoretical predictions are all over the board
• Can y ~ 1% be convincingly accommodated?
• Is it possible to have y >> x?
• Does it still mean that y ~ x?
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical estimates IA. Short distance gives a tiny contribution, consider y as an example
12
221
1
122
22
1
2
122
21
2
22
2'
2121
222
22
2
222
C
CC
uc
D
D
D
C
C
Cc
ds
c
dsD
C
Csd
N
N
C
C
C
CN
mm
CM
B
B
N
N
NCCCCm
mm
m
mmX
N
Ny
001DΤD
my
D
… as can be seen form the straightforward computation…
with .,2
41 2200 etcB
m
mF
N
NDcucuD D
D
DD
C
C
4 unknown matrix elements
similar for x (trust me!)
mc is quite large !!!
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical estimates IA. Short distance + “subleading corrections” (in 1/mc expansion):
4422
222)6(
6622
22
2
222)6(
shadc
dssd
shadc
ds
c
dssd
mm
mmx
mm
mm
m
mmy
…subleading effects?
4 unknown matrix elements
33)9(
33)9(
ssd
ssd
mx
my15 unknown matrix elements
22)12(
2220
)12(
sSsd
ssd
mx
myS
Twenty-something unknown matrix elements
Guestimate: x ~ y ~ 10-3 ?Leading contribution!!!
Georgi, …Bigi, Uraltsev
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Resume: model-independent computation with model-dependent result
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical estimates IIB. Long distance might give a large result? Let’s see…
KDBrKDBr
DBrKKDBry
00
002
cos2
If every Br is known up to O(1%) the result is expected to be O(1%)!
mc is NOT large !!!
… with n being all states to which D0 and D0 can decay. Consider K, KK intermediate states as an example…
01100110
2
1DHnnHDDHnnHDy C
WC
WC
WC
Wn
n
cancellation expected! The result here is a series of large numbers with alternating signs, SU(3) forces 0
need to restructure the calculation… x = ? Extremely hard…
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Resume: model-dependent computation with model-dependent result
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Questions:
1. Can any model-independent statements be made for x or y ?
2. Can one claim that y ~ 1% is natural?
What is the order of SU(3) breaking? i.e. if what is n?
nsmyx ,
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical expectationsAt which order in SU(3)F breaking does the effect occur? Group theory?
))(())(())(())((
))(())(())(())((
))(())(())(())((
))(())(())(())((
21
2111
116
21
2111
1115
sdcussucdssscussucss
ddcusducdsdscududsO
sdcussucdssscussucss
ddcusducdsdscududsO
0000 DHHDDHHD WWWW
is a singlet with that belongs to 3 of SU(3)F (one light quark)
Introduce SU(3) breaking via the quark mass operator
ijkkji Heiqqcq 33615333..,
All nonzero matrix elements built of must be SU(3) singlets
iDD
The C=1 part of HW is
),,( sduij mmmdiagM
ij
ijki MHD ,,
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical expectations
0000 DHHDDHHD WWWW
note that DiDj is symmetric belongs to 6 of SU(3)F
36152486
D mixing is prohibited by SU(3) symmetry
Explicitly,
WW HH6
'154260
6
OOOHH
DDD
WW
1. No in the decomposition of no SU(3) singlet can be formed
2. Consider a single insertion of transforms as still no SU(3) singlet can be formed
MDM ij 6
NO D mixing at first order in SU(3) breaking
3. Consider double insertion of
6)361524(
)61515244260()88(6:
SDDMM
D mixing occurs only at the second order in SU(3) breaking
A.F., Y.G., Z.L., and A.A.P.
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical expectations
iSUi AA )3(
KDandD 44 00
Most probably don’t exists…
• Does it always work? SU(3) breaking must enter perturbatively…
• Known counter-examples:
1. Very narrow light quark resonance with mR~mD
RD
DR
RD
DR
mmm
g
mm
gyx
020
2
2
22
2
2~~,
2. Part of the multiplet is kinematically forbidden
see E.Golowich and A.A.P.
Example: both are from the same multiplet, but the latter is kinematically forbidden
see A.F., Y.G., Z.L., and A.A.P.
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Theoretical expectations
... mmmK
• Two major sources of SU(3) breaking
1. phase space
2a. matrix elements (absolute value)
2b. matrix elements (phases aka FSI)
...ffK
0
)(Im 0
0
KDA
KDA
Take into account only the first source (computable)!
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
SU(3) and phase space
RRR FnF
RFRF
RF nDyFDBryy 0,
0,
1~
• “Repackage” the analysis: look at the complete multiplet contribution
• Does it help? If only phase space is taken into account: no (mild) model dependence
Each is 0 in SU(3)y for each SU(3) multiplet
R
R
R
R
Fn
FnWnW
FnWnW
FnWnW
RF
nD
DHnnHD
DHnnHD
DHnnHD
y
)( 0
00
00
00
,
if CP is conserved
Can consistently compute !
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Results
• Product is naturally O(1%)• No (symmetry-enforced) cancellations• Does NOT occur for x
naturally implies that y~1% and x < y !
Alexey Petrov (Wayne State Univ.)
FPCP 2002 May 16-18
Conclusions
• x,y=0 in the SU(3) limit (as Vub is very small)
• it is a second order effect
• it is quite possible that y ~ 1% with x<y
• expect new data from BaBar/Belle/CLEO/CLEOc/CDF(?)
• currently: (allowing NP)
• CP-violation in mixing is a “smoking gun” signal for New Physics