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Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Alexey A. Petrov
Wayne State University
Table of Contents:
• Introduction• Mixing: current/future experimental constraints• Mixing: theoretical expectations• CP violation in charm• Conclusions and outlook
Mixing and CP violation in charm
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Murphy’s law:
Modern charm physics experiments acquire ample statistics; many decay rates are quite large.
THUS:
It is very difficult to provide model-independent theoretical description of charmed quark
systems.
Introduction
27
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Charm transitions serve as excellent probes of New Physics
1. Processes forbidden in the Standard Model to all orders (or very rare)
Examples:
2. Processes forbidden in the Standard Model at tree level
Examples:
3. Processes allowed in the Standard Model
Examples: relations, valid in the SM, but not necessarily in general
0 0,D p D e
XDXDDD ,,mixing00
1
0
0
D
D
Introduction: charm and New Physics
26
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Introduction: mixing
Q=2: only at one loop in the Standard Model: possible new physics particles in the loop Q=2 interaction couples dynamics of D0 and D0
00 )()()(
)()( DtbDta
tb
tatD
)()(2
)(2
2
tDAq
pAtD
iMtD
ti
Time-dependence: coupled Schrödinger equations
002,1 DqDpD
Diagonalize: mass eigenstates flavor eigenstates
2
, 1212 yMM
xMass and lifetime differences of mass eigenstates:
25
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Introduction: mixing
Q=2: only at one loop in the Standard Model: possible new physics particles in the loop Q=2 interaction couples dynamics of D0 and D0
00 )()()(
)()( DtbDta
tb
tatD
)()(2
)(2
2
tDAq
pAtD
iMtD
ti
Time-dependence: coupled Schrödinger equations
Diagonalize: mass eigenstates flavor eigenstates
2
, 1212 yMM
xMass and lifetime differences of mass eigenstates:
1 0 0No CPV:1,2 2
D D D DCP
25
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Introduction: why do we care?
mixing mixing
• intermediate down-type quarks
• SM: b-quark contribution is negligible due to VcdVub
*
• (zero in the SU(3) limit)
• intermediate up-type quarks
• SM: t-quark contribution is dominant
• (expected to be large)
1. Sensitive to long distance QCD2. Small in the SM: New Physics! (must know SM x and y)
1. Computable in QCD (*)2. Large in the SM: CKM!
00 DD 00 BB
)()( ds mfmfrate 2tmrate
(*) up to matrix elements of 4-quark operators
Falk, Grossman, Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002
2nd order effect!!!
24
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
How would new physics affect mixing?
I ID
jC
WC
Wi
Dj
CWi
DijD
ij imm
DHIIHD
mDHD
mm
iM
22
0110
020)0(
2
1
2
1
2
Real intermediate states, affect both x and y Standard Model
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
)()(2
)(2
2
tDAq
pAtD
iMtD
ti
Look again at time development:
Expand mass matrix:
Local operator, affects x, possible new phsyics
00 DD
new CP-violating phase
23
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
How would CP violation manifest itself in charm?
Possible sources of CP violation in charm transitions:
CPV in decay amplitudes (“direct” CPV)
CPV in mixing matrix
CPV in the interference of decays with and without mixing
f
fim
f
ff A
AeR
A
A
p
q
fDAfDA
00 DD
12
2
1212
1212
2
2
iM
iM
q
pRm
22
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Experimental constraints on mixing
2
1sincos1 m
CP
Rxy
KKD
KDy
1. Time-dependent or time-integrated semileptonic analysis
2. Time-dependent analysis (lifetime difference)
3. Time-dependent analysis KtD )(0
22 yxrate Quadratic in x,y: not so sensitive
KKtD )(0
Sensitive to DCS/CF strong phase
Idea: look for a wrong-sign final state
sincos',sincos' xyyyxx
2222
20
4sin'cos')( txy
RtxyRRRAeKtD m
mK
t
2
2 ,m
qR
p
21
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Example: experimental constraints on yCP
Several groups have measured yCP
Experiment Value, %
FOCUS (2000) 3.4 ± 1.4 ± 0.7
E791(2001) 0.8 ± 2.9 ± 1.0
CLEO (2002) -1.2 ± 2.5 ± 1.4
Belle (2002) -0.5 ± 1.0 ± 0.8
BaBar (2003) 0. 2± 0.5 .
Belle (2003) 1.2 ± 0.7 ± 0.4
BaBar (2003, K+K-)
1.2 ± 0.7 ± 0.4
BaBar (2003, +-) 1.7 ± 1.2 .
0.50.4
1.20.6
World average: yCP = (0.9 ± 0.4)%
a. What if time-dependent studies are not possible?b. What are the expectations for x and y?
B. Yabsley
20
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
What if time-dependent studies are not possible I?
f3
f1
f2
1 2D f f
0 0 00 0 01 2 2 1
1
1( ) ( ) ( ) ( )
2LD D D k D k D k D k
-charm factory (CLEO-c)
3 4D f f
f4
Time-integrated analysis: DCSD contribution cancels out for double-tagged
decays!
KD0
))((00 KKDD
0000200
2
1
2
1DDΗKKDDΗKKKDDA effeff
CF DCS
2
2
222
2 q
pr
q
pyx
KK
KKR D
Quadratic in x,y: not so sensitive wanted: linear in x or y
H. Yamamoto; I. Bigi, A. Sanda
19
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
What if time-dependent studies are not possible II?
If CP violation is neglected mass eigenstates = CP eigenstates CP eigenstates do NOT evolve with time, so can be used for “tagging”
KS
0
CP Eigenstate (-)
f1
f2
21)( ffDCP
)()()1()()(
2
11
0
20
2
0
1000 kDkDkDkDDD L
L
CLEO-c has good CP-tagging capabilities CP anti-correlated (3770): CP(tag) (-1)L = [CP(KS) CP(0)] (-1) = +1 CP correlated (4140)
(-)
-charm factory (CLEO-c)
Can still measure y:
tot
CPl XlDB
l
l
l
l
B
B
B
By
4
1cos
D. Atwood, A.A.P., hep-ph/0207165
18
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Mixing: theoretical estimates
Theoretical predictions are all over the board… so:
Can x,y ~ 1% be convincingly accommodated?
What is the relationship between x and y (x ~ y, x > y, x < y?) in the Standard Model? • x from new physics
� y from Standard Model Δ x from Standard Model(papers from SPIRES )
Standard Model mixing predictions
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1 4 7 10 13 16 19 22 25 28 31 34 37 40
Reference Index
|x|
or
|y|
New Physics mixing predictions
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Reference Index
|x|
Updated predictionsA.A.P. hep-ph/0311371
17
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Theoretical estimates I
A. Short distance gives a tiny contribution, consider y as an example
22 2 2 22 22 1 2 14 2
' 2 2 22 1 1
2 22 2
12
2
2 2 1 21 2
1 2 1
s dC s dsd D C
C c c
C CD DC
C D Cc u
m mN m my X C C C C N
N m m
N NB M C C CN
N B C C Nm m
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 large !!!
16
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Theoretical estimates I
A. 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!!!
H. Georgi, …I. Bigi, N. Uraltsev
15
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Resume: model-independent computation with model-dependent
result
14
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Theoretical estimates II
B. Long distance physics dominates the dynamics…
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
x = ? Extremely hard…
J. Donoghue et. al.P. Colangelo et. al.
Need to “repackage” the analysis: look at the complete multiplet contribution
13
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Resume: model-dependent computation with model-dependent result
12
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Theoretical expectations
Let’s compute both x and y. Consider the correlator
4 0 D
D
i q p zp D w w Dq i d z D p T H z H D p e
1
2 2Dp DD
ip m
m
pD(q) is an analytic function of q. To write a disp. relation, go to to
HQET:
A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204
...D p mv m H v
1 2
( ) ( )4 ˆ ...2
c cim v z im v zc cFw cq uq i i w v v
i
GH V V C O H e h e h
Now we can interpret pD(q) for all q
11
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Theoretical expectations
…this implies for the correlator
4 ( ) ( )
4 ( ) ( )
ˆ ˆ, 0
ˆ ˆ, 0 ...
D c
D
D c
i q p m v z c cp w v w v
i q p m v z c cw v w v
q i d z H v Te H h z H h H v
i d z H v Te H h z H h H v
2v q m E i E
HQ mass dependence drops out for the second term, so for v(q) = p
D(q)/mD
2
1
2QCD
Dm
Em P dE O
E m E
mass and width difference of a heavy meson with mass E
Rapidly oscillates for large mc
Thus, a dispersion relation
Compute , then find m!
10
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Results:
Product is naturally O(1%)No (symmetry-enforced) cancellations
Naturally implies that y ~ 1%! What about x?A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002
RRR FnF
RFRF
RF nDyFDBryy 0,
0,
1~From each
multiplet:
9
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Results: m/=x/y:
Computation naturally implies that y ~ x ~ 1%!
2
1R R R
R
R R R
F F FF
F D F D F Dm
x y E EdEr
y E m y m m
Also:
1. Assume 2-parameter model for
2. Compute rF for 4-body and 2-body intermediate multiplets
3. Model dependence remains…
/ forD Dg E E m E m
A. Falk., Y. Grossman, Z. Ligeti, Y. Nir and A.A.P., hep-ph/0402204
8
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
A bit more about CP violation in charm
7
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
CP violation: experimental constraints
2
2
1
1
CP
f f
f f
D f D fA f
D f D f
A A
A A
1. Standard analysis: rate asymmetries
Mode E791, % FOCUS, % CLEO, %
D0 → K+K- -1.0±4.9±1.2-
0.1±2.2±1.5
0.0±2.2±0.8
D0 → +- -4.9±7.8±3.04.8±3.9±2.
51.9±3.2±0.
8
D0 → KS0 0.1±1.3
D0 → 0+K- -3.1±8.6… which is of the first order in CPV parameters, but requires tagging
2. Recall that CP of the states in are anti-correlated at (3770):
a simple signal of CP violation:
2222222 2121
21
2112
2 FFFFm
FFFF yxyx
R
))((3770 00 CPCPDD))(( 21
00 FFDD
f
ff A
A
p
q … which is of the second order in CPV parameters, i.e. tiny
6
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
CP violation: new experimental possibilities 1
1. Time dependent (lifetime difference analysis):
separate datasets for D0 and D0
This analysis requires 1. time-dependent studies2. initial flavor tagging (“the D* trick”)
0 0
0 0cos sin
2m
CP
D K K D K K AA f y x
D K K D K K
KKtD )(0
Cuts statistics/sensitivity
5
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
CP violation: new experimental possibilities 2
2. Look for CPV signals that are 1. first order in CPV2. do not require flavor
tagging
Consider the final states that can be reached by both D0 and
D0, but are not CP eigenstates (, KK*, K, K, …)
where
,f fU
CPf f
A f t
0 0f D f t D f t
A.A.P., PRD69, 111901(R), 2004hep-ph/0403030
4
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
CP violation: untagged asymmetries
Expect time-dependent asymmetry…
0
0
iA D f
ReA D f
2 22 22 sin sin cos cos ,f ff f
B y R A A A A
21,U t
CPA f t e A B t C tD t
… whose coefficients are computed to be
22 22 21 1 ,f ff f f
A A A A R A A
This is true for any final state f
2
.2
xC A
… and time-integrated asymmetry 1
, 2UCPA f t A B C
D
3
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
CP violation: untagged asymmetries (K+)
For a particular final state K, the time-integrated asymmetry is simple
This asymmetry is1. non-zero due to large SU(3) breaking2. contains no model-dependent hadronic parameters (R and are experimental
observables)3. could be as large as 0.04% for NP
sin sinUCPA K y R
Note: larger by O(100) for SCS decays (, …) where R ~ 1
A.A.P., PRD69, 111901(R), 2004hep-ph/0403030
2
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Conclusions
Charm provides great opportunities for New Physics studies– large available statistics – mixing: x, y = 0 in the SU(3) limit (as V*
cbVub is very small)– mixing is a second order effect in SU(3) breaking– it is quite possible that y~ x ~ 1% in the Standard Model
Expect new data from BaBar/Belle/CLEO-c/CDF Quantum coherence will allow CLEO-c/BES to perform new
measurements of strong phases in charm mixing studies– important inputs to time-dependent studies of mixing
Quantum coherence will allow CLEO-c to perform new studies of mixing – no DCSD contamination in double-tag K studies– new mixing measurements unique to CLEO-c
Observation of CP-violation or FCNC transitions in the current round of experiments provide “smoking gun” signals for New Physics - untagged asymmetries are more sensitive to CPV
1
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Additional slides
0
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
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 ,
-1
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Theoretical expectations
At 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 ,,
-2
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
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:
SDMMM
D mixing occurs only at the second order in SU(3) breaking
A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002
-3
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Example: PP intermediate states
,,,6
1,
6
1,
,,,3
1,
2
1,
2
1
00
0000021
2
8, 0
KKKKKK
KsAAN
• n=PP transforms as , take 8 as an example:
• This gives a calculable effect!
Numerator:
1. Repeat for other states2. Multiply by BrFr to get y
182788 S
Denominator:
)(,2
1,,
6
1 21
0002
8, 0sOKKKAAD
421
8,
8,8,2 108.1038.0 s
A
Ay
D
N
phase space function
-4
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
: 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
A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002
-5
Alexey Petrov (Wayne State Univ.)
BEACH 2004, IIT, Chicago
Quantum coherence: supporting measurements
2222
20
4sin'cos')( txy
RtxyRRRAeKtD m
mK
t
Time-dependent analysis KtD )(0
2
K
K
A
AR
sincos'
sincos'
xyy
yxx
A. Falk, Y. Nir and A.A.P., JHEP 12 (1999) 019
Strong phase can be measured at CLEO-c!
where and
Strong phase is zero in the SU(3) limit and strongly model-dependent
KDAKDAKDA CP
002
KDBrR
KDBrKDBr CPCP02
cos With 3 fb-1 of data cos can be
determined to | cos | < 0.05!Silva, Soffer;Gronau, Grossman, Rosner