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Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Alexey A. Petrov
Wayne State University
Table of Contents:
• Introduction• Mixing: current/future experimental constraints• Mixing: theoretical expectations
• Standard Model• New Physics
• Conclusions and outlook
Charm mixing in the Standard Model and Beyond
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Charm transitions serve as excellent probes of New Physics
1. Processes forbidden in the Standard Model to all orders
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
0D p
XDXDDD ,,mixing00
1. Introduction: charm and New Physics
30
CKM triangle relations
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
D-mixing is the last chance to see New Physics in meson oscillations!!!
29
With the recent measurement of ms in Bs-mixing…
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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:
28
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
28
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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!!!
27
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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 SM, C=1 NP!
1. : signal for New Physics? : Standard Model?
2. CP violation in mixing/decay
yx yx
)()(2
)(2
2
tDAq
pAtD
iMtD
ti
Look again at time development:
Expand mass matrix:
Local operator, affects x, possible C=2 new physics
00 DD
new CP-violating phase
26
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
New Physics in x and y
I ID
jC
WC
Wi
Dj
CWi
DijD
ij imm
DHIIHD
mDHD
mm
iM
22
0110
020)0(
2
1
2
1
2
Local C=2 piece of the mass matrix affects x:
25
Double insertion of C=1 affects x and y:
0 1 1C C SM NPn SM NP n nA D H H n A A
Example: 1 1 1
2 2 2
SM NP SM SM NPSM NP SM NP SMn n n n nn n n n n n n n
n n n
y A A A A A A A A A A
exp. uncertainty 10%NP SMn nA A O Suppose
1TeV 1GeV
Zero in the SU(3) limitFalk, Grossman, Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002
2nd order effect!!!
Can be significant!!!
Amplitude
phase space
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
How would CP violation manifest itself in charm?
Possible sources of NP in 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
24
With b-quark contribution neglected: only 2 generations contribute real 2x2 Cabibbo matrix
At this point CP-violating signal is a “smoking gun” signature of New Physics
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
2. 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
23
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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 (BES/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
22
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
-charm factories have good CP-tagging capabilities CP anti-correlated (3770): CP(tag) (-1)L = [CP(KS) CP(0)] (-1) = +1 CP correlated (4140)
(-)
-charm factory (BES/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/0207165D. Asner, W. Sun, hep-ph/0507238
21
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
3. Mixing: theoretical estimates
Theoretical predictions are all over the board… so:
Can x,y ~ 0.5% be a SM signal?
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
20
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Theoretical estimates I
A. Short distance gives a tiny contribution
… as can be seen from a “straightforward computation”…
with .,2
41 2200 etcB
m
mF
N
NDcucuD D
D
DD
C
C
mc IS large !!!
19
Notice, however, that at NLO in QCD (xNLO,yNLO) >> (xLO, yLO) :
Similar for x (trust me!)Example of NLO contribution E. Golowich and A.A.P.Phys. Lett. B625 (2005) 53
6 6
4 4
s
s
m
m
2
2s
c
mz
m
… xLO >> yLO !!!
xNLO ~ yNLO!
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Theoretical estimates I
A. Short distance + “subleading corrections” (in {ms, 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
18
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Resume: model-independent computation with model-dependent
result
17
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
16
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
15
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
14
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Results
• Product is naturally O(1%)• No (symmetry-enforced) cancellations• Disp relation: compute x (model-dependence)
naturally implies that x,y ~ 1% is not excluded in the Standard Model
13
E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998
A.F., Y.G., Z.L., Y.N. and A.A.P.Phys.Rev. D69, 114021, 2004
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Resume: model-dependent computation with model-dependent result
12
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Summary of SM theoretical expectations
11
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|
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
10
Attacking New Physics
1TeV
1GeV
Multitude of various models of New Physics can affect x
1TeV
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
10
Attacking New Physics
“ Four amigos”
1TeV
1GeV
Multitude of various models of New Physics can affect x
1TeV
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Global Analysis of New Physics in x
9
Let’s write the most general C=2 Hamiltonian
… with the following set of 9 independent operators…
1GeV
1TeV
RG-running relate Ci() at NP scale to the scale of ~ 1 GeV, where ME are computed (on the lattice)
E.Golowich, J. Hewett, S. Pakvasa and A.A.P.
Each model of New Physics provides unique matching condition for Ci(NP)
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
New Physics in x and y: lots of extras
Extra gauge bosons
8
Extra scalars
Extra fermions
Extra dimensions
Extra global symmetries
Left-right models, horizontal symmetries, etc.
Two-Higgs doublet models, leptoquarks, technicolor, etc.
4th generation, vector-like quarks, little Higgs, etc.
Universal extra dimensions, split fermions, warped ED, etc.
SUSY: MSSM, alignment models, split SUSY, etc.
Example: two-Higgs doublet model:
2 2
22 4,2
tan ,2
C F WR Rub cb HH b H c L L
G mH V V A x x x u c u c
1LL
NPC 1LL
NPQ
E.Golowich, J. Hewett, S. Pakvasa and A.A.P.
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Summary of NP theoretical expectations
7
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|
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
5
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
CP violation: new experimental possibilities
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 (WSU) Charm 2006, June 5-7, Beijing
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 (WSU) Charm 2006, June 5-7, Beijing
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 (WSU) Charm 2006, June 5-7, Beijing
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 conceivable that y ~ x ~ 1% in the Standard Model– it is possible for y to be dominated by New Physics
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 and 1/
Quantum coherence will allow BES/CLEO-c to perform new studies of mixing – no DCSD contamination in double-tag K studies– new mixing measurements unique to tau-charm factories
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 (WSU) Charm 2006, June 5-7, Beijing
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 (WSU) Charm 2006, June 5-7, Beijing
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 (WSU) Charm 2006, June 5-7, Beijing
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 (WSU) Charm 2006, June 5-7, Beijing
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
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
Theoretical expectations
iSUi AA )3(
KDandD 44 00
Most probably don’t exists…
• If SU(3) breaking enters perturbatively, it is a second order effect…
• Known counter-example:
1. Very narrow light quark resonance with mR~mD
RD
DR
RD
DR
mmm
g
mm
gyx
020
2
2
22
2
2~~,
• What happens if part of the multiplet is kinematically forbidden?
see E.Golowich and A.A.P. Phys.Lett. B427, 172, 1998
Example: both are from the same multiplet, but the latter is kinematically forbidden
see A.F., Y.G., Z.L., and A.A.P.Phys.Rev. D65, 054034, 2002
A. Falk, Y. Grossman, Z. Ligeti, and A.A.P.Phys.Rev. D65, 054034, 2002
Alexey Petrov (WSU) Charm 2006, June 5-7, Beijing
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
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