Theory introduction to charm physics
Alexey A. Petrov
Wayne State University
Table of Contents:
1.
2.
3.
4.
5.
Introduction
Spectroscopy
Leptonic and semileptonic decays
Mixing and Rare decays
Conclusions and outlook
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
1. Introduction: role of charm
1. 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.
D0   e
D0  D0 mixing , D  X , D  X
Processes allowed in the Standard Model
Examples: relations, valid in the SM, but not
necessarily in general
2. Provide unique QCD laboratory
Start from the bottom…
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Introduction
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.
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
2. Charm Spectroscopy
 HQL: Charm spectroscopy is “simple”
S  J l  S Q , J l  S l  Ll
decouples
good quantum numbers
 All states appear as doublets classified
by parity and spin of light DoF:
Spin
1
S J 
2
P
P
l
L
0
1
Jl
1/2
1/2
3/2
3/2
5/2
S
0,1
0,1
1,2
1,2
2,3
Jl P
SP
state
M
G
1/2-
0-
Ds
1969
0.49 ps
1-
Ds*
2110
<1.9
0+
D0*
1+
D1’
1+
Ds1
2536
<2.3
2+
Ds2
2572
15
2
Alexey Petrov (Wayne State Univ.)
Exp. Data, MeV
1/2+
3/2+
FPCP 03, June 3-6 2003 (Paris)
Charm Spectroscopy: new states
 BaBar/Belle/CLEO see
new DsJ* states:

DsJ* (2463)
DsJ* (2317)
p0
Ds (1969)
Alexey Petrov (Wayne State Univ.)
p0

Ds* (2112)
fp
FPCP 03, June 3-6 2003 (Paris)
Charm Spectroscopy: problem?
 BaBar/Belle/CLEO report new DsJ states
DsJ (2317)  Ds p 0 , DsJ (2463)  Ds p 0
 Ds , Ds , Dsp p 
 Interpretation? 0+ and 1+ p-wave Qq states?
Possible problems:
1. Mass is too low?
2. Width is too narrow?
non-Qq state?
Barnes, Close, Lipkin;
Szczepaniak, Bali
4-quark (“baryonium”) state

DK or Dp molecule?
1. mass is naturally in the vicinity of DK threshold
2. since M(DsJ(2130)) < M (D+K) width is naturally small
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Charm Spectroscopy: problem?
 BaBar/Belle/CLEO report new DsJ states
DsJ (2317)  Ds p 0 , DsJ (2463)  Ds p 0
 Ds , Ds , Dsp p 
 Interpretation? 0+ and 1+ p-wave Qq states!
Possible problems:
1. Mass is too low?
2. Width is too narrow?
Broken chiral symmetry: positive
parity-partners of Ds Ds*
Reference
Mass
Ebert et. al. (98)
2.51 GeV
Godfrey-Isgur (85)
2.48 GeV
DiPierro-Eichten (01)
2.49 GeV
Gupta-Johnson (95)
2.38 GeV
Zeng et. al. (95)
2.38 GeV
Bardeen, Eichten, Hill
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Charm Spectroscopy
New states:
1. Why is M(DsJ*(2130)) < M (D+K) and
M(DsJ*(2130)) < M (D*+K) ?
Van Beveren and Rupp
2. Interpretation? Radiative decays?
Godfrey; Colangelo and De Fazio
3. Similar states in D and B systems?
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
|fD|2
3. Leptonic and semileptonic decays
|VCKM|2
l

Form-factors and decay constants

Heavy quark symmetry relates observables in B and D transitions
0 A 0 X  p   f X p
Example 1: decay constants
fB
MD

 O1 / M 
fD
MB
HQS requires:
f Bs f B
HQS+Chiral symmetry:
f Ds f D
2
M d  BBd f Bd   Vtd
 

M s  BBs f Bs   Vts


Alexey Petrov (Wayne State Univ.)



Large!
 1  Oms  O1 mb  1 mc 
2
f Ds
fD




5
M K2
2
 1  1  3g
log M K2  2  ...
2 2
6
16p f
D* Dp coupling constant
FPCP 03, June 3-6 2003 (Paris)
 CLEO-c is expected to provide accurate measurements
f Ds
f Ds
Reaction
CLEO-c CM
Energy (MeV)
L fb-1
PDG
CLEO-c
Ds+  
Ds+  t
4140
4140
3
3
17%
33%
1.7%
1.6%
3770
3
UL
2.3%
D+  
f D+

If charm production data is used to obtain Vcs (dVcs/Vcs~1.3%), the
ratio gives information about decay constants
 input for lattice calculations
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
|VCKM|2 |f+(q2)|2
Form-factors and decay constants

Heavy quark symmetry relates observables in B and D transitions
Example 2: decay form-factors
 
 
P j X  p   f XP q 2  p X  pP   f XP q 2  p X  pP 

dG
G 2F
2 3
2 2

|
V
|
p
|
f
(q
)|
cs
K

2
3
dq 24p
Alexey Petrov (Wayne State Univ.)
If charm production data is used to obtain Vcs
(dVcs/Vcs~1.3%), the ratio gives information about
decay form factors
q2 shape can be measured
input for lattice calculations
FPCP 03, June 3-6 2003 (Paris)
4. D0-D0 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
 a(t ) 
0
0
D(t )  
 b(t ) 
  a(t ) D  b(t ) D


• Time-dependence: coupled Schrödinger equations
A

i 

i
D(t )   M  G  D(t )   2
t
2 

q
• Diagonalize: mass eigenstates
p2 
 D(t )
A
 flavor eigenstates
D1, 2  p D 0  q D 0
Mass and lifetime differences of mass eigenstates:
Alexey Petrov (Wayne State Univ.)
x
M 2  M1
G  G1
, y 2
G
2G
FPCP 03, June 3-6 2003 (Paris)
CP violation in charm
• Possible sources of CP violation in charm:
 CPV in decay amplitudes (“direct” CPV)

AD  f   A D  f
 CPV in

D0  D0 mixing matrix
2
Rm2 
p
2M 12  iG12

1


q
2M 12  iG12
 CPV in the interference of decays with and without mixing
Af
q Af
i f d 
f 
 Rm e
p Af
Af
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Mixing: why do we care?
D0  D0 mixing
B0  B0 mixing
• intermediate down-type quarks
• intermediate up-type quarks
• SM: b-quark contribution is
negligible due to Vub
• SM: t-quark contribution is
dominant
• rate  f (ms )  f (md )
(zero in the SU(3) limit)
•
rate  mt2
(expected to be large)
Falk, Grossman, Ligeti, A.A.P.
(Phys.Rev. D65, 054034, (2002)):
2nd order in SU(3) breaking!!!
1. Sensitive to long distance QCD 1. Computable in QCD (*)
2. Small in the SM: New Physics! 2. Large in the SM: CKM!
(must know SM x and y)
(*) up to matrix elements of 4-quark operators
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
How would new physics affect mixing?
• Look again at time development:
A

i 

i
D(t )   M  G  D(t )   2
t
2 

q
p2 
 D(t )
A
• Expand D0  D0 mass matrix:
i 
1
1

(0)
Di0 H WC  2 D 0j 
 M  G   mD d ij 
2 ij
2 mD
2 mD

Local operator, affects x,
possible new phsyics

I
Di0 H WC 1 I I H WC 1 D 0j
mD2  mI2  i
Real intermediate states, affect
both x and y  Standard Model
1. x  y : signal for New Physics?
x  y : Standard Model?
2. CP violation in mixing/decay
new CP-violating phase f
Alexey Petrov (Wayne State Univ.)
With b-quark contribution neglected:
only 2 generations contribute
 real 2x2 Cabibbo matrix
FPCP 03, June 3-6 2003 (Paris)
Experimental constraints
1.
0
 
Time-dependent D (t )  K p analysis

G D (t )  K p

0

 e
Gt
AK p 
2

Rm2 2
2
2




R

R
R
y
'
cos
f

x
'
sin
f
G
t

y

x
G
t
m


4




Sensitive to DCS/CF strong phase
2.
yCP
3.


Time-dependent D (t )  K K analysis (lifetime difference)
0
Am
t D  p  K  


1

y
cos
f

x
sin
f
t D  K  K  
2
Semileptonic analysis
rate  x 2  y 2
Quadratic in x,y: not so sensitive
4.
Time-independent analysis at tau-charm factory: (QM) entangled initial state
RL  1
y cos f  (1) 
RL
L
RL 
G[ L  ( D  [CP] )( D  Xl )]
1
Br ( D  Xl ) G[ L  ( D  [CP] )( D  X )]
0
D. Atwood and A.A.P., hep-ph/0207165
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Experimental constraints 1
0
 
1. Time-dependent D (t )  K p analysis
GD (t )  K p   e

0

 Gt
AK p 
2

Rm2 2
2
  R  R Rm  y ' cos f  x' sin f  Gt 
y  x 2 Gt  
4



R
AK p 
A K p 
2

x'  x cos d  y sin d
for D 0  D 0 :
y '  y cos d  x sin d
Rm  Rm1 , x'   x'
Strong phase is zero in the
SU(3) limit
A. Falk, Y. Nir and A.A.P.,
JHEP 12 (1999) 019
Can be measured at CLEO-c!
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Experimental constraints 2
0


2. Time-dependent D (t )  K K analysis
Experiment
FOCUS (2000)
What are the expectations for x and y?
Alexey Petrov (Wayne State Univ.)
Value
(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 0.8 )%
BaBar (2002)
(1.4±1.0 0.7 )%
 0 .7
 0 .6
World average: yCP = (1.0±0.7)%
FPCP 03, June 3-6 2003 (Paris)
Theoretical estimates
 Theoretical predictions are all over
the board…
 Nevertheless, it can be that y ~ 1%!
Falk, Grossman, Ligeti, A.A.P., Phys.Rev. D65, 054034, (2002)
 Seems like D-system is unique in
that y >> x!
 … but sensitivity to new physics is
reduced
•
(papers from SPIRES )
Alexey Petrov (Wayne State Univ.)
x from new physics
• y from Standard Model
Δ x from Standard Model
FPCP 03, June 3-6 2003 (Paris)
Theoretical estimates I
A. Short distance gives a tiny contribution, consider y as an example
y
mc IS large !!!
1
D0 Τ D0
mD G
… as can be seen form the straightforward computation…

NC  1
ms2  md2  ms2  md2
2
2

XD
C

2
C
C

C
NC
2
1
2
1
2
2
2p NC G
mc
mc
2
y sd
22 N C  1 BD'
M D2 C22

1  NC
BD mc  mu 2
with
D
0

u G c uG c D
0

2


C
1
1   N C 2  2 C1


C2
C2


1  N C 4 FD2 mD2

BD , etc.
NC
2 mD
 2  NC 



 2 NC 1 
4 unknown matrix elements
similar for x (trust me!)
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Theoretical estimates I
A. Short distance + “subleading corrections” (in 1/mc expansion):
(6)
y sd
(6)
xsd
m

m

2
s
 md2  ms2  md2  2
 had  ms6 6
2
2
mc
mc
2
2
s
 md2 
2
 had
 ms4  4
2
mc
2
4 unknown matrix elements
…subleading effects?
(9)
ysd
 ms3 3
15 unknown matrix elements
(9)
xsd
 ms3 3
(12)
y sd
  0  2S   ms2 2
x
(12)
sd

 S   m 
2
s
2
Leading contribution!!!
Alexey Petrov (Wayne State Univ.)
Georgi, …
Bigi, Uraltsev
Twenty-something unknown
matrix elements
Guestimate:
x ~ y ~ 10-3 ?
FPCP 03, June 3-6 2003 (Paris)
Resume: model-independent computation with modeldependent result
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Theoretical estimates II
mc is NOT large !!!
B. Long distance physics dominates the dynamics…
y
1
 n
2G n

D 0 HWC 1 n n HWC 1 D 0  D 0 HWC 1 n n HWC 1 D 0

… with n being all states to which D0 and D0 can decay. Consider pp, pK, KK
intermediate states as an example…



y2  Br D 0  K  K   Br D 0  p p 
 2 cos d
cancellation
expected!

 
Donoghue et. al.
Colangelo et. al.

Br D 0  K p  Br D 0  p  K 
If every Br is known up to O(1%)

the result is expected to be O(1%)!
The result here is a series of large numbers with alternating signs, SU(3) forces 0
x = ? Extremely hard…
Alexey Petrov (Wayne State Univ.)
need to restructure the calculation…
FPCP 03, June 3-6 2003 (Paris)
Resume: model-dependent computation with modeldependent result
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Theoretical expectations: SU(3) breaking
• Neglecting the third generation, mixing arises at second order in SU(3) breaking
2
x, y ~ sin 2 C  SU
( 3)
• Known counter-example:
Does not work if there is a very narrow light quark resonance with mR~mD
2
2
g DR
g DR
x, y ~ 2
~ 2
2
mD  mR mD  m02  2m0d R
Most probably don’t exists…
see E.Golowich and A.A.P.
Phys.Lett. B427, 172, 1998
• What happens if part of the multiplet is kinematically forbidden?
0
0
Example: both D  4p and D  4 K are from the same multiplet, but the
latter is kinematically forbidden
Mixing is dominated by 4-body intermediate
state contribution, incomplete cancellations
naturally imply that y ~ 1%
Alexey Petrov (Wayne State Univ.)
see A.F., Y.G., Z.L., and A.A.P.
Phys.Rev. D65, 054034, 2002
FPCP 03, June 3-6 2003 (Paris)
FCNC in charm: why do we care?
Rare charm decays
Rare beauty decays
• intermediate down-type quarks
• intermediate up-type quarks
• SM: b-quark contribution is
very small due to Vub
• SM: t-quark contribution is
dominant
•
rate  f (ms )  f (md )
(zero in the SU(3) limit)
• rate  f ( mt )
(expected to be large)
2
1. Sensitive to long distance QCD 1. Computable in QCD (*)
2. Sensitive to New Physics!
2. Large in the SM: CKM!
(*) depending on the process: OPE, factorization, …
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
FCNC charm decays
1. In many cases NP contribution “gives a
larger contribution” than the Standard Model
2. Example: R SUSY
~
dH  
~
 'i 2 k  'i1k
2m ~2 k
u  c l  l 
L  L
L

L
dR
…or MSSM for different values of squark masses
see Burdman, Golowich, Hewett and Pakvasa
Phys.Rev. D66, 014009, 2002
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
5. Conclusions
 Did not talk about:
– Lifetimes and inclusive semileptonic decays
– applications of 1/m techniques
– Charmed baryons and double-charmed baryons
– issues in double-charmed baryon production
– Exclusive nonleptonic charm decays
– direct CP violation
– Charmonium production and polarization
– J/ production in e+e- collisions
– …
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Conclusions
 Spectroscopy: what are the new DsJ* states?
– low mass triggers many possible explanations
 Leptonic and semileptonic decays
– important inputs to B-physics/CKM extractions
 Charm mixing:
–
–
–
–
x, y = 0 in the SU(3) limit (as V*cbVub 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/CLEO-c/CDF
 Observation of CP-violation or FCNC transitions in the current round
of experiments are still “smoking gun” signals for New Physics
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Additional Slides
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Questions:
1. Can any model-independent statements be made for x or y ?
What is the order of SU(3) breaking?
n
i.e. if x, y  ms what is n?
2. Can one claim that y ~ 1% is natural?
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Theoretical expectations
At which order in SU(3)F breaking does the effect occur? Group theory?
D 0 HW HW D 0  0 D HW HW D 0
is a singlet with D  Di that belongs to 3 of SU(3)F (one light quark)
The C=1 part of HW is
q cq q , i.e. 3  3  3  15  6  3  3  H
i
j
k
ij
k
O15  ( sd )(ud )  (uc )( sd )  s1 ( d c )(ud )  s1 (uc )( d d )
 s1 ( sc )(us )  s1 (uc )( ss )  s12 ( d c )(us )  s12 (uc )( d s )
O6  ( sd )(ud )  (uc )( sd )  s1 ( d c )(ud )  s1 (uc )( d d )
 s1 ( sc )(us )  s1 (uc )( ss )  s12 ( d c )(us )  s12 (uc )( d s )
i
Introduce SU(3) breaking via the quark mass operator M j  diag (mu , md , ms )
All nonzero matrix elements built of Di , H kij , M ij must be SU(3) singlets
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
Theoretical expectations
note that DiDj is symmetric

belongs to 6 of SU(3)F
D 0 HW HW D 0  0 D HW HW D 0
Explicitly,
DD  D6
H W H W  O60  O42  O15'
1. No 6 in the decomposition of HW HW  no SU(3) singlet can be formed
D mixing is prohibited by SU(3) symmetry
2. Consider a single insertion of M ij  D6 M transforms as 6  8  24  15  6  3 
still no SU(3) singlet can be formed
NO D mixing at first order in SU(3) breaking
3. Consider double insertion of M  DMM : 6  (8  8) S  (60  42  24  15  15  6)
 (24  15  6  3)  6
D mixing occurs only at the second order in SU(3) breaking
Alexey Petrov (Wayne State Univ.)
A.F., Y.G., Z.L., and A.A.P.
Phys.Rev. D65, 054034, 2002
FPCP 03, June 3-6 2003 (Paris)
Theoretical expectations: SU(3) breaking
• Two major sources of SU(3) breaking
1.
phase space
mK  mp  m ...
2a. matrix elements (absolute value)
f K  fp ...
2b. matrix elements (phases a.k.a. FSI)
Im

A D 0  K p 
0
0
A( D  K p  )
Take into account only the first source…
Alexey Petrov (Wayne State Univ.)
FPCP 03, June 3-6 2003 (Paris)
SU(3) and phase space
• “Repackage” the analysis: look at the complete multiplet contribution


y   yF , R Br D 0  FR ~  yF , R
FR
FR

1
0
G
D
n

G nFR
y for each SU(3) multiplet

Each is 0 in SU(3)
• Does it help? If only phase space is taken into account: no (mild) model dependence
yF ,R 

D 0 HW n  n n HW D 0

D 0 HW n  n n HW D 0

D 0 HW n  n n HW D 0
nFR
nFR
if CP is conserved

nFR
 G( D
nFR
Alexey Petrov (Wayne State Univ.)
0
 n)
Can consistently compute
FPCP 03, June 3-6 2003 (Paris)
Example: PP intermediate states
• n=PP transforms as 8  8S  27  8  1 , take 8 as an example:
Numerator:











0
1
1
2
1
AN ,8  A0 s12    ,    p 0 , p 0    , p 0   p  , p    K , p 0
2
3
2
0
1
1
  K  , K    , K 0   , K
  K  ,p    K  ,p 
6
6




Denominator:


phase space function






1
2 1

AD ,8  A0    , K 0   K  , p    K 0 , p 0  O ( s12 ) 
2
6

• This gives a calculable effect!
y 2 ,8 
AN ,8
AD ,8
Alexey Petrov (Wayne State Univ.)
 0.038s12  1.8 10  4
1.
2.
Repeat for other states
Multiply by BrFr to get y
FPCP 03, June 3-6 2003 (Paris)

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 03, June 3-6 2003 (Paris)