Introduction to Charm
S.Olsen
Hawaii
&
高能物理研究所
BESIII物理分析讲习班
2008年6月23日-7月4日
中关村教学园区教学楼大厅
S. Olsen’s
A brief history of the charmed
quark
Hadrons in 1963
“stable” hadrons
Two “classes” of hadrons
“non-strange:” n, p, p, r, …
“strange:” L, S, K, K*, …
meson resonances
baryon resonances
“Three quarks for Muster Mark”
3 quarks 夸克
Gell-Mann
u+2/3
Zweig
d-1/3
u-2/3
s-1/3
non-strange: no s quarks
p:
p-:
u+2/3 u+2/3
d-1/3
u-2/3
d-1/3
(& 3 antiquarks) 反夸克
d+1/3
s+1/3
strange: contains s quark(s)
L:
K-:
u+2/3 s-1/3
d-1/3
S-1/3
u-2//3
Weak decay’s in the 3-quark era
3 quarks:
u 
 
q=-1/3
d 
q=+2/3
|DS|=0
4 leptons:
Flavorchanging
decays
|DS|=1
s
e   
 ~
  
 e  
-
-
(1964—1974)




Flavorpreserving
decays
Problems
Problem 1: Different weak decay “charges”
for leptons & hadrons:

du
Gd 0.98GF
d
n
Gd G
Fermi Constant
-
GF
F
u
Flavor preserving decay
p
K-
GF
su
Gs 0.21GF

s
Gs
GF
u
Flavor changing decay
p0
flavor mixing
Cabibbo’s sol’n:
N.Cabibbo
Weak Int
flavor state
Flavor mass
eigenstates
d = a d + b s
GF
d’
u =
W-
a=cosqc=0.98
aGF
d
Unitarity: |a|2 + |b|2 = 1
b=sinqc=0.21
u
+
W-
bGF
s
u
W-
a=cosqc; b = sinqc
qc=“Cabibbo angle” ≈ 12o
Missing neutral currents
Problem 2: no flavor-changing
“neutral currents” seen.
Discovered at CERN
s
GN
d,u
d,u
K-
flavor-preserving neutral
currents (e.g. NX) are
allowed
d
p-
flavor-changing neutral
currents (e.g. Kp l+l-)
are strongly suppressed
GIM sol’n:
Introduce 4th quark
2 quark doublets:
charmed quark
 u  c 
  
 d '  s' 
 u  c 
  
 d  s 
Weak
eigenstates
GIM:
Mass
eigenstates
Glashow Iliopoulis Maiani
d’ & s’ are mixed d & s
4-quark
flavor-mixing
matrix
Weak
eigenstates
 d '  a b  d 
   
  Mass
 s'      s eigenstates
Mixing matrix must be Unitary
UU†
= 1
a
U  

GF
a


b  a    1 0 

 *





*
  b    0 1 
*
*
b   a b   cos qC
  
  
   - b a   - sin qC
|a|2 + |b|2 = 1 & a*b - ab* =0
sin qC 

cos qC 
Charged currents (u-quark)
3


|DS|=1
u
 -1

 ad 3 + b s -13 


2
d
aGF
u
s
W-
du: GF modified by a
Cabibbo
favored
(cosqc)
bGF
u
W-
(sinqc)
su: GF modified by b
Cabibbo
suppressed
N.Cabibbo
N.Cabibbo
Charged currents (c-quark)
3
|DC|=1


c
|DS|=1


 - b d -13 + as -13 


2
|DC|=1
|DS|=0
-b GF
d
c
W-
dc: GF modified by b
(sinqc)
suppressed
N.Cabibbo
s
aGF
c
W(cosqc)
sc: GF modified by a
Favored
Flavor preserving Neutral Current
|a|2+|b| 2
d,(S)
GN
d,(s)
d  a d  - b s
s  a s + b d 
Z0
d d  a d  - b s a d  - b s
*
a
2
*
d  d  - a * b d  s - b a s d  + b
*
a +b
2
allowed
2
=1
2
s s
From Unitarity
Flavor changing Neutral Current
a*b-ba*
GN
s(d) Z0
a
2
d  a d  - b s
d(s)
s  a s + b d 
s d  a * s - b * d  a d  + b s
s d  + a * b s s - b a d  d  + b
*

 a b -b a
*
*

=0 From
FCNC forbidden by Unitarity
2
d  s
Unitarity
“GIMmechanism”
GIM Mechanism
GIM: Glashow Iliopoulis Maiani
FCNC forbidden by Unitarity
if quarks come in pairs
Discovery of the 4th quark (charm)
p+Bee+e- + X @ BNL
e+e- @ SLAC
J/y
s(e+e-  hadrons)
cc bound state
Ting (丁)
Richter
s(e+e-  e+e-)
1976 Nobelists
PRL 33, 1404 (1974)
s(e+e-  +-, p+p- & K+K-)
M(e+e-)
PRL 33, 1406 (1974)
Ecm(e+e-)
Glashow won the 1979
Physics Nobel prize for
predicting the c-quark
No prize for
Iliopoulis & Maiani
Status in 2008
6 quarks
(3 doublets)
 u  c  t 
   
 d  s  b 
+2/3 e
-1/3 e
 cos qC
 
 - sin qC
3x3 flavor-mixing
(CKM) matrix
 d '  VudVusVub  d 
 
  
 s '   VcdVcsVcb  s 
 b'  V V V  b 
   td ts tb  
sin qC 

cos qC 
Mesons formed from c quarks
“charmonium” mesons are cc pairs
Charmonium mesons
y(4415)
y(4150)
y(4040)
c’c2
y”
h’c
y’
hc
cc0
cc1
cc2
J/y
hc
Discovered by Ting & Richter
The 1-- states are produced
directly n e+e- annihilations
“Open-charm” mesons contain one c quark
+2/3
D+: c d+1/3
+2/3
D0: c u-2/3
+2/3
D+s: c s+1/3
“Ds meson”
“D meson”
D0 meson discovered at SLAC 1975
c+2/3
u-2/3
G. Goldhaber
D0K-p+
Phys Rev Letts
37, 255 (1976)
(& D0K+p-)
K-
p+
1865 MeV
D+ discovered
in 1976
c+2/3
d+1/3
“Invariant mass:”

 2
M inv  ( EK + Ep ) - ( pK + pp )
2
Ds meson discovered at Cornell
c+2/3
s+1/3
Y. Kubota
Ds+fp+
(& Ds-fp-)
1970 MeV
fp invariant mass
Phys Rev Letts
51, 634 (1983)
How do D mesons decay?
Dominant hadronic decay modes
“Cabibbo-allowed”
hadronic decays
u
*
ud
V
c
q
Vcs
d
W
s
q
K, K*, etc
(=u or d)
some D+ Bf’s
& D0 Bf’s
K0p+
2.9%
K-p+
3.8%
K0r+
9.6%
K-r+
11%
K*0p+
2.0%
K*-p+
3.4%
K*0r+
1.8%
K*-r+
6.5%
Vcs  cos q c
Vud  cos q c
“singly” Cabibbo-suppressed hadronic modes
Vus  -Vcd  sin qc  0.21
u
*
us
V
Vcs
c
q
W
s
s
q
K, K*, etc
or
(=u or d)
V
c
q
Vcd
& D0 Bf’s
K0K+
0.6%
K-K+
0.4%
K0K*+
1.2%
K-K*+
0.4%
p+p0
0.1%
p+p-
0.1%
r0p+
0.1%
r+p-
~1%
Vus
d
W
(=u or d)
some D+ Bf’s
u
*
ud
2
Expected suppression factor ~ V ≈ tan2qC = 0.05
ud
d
q
p, r, etc
“doubly” Cabibbo suppressed nodes
Vus  -Vcd  sin qc  0.21
Vcd
c
q
u
*
us
V
W
s
d
q
p, r, etc
(=u or d)
some Bf’s
D0K+p-
0.014%
D0K*+p-
0.01%
D+K+p0
<0.04%
D+K+p+p-
0.06%
“Expected” suppression factor ~
Vus
Vud
4
≈ tan4qC = 0.003
color suppressed nodes
Internal W bosons
c
Vcs
c
s
d
W
Vud*
u
u
u
K0,K*0, etc
p0,
r0,
s
d
W
Vud*
u
etc
c
quark colors
must match
W
Vud*
The nominal suppression factor is (1/3)2;
observed suppression are typically less
some Bf’s
u
u
u
s
d
u
u
color mismatches
are not allowed
For comparison
D0K0p0
2.2%
D0K-p+
3.8%
D0K*0p0
1.2%
D0K*-p+
3.4%
D0K0r0
1.5%
D0K-r+
11%
D0K*0r0
1.5%
D0K*-r+
2.1%
The trouble with these simple
arguments
u
d
u
d
c
Vcs
W
q
s
q
We draw diagrams
that look like this
c
W
s
q
q
But nature does this
Semileptonic decays are “cleaner”


Vcs
W
c

s
c
Vcd
W
d
K, K*, etc
q
q
(=u or d)
Vcs
p, r, etc
q
q
(=u or d)
“Cabibbo-allowed”
semileptonic decays
“Cabibbo-suppressed”
semileptonic decays
some Bf’s
some Bf’s
D0K-e+
3.5%
D0p-e+
0.3%
D0K*-e+
2.2%
D0r-e+
0.2%
D+K0e+
8.6%
D+p0e+
0.4%
D+K*0e+
5.6%
D+r0e+
0.2%
Vcs
Vus
2
suppression factor ~ V
≈ tan2qC = 0.05
ud
Cleanest modes: purely leptonic
D+e+
<0.002%
D++
0.04%
D+t+
<0.21%
(s)
(Vcs)
(s)
Ds+e+
<0.013%
Ds++
0.64%
Ds+t+
8.0%
(s)
SM theory calculates this unambiguously to be:
Use |Vcd| from elsewhere: measure fD+
Helicity suppression factor
detecting D mesons at BES-III
y(3770)
Run at the y(3770)
If a D meson is produced
here it must recoil from a
D meson & nothing else
(not enough energy to
make any other particles)
2mD
mD+mD*
BES-II PLB 660, 315 (2007)
Kinematic variables for y(3770)DD
Tagged-D
ED  Ep + EK  ECM 2
K
e+
recoil-D
invariant mass:
Beam-constrained
mass:
D0
D0
e+y(3770)eE=Ecm/2
p
e-
E=Ecm/2
in CM:

 2
minv  ( Ep + EK ) - ( pp + pK )
2
mbc  ( ECM

 2
2) - ( pp + pK )
2
Mbc
s=6~12 MeV
mode-dependent
DE
3.57
3.61
3.65
s =1.2~2
Energy difference:
DE  Ep + EK - ECM 2
Beam-constrained mass:

 2
2
mbc  ( ECM 2) - ( pp + pK )
3.69
MeV
3.73 3.77
D meson “beam”
E=½Ecm
D0
recoil-D
Tagged-D
D0
p+
K-
E=½Ecm
Kp+
•its energy E
•its 3-momentum: p
•flavor (D or D)
For the recoil-D we know: •which tracks come from it
(no *combinatoric” background)
CLEO-c D- Tagging modes
Measurements with tagged D mesons
• Absolute branching fractions
• Semileptonic decays
– |Vcs| and |Vcd| CKM matrix elements
• Purely leptonic decays
– fD and fDs decay constants
• D-D oscillations
– Exploiting quantum correlations @ the y(3770)
• CP violation
• …
Absolute branching fractions
Nj = number of single tags Dfj
 N DD Br ( D  f j )eff f j
Njk = number of double tags Dfj and Dfk
 N DD Br ( D  f j )eff f j Br ( D  f k )eff fk
Absolute branching fractions
N jk
Nj


N DD Br ( D  f j )eff f j Br ( D  f k )eff fk
N DD Br ( D  f j )eff f j

N jk 1
Br ( D  f k ) 
N j eff fk
No dependence on NDD or efffj
CLEO-c with 281 pb-1
Factors of 2~4
improvement
BES-III should
do even better
Semileptonic decays
(neutrino reconstruction)

c
ℓ+
Vcs

K, K*, etc
s
c
Vcd
ℓ+
d
p, r, etc
K, K*, etc
q
Vcd
q
q
q
(=u or d)
Vcs measurements of Vcs and Vcd
Goal: precise
Why are these important?
Wolfenstein parameterization of the CKM matrix
- 12qC2
VudVusVub    1cos
sin qC 


 
2
1


V
V
V


1


 cd cs cb 
- sin qC cos qC2 

V V V   A3 (1 - r - ih ) - A2
 td ts tb  
A3 ( r - ih ) 

2
A
 + (4 )
 ≈sinq ≈
1
C

0.21
4 = 0.002
So, to good precision, SM predicts:
World avg
Errors:
Vcs = Vud
Vcd = -Vus
~10%
~5%
0.02%
~1%
Checking these relations by improving the Vcs and Vcd precision
will provide an important test of the Standard Model.
(Needs a combined theory & experimental effort.)
Neutrino reconstruction

K-
K+
pe+
D0
By tagging the
meson, we can
know p & E for the recoil D0:
Ke+

D0
D0 K+
p-
p = pD – pK – pp
E = ½Ecm – EK – Ep
E–| p|= “Umiss” = 0
Umiss in CLEO-c
Cabibbo-favored
Cabibbo-suppressed
D0K-e+
Signal is well separated from background,
even in the Cabibbo-suppressed modes
|Vcs| and |Vcd| from CLEO-c
Expected experimena’l
precision from BES-III
Purely leptonic D+ & Ds+ decays
SM value for fD+ can be calculated by lattice QCD
(s)
(Vcs)
H +?
(s)
This could be modified by the presence of
other heavy particles. (A charged Higgs
Would make the value lower than the SM
prediction.)
New CLEO Measurements
arXiv:0806.2112v2
≈4 %
precision
205.8±8.9 MeV
Theory seems
to get it right
206±4 MeV
Does fDs differ from SM predictions?
Vcs
Ds
s
Kronfeld & Dobrescu
arXiv: 0803.0512
H+as well?
a hot (the hottest?) topic for BES-III
Talk by
at
A. Kronfeld
Measuring D+ + decays
Use charged D+ tagged sample
+

D+
Single track on
the recoil side
-identify it
as a muon-
CLEO-c
D- K+
p-
L
p-
p = pD – p
E = ½Ecm – E
2
2
E–| p| = MM2= 0
CLEOc doesn’t have a muon detector
Systematic errors
BES-III statistical error will be ~2%
Source of Error
(for CLEO-c)
Finding the + track
Minimum ionization of + in EM cal
Particle identification of +
MM2 width
Extra showers in event > 250 MeV
Background
Number of single tag D+
Monte Carlo statistics
Total
%
0.7
1.0
1.0
1.0
0.5
0.6
0.6
0.4
2.1
BES-III precision on fD+
+
+

(
D


)
+
+
Br ( D    ) 
 t D + ( D +   + )
tot
f D+ 
8pBr ( D +   + )
t D GF Vcd m M D (1 - M )
+
+
m2
2
D+
≈ 2.0%
0.6%
1.5%
1.1%
Measuring Br(D+t+)
Now there are 2 or 3 ’s on the
recoil side. The measurement
Is dirtier, but the Bf is larger
p+


t+ D+
+
D- K+
p-
Single track on
the recoil side
-identify it as a
as a pion or muon-
p-
D+p+KL
pmiss = pD – pp
Emiss = ½Ecm – Ep
2
2
Emiss–| pmiss|  0<
MM2
2
<mK 0
p+
Ds leptonic decays
Big question: what energy to run at?
Ds production
cross section
(nanobarns)
CLEO-c
Here s(e+e-Ds+Ds-)≈0.9nb. A
modified tagging technique is needed
Here s(e+e-Ds+Ds-)≈0.3nb. The
standard tagging techique applies
Ds leptonic decays @ 4170 MeV
e+e-DsDs*
Ds
+

Ds-
The  can come from either Ds

Ds*p-
f
Since the Ds and Ds have different
energies, the n-reconstruction
method we use @ the y(3770)
do not work.
CLEO-c used two techniques:
one required detecting the , the other didn’t
Technique -1 (detect the )
First select a tagged-Ds sample:
Invariant mass: M inv  ( Ei ) 2 - ( p i ) 2
Then compute the  + tag-Ds
missing mass2:

MM 2Ds  E + EDs
 -  p
2


+ pDs

2
11880±399±504 tags
E and p for the recoil Ds is determined
For events with 1 + (or p+) on the recoil side,


 2
2
2
compute: MM  Ecm - ED - E - E  - - pD - p - p 
s
s
D++ (MC)
+ Data
Ds+ signal
D+p+KL
D+t+ (MC)
p+ Data
Dst+ signals?
D+p+KL
e+ Data
MM2 (GeV)
Technique-1 systematic errors
on Br(Ds+)
Mostly from uncertainties
in fitting this peak
??
11880±399±504 tags
BES-III will have to figure out how to improve this
Technique-2 (for Dst+):
Ignore the  but require a single
e+ on the recoil side
Tag-Ds signals with a single recoil electron (or positron)
Look at the “extra” EMC energy
recoil-Dst+
e+
K
e+
p

K+
tag-Ds
tracks
After the EMC signals
associated with the
e+ and the tag-D trks
are removed, only ’s
remain.
DsKLe+ bkgd looks just like the signal
& must be well understood.
For CLEOc this is the dominate syst error (~5%)
Expected precision (Dsℓ+)
CLEOc’s weighted average (281 pb-1): fDs=274±10±5 MeV
~4%
~2%
•BES-III can easily improve the statistical error to 1%
•>10x more data
•good Muon detection
•Need to improve systematic error by at least factor of 2
•restrict analyses to cleaner tag modes?
particle-antiparticle oscillations
First seen in the K0 system
Short distance contribution: ≈ 1/MW ≈ 10-3fm
K0
K0
long distance contribution: ≈ 1/Mp ≈ 1fm
p+
K0
p-
K0
This part is most
interesting since
non-SM heavy
particles could
occur in the loop
Neutral D meson phenomenology
SM: CPV is very small: q ≈ p ≈1/2
What happens when two identical
systems are coupled?
D0D0 D0 D0
Energy transfers
…. back-and-forth
between the two
oscillators
•In general, part of x = DM/ originates from short
distance terms and is, thus, interesting.
• y = D/2 is produced by long distance terns & is
less interesting
• when mixing occurs, it’s important to sort out x & y
Historically, particleantiparticle mixing has been a
good indicator of new physics
1st hint of charm came from K0K0
Vus*
Dms 
K0
u
u
Vud
+ Si
c
+ Si
t
Vus*
Vud
qi
qi
Vus*
K0
+
K0
Vus*
Vcd
u
c
K0
+
K0
u
Vcs*
Vud
Vud
Vtd≈0
K0
t
Vts*≈0

Dms  Vus*Vud f (mu )Vus*Vud + f (mc )Vcs*Vcd
in the limit mu=mc (=mq):

Dms  Vus*Vud f (mq ) Vus*Vud + Vcs*Vcd


=0 (GIM mechanism)
K0K0 mixing parameter Dm is determined by the difference
in mass between the c-quark and u-quark: mc≈150xmu
1st sign of a heavy t-quark came
from B0B0 mixing
Discovered at DESY
B0
B0
B0
H.Schroeder
B0
B0
~20ps
a heavy t-quark  large Dmb
b
Dmb 
B0
Vub*
u
Vub*
Vud
b
B0
u
+
Vub*
Vcd
b
B0
u
c
B0
b
Vud
+…
+…
Vub*
Vtd
+
B0
u
t
b
Vud
b
Vcb*
Vud

Vts*
Dmb  Vub* Vud f (mu )Vub* Vud + f (mc )Vcb* Vcd + f (mt )Vtb*Vud
Vub* Vud + Vcb* Vcd + Vtb*Vud  0

 Unitarity (GIM)
Vud* Vcd* Vtd* VudVusVub   1 0 0 


 

* * *
VusVcsVts VcdVcsVcb    0 1 0 
 * * * 
VubVcbVtb VtdVtsVtb   0 0 1 


Dmb is large because of the huge t-quark mass:
i.e. f(mt) is very much different than f(mu) & f(mc)
B0
mu≈10 MeV
mc≈1500 MeV
mt≈175,000 MeV
x150
x120
The “Flavor Problem”
SUSY’s Problem with K0K0 mixing
SM:
Weak-int vertices
2nd order EW:
Δm  3 x 10-12 MeV
NP (SUSY):
QCD-vertices
6x6 matrix
Dm should be huge:
but it is not
quark-squark “Alignment”
Invoke a symmetry that results in small
values for the down-type squark mixing
This requires up-type squark mixing elements  sinqC (~0.2)
Expect large effects in D0-D0 mixing
e.g. Δm ~ 6x10-11 MeV
Nir & Raz PRD 66, 035007 (2002)
D0D0 & K0K0 comparison
c
D0
d,s
d,s
D0
K0
u,c
u,c K0
c
charge=-1/3 virtual quarks (d,s,b)
md≈10 MeV
ms≈150 MeV
x15
charge=+2/3 virtual quarks (u,c,t)c
mu≈10 MeV
mc≈1500 MeV
SM: D0D0 mixing is very small
(at least the part from short-distance terms)
x150
BaBar: study of D0K+p(“wrong-sign” decays)
u
*
ud
V
D0K-p+
is a Cabibbo-allowed
favored decay mode (Br=3.8%)
c
u
Vcs
d
W
s
u
K-
There are 2 ways that a D0 can decay to the opposite combination K+p-:
1) Doubly Cabibbo-suppressed decays
(DCS)
u
*
Vus
s
c
0
D u
Vcd
W
Br ~ 0.014%
d
u
p-
2) D0  D0; D0K+p- decays
*
cs
V
u
0
c D
mixing
c
D0
u
d
Vud
u
W
s
u
K+
Cabibbo-allowed D0 decay
(CA)
Distinguish DCS from mixing
using t-dependence
 ws ( D  K p )  ADCS + Amix ACA
0
+
-
2
2
2

(
x
+
y
)
2
2 2  -t t
*
ws   ADCS + yADCS ACAt +
ACA t e
4 pure mixing
 DCSD

interfence
usually use : ADCS  re i ACA
 rs  ACA e -t t
2
(" right sign" rate)
ws 
( x 2 + y 2 ) 2  -t t
 1 + y' rt +
t e
rs 
4

y '  y cos  + x sin 
This is what
BaBar measures
BaBar’s fit
y’ = (9.7  4.4  3.1) x 10−3
y '  y cos  + x sin 
long-distance effect?
short-distance effect?
Dm??? D???
Need to translate y’ into x & y,
for this we have to determine 
Time-dependence of D0K+p-
What can BES-III do?
We can’t measure t-dependence because our D0 mesons at almost at rest
But in y(3770)D0D0 decays, the D0 and D0 are in a coherent Quantum state
So, for example:
When one D0 decays to a CP=+1 eigenstate (D1K+K- or D1p+p-),
the rate for the other DK∓p± is “enhanced” by f=1+(2rcos+y)
BES-III can measure f with
a ~1% statistical error
r≈tan2qc≈0.05
When one D0 decays to a CP=-1 eigenstate (D2KSp0 or D1KSh),
the rate for the other D2K∓p± is “reduced” by f=1-(2rcos+y)
other quantum correlations @ the y(3770)
ℓ
+
ℓ-
CLEO-c Results
1st measurement of Kp
•essential input to D-mixing studies
•unique to the y(3770) (BES-III)
•BES-III will do much better
•plus other modes
CP violation in c-quark sector?
the most exciting quantum correlation
Expected to be very small in the SM
in y(3770)D0D0, the D0 and D0 are in a coherent CP=-1 Quantum state
When one D0 decays to a CP eigenstate, the other D
cannot decay to a CP eigen state with the same CP
unless CP is violated
For example, y(3770) DD
CP violation!!!
Summary
• Charm physics has had an illustrious history
• New results (mixing, fDs) have revived interest
• Many unique opportunities for BES-III
–
–
–
–
challenge SM with improved f D+& fDs values
Important contributions to D-mixing studies
Search for CP violation in D-meson decays
…
• Many, many thesis topics for PhD students
Lots to do
加油
謝謝
Back-up slides
SM expectation for Dmc
Vcd
Dmc 
c
D0
u
+…
Vud*
u
d
d
*
ud
V
Vcd
D0
c
Vcd
c
+
D0
d
u
*
us
V
s
*
ud
V
Vcd
u
D0
c
Vub* ≈0
u
c
D0
+
d
u
Vcs
b
*
ud
V

Vcb≈0
Dmc  Vud* Vcd f (md )Vud* Vcd + f (ms )Vus*Vcs
+…
not so different
Expect D0D0 mixing is very small
(at least from short-distance terms)
D0

c
How to make Δm small?
PLB 309, 337 (1993)