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Charmed Baryons. Charmed Baryons. Hai-Yang Cheng Academia Sinica, Taipei Spectroscopy Strong & EM decays. Charm 2007, Cornell, August 5-8, 2007. Spectroscopy. In SU(3) representation, diquark = 3 3 = 3 +6 - PowerPoint PPT Presentation
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Charmed Baryons Charmed Baryons
Hai-Yang Cheng Academia Sinica, Taipei
Spectroscopy Strong & EM decays
Charm 2007, Cornell, August 5-8, 2007
2
Spectroscopy
Many new resonances observed:
Ground state: c
*(2770) with mass = 2768.33.0 MeV (BaBar)
Orbitally excited p-wave states: L=1
e.g. c(2593), c(2625), … etc. (CLEO)
Positive parity excitations: L=2,1,0
e.g. JP[c(2880)]=5/2+ (Belle)
In SU(3) representation, diquark = 33 = 3+6
3: c+,c
+,c0, all decay weakly
6: c0,’+
c,’0c,c
++,+,0 only c0 decays weakly
c*0,*+
c,*0c,c
*++,+,0 S=0 S=1
3
Orbitally excited charmed baryon states
L½+L¸=Ll (not L½+L¸=L !)
Two possible p-wave states (L+L=1):
1. L½=1, L¸=0; antisymmetric under q1q2
2. L½=0, L¸=1; symmetric under q1q2
Jl=Sl+Ll, J=Sc+Jl
symmetric
antisymmetric
(denoted by a tilde)
¤cJ ` (JP )
In HQ limit, Jl & Sc are separately conserved
4
First positive parity excitations (L+L=2):
1. L½=2, L¸=0; L½=0, L¸=2 symmetric under q1q2; Ll=2
2. L½=L¸=1 antisymmetric under q1q2; Ll=2,1,0
5
½-
½-
½-
3/2-
3/2-
Only the parity of c & c(2880) has been measured
3/2-
3/2-
3/2-
3/2-
6
c(2595), c(2625) → c1(1/2-,3/2-)
c1(1/2-)![c]S, c1(3/2-)![¤c¼¼]P, [c]D
⇒ ¤c(2625) is narrower than ¤c(2595)
c0→[c]S, c1→[c]
P, c2→[
c]D
Since c(2880) observed in c spectrum has a width 65 MeV, and (c0→c) 405 MeV from HHChPT ⇒ c(2880) is most likely to be a c2(3/2-)
c(2800): c2(3/2-), c1(3/2-), c0(1/2-)
Antitriplet charmed baryons:
½+ (c, c+, c
0)
½- (c(2595)+, c(2790)+, c(2790)0)
3/2- (c(2625)+, c(2815)+, c(2815)0)
c(2790), c(2815) → c1(1/2-,3/2-)
7
c(2880): first positive parity excited charmed baryon
Candidates for spin-5/2 states:
2/5~
,2/5~
,2/5~
,2/5~
,2/5 ''3
''2
'222 ccccc
45.142.02
7
))2880((
))2880((
2
7
)][)2/5(~
(
)][)2/5(~
(5
*5
2
*2
cc
cc
Dcc
Dcc
p
p
23.029.05
4
))2880((
))2880((
5
4
)][)2/5((
)][)2/5((7
*7
2
*2
cc
cc
Fcc
Fcc
p
p
36.029.04
5
))2880((
))2880((
4
5
)][)2/5(~
(
)][)2/5(~
(7
*7
3
*''3
cc
cc
Fcc
Fcc
p
p
)%4.61.24())2880((
))2880(( 1.15.4
*
cc
cc ⇒ parity assignment for c(2880)
Angular analysis of c(2880)→ cby Belle ⇒ J=5/2 is preferred
JP=5/2- is
disfavored
However, c2(5/2+) can decay into c* in a P-wave
robust prediction
c(2880) could be an admixture of 2/5~
& 2/5 ''32 cc
HQS
Chua,HYC (’07)
8
Remarks:
Based on the diquark idea, JP[c(2880)]=5/2+ has been predicted by
Wilczek and Selem before Belle experiment
Peking group (Zhu et al., hep-ph/0704.0075) has studied the strong
decays of charmed baryons using 3P0 model
⇒ Since c(2880) decays into D0p, it cannot be a radial excitation
⇒ c(2880) is a pure state
c2(5/2+) leads to too large ratio of c*/c for L=0, L=2,
and too large width ( 78 MeV) for L=2, L=0
2/5~ ''
3c
2/5~ ''
3c
An issue about mass: According to QM, m[c2(5/2+)] 2910MeV,
The mass of is even higher
9
Other even-parity excitated states ?
c(2765): even-parity orbital excitation ½+, supported by
QM (Capstick, Isgur ‘86) & Skyrme model (Oh & Park ‘96)
radial excitation 2½+ (Ebert, Faustov, Galkin ‘07)
c(2940): 3/2+, 5/2-, can be tested by measuring the ratio c*/c
m(D*0)+m(p)=2945 MeV ⇒ a D*0p molecular ½- state for
c(2940) with binding energy 5 MeV ? (X.G. He et al.)
first radial excitation of c with JP=3/2+ (Ebert et al.)
M(c)-M(c) 180200 MeV for JP= ½+, ½-,3/2-
⇒ c(2980) & c(3077) considered as counterparts of c(2765) & c(2880)
c(2980): ½+, or 2½+
c(3077): 5/2+,
c(3055): ? c(3123): ?
c(2980) is broader than c(3077); both are above D threshold
or c(2765)
10
½+,2½+
3/2+,5/2-
5/2+
5/2+
½+,2½+ ½+,2½+
11
5/2+
3/2-
3/2+1/2+
c c c c
1/2+5/2+
12
An ideal place for testing heavy quark symmetry and chiral symmetry: heavy hadron chiral perturbation theory (HHChPT)
Strong decays of s-wave charmed baryons are governed by two couplings g1 & g2. While info on g1 is absent due to the lack of c
*→c, g2 is fixed to be 0.61±0.04 by the measured rate of c
++→c++
(in units of MeV)
Wise; Yan et al.; Burdman, Donoghue (’92)
(c*) 7(c), though they have same widths in HQ limit
13
S-wave (D-wave) transitions between s-wave and p-wave baryons are described by six couplings h2,…,h7 (eight couplings h8,…,h15)
Pirjol, Yan (’97)
h2
h10
h10 &
h8=h
10
1308.010.010
114.0102.02 MeV 10)86.0( ,437.0
hh Chau, HYC
14
Strong decays of p-wave charmed baryons
⇒ isospin violation: c+0 2 c
0+ , c00 c+- as 0 is lighter than
Strong decays of c(2593) are near threshold⇒ sensitive to masses
(c0(1/2-)→c) 405 MeV
15
Electromagnetic decays
cccccc
cccc
cccc
BB
BB
BB
*''**6
*6
'**3
*6
'36
, , :
, :
, :
suitable framework: HHChPT+ QM (Yan et al. ’94)
(in units
of keV)
It will be very difficult to measure EM decay rates
16
Other topics:
Hadronic weak decays of c+,c
+,c0,c
0
Charm-flavor-conserving weak decays
Lifetime differences
Semileptonic decays
Weak radiative decays
discussed in back-up slides
See review article on charmed baryons in Tau-Charm
Physics Book at BESIII. Hope it will be posted on archive soon
17
Conclusions
HQS & S can be nicely tested in charmed baryon sector.
Strong couplings g2, h2 & h10 are updated
Many orbitally excited charmed baryons have been observed
Some form multiplets
c(2880) is a first even-parity excited state. It could an
admixture of 2/5~
& 2/5 ''32 cc
We need more strong decay measurements to pin down spin-
parity assignment
18
Back-up Slides
19
Lifetimes
c+ 44226
c+ 2006
c0 112+13
-10
c0 6912
10-15s
...)(192
)(33
22
03
52
cc
CKMcF
c m
A
m
AAV
mGfB
D+ 10407
Ds+ 5007
D0 410.11.5
heavy quark expansion:
Pauli interference & W-exchange are 1/mc3
corrections, enhanced by p.s. enhancement factor of 162
c decay W-exchange
destructive P.I.
constructive P.I.
20
Dec Ann Int(-)
Int(+) Semi-inclusive
(10-13s) Expt
c+ 1 s2 1 c2 small P.I. 3.68 4.420.26
c+ 1 c2 1 s2 2.64 2.000.06
c0 1 1 1 1 small P.I. 1.93 1.12+0.13
-0.10
c0 1 6s2 10/3c2 large P.I. 1.71 0.690.12
s=sinC, c=cosC
Lifetime hierarchy (c+)>(c
+)>(c0)>(c
0) is qualitatively understandable, but not quantitatively.
It has been claimed that lifetimes can be accommodated (except c
+) provided that hybrid renormalization is employed and replacement of fD by FD is made (Shifman, Blok, Guberina, Bigi…..)
It is difficult to explain (c+)/(c
+)=2.210.15
1/mc expansion is not well convergent and sensible
21
Hadronic weak decays
Complications:
Baryons are made of three quarks
Factorization approximation generally doesn’t work
W-exchange is not subject to helicity & color suppression
Current algebra is no longer applicable as the outgoing meson is
far from being “soft”. Also this soft-meson technique is not
applicable to vector meson production
22
Hadronic weak decays
Diagrammatic scheme (Chau, HYC, Tseng ‘96)
Two distinct internal W emission diagrams, three different W exchange diagrams
Need information of decay asymmetry to extract s-wave and p-wave amplitudes separately
23
Dynamical model calculation
pole model:
Consider low-lying pole contributions:
s-wave is governed by ½- resonances
p-wave is dominated by ½+ ground-state baryons
Relativistic QM: Korner, Kramer, Ivanov,…
iffi uBAuiPBBM )()( 5
24
BRs of Cabibbo-allowed decays
W-exchange plays an essential role
25
Decay asymmetry for Cabibbo-allowed decays
??
Longitudinal pol. of daughter baryon from unpol. parent baryon
⇒ information on the relative sign between s- and p-waves
26
Decay modes that proceed through factorizable diagrams
c+→ p ⇒ |a2|=0.600.10, close to c2
1/Nc is also applicable to charmed baryon sector
c0→-+ ⇒ a1
c0→*0K0 ⇒ a2
27
Charm-flavor-conserving weak decays:
Light quarks undergo weak transitions, while c quark behaves as a “spectator” e.g. cc, c’c
Br(c0c
+-) = 2.9 10-4
Br(c+c
+0) = 6.7 10-4
Br(c0’+
c-)= 4.5 10-6
should be readily accessible soon
28
Semileptonic decays
Semileptonic rate depends on Bc→B form factors
|→ NRQM | RQM LFQM QSR QSR
in units of 1010s-1
Six form factors are reduced to two in mQ limit
29
Weak radiative decays
Charm-flavor-changing
c+→+, c
0→0
Charm-flavor-conserving
c→c, c→c
i) e.m. penguin cu
ii) emission from external quark in W-exchange
emission from W boson in W-exchange
0.86 ,106.3)(
0.86 ,109.4)(500
5
c
c
Br
Br