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Quark dynamics studied in charmed baryons
April 20, 2015 ASRC Seminar 1
Atsushi Hosaka, RCNP, Osaka ASRC Seminar
Contents1. Introduction2. Structure: How ρλ modes appear in the spectrum
3. Charmed baryon productions and decays
Baryons with heavy quark(s) may disentangle light quark dynamics
With Noumi, Shirotori, Kim, Sadato, Yoshida, Oka, Hiyama
1. Introduction
April 20, 2015 ASRC Seminar 2
Quark model and EXOTICS: Now 51 years old
But no colors ~ glues
Fermi Lab
SLAC
LHC
April 20, 2015 ASRC Seminar 3
BES
Quarks bonding differently at LHCb
April 20, 2015 ASRC Seminar 4
http://www.theguardian.com/science/life-and-physics/2014/apr/13/quarks-bonding-differently-at-lhcb
So until last week there were two known types of hadron. ......LHCb has just confirmed what data from other experiments had already led us to suspect. There is a third way.
Phys. Rev. Lett. 112, 222002
Z+(4430)
Z(3900)
Z(4430)
5
X(3872)
Above the threshold qq creation and rearrangement of multiquarks
? ?
• What governs them ?• Constituent quarks, mesons, diquarks ...• Are heavy quarks useful to know it?
2.8
3.0
3.2
3.4
3.6
3.8
4.2
April 20, 2015 ASRC Seminar
Meson-like Diquarks
April 20, 2015 6
2. Charmed baryons
HO and no ss
Degenerate λ and ρ Distinguished
Isotope-shift: Copley-Isgur-Karl, PRD20, 768 (1979)
A heavy quark may distinguish the fundamental modes λ and ρ place to look at diquark correlations
Mixing of
ASRC Seminar
Harmonic oscillator
April 20, 2015 ASRC Seminar 7
x1x2
x3
String
April 20, 2015 ASRC Seminar 8
ρ-mode λ-mode
120°
120°
QCD sum rule
April 20, 2015 ASRC Seminar 9
PRD91, 054034 (2015)
Diquark Density correlations
April 20, 2015 ASRC Seminar 10
Alexandrou, deForcrand, LuciniPRL 97, 222002 (2006)
cosθ 1.0
r
θ
r = 0.69 fm
r = 0.47 fm
r = 0.35 fm
Good diquarkBad diquark
Indicates significant attraction between quarks in good diquark pair
See also recent QCD sum rule study, Chen et alarXiv:1502.01103 [hep-ph], To appear in PRD
S=3/2
S=1/2
1/2+
1/2 –
1/2+
3/2+
1/2–
1/2+
3/2+
3/2 –
5/2+
?
ΞC
[GeV]
?
1/2+
3/2+
ΩC
csq
cssΞC
Ξ’C
1hω
?
1 Ξ+cc
April 20, 2015 ASRC Seminar 11
Spectroscopy: More states at J-PARC
• Excited energies, decay widths are smaller• Two distinct modes may be different
Spectrum and WF's as MQ is varied
April 20, 2015 ASRC Seminar 12
Yoshida, Sadato, Hiyama, Oka, Hosaka
• Model Hamiltonian
• Solved by the Gaussian expansion method
Roberts-Pervin, IJMPA, 23, 2817 (2008)
Excitation spectrum
Σ(1/2+)
Λ(1/2+)
Σ(3/2+) Λ(1/2-, 3/2-)
ΛΣΣ
ΣΛHyperons
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Charmed baryons
Σc(1/2+)
Λc(1/2+)
Σc(3/2+)
Λc(1/2-, 3/2-)
Λc
Σc
Λc
Σc
Σc
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l = 0, ground states
l = 1, excited states
Excitation spectrum
Σ(1/2+)
Λ(1/2+)
Σ(3/2+) Λ(1/2-, 3/2-)
ΛΣΣ
ΣΛ
April 20, 2015 14
Σc(1/2+)
Λc(1/2+)
Σc(3/2+)
Λc(1/2-, 3/2-)
Λc
Σc
Λc
Σc
Σc
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
MQ [GeV/c2]
s cHyperons Charmed baryonsSU(3) HQ
Wave function
April 20, 2015 ASRC Seminar 15
MQ [GeV]
Pro
babi
lity
|c|2
Mixing ofe.g. λ-mode dominant state: How much the other mode mixes?
Λc* is almost
pure λ modeReflect more
qq nature
Λ solid Σ dashed
April 20, 2015 16
SU(3)
spin
Flavor
Orbital
u d
s
u
d
s
. . . ,
To understand better -- Wave functions
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April 20, 2015 17
SU(3)
HQ
To understand better -- Wave functions
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April 20, 2015 18
SU(6)
HQ
mix
To understand better -- Wave functions
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Intermediate summary
April 20, 2015 ASRC Seminar 19
• Heavy quark spectroscopy will reveal uniquely the dynamics of constituents
• Isotope shift may resolve two diquark modes collective and internal
• Λ baryons may have more chance to see the two modes separately
• Systematic study from strange to heavy is needed
3. Productions
April 20, 2015 ASRC Seminar 20
Production rate (Λc/Λ) and Ratios (Bc*/Bc)
π + N D* + Λc reactions
Strategy: Forward peak (high energy) t-channel dominant
We look at:(1) Rates (Λc/Λs) by the Regge model, D* Reggeon
(2) Ratios of Bc*(λ modes) / Bc
by a one step process of Qd picture for λ-mode
21
Pion-induced reactionπ + p D* + Bc
*
π D*
Bc*p
D* Reggeon
April 20, 2015 ASRC Seminar 21
pπ, Lab = 4.5 GeV
cosθ cosθ
1
10
0.1
–1.0 0 +1.0 –1.0 0 +1.0
D.J. Krennel et alPRD6, 1220 (1972)
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Absolute values
April 20, 2015 ASRC Seminar 23
Regge model (Sang-Ho Kim, in preparation)
Charm/strangeness ratio: 10–4 ~ 10–6
several nb near the threshold
strangeness
charm
~ 10–5
We have examined:• K*(strange) productions• D and D* Reggeon• Angular dependence• Small u-channels ~ Baryon Regge• Normalizations
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Effective Lagrangian method
Cross section does not fall off ↔Unitarity
April 20, 2015 ASRC Seminar 25
Vector Reggeon dominance
K(p-scalar)
K*(vector)
• Angular dependence prefers vector-Reggeon• Energy dependence seems• There is some discrepancy in the very forward region
April 20, 2015 ASRC Seminar 26
Relative rates of (Bc*/Bc)
One step process for Qd λ-mode
λ
D*-exchanges
π
Bc*
D* ~ Transverse
= (Geometric) × (Dynamic)CG coefficients
Quark model estimate
N
Dynamical part ~ radial integral
April 20, 2015 ASRC Seminar 27
GS
Transitions to excited states are not suppressed
Excited states
qeff: the momentum transfer ~ Large
Results
Strange kπCM = 1.59 [GeV], kπ
Lab = 5.8 [GeV]
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1.00 0.02 0.16
0.90 1.70 0.02 0.03 0.04 0.19 0.18
0.50 0.88 0.02 0.02 0.01 0.03 0.07 0.07
Charm kπCM = 2.71 [GeV] , kπ
Lab = 16 [GeV]
1.00 0.067 0.44
0.11 0.23 0.007 0.01 0.01 0.07 0.067 0.13 0.20 0.007 0.01 0.004 0.02 0.038 0.04
HQ doublet HQ doublet
l = 1
l = 2l = 0
1 : 2 3 : 2
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4. Decays
April 20, 2015 ASRC Seminar 30
ρ-modeλ-mode
Bc*
Mc
N π
Bc*
Bc
Pion emission – quark model --on going
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Λc*(2595, 1/2–)
Λc*(2625, 3/2–)
Σc(2455, 1/2+)
Σc*(2520, 3/2+)
π
~ 140 MeV
Things to be looked at:• Pion emission ~ very near the threshold
Place to look at the two independent operators
Λc* Σc
*
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Pion emission by the λ motion
Pion emission – quark model --on going
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Diquark correlation may suppress pion emission
λ-mode decayπ
Λc*(2625, 3/2–) π Σc(2455, 1/2+)
overlap vanishes with strong correlation
Σc(2455, 1/2+) + π Λc*(2625, 3/2–)
if
Possible selection rules
April 20, 2015 ASRC Seminar 33
ρ-modes
Two conditions must be satisfied for baryons and for diquarks
Possible selection rules
April 20, 2015 ASRC Seminar 34
Example:
This is a forbidden process
Possible selection rules
April 20, 2015 ASRC Seminar 35
Example:
April 20, 2015 ASRC Seminar 36
Radiative decay: 1/2– 1/2+ E1
λ mode
Good diquark 0+
lλ = 1
3P0 diquark 0–
lρ = 1
ρ mode
0– 0+ is forbidden
Good diquark 0+
April 20, 2015 ASRC Seminar 37
Radiative decay: 5/2– 1/2+ M2, E3
λ mode3S1 diquark 1+
lλ = 1
3P2 diquark 2–
lρ = 1
ρ mode
2– 0+ is only M2
Good diquark 0+
Both M2 E3
Summary• Charmed baryons: yet unexplored region• J-PARC plans to observe them
• Production rate: Charm/Strangeness: 10–4 – 10–6
• Abundant production of excited states
• Decay selection rules are helpful
April 20, 2015 ASRC Seminar 38