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λ
ρ
Produc'ons and decays of charmed baryons
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 1
Atsushi Hosaka, RCNP, Osaka Progress on J-‐PARC hadron physics in 2014, J-‐PARC
Contents 1. Introduction -- Exotics with heavy quarks 2. Charmed baryons: to probe ρλ modes diquark 3. Productions 4. Decays
With Noumi, Shirotori, Kim, Sadato, Yoshida, Oka, Hiyama Prog. Theor. Exp. Phys. (2014) 103D01
1. Introduction
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 2
50 year of quarks
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 3
Already proposed by
12 year of quarks
Fermi Lab
SLAC
LHC
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 4
Quarks bonding differently at LHCb
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 5
hJp://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. LeJ. 112, 222002
Zb(10610, 10650)@KEK 2012 1/10
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 6
Bファクトリー実験において、ボトム・クォークを含む新種のハドロン粒子を発見した。この新粒子は電荷を持ち、4個以上のクォークが結合してできたハドロン粒子と考えられる。... 今回の発見は、4個以上のクォークが結合したエキゾチックハドロンが、ボトム・クォークを含む粒子系にも存在することを明らかに示したものである。
Z(3900)
Z(4430)
7
X(3872)
qq qq
What we expect: Creation and rearrangement of multiquarks
ηc
′ηc
J ψ
′ψ
χc0χc1
χc2
N=0
N=1
N=2
N=3 qqqq
? ?
creation (constituent) Clustering Meson-like Diquarks
What governs them ? 2.8
3.0
3.2
3.4
3.6
3.8
4.2
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron
S=3/2
S=1/2
14c +1cc << 80uds (6excited)
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
cqq cqq
csq
css ΞC
Ξ’C
1hω
?
1 Ξ+cc
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 8
Ground states
More states at JPARC
2. Charmed baryons
What do we expect for heavy quarks?
• Qqq distinguishes the two modes of λ and ρ Diquark motions in the baryon mass spectrum • It could expose light flavor (chiral) dynamics
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 9
From hadron to diquark (spectroscopy)
λ
ρ
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 10
λ, ρ modes appear in the spectrum
λ
ρρ > λ
λ
ρ ρ = λ
HO and no ss λ
ρ
Degenerate ß Two diquark motions à Distinguished Isotope-shift
mQ = mu,d mQ →∞
qqQ systems
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 11
Quark model calculation with spin-spin interaction: Yoshida, Sadato, Hiyama, Oka, Hosaka
Quark model hamiltonian
H = p12
2mq+ p2
2
2mq+ p3
2
2MQ− P2
2Mtot
+Vconf (HO)+Vspin−spin (Color −magnetic)+ ...Solved by the Gaussian expansion method
See how systems change as MQ is varied
Excitabon spectrum
Σ(1/2+)
Λ(1/2+)
Σ(3/2+) Λ(1/2-, 3/2-)
Λ Σ Σ
Σ Λ
Hyperons
Nov.30 -‐-‐ Dec.1, 2014 12
Charmed baryons
Σc(1/2+)
Λc(1/2+)
Σc(3/2+)
Λc(1/2-, 3/2-)
Λc
Σc
Λc
Σc
Σc
L=1 excited states: spin-‐spin interacbon
Progress on J-‐PARC hadron
ß l = 0, ground states à
ß l = 1, excited states à
Excitabon spectrum
Σ(1/2+)
Λ(1/2+)
Σ(3/2+) Λ(1/2-, 3/2-)
Λ Σ Σ
Σ Λ
Hyperons
Nov.30 -‐-‐ Dec.1, 2014 13
Charmed baryons
Σc(1/2+)
Λc(1/2+)
Σc(3/2+)
Λc(1/2-, 3/2-)
Λc
Σc
Λc
Σc
Σc
L=1 excited states: spin-‐spin interacbon
Progress on J-‐PARC hadron
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 MQ [GeV/c2]
s c
Excitabon spectrum
Σ(1/2+)
Λ(1/2+)
Σ(3/2+) Λ(1/2-, 3/2-)
Λ Σ Σ
Σ Λ
Hyperons
Nov.30 -‐-‐ Dec.1, 2014 14
Charmed baryons
Σc(1/2+)
Λc(1/2+)
Σc(3/2+)
Λc(1/2-, 3/2-)
Λc
Σc
Λc
Σc
Σc
L=1 excited states: spin-‐spin interacbon
Progress on J-‐PARC hadron
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 MQ [GeV/c2]
s c SU(3) HQ
Wave funcbon
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron
15 mQ [GeV]
mud = 300 MeV
Prob
abili
ty |c
|2 Mixing of
e.g. λ-mode dominant state: How much the other mode mixes? Λ(phys) = cλΛ(
2λ)+ cρΛ(2 ρ)
| cλ (Λ(1 / 2− )) |2
| cλ (Σ(1 / 2− )) |2
| cρ (Λ(1 / 2− )) |2
| cρ (Σ(1 / 2− )) |2
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2
SU(3) limit
Λc* is almost
pure λ mode è Reflect more diquark nature
3. Charmed baryon Productions
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 16
Production rate (Λc/Λ) and Ratios (Bc*/Bc)
π + N à D* + Λc reactions
Strategy: At high energies: Forward peak à t-channel dominant Theory: • Rates (Λc/Λ) by the Regge model, D* Reggeon • Relative ratios of (Bc
*(λ modes)/Bc) by a One step process of Qd picture
APS-‐JPS joint meebng 17 d
q(pi ) c(p f )Pion-induced reaction π + p D* + Bc
*
π D*
Bc* p
D* Reggeon
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 17
pπ, Lab = 4.5 GeV
π − p→ΛK*0 π − p→ ΣK*0
cosθ cosθ
1
10
0.1 –1.0 0 +1.0 –1.0 0 +1.0
dσdΩ[µb / sr]
D.J. Krennel et al PRD6, 1220 (1972)
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 18
Absolute values
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 19
Regge model ~ Sang-Ho Kim's talk
strangeness
charm
10–2
10–5
Charm/strangeness productions: 10–2 ~ 10–5
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 20
Relative rates of (Bc*/Bc) ���
One step process of Qd pictire
t fi ~kπ × e ⋅
J fi
~ Bc* e⊥ ⋅
σ ei
qeff ⋅x N
Transverse = (Geometric) × (Dynamic) CG coefficients
d
q(pi ) c(p f )λ
V-exchanges
D*π
Bc*
Kim et al, PTEP (2014) 103D01
Dynamical part ~ radial integral
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 21
GS
Transitions to excited states are not suppressed
Bc(S-wave)
e⊥ ⋅σ ei
qeff ⋅x N (S-wave) radial ~1× exp −
qeff2
4A2⎛
⎝⎜
⎞
⎠⎟
Bc(P-wave)
e⊥ ⋅σ ei
qeff ⋅x N (S-wave) radial ~
qeffA
⎛⎝⎜
⎞⎠⎟
1
× exp −qeff2
4A2⎛
⎝⎜
⎞
⎠⎟
Bc(D-wave)
e⊥ ⋅σ ei
qeff ⋅x N (S-wave) radial ~
qeffA
⎛⎝⎜
⎞⎠⎟
2
× exp −qeff2
4A2⎛
⎝⎜
⎞
⎠⎟
Excited states
d
q(pi ) c(p f )qeff: the momentum transfer ~ Large
Results
Strange kπCM = 1.59 [GeV], kπLab = 5.8 [GeV]
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 22
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] , kπLab = 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
Yasui's talk, wed à 1/ 2+ 1/ 2− 3 / 2− 3 / 2+ 5 / 2+
HQ doublet HQ doublet
l = 1 l = 2 l = 0
1 : 2 3 : 2
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 23
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 24
Meson analogue
d
q(pi ) c(p f )
D*π
Bc λ
r
How similar the λ baryon mode and r meson mode?
4. Charmed baryon decays
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 25
ρ-mode λ-mode
Bc*
Mc
N π
Bc*
Bc
Chiral dynamics
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 26
Spontaneously broken = SU(2)L x SU(2)R à SU(2)V Non-linear realization with only ispsoin symmetry S. Weinberg, Phys.Rev.166, 1568 (1968)
U = exp ifπ
τ ⋅ π⎛⎝⎜
⎞⎠⎟, U→ gLUgR
†
ξ = exp i2 fπ
τ ⋅ π⎛⎝⎜
⎞⎠⎟, ξ → gLξh
† = hξg†L , h = h(gL ,gR ,π )
vµ , aµ = i2
ξ† ∂µξ ±ξ ∂µξ†( )
N→ξN , DµN ≡ (∂µ− ivµ )N→ξDµN• • • •
Linear descripbon
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 27
Again by S. Weinberg, Algebraic realization, Phys.Rev.177, 2604 (1969) Mended symmetries, PRL65, 1177 (1990)
• Assign chiral representations to hadrons • Then write a chiral invariant Lagrangian terms
etc
N ~ 12 , 0( )⊕ 0, 12( ); NL,R → gL,RNL,R , NL,R = 1+ γ 5
2N
(σ , π ) ~ 12 ,
12( ), (ρ, a1) ~ 1, 0( )⊕ 0,1( )
NLUNR + NRU†NL = N σ + iτ ⋅ πγ 5( )N
Meson-‐baryon coupling
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 28
Light meson qq (½, ½) Nucleon qqq (½, 0), (1, ½) Heavy meson (quark) Qq (½, 0) Heavy baryon (diquark) Qqq (0, 0), (½, ½), (1, 0)
Diquark JP Chiral Isospin Baryons S 1S0 0+ (0, 0) 0 Λ, Λ*(λ) P 3P0 0– (0, 0) 0 Λ*(ρ) V 3P1 1– (½, ½) 0 Λ*(ρ) A 3S1 1+ (½, ½) 1 Σ, Σ*(λ) T 3D1, 1P1 1+, 1– (1, 0) 1 Σ, Σ*(ρ)
qqqγ 5qqγ µqqγ µγ 5
τ qqσ µνγ 5
τ q
q =T qiγ 0γ 2γ 5iτ 2
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 29
Bc* à π Bc
π Bc (½, ½)×(0, 0) (½, ½)×(½, ½) (½, ½)×(0, 1) [1] (0, 0) --- OK --- [2] (½, ½) OK --- OK [3] (1, 0) --- OK ---
Bc*
[1] Λ*(λ) à πΣ [2] Λ*(ρ), Σ*(λ) à πΛ, πΣ, these are related [3] Σ*(ρ) à πΛ, πΣ
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 30
Bc* à Mc N(½,0), (1,½)
Mc N (0, ½)×(0, ½) (0, ½)×(½, 1) [1] (0, 0) OK --- [2] (½, ½) --- OK [3] (1, 0) --- OK
Bc*
[1] Λ*(λ) à KN [2] Λ*(ρ), Σ*(λ) à KN [3] Σ*(ρ) à KN
• Chiral selection rules may explain small widths • explore more on the nucleon
Summary • Evidences of new mulbquark configurabons è Molecule + ... • To pin down the dynamics, J-‐PARC will help
• ρ and λ modes are disbnct (Isotope shin) beJer in Λ than in Σ à can we approach di-‐quark ? • Systemabc study in strangeness is important
• Higher excited (Λ) states may be produced as many as the ground states, analogue for mesons • Chiral selecbon rules may be relevant to small width
• More on the chiral structure of the nucleon
Nov.30 -‐-‐ Dec.1, 2014 Progress on J-‐PARC hadron 31