Produc'ons	  and	  decays	  of	  charmed	  baryons	  Atsushi	  Hosaka,	  	  	  RCNP,	  Osaka	  	  Progress	  on	  J-­‐PARC	  hadron	  physics	  in	  2014,	  J-­‐PARC	  With Noumi, Shirotori, Kim, Sadato, Yoshida, Oka, Hiyama	Prog.	  Theor.	  Exp.	  Phys.	  (2014)	  103D01	  ρContents	

1. Introduction -- Exotics with heavy quarks	

2. Charmed baryons: to probe ρλ modes diquark 	

3. Productions 	

4. Decays	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

λ1	1. Introduction	
50 year of quarks	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	2	Already proposed by 	

12 year of quarks	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

3	Fermi Lab	SLAC	
LHC	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	  Progress	  on	  J-­‐PARC	  hadron	  4	  Quarks bonding differently at LHCb	
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	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	  Progress	  on	  J-­‐PARC	  hadron	  5	  Zb(10610, 10650)@KEK 2012 1/10	
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。		

Nov.30	  -­‐-­‐	  Dec.1,	  2014	  Progress	  on	  J-­‐PARC	  hadron	  6	  What we expect:
Creation and rearrangement of multiquarks	
N=3qqqq

qqZ(4430)	

qq

4.2	Z(3900)	

N=23.8	
3.6	
N=1X(3872)	

ηc′ψ′χ c0

3.4	
3.2	
N=0
3.0	? ?	

χ c1

χ c2

qq creation (constituent)	

Clustering 	

Meson-like	

Diquarks			 What governs them ?	

JψηcNov.30	  -­‐-­‐	  Dec.1,	  2014	
2.8	

Progress	  on	  J-­‐PARC	  hadron	7	2. Charmed baryons	(6excited)	
14c ＋1cc <<80uds states
Moreat JPARC	[GeV]	

?	
5/2+	?	
?	

1hω	

cqq	

1/2+	

3/2+	

Ξ’C	
1/2+	 ΞC	

1/2+	

csq	

1/2+	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

3/2+	

3/2+	3/2	  –	1/2	  –		  1/2–	ΩC	

S=3/2	

Ground	states	css	ΞC	

S=1/2	

1 Ξ+cc	cqq	Progress	  on	  J-­‐PARC	  hadron	

8	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	ρλFrom hadron to diquark (spectroscopy)	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	9	λ, ρ modes appear in the spectrum	

ρ

ρ=λλ

HO and no ss	ρλλmQ → ∞

mQ = mu,dDegenerate

ρ>λρß Two diquark motions à Distinguished	
Isotope-shift	Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

10	qqQ	  systems	

Quark model calculation	

with spin-spin interaction: 	

Yoshida, Sadato, Hiyama, Oka, Hosaka	

Quark model hamiltonian	
2p1

2p2

2p3

2

P
H=++−2mq 2mq 2M Q 2M tot+ Vconf (HO) + Vspin−spin (Color − magnetic) + ...
Solved by the Gaussian expansion method 	See how systems change as MQ is varied	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

11	

Excitabon	  spectrum	
L=1	  excited	  states:	  spin-­‐spin	  interacbon	
Charmed baryons	Hyperons	Λ	Σ	Λc	Λc	Σc	  Σc	  Σc	  ß l = 1, excited states à	Λ	  Σ	  Σ	  Λ(1/2-,	  3/2-)	
Σ(3/2+)	  	Λc(1/2-,	  3/2-)	
Σc(3/2+)	  	Σ(1/2+)	  	ß l = 0, ground states à	Λ(1/2+)	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	Σc(1/2+)	  	Λc(1/2+)	

Progress	  on	  J-­‐PARC	  hadron	

12	

Excitabon	  spectrum	
L=1	  excited	  states:	  spin-­‐spin	  interacbon	
Hyperons	Λ	Σ	Λ	  Σ	  Σ	  0.8s	c	Charmed baryons	

0.7

Λc	0.6Λc	

Σc	  Σc	  Σc	  0.5Λ(1/2-,	  3/2-)	
Σ(3/2+)	  	0.4Λc(1/2-,	  3/2-)	

0.3

Σc(3/2+)	  	0.2Σ(1/2+)	  	Λ(1/2+)	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	Σc(1/2+)	  	0.100 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5M 	  [GeV/c2]	

Progress	  on	  J-­‐PARC	  Q hadron	Λc(1/2+)	
13	

Excitabon	  spectrum	
L=1	  excited	  states:	  spin-­‐spin	  interacbon	
Hyperons	Λ	Σ	Λ	  Σ	  Σ	  0.8s	SU(3)	

c	HQ	

Charmed baryons	

0.7

Λc	0.6Λc	Σc	  Σc	  Σc	  0.5Λ(1/2-,	  3/2-)	
Σ(3/2+)	  	0.4Λc(1/2-,	  3/2-)	

0.3

Σc(3/2+)	  	0.2Σ(1/2+)	  	Λ(1/2+)	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	Σc(1/2+)	  	0.100 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5M 	  [GeV/c2]	

Progress	  on	  J-­‐PARC	  Q hadron	Λc(1/2+)	
14	

Wave	  funcbon	
22
Λ(phys)=c
Λ(λ)+cΛ(ρ)
Mixing of	λρe.g. λ-mode dominant state: How much the other mode mixes? 	

Probability |c|2	1| cλ (Λ(1 / 2 − )) |20.8

Λc* is almost 	

| cλ (Σ(1 / 2 − ))pure|2 λ mode	è	

mud = 300 MeV	
more	| cρ (Σ(1 / 2 − ))Reflect|2diquark nature	

0.6
0.4
0.2−2|c(Λ(1/2))|ρSU(3) limit	

00
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

0.5

1

1.5on	  J-­‐PARC	  hadron	mQProgress	  [GeV]	

215	

3.	  Charmed baryon
Productions	π + N à D* + Λc reactions 	
Production rate (Λc/Λ) and Ratios (Bc*/Bc) 	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

16	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	π	D*	Pion-induced reaction	

π + p  D* + Bc*	q( p )D* Reggeon	p	 diAPS-­‐JPS	  joint	  meebng	  	Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	c( p f )Bc*	

17	17	

−π p → ΛKdσ
[ µb / sr]dΩ*0

π − p → ΣK *0pπ, Lab = 4.5 GeV	 10	D.J. Krennel et al	

PRD6, 1220 (1972)	
1	0.1	
–1.0
Nov.30	  -­‐-­‐	  Dec.1,	  2014	0cosθ	+1.0	

Progress	  on	  J-­‐PARC	  hadron	–1.00cosθ	+1.0	18	

Absolute values	
Regge model ~ Sang-Ho Kim's talk 	
strangeness	
10–2	
charm	

10–5	–2 ~ 10–5 	
Charm/strangenessproductions:10Nov.30	  -­‐-­‐	  Dec.1,	  2014	
Progress	  on	  J-­‐PARC	  hadron	

19	

Relative rates of (Bc*/Bc) One step process of Qd pictire	

Kim	  et	  al,	  PTEP	  (2014)	  103D01	  *π	DV-exchanges 	q( pi )c( p f )λ	Bc*	d  t fi ~ kπ × e ⋅ J fi iqeff ⋅x*~ Bc e⊥ ⋅ σ eN = (Geometric) × (Dynamic)	
Transverse	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

CG coefficients	

Progress	  on	  J-­‐PARC	  hadron	20	

Dynamical	  part	  ~	  radial	  integral	
qeff: the momentum transfer ~ Large	c( p f )q( pi )dGS	 Bc (S-wave) e⊥ ⋅ σ e

Excited states	 
Bc (P-wave) e⊥ ⋅ σ e iqeff ⋅x

2 ⎞⎛ qeffN(S-wave) radial ~ 1× exp ⎜ − 2 ⎟⎝ 4A ⎠ iqeff ⋅x

12 ⎞⎛
qq
⎛ eff ⎞eff
N(S-wave) radial ~ ⎜×exp−⎜2⎟⎝ A ⎟⎠⎝ 4A ⎠ iqeff ⋅x2 ⎞⎛ qeff
⎛ qeff ⎞N(S-wave) radial ~ ⎜× exp ⎜ − 2 ⎟⎟⎝ A ⎠⎝ 4A ⎠ 
Bc (D-wave) e⊥ ⋅ σ e

2Transitions to excited states are not suppressed	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

21	Results	
Charm	 kπCM = 2.71 [GeV] , kπLab = 16 [GeV] 	
1.00	  	  	  	  	  	  	  	  0.02	  	  	  	  	  	  	  	  0.16	  	  	  	  	  0.90	  	  	  	  	  	  	  	  1.70	  	  	  	  	  	  	  	  0.02	  	  	  	  	  	  	  	  0.03	  	  	  	  	  	  	  0.04	  	  	  	  	  	  	  0.19	  	  	  	  	  	  	  0.18	  	  	  	  	  Nov.30	  -­‐-­‐	  0.50	  Dec.1,	  2014	
-­‐PARC	  h	  adron		  	  	  	  	  	  	  0.88	  	  	  	  	  	  	  	  0.02	  Progress	  	  	  	  	  	  	  	  o0n	  J.02	  	  	  	  	  	  0.01	  	  	  	  	  	  	  	  0.03	  	  	  	  	  	  0.07	  	  	  	  	  	  022	.07	Strange	 kπCM = 1.59 [GeV], kπLab = 5.8 [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 	 HQ doublet	
1 / 2+

l = 0	

1 / 2−

3 / 2−l = 1	

1 : 2	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	

HQ doublet	
3 / 2+

5 / 2+

l = 2	

3 : 2	23	Meson analogue 	π	c( p f )q( pi )
dD*r	

λ	Bc	

How similar the λ baryon mode and r meson mode?	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	24	

4.	  Charmed	  baryon	  decays	
λ-mode	ρ-mode	N	
Bc*	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Mc	

Progress	  on	  J-­‐PARC	  hadron	π	Bc*	
Bc	 25	Chiral dynamics 	

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)	

⎛ i  ⎞U = exp ⎜ τ ⋅ π ⎟ , U → gLUgR†⎝f⎠π⎛ i  ⎞††ξ = exp ⎜τ ⋅ π ⎟ , ξ → gLξ h = hξ g L , h = h(gL , gR , π )
⎝2f
⎠
π()

i †vµ , a µ = ξ ∂ µ ξ ± ξ ∂ µ ξ †2
N → ξ N, Dµ N ≡ (∂ µ − ivµ )N → ξ Dµ N••••Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	26	Linear	  descripbon	
Again by S. Weinberg, 	

Algebraic realization, Phys.Rev.177, 2604 (1969)	

Mended symmetries, PRL65, 1177 (1990)	
• Assign chiral representations to hadrons		

1+ γ 51 , 0 ⊕ 0, 1 ; NN~→
gN,N=( 2 ) ( 2 ) L,R L,R L,R L,R 2 N		(σ , π ) ~ ( 12 , 12 ) , ( ρ , a1 ) ~ (1, 0 ) ⊕ ( 0, 1)	

• Then write a chiral invariant Lagrangian terms	 	†N UN + N U N = N (σ + iτ ⋅ πγ ) NL	RRL

5etc	

Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	27	

Meson-­‐baryon	  coupling	Light meson
NucleonHeavy meson (quark)Heavy baryon (diquark)Diquark
S qq
P qγ 5 q
V qγ µ q
qγγ
τµ 5 q
AT qσ µν γ 5τ qqq(½, ½) 	

qqq (½, 0), (1, ½) 	Qq(½, 0)	

Qqq (0, 0), (½, ½), (1, 0)

JP

ChiralIsospin

00+(0, 0)

0Λ, Λ*(λ)	

0

0–(0, 0)

0

Λ*(ρ)	

3P1

1–(½, ½)

0

Λ*(ρ)	

1

1+(½, ½)

1

Σ, Σ*(λ)	

1+, 1–(1, 0)

1

Σ, Σ*(ρ)	

1S
3P

3S

3D , 1P
11

Baryons	q = T qiγ 0γ 2γ 5iτ 2Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	28		Bc* à π Bc	
π Bc* 	B	 c[1] (0, 0)[2] (½, ½)[3] (1, 0)(½, ½)×(0, 0) (½, ½)×(½, ½)
--OK
---

OK--OK(½, ½)×(0, 1)	

---	

OK	

---	

[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	29	Bc* à Mc N(½,0), (1,½)	
Bc*		

Mc N

[1] (0, 0)[2] (½, ½)[3] (1, 0)(0, ½)×(0, ½)(0, ½)×(½, 1)	

OK-------OKOK			

[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	
Nov.30	  -­‐-­‐	  Dec.1,	  2014	

Progress	  on	  J-­‐PARC	  hadron	30	

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