Charmed	  baryons	  -­‐	  Structure,	  produc5ons	  and	  decays	  -­‐	  	  Atsushi	  Hosaka,	  	  	  RCNP,	  Osaka	  	  HHIQCD	  -­‐	  symposium,	  YITP,	  Kyoto,	  2/15-­‐3/21	  With Noumi, Shirotori, Kim, Sadato, Yoshida, Oka, 	Hiyama, Yasui, Nagahiro	

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	
Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	

λ1	

1. Introduction	
Quark model and EXOTICS: Now 51 years old	Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	

2	

Fermi Lab	

SLAC	
LHC	

Feb.16	  -­‐	  Mar.21,	  2015	  HHIQCD,	  YITP	  3	  Quarks bonding differently at LHCb	
Z+(4430)	
hOp://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.	  LeO.	  112,	  222002	

Feb.16	  -­‐	  Mar.21,	  2015	  HHIQCD,	  YITP	  4	  EXOTIC threshold (and above)

qq creation and rearrangement of multiquarks	
Meson-like	
N=3Diquarks	

qqZ(4430)	

qq

4.2	
Z(3900)	

N=2

3.8	
3.6	
N=1? ?	

X(3872)	

ηc′ψ′
χ c0

3.4	
3.2	
N=0
3.0	

qqqq

χ c1

χ c2

• What governs them ?	

• Are heavy quarks 	

useful to know it?	

• Constituent quarks,	

mesons, diquarks ...	

JψηcFeb.16	  -­‐	  Mar.21,	  2015	
2.8	

HHIQCD,	  YITP	

5	2. Charmed baryons	(6excitedat)	 J-PARC	

More states[GeV]	?	
5/2+	?	
?	

1hω	cqq	

1/2+	3/2+	

Ξ’C	
1/2+	 ΞC	

1/2+	csq	

1/2+	

Feb.16	  -­‐	  Mar.21,	  2015	

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	

HHIQCD,	  YITP	

6	

Qqq distinguishes the fundamental modes	

λ and ρ è place to look at diquarks 	

Isotope-shift	ρρ=λλHO and no ss	

ρ>λ

ρ

ρ

λ

λmQ → ∞

mQ = mu,dDegenerate

λ and ρFeb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	Distinguished	
7	Quark model calculation	

Yoshida, Sadato, Hiyama, Oka, Hosaka	• Model Hamiltonian	
2p12p22p32

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	
Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	

8	

Excitadon	  spectrum	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+)	
Feb.16	  -­‐	  Mar.21,	  2015	Σc(1/2+)	  	Λc(1/2+)	

HHIQCD,	  YITP	

9	

Excitadon	  spectrum	
Hyperons	Λ	Σ	Λ	  Σ	  Σ	  0.8s	c	Charmed baryons	

0.7

Λc	

0.6

Λc	

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+)	
Feb.16	  -­‐	  Mar.21,	  2015	Σc(1/2+)	  	0.1
00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5M 	  [GeV/c2]	

HHIQCD,	  Q
YITP	Λc(1/2+)	
10	

Excitadon	  spectrum	
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+)	
Feb.16	  -­‐	  Mar.21,	  2015	Σc(1/2+)	  	0.1
00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5M 	  [GeV/c2]	

HHIQCD,	  Q
YITP	Λc(1/2+)	
11	

Wave	  funcdon	
22
Λ(phys)=cΛ(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| cλ (Σ(1 / 2 − )) |20.6

mud = 300 MeV	
0.4

| cρ (Σ(1 / 2 − )) |20.2−2|c(Λ(1/2))|ρSU(3) limit	

00Feb.16	  -­‐	  Mar.21,	  2015	

0.5

11.5

HHIQCD,	  YITP	mQ [GeV]	

212	

Wave	  funcdon	
22Λ(phys)=cΛ(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 − )) |2pure λ mode	è	mud = 300 MeV	| cρ (Σ(1 / 2 − )) |2Reflect more	qqnature	−
2

0.6
0.4
0.2

SU(3) limit	| cρ (Λ(1 / 2 )) |00Feb.16	  -­‐	  Mar.21,	  2015	

0.5

1

1.5

HHIQCD,	  YITP	mQ [GeV]	

213	

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

Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	

14	

Strategy: 	

Forward peak (high energy) à t-channel dominant		

We look at:	• Rates (Λc/Λ) by the Regge model, D* Reggeon	• Relative ratios of Bc*(λ modes) / Bc 	by a one step process of Qd picture for λ-mode	π	D*	

Pion-induced reaction	

π + p  D* + Bc*	q( p )D* Reggeon	

p	 dFeb.16	  -­‐	  Mar.21,	  2015	iHHIQCD,	  YITP	c( p f )Bc*	

15	15	

−dσ
[ µb / sr]dΩπ p → ΛK

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

PRD6, 1220 (1972)	
1	0.1	
–1.0
Feb.16	  -­‐	  Mar.21,	  2015	

0cosθ	HHIQCD,	  YITP	

+1.0	

–1.00

cosθ	+1.0	16	Absolute values	
Regge model (Sang-Ho Kim, in preparation) 	

We have examined:	

• K*(strange) productions	• D and D* Reggeon	• Angular dependence	• u-channels 	

~ Baryon Regge	• Normalizations	

~ 10–5	

strangeness	
charm	

Charm/strangeness ratio: 10–4 ~ 10–6	

nearYITP	the threshold	Feb.16	  -­‐	  Mar.21,	  2015	 è several nb HHIQCD,	  17	

Relative rates of (Bc*/Bc) One step process for Qd λ-mode	π	D*D*-exchanges 	q( pi )
N	dc( p f )λ	Bc*	

Quark model estimate	  t fi ~ kπ × e ⋅ J fi iq*eff ⋅x~ Bc e⊥ ⋅ σ e
N = (Geometric) × (Dynamic)	
D* ~ Transverse	

Feb.16	  -­‐	  Mar.21,	  2015	

CG coefficients	

HHIQCD,	  YITP	18	

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 ⋅x2 ⎞⎛ qeffN(S-wave) radial ~ 1× exp ⎜ − 2 ⎟⎝ 4A ⎠ iqeff ⋅x

12 ⎞⎛qq⎛ eff ⎞eff
N(S-wave) radial ~ ⎜×exp−⎜2⎟⎝ A ⎟⎠⎝ 4A ⎠ iqeff ⋅x

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

2Transitions to excited states are not suppressed	

Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	19	

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	  	  	  	  	  Feb.16	  -­‐	  Mar.21,	  2015	
YITP	0.50	  	  	  	  	  	  	  	  0.88	  	  	  	  	  	  	  	  0.02	  	  	  	  	  HHIQCD,	  	  	  	  0.02	  	  	  	  	  	  	  0.01	  	  	  	  	  	  	  	  0.03	  	  	  	  	  	  0.07	  	  	  	  	  	  020	.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	

HQ doublet	
1 / 2+

l = 0	

1 / 2−

3 / 2−

l = 1	

1 : 2	

Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	HQ doublet	
3 / 2+

5 / 2+

l = 2	

3 : 2	21	

4.	  Decays	
λ-mode	ρ-mode	N	
Bc*	
Feb.16	  -­‐	  Mar.21,	  2015	

Mc	π	
Bc*	
HHIQCD,	  YITP	

Bc	 22	

Pion	  emission	  –	  quark	  model	  -­‐-­‐on	  going	
Things to be looked at:	• Pion emission ~ very near the threshold	• D-meson emission ~ The coupling of D-meson to cq	

Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	23	

Pion	  emission	  –	  quark	  model	  -­‐-­‐on	  going	
Things to be looked at:	• Pion emission ~ very near the threshold	π	

Λc*(2625, 3/2–)	
Λc*(2595, 1/2–)	

Σc*(2520, 3/2+)	

~ 140 MeV	Σc(2455, 1/2+)	

Place to look at the two independent operators	 
qγ 5 qφπ , qγ µγ 5 q ∂ µ φπ
     σ ⋅ pi , σ ⋅ p f (σ ⋅ q)
Feb.16	  -­‐	  Mar.21,	  2015	

Λc*	
HHIQCD,	  YITP	

piq
pf

Σc*	
24	

Pion	  emission	  –	  quark	  model	  -­‐-­‐on	  going	
Diquark correlation may suppress pion emission	π	λ-mode decay	λΛc*(2625, 3/2–)

π Σc(2455, 1/2+) 	

overlap vanishes 	with strong correlation	

′	Feb.16	  -­‐	  Mar.21,	  2015	Σc(2455, 1/2+) + π ß
Λc*(2625, 3/2–) 	
YITP	
25	
PionHHIQCD,	  emission
by the λ motion	

Radiative decay: 1/2– à 1/2+ E1 	λ mode	ρ mode	Good diquark 0+	

3P0 diquark 0–	lρ = 1	lλ = 1	0– à 0+ is 	forbidden	
Good diquark 0+	

05/11,	  2013	

JPARC-­‐discussions	26	

Radiative decay: 5/2– à 1/2+ M2, E3 	λ mode	3Sρ mode	+	diquark
1
13P–	diquark
22lρ = 1	
lλ = 1	Both M2 E3	

2– à 0+ is 	

only M2	

Good diquark 0+	

05/11,	  2013	

JPARC-­‐discussions	27	Summary	•	  Charmed	  baryons:	  yet	  unexplored	  states	  •	  J-­‐PARC	  plans	  to	  observe	  them	  •	  ρ	  and	  λ	  modes	  are	  disdnct	  (Isotope	  shin)	  	  	  	  beOer	  chance	  to	  look	  at	  in	  Λ*	  than	  in	  Σ*	  	  à	  diquarks	  •	  Systemadc	  study	  in	  strangeness	  is	  important	  •	  Higher	  excited	  (Λ)	  states	  may	  be	  produced	  a	  lot	  •	  Pion	  decay	  provides	  unique	  opportunity	  •	  Radiadve	  decay	  selecdon	  rules	  are	  also	  helpful	  Feb.16	  -­‐	  Mar.21,	  2015	

HHIQCD,	  YITP	

28