Quark dynamics studied in charmed baryons April 20, 2015ASRC Seminar1 Atsushi Hosaka, RCNP, Osaka...

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

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Quark model and EXOTICS: Now 51 years old

But no colors ~ glues

Fermi Lab

SLAC

LHC

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BES

Quarks bonding differently at LHCb

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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

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Meson-like Diquarks

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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

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Harmonic oscillator

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x1x2

x3

String

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ρ-mode λ-mode

120°

120°

QCD sum rule

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PRD91, 054034 (2015)

Diquark Density correlations

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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

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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

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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

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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

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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

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SU(3)

spin

Flavor

Orbital

u d

s

u

d

s

. . . ,

To understand better -- Wave functions

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SU(3)

HQ

To understand better -- Wave functions

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SU(6)

HQ

mix

To understand better -- Wave functions

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Intermediate summary

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• 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

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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

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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

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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

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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

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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

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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

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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

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ρ-modes

Two conditions must be satisfied for baryons and for diquarks

Possible selection rules

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Example:

This is a forbidden process

Possible selection rules

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Example:

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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+

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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

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