How are hadrons formed from quarks?
Transcript of How are hadrons formed from quarks?
1
How are hadrons formed from quarks?
Hiroyuki NoumiRCNP, Osaka University
Institute of Particle and Nuclear Studies, KEK
Seminar at RCNP, Osaka University7- 9March, 2019
Part I: Introduction
Part II: Experimental Study of Hadrons
II-1: ฮ๏ผ1405๏ผ and KbarN Interaction
II-2: Charmed Baryons
Contents
Part I: Introduction
I-1: Standing Point of this Lecture
I-2: Basic Introduction of Hadrons
Part II: Experimental Study of Hadrons
II-1: ฮ๏ผ1405๏ผ and KbarN Interaction
II-2: Charmed Baryon and diquark correlation
2
Contents
Part I: Introduction
I-1: Standing Point of this Lecture
I-2: Basic Introduction of Hadrons
Part II: Experimental Study of Hadrons
II-1: ฮ๏ผ1405๏ผ and KbarN Interaction
II-2: Charmed Baryon and diquark correlation
3
4
Dense Nucl. Matter
How does Matter Evolve in the Universe?- Roles of the Strong Int. -
Quark
Nucleus
QCD
BB Int. ๏ผ2BF, 3BF, โฆ๏ผBB scattering, Nuclear Structure
Nuclear Matter: EoSNuclear Response, Single Particle Energy
Nuclear SynthesisMagic No., Drip-line, S.H.E.,โฆ
Q Hadron
AtomโMoleculeโStarโGalaxyโUniverse
Mystery of Heavy NS: NS Merger as a Factory of H.E.
QCD dynamicsQGP at High-T, High-rho, Phase Border
Form of HadronHadron Spectroscopy, TomographyHadron at High-T, High-rho
How Hadrons are formed?
9
๐ผ๐ = โat LQCD
High E Low E
Quarks drastically change themselves below LQCD.
Meson
Baryon
How Hadrons are formed?
10
๐ผ๐ = โat LQCD
High E Low E
Quarks drastically change themselves below LQCD.
Meson
Baryon
How Hadrons are formed?
11
High E Low E
Meson
Baryon
โEffective DoFโ
โConstituent Quarksโ seem to work rather wellas good building blocks of hadronsโฆ
How Hadrons are formed?
12
High E Low E
Meson
Baryon
โEffective DoFโ
โConstituent Quarksโ seem to work rather wellas good building blocks of hadronsโฆ Saturation of โEffective Chargeโ at low k.
(PRD96,054026(2017)
How Hadrons are formed?
13
High E Low E
Pentaquark?
Tetraquark?
โEffective DoFโ
โExotic hadronsโ require a new aspectin describing hadrons beyond the โstandard pictureโ.
15
Hadron Physics at J-PARC
๐ผ๐ = โat LQCD
High E Low E
How are they excited?
How do they change properties in medium?
Quasi-Particles (= Effective DoF) emerging at Low E describe hadron properties effectively.
16
What are good building blocks of Hadrons?
Constituent Quarkq
q
q
Diquark?[qq]
q(Colored cluster)
hadron (colorless cluster)
q
q
q
Contents
Part I: Introduction
I-1: Standing Point of this Lecture
I-2: Basic Introduction of Hadrons
Part II: Experimental Study of Hadrons
II-1: ฮ๏ผ1405๏ผ and KbarN Interaction
II-2: Charmed Baryon and diquark correlation
17
Classification of Hadrons
18
Observable Relevant Physics Quantity What we learn
Mass Spectrum Mass, Width(pole:๐๐ โ ๐ฮ/2)
Particle stateResonant state
Classification
Angular Correl.(decay)
Spin, Parity
In 1964 Quark ModelM. Gell-mann๏ผNobel Prize in 1969๏ผG. Zweig
Baryon Family Meson Family
IntroducedFractional electric chargeColor charge
๐ + ๐ + ๐ ๐ + เดค๐
Hadron
QuantumChromoDynamics
ntnm
t
b
t
c
s
m
u
d
ne
e
g
g
Z, Wยฑ
๏ผG๏ผ
Quark
Lepton
Gauge Boson
Strong
Electro-magnetic
Weak
gravity
+2/3
-1/3
-1
0
charge
Elementary particle Mediating โForceโ
+Anti-particle๏ผopposite charge, same mass๏ผ
Higgs
Why are quarks confined๏ผ
โข Force independent in a distance (Linear Potential)
โข Coulomb-like in a close distance (1/r Potential)
โข Cornel Potential: V=ar-b/r
๐ เดค๐
How are quarks confined๏ผ
โข Force independent in a distance (Linear Potential)
โข Coulomb-like in a close distance (1/r Potential)
โข Cornell Potential: V=ar-b/r
๐ เดค๐
Form of Hadrons
Observable Relevant Physics Quantity What we learn
Mass Spectrum Mass, Width(pole:๐๐ โ ๐ฮ/2)
Particle stateResonant state
Classification
Angular Correl.(decay)
Spin, Parity
Level structure Internal (effective) DoF Form(Dynamics of effective DoFin Hadron)
Production Rate(Diff. Cross Sect.)
Response Function(Transition) Form Factor
Reaction MechanismInternal Motion/Corr.
Partial Width Internal Correlation(Wave function)
Decay MechanismInternal Motion/Corr.
32
How Hadrons are formed?
33
๐ผ๐ = โat LQCD
High E Low E
Quarks drastically change themselves below LQCD.
Meson
Baryon
Quark Mass
34
1 MeV 1 GeV 1 TeVLQCD
u d s c b tโBearโQuark
(E>>LQCD)
โDressedโQuark
(E<LQCD) u d sc b t
Proton(uud)
Wยฑ
Z
Heavy QuarkLight Quark
๐๐2๐๐
2 = ๐๐ ๐ เดค๐
็ฉ่ณชใฎ่ณช้ใฎ่ตทๆบใฎใชใ
1965ๅนด ใใซใคใฉใซๅฏพ็งฐๆงใฎ่ช็บ็็ ดใใๆๅฑๅ้จ้ฝไธ้ใซใใใใใๅฏพ็งฐๆงใ็ ดใใใใจใซใใฃใฆใใจใใจ่ณช้ใใชใใฃใ็ฒๅญใซ่ณช้ใ็ใใๆฉๆงใ่งฃๆใ็ฒๅญใซๅใ็ธไบไฝ็จใซใใฃใฆๅฏพ็งฐๆงใ็ ดใใๅๆใซ่ณช้ใ็ใใใ
ใใใญใณ๏ผ้ฝๅญใไธญๆงๅญใชใฉ๏ผๅฝขๆใฎใชใ๏ผใฏใฉใผใฏ้ใฎๅผทใ็ธไบไฝ็จใซใใฃใฆใ็็ฉบไธญใซ๏ฝใจๅ๏ฝใๅ็ธฎใใฆ่ณช้ใ็ฒๅพใๅๆใซใ่ช่บซใฎ็ธไบไฝ็จใงใฏใฉใผใฏใฏใใใญใณๅ ้จใซ้ใ่พผใใใใใ
ใใใญใณใฏใฉใผใฏใๅ็ฌใงๅใๅบใใชใ็็ฑใ
ใกใซใใบใ ใฎๆค่จผใฏใพใ ไธๅๅ
Constituent Quark Model
โข Successful to describe nature of hadrons in the ground stateโ Mass
โ Spin-Isospin(flavor) classification
โ Magnetic moment of baryons
โข Sometimes fails in excited stateโ Missing resonance problem
โ Exotic states
โข Provides a Good Guide Line to insight Hadrons
36
Classification of Light MesonSUF(3)
โข เดค๐๐~(เดค๐ข, าง๐, าง๐ )โจ(๐ข, ๐, ๐ )
๐โ
(เดค๐ข๐)
๐พโ(เดค๐ข๐ ) ๐พ0( าง๐ ๐)
๐พ0( าง๐๐ ) ๐พ+( าง๐ ๐ข)
๐+
( าง๐๐ข)
๐0๐โฒ
๐
Classification of Light MesonSUF(3)
โข เดค3 โจ 3 = 1โจ8
๐โ
(เดค๐ข๐)
๐พโ(เดค๐ข๐ ) ๐พ0( าง๐ ๐)
๐พ0( าง๐๐ ) ๐พ+( าง๐ ๐ข)
๐+
( าง๐๐ข)
๐0๐โฒ
๐
Classification of Light BaryonSUF(3)
โข ๐๐๐~(๐ข, ๐, ๐ )โจ(๐ข, ๐, ๐ )โจ(๐ข, ๐, ๐ )
๐(๐ข๐๐)
ฮโ(๐๐ ๐ )
ฮ, ฮฃ0
(๐ข๐๐ )
๐(๐ข๐ข๐)
ฮฃโ
(๐๐๐ )ฮฃ+
(๐ข๐ข๐ )
ฮโ
(๐๐๐)ฮ++
(๐ข๐ข๐ข)
ฮฉโ(๐ ๐ ๐ )
ฮฃโโ
(๐๐๐ )
ฮ0(๐๐ ๐ )
ฮโโ
(๐๐ ๐ )
ฮโ0
(๐๐ ๐ )
ฮฃโ+
(๐ข๐ข๐ )ฮฃโ0
(๐ข๐๐ )
ฮ0
(๐๐๐ข)
ฮ+
(๐๐ข๐ข)
Classification of Light BaryonSUF(3)
โข 3 โจ 3 โจ 3 = 10โจ8โจ8โจ1
๐(๐ข๐๐)
ฮโ(๐๐ ๐ )
ฮ, ฮฃ0
(๐ข๐๐ )
๐(๐ข๐ข๐)
ฮฃโ
(๐๐๐ )ฮฃ+
(๐ข๐ข๐ )
ฮโ
(๐๐๐)ฮ++
(๐ข๐ข๐ข)
ฮฉโ(๐ ๐ ๐ )
ฮฃโโ
(๐๐๐ )
ฮ0(๐๐ ๐ )
ฮโโ
(๐๐ ๐ )
ฮโ0
(๐๐ ๐ )
ฮฃโ+
(๐ข๐ข๐ )ฮฃโ0
(๐ข๐๐ )
ฮ0
(๐๐๐ข)
ฮ+
(๐๐ข๐ข)
Classification of Light BaryonSUF(4): (heavily broken due to ๐๐ โซ ๐๐ข,๐,๐ )
โข ๐๐๐~(๐ข, ๐, ๐ , ๐)โจ(๐ข, ๐, ๐ , ๐)โจ(๐ข, ๐, ๐ , ๐)
๐๐๐ด๐๐๐บ
Relativistic Quark Model
โข unobserved states
โข unexpected states42
T. Melde, W. Plessas, and B. SenglPhys. Rev. D77, 114002(2008)
Red: RQMGreen: Exp.
44
Magnetic Moment of Octet Baryons
Constituent Quark Model Picture works well!
q
q
q
zqz msq /ห m
In the framework of spin-flavor SU(6)
BB zB mm ห
Only 3 parameters: mu, md, ms
Spontaneous c Symmetry Breaking
Current quark:mq~0 -> Constituent quark:mq~MN/3
Partial restoration of c Sym. in finite density?
Magnetic Moment
โข m of Dirac particle โ spinรcharge/mass
ฮผN
neutronproton
0
๐๐๏ผ๐โ
2๐๐๐
ฮผN
๐๐๏ผ๐โ
2๐๐๐
Magnetic Moment
โข m of Dirac particle โ spinรcharge/mass
โข CQM explains the measured values of nucleons
2.79ฮผN -1.91ฮผN
neutronproton
47
Magnetic Moment of Octet BaryonsAnalytically deduced, based on Lattice QCD data
In cooperation with ChPT
EXP., Full QCD, QQCD
D. B. Leinweber et al., PRL94, 212001(2005).
QM [SU(6)]
Essence of
Non-relativistic Formulation in CQM
๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + ๐๐๐ + ๐๐ โฆ
โ ๐ป0: kinematic term
โ ๐๐: confinement potential
โ ๐๐ ๐ : spin-spin interaction
โ ๐๐๐: spin-orbit interaction (LS force)
โ ๐๐: Tensor interaction
48
Q3
rq1 q2
l
Coordinate: r1, r2, r3
๐ = (๐1 โ ๐2)/ 2
๐ = (๐1 + ๐2 โ 2๐3)/ 6๐๐ = ๐๐
๐๐ = 3๐๐๐๐/(2๐๐ + ๐๐)
โข ฮป and ฯ motions split (Isotope Shift)
โข HQ spin multiplet ๏ผ เดฑ๐ ๐ป๐ ยฑ เดฑ๐๐ต๐๐๐ค๐ ๐๐ข๐๐๏ผ
Schematic Level Structure of Heavy Baryons
49
ฮป mode
ฯ mode
G.S.
P-wave
Q
l
[qq]
Q
r(qq)
mQ = mq mQ > mq
q
q
qเดฑ๐ ๐ป๐ ยฑ เดฑ๐๐ต๐
......
Spin-dep. Int.
โ๐๐
โ๐๐=
3๐๐
2๐๐ + ๐๐โ 3 (๐๐ โ โ)
Confinement
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐๐๐ผ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2 โ analytic (<-> cornell potential ฯ(
๐
๐๐๐+ ๐๐๐๐ ) )
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
๐ = 0.332๐๐/3, at ๐๐ = 1.5 GeV/c2
c.f. 1โ๐๐~ฮ๐
1
2
โ+2ฮ๐
3
2
โ
3โ ฮ๐
1
2
+~ 0.33 GeV/c2
50
[
P-wave (r, l-mode excitations)
51
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
w (
GeV
)
MQ (GeV/c2)
l-mode
r-mode
isotope shift
3)2/(3/ Qm
QqQ mmmlr ww
Spin-spin Interaction
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐๐๐ผ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
โข ๐๐ ๐ = ๐๐ ฯ๐๐โ๐๐
๐๐๐๐๐ฟ ๐๐๐ ๐๐ ๐๐ ๐ ๐๐ :
ฮ1
2
+= ๐0 โ 3๐๐ /๐๐
2
ฮฃ1
2
+= ๐0 + ๐๐
1
๐๐2 โ
4
๐๐๐๐
ฮฃโ 3
2
+= ๐0 + ๐๐
1
๐๐2 +
2
๐๐๐๐
52
[
(๐, ๐๐) : โqqโ-spin anti-symm.
(๐, ๐๐) : โqqโ-spin symm., [qqQ]1/2
(๐, ๐๐ ) : โqqQโ spin symm.
Spin-spin Interaction
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐๐๐ผ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
โข ๐๐ ๐ = ๐๐ ฯ๐๐โ๐๐
๐๐๐๐๐ฟ ๐๐๐ ๐๐ ๐๐ ๐ ๐๐ :
ฮ1
2
+= ๐0 โ 3๐๐ /๐๐
2
ฮฃ1
2
+= ๐0 + ๐๐
1
๐๐2 โ
4
๐๐๐๐
ฮฃโ 3
2
+= ๐0 + ๐๐
1
๐๐2 +
2
๐๐๐๐
53
[
โฮฃ + 2ฮฃโ
3โ ฮ = ๐๐
4
๐๐2
~0.2 GeV/c2}
Spin-spin Interaction
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐๐๐ผ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
โข ๐๐ ๐ = ๐๐ ฯ๐๐โ๐๐
๐๐๐๐๐ฟ ๐๐๐ ๐๐ ๐๐ ๐ ๐๐ :
ฮ1
2
โ,
3
2
โ= เต
๐๐ + ๐๐ 1
๐๐2 โ
4
๐๐๐๐
๐๐ โ 3๐๐ /๐๐2
(โ๐ = 1, ๐๐)
(โ๐ = 1, ๐๐)
ฮ1
2
โ,
3
2
โ,
5
2
โ= ๐๐ + ๐๐
1
๐๐2 +
2
๐๐๐๐(โ๐ = 1, ๐๐ )
54
[
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
w (
GeV
)
MQ (GeV/c2)
Isotope shift
L(P,c) (r, l-mode excitations w/ Vss)
55
L(Pr,cs)
L(Pr,cl)
L(Pl,cr)
22 /1/2/1 q
m
Qqq mmmm Q
6/๐๐2
4/๐๐2
Lambda Baryons (P-wave)
56
c(1/2+)
c*(3/2+)
Lc(2595, 1/2)Lc(2625, 3/2)
Lc o๏ฝ c (2765, ??)
Lc(2880, 5/2)
Lc(2940, ??)
Lc(GS)
L(1520, 3/2)
(1/2+)
L(1/2+)
*(3/2+) L(1405, 1/2)
L(1830, 5/2)
L(1690, ??)L(1670, 1/2)
L(GS)
b(1/2+) b
*(3/2+)
Lb(5920, 3/2)Lb(5912, 1/2)
Lb(GS)
strange charm bottom
0
100
200
300
400
500
600
700
800
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Y* -
YG.S
.[M
eV]
MQ [GeV/c2]
Lambda Baryons (P-wave)
57
s c
non-rel. QM:H=H0 +Vconf +VSS+VLS+VT
rl mixing (cal. By T. Yoshida)
c(1/2+)
c*(3/2+)
Lc(2595, 1/2)Lc(2625, 3/2)
Lc o๏ฝ c (2765, ??)
Lc(2880, 5/2)
Lc(2940, ??)
Lc(GS)
L(1520, 3/2)
(1/2+)
L(1/2+)
*(3/2+) L(1405, 1/2)
L(1830, 5/2)
L(1690, ??)L(1670, 1/2)
L(GS)
l
r
b
r
b(1/2+) b
*(3/2+)
Lb(5920, 3/2)Lb(5912, 1/2)
Lb(GS)
Q
l
r
T. Yoshida et al.,Phys. Rev. D92, 114029(2015)
L,(P,c) (r, l-mode mixing w/ Vss)
58
๐ฒ๐
๐ฒ๐
๐บ๐
๐บ๐
T. Yoshida et al., Phys. Rev. D92, 114029(2015)
L,(P,c) (r, l-mode mixing w/ Vss)
59
๐บ๐
๐บ๐
T. Yoshida et al., Phys. Rev. D92, 114029(2015)
L,(P,c) (r, l-mode mixing w/ Vss)
60
๐ฒ๐
๐ฒ๐
T. Yoshida et al., Phys. Rev. D92, 114029(2015)
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
w (
GeV
)
MQ (GeV/c2)
(P,c) (r, l-mode excitations w/ Vss)
61
(Pl,cs)
(Pl,cl)
(Pr,cr)
0/6 Qm
Qqmm
22 /4)/1/1(4 q
m
Qqq mmmm Q
L,(1/2-) (r, l-mode excitations w/ Vss)
62
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
w (
YL
GS)
[G
eV]
MQ (GeV/c2)
(Pl,cs)
(Pl,cl)
(Pr,cr)
(S,cs)
(S,cl)
L(Pr,cs)
L(Pr,cl)
L(Pl,cr)
0
100
200
300
400
500
600
700
800
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Y* -
YG.S
.[M
eV]
MQ [GeV/c2]
CQM calculation (P-wave Sigma)
63
s c
non-rel. QM:H=H0 +Vconf +VSS+VLS+VT
rl mixing (cal. By T. Yoshida)
c(1/2+)
Lc(1/2+)
c(3/2+)
c(1/2,3/2)
c(1/2,3/2,5/2)
c(1/2,3/2)(1/2,3/2,5/2)
(1/2,3/2)
(1/2+)
L(1/2+)
(3/2+)
(1/2,3/2)
l
r
Strange baryons Charmed baryons
l
T. Yoshida et al.,Phys. Rev. D92, 114029(2015)
0
100
200
300
400
500
600
700
800
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Y* -
YG.S
.[M
eV]
MQ [GeV/c2]
Lambda Baryons (P-wave)
64
s c
non-rel. QM:H=H0 +Vconf +VSS+VLS+VT
rl mixing (cal. By T. Yoshida)
c(1/2+)
c*(3/2+)
Lc(2595, 1/2)Lc(2625, 3/2)
Lc o๏ฝ c (2765, ??)
Lc(2880, 5/2)
Lc(2940, ??)
Lc(GS)
L(1520, 3/2)
(1/2+)
L(1/2+)
*(3/2+) L(1405, 1/2)
L(1830, 5/2)
L(1690, ??)L(1670, 1/2)
L(GS)
l
r
b
r
b(1/2+) b
*(3/2+)
Lb(5920, 3/2)Lb(5912, 1/2)
Lb(GS)
Q
l
r
?
T. Yoshida et al.,Phys. Rev. D92, 114029(2015)
โข ฮป and ฯ mode excitations interchange
sqsQQ, SO
(1/2-,3/2-)
(1/2-, 3/2-, 5/2-)
(1/2-, 3/2-)
*(3/2+)
(1/2+)
Level Structure of double-strange baryons
Q
ฮป mode
ฯ mode
G.S.
P-wave
66
q
lQQ
r Q-Q
q
Confinement
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐ ๐ผ๐ ๐๐ ๐๐๐ โ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
67
[
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
w (
GeV
)
MQ (GeV/c2)
P-wave (r, l-mode excitations)
68
l-mode
r-mode
isotope shift
0)2/(3/ Qm
qQq mmmlr ww
Spin-spin Interaction
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐ ๐ผ๐ ๐๐ ๐๐๐ โ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
โข ๐๐ ๐ = ๐๐ ฯ๐๐โ๐๐
๐๐๐๐๐ฟ ๐๐๐ ๐๐ ๐๐ ๐ ๐๐ :
ฮ1
2
+= ๐0 + ๐๐
1
๐๐2 โ
4
๐๐๐๐
ฮโ 3
2
+= ๐0 + ๐๐
1
๐๐2 +
2
๐๐๐๐
69
[
(๐, ๐๐) : โQQโ-spin symm., [QQq]1/2
(๐, ๐๐ ) : โQQqโ spin symm.
Spin-spin Interaction
โข ๐ป = ๐ป0 + ๐๐ + ๐๐ ๐ + โฏฮจ~๐โ๐๐ ๐ผ๐ ๐๐ ๐๐๐ โ ๐๐๐๐๐ โ symmetrize (anti-symm.)
โข ๐๐ = ๐/2 ฯ ๐๐๐2
๐๐,๐ = 3๐/๐๐,๐, ๐๐ =3๐๐๐๐
2๐๐ + ๐๐, ๐๐=๐๐
โข ๐๐ ๐ ~๐๐ ฯ๐๐โ๐๐
๐๐๐๐๐ฟ ๐๐๐ ๐๐ ๐๐ ๐ ๐๐ :
ฮ1
2
โ,
3
2
โ= เต
๐๐ โ 3๐๐ /๐๐2
๐๐ + ๐๐ 1
๐๐2 โ
4
๐๐๐๐
(โ๐ = 1, ๐๐)
(โ๐ = 1, ๐๐)
ฮ1
2
โ,
3
2
โ,
5
2
โ= ๐๐ + ๐๐
1
๐๐2 +
2
๐๐๐๐(โ๐ = 1, ๐๐ )
70
[
(r, l-mode excitations w/ Vss)
71
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
w(
GS)
[G
eV]
MQ (GeV/c2)
(Pl,cs)
(Pl,cl)
(Pr,cr)
(S,cs)
โข ฮป and ฯ mode excitations interchange
sqsQQ, SO
(1/2-,3/2-)
(1/2-, 3/2-, 5/2-)
(1/2-, 3/2-)
*(3/2+)
(1/2+)
Level Structure of double-strange baryons
Q
ฮป mode
ฯ mode
G.S.
P-wave
72
q
lQQ
r Q-Q
q
Form of Hadrons
Observable Relevant Physics Quantity What we learn
Mass Spectrum Mass, Width(pole:๐๐ โ ๐ฮ/2)
Particle stateResonant state
Classification
Angular Correl.(decay)
Spin, Parity
Level structure Internal (effective) DoF Form(Dynamics of effective DoFin Hadron)
Production Rate(Diff. Cross Sect.)
Response Function(Transition) Form Factor
Reaction MechanismInternal Motion/Corr.
Partial Width Internal Correlation(Wave function)
Decay MechanismInternal Motion/Corr.
74