强作用物质性质研讨会, 遵义, 2014.8 Before and after the discovery of d* dibaryon Hongxia Huang, Jialun Ping Nanjing Normal University Fan Wang Nanjing University

, , 2强作用物质性质研讨会遵义014.8

Before and after the discovery of d* dibaryon

Hongxia Huang, Jialun PingNanjing Normal University

Fan WangNanjing University


Outline

Introduction Quark cluster model approach of NN intera

ction Quark delocalization color screening model Comprehensive studies of d* dibaryon The discovery of d* dibaryon After the discovery of d* dibaryon


IntroductionSimilarity of nuclear force and molecular force

call for an understanding

electron percolation quark delocalization


Molecular force is due to atom mutual polarization caused by electron delocalization.

Meson exchange between point nucleon picture is totally different from the mechanism of molecular bond.

Color singlet quark model of nucleon provide a possibility to understand the similarity of nuclear force and molecular force.


Quark cluster model approach of NN interaction

1975 we did SU(4) analysis of charm quark states with Lu Tan et al.

1976 we did resonating group method (RGM) nuclear data calculation.

I extended quark model for single hadron to two-baryon developed the quark cluster model to calculate NN interaction with RGM in 1976.

Checked with C.N. Yang in 1977. 1978 Lushan conference I reported this quark cluster mode

l approach of NN interaction. Oka and Yazaki first RGM calculation cited our 1980 Bolog

na international conference contribution. Faessler brought our paper to Beijing winter school.


1984 I studied 4-quark states with C.W.Wong at UCLA

Multi-quark strings, Nuovo Cim. A86(1985)283. 1986 I studied SU(3) 6-quark states with T. Goldman at LANL.

Strangeness-3 dibaryons, PRL 59(1987)627.

An ‘inevitable’ non-strange dibaryon, PRC39(1989)1889.

Why d* is inevitable?1.Quark delocalization reduce the kinetic energy of quark and prov

ide effective attraction for dibaryon.

2.Color magnetic interaction provide repulsion (attraction) for spin triplet (singlet) quark pair for single baryon states, which provide the repulsive core for Octet dibaryons and effective attraction for decuplet dibaryons.


Quark delocalization color screening model

We have to develop a quantitative model to check the above qualitative model predictions. This model must be able to describe the vast NN interaction data, including both bound and scattering data. Then apply to dibaryon states.

1988 I spent 9 months to make a transit-world academic trip to meet experts in this field almost all over the world, including T.D.Lee, G.t’Hoft, E. Lomon, N.Isgur, T.E.O.Ericson, J. de Swart, M. Locher, Vin Mauo, Chemtob, Holinder, J.Speth, Y.Simonov, V.Neuydachin and others.


After coming back in China, I collecting informations what I got in this round-world trip to develop a quark model for multiquark systems.

Unfortunately I had been partially employed in the education department so this project took quite a long time. Finally collaborating with G.H. Hu and L.J. Teng to complete the numerical calculation.

Quark delocalization, color screening and nuclear intermediate range attraction, PRL 69(1992)2901.


Quark delocalization:

the parameter εis determined by system dynamics 。 The main advantage of QDCSM : the delocalization parameter is determined through its ow

n dynamics, so multi-quark system choose its most favorable configuration in the course of interaction. For example in the NN scattering process, the two nucleons vary from two independent spherical nucleons through polarized two nucleons, merge into a peanut finally a 6-quark spherical ball.

2

2

2

2

2

)2/(4/3

22

)2/(4/3

2 2

1,

2

1

/)(,/)(

br

bl

lrrrll

eb

eb

NNsrsr


Color screening ： qq interaction: inside baryon outside baryon different

the color structure is taken into consideration three gluons exchange 0 (inside baryon) = 0 (outside baryons)


We did a hidden color channel coupling calculation with normal color confinement and obtained the same quality fit to the deuteron and NN scattering data, so the color screening might be an effective description of hidden color channel effect.

Hidden color channel effect in NN scattering,

PRC 84(2011)064001. We also did a comparative study with QDCSM and

CHQM use exact same model parameters but replace the sigma meson in CHQM with color screening and quark delocalization in QDCSM and proved these two models gave quantitatively the same NN interaction.

An alternative approach for nuclear intermediate range attraction, PRC 76(2007)014001.


QDCSM vs ChQM PRC 76(2007) 014001


Comprehensive studies of d* dibaryon

In order to do comprehensive calculation of multi-quark system especially dibaryons, we develop a systematic group theory method.

An extension of the fractional parentage expansion to nonrelativistic and relativistic SU^f(3) dibaryon calculation, PRC 51(1995)1648.

in collaboration with J.L.ping


We use three quark model to check the reliability of these model calculation, QDCSM, ChQM, Relativistic QM, also Zhang et al ChQM in cases.

First Adiabatic calculation to do an overall search in SU(3) flavor world, then single channel dynamical calculation for special interesting channels, and finally multi-channel coupling calculation to study the baryon and dibaryon resonances.


Comprehensive studies of d*

Quark delocalization color screening model: PRC51 (1995) 3411;

Relativistic QM: Ping, Mod. Phys. Lett., A13 (1998) 59; QDCSM d* decay: NPA688 (2001) 871; Extended QDCSM d* decay: PRC65 (2002) 044003; d* production and decay: PRC57 (1998) 1962; three-body decay of d*: PRC58 (1998) 2414; d* decay: PRC70 (2004) 035201;

NN scattering and d*: QDCSM and ChQM: PRC 79 (2009) 024001

Symmetry analysis: Dyson and Xuong, PRL13 (1964) 815; Bashkanov, Brodsky and Clement: PLB727 (2013) 438; HX Huang, JL Ping & F Wang: PRC89 (2014) 034001.


Proposals for d* experimental searching In 1990, LAMPF: four proposed experiments in 1990-2000 A better dibaryon than H particle

In 1997, TRIUMF: Search for the \Delta - \Delta Dibaryon S. Yen, … (TRIUMF), T. Goldman (LANL), C.W. Wong, … (UCLA), T.E. Drake, … (U.Toronto), F. Wang, … (Nanjing U.), Y. Ye, … (Peking U.), W.R. Falk (U.Manitoba), C. Rangacharyulu (U.Saskatchewan), E.G. Auld, … (UBC), G.V. O'Rielly, … (UNBC), T.G. Walton (Cariboo U. College), A.K. Opper (Ohio U.), R.D. Bent (Indiana U.), I.I. Strakovsky (Virginia Tech), D. Frekers, M. Hartig (Muenster U.)


d* in QDCSM

d* (IJP=03+) as a resonance in NN scattering

Mass 2270—2400 MeV

ΓNN= 14 –17 MeV Γinel= 33 - 144 MeV

Total width Γ= 50 – 158 MeV

agrees with WASA-at-COSY measurements.


Other dibaryons in QDCSM

D12 (IJP=12+): M=2168 MeV, Γ=121 MeV

Experimental signal: M=2148 MeV, Γ=118 MeV

NΩ(IJP=1/2 2+): M=2549--2566 MeV, Γ< 1 MeV

ΩΩ(IJP=00+): M ~ 3300 MeV


The discovery of d* dibaryon

baryon number = 2 “d* (IJP=03+) ”: M=2380 MeV, Γ=70 MeV reported continuously by WASA-at-COSY collaboration

PRL 102, 052301 (2009); PRL 106, 242302 (20

11); PLB 721, 229 (2013); PRL 112, 202301 (20

14); PRC 88, 055208 (2013)


WASA-at-COSY measurements







CERN Courier 2011 http://cerncourier.com/cws/article/cern/46855


CERN Courier 2014 http://cerncourier.com/cws/article/cern/57836


After thr discovery of d* dibaryon

Dibaryon had been discovered and disappeared few times, so this community is very cautious on the new discovery.

We must have an independent check of the existence of d* dibaryon.

WASA-at-COSY collaboration plan to use their collected data to search the company dibaryon IJP=30+.


They also plan to use Meinz electron beam to do ed->ed* production measurements.

Y.J. Mao group started an analysis of DESY ed scattering data.

H.Y.Gao plan to propose to do ed->ed* at Jlab. H.Z. Huang group started STAR data analysis to s

earch N\Omega resonance. Y.G Ma group started the \Lambda\Ksi invariant m

ass analysis and 3 days ago we discussed at Shanghai to extend to analyse the \Lambda\Ksi and p\Omega correlation.


Theoretical study of the properties of d* especially the decay width.

Our understanding is because our Feshbach resonance channel coupling calculation obtained almost the right resonance width so it is produced through such a process, but the other decay widths is smaller than a naïve bound \delta width estimate, the binding energy is large (~80 MeV), the size is small (~1 fm), so it should be a compact 6 quark state. J.L. Ping will give a critical analysis about the large hidden component assumption.


A lesson

Strong scattering channel coupling to an otherwise bound hadron states might change the energy drastically.

IJP=01+ NN scattering channel coupling push the otherwise deep bound dibaryon to

Continuum(push up 300MeV).

\pi N scattering channel coupling lower the

1.5 GeV \Delta to 1.2 GeV.


To do quark model or lattice hadron spectroscopy calculation, to study the near threshold resonance have to taking this channel coupling effect into account.


Dynamical symmetry

Gell-Mann-Zweig quark model:

classification system -- Eightfold Way

SU(3) flavor symmetry Ω IBM: Arima and Iachello FDSM: D.H. Feng, C.L. Wu and J.Q. Chen


Dynamical symmetry:

H: Hamiltonian of a system

can be expressed in terms of

C,C1,C2,……: Casimir operators or class

operators of group chain

Eigenenergy of the system can be obtained directly

from the eigen value of these operators

1 2( , , ,......) ( , ( ))H F C C C F C C s

1 2 ......G G G

1 2( , , ,......) ( , )E F m m F m

[ , ] 0, [ , ] 0, [ , ( )] 0H G H C H C s


Group chain of quark model

Hadron ground states:

orbital: Ux(1)

color: SUc(3)

flavor: SUf(3)

spin: SUσ(2)

Group chain:

(18) (3) ( (6) ( (3) (2) (1)) (2))

[1 ] [ ] [ ] [ ]

c f f I Y

n

SU SU SU SU SU U SU

c f I Y J


Dynamical symmetry applied to quark model

Color: singlet, [c] fixed

Gursey-Radicati mass formula (PRL13(1964)173)

(6) (3) (2) (1) (2)( , , , , )f f I YSU SU SU U SU

H F C C C C C

0 (3) (2) (1) (2)f Y ISU SU U SUM M AC B C C C D C

20 (3)

( 1) ( 1) / 4fSUM M AC B J J C Y D I I Y


Parameters the masses of baryons

A=9.2962 B=48.238 C=-196.34 D=35.080

(unit: MeV)


Baryon: qqq

Group chain:

[μ]=[3], dim=56

[μ]=[ f ] x [ σ]: [21] x [21], [3] x [3] octet decuplet

M0=1021.9 MINUIT err

3

(18) (3) ( (6) ( (3) (2) (1)) (2))

[1 ] [111] [ ] [ ]

c f f I YSU SU SU SU SU U SU

f I Y J



N Λ Σ Ξ Δ Σ* Ξ* Ω

Y 1 0 0 -1 1 0 -1 -2

I ½ 0 1 ½ 3/2 1 ½ 0

J ½ ½ ½ ½ 3/2 3/2 3/2 3/2

[f] [21] [21] [21] [21] [3] [3] [3] [3]

theo 935 1114 1184 1328 1241 1384 1528 1672

err 2.6 1.9 2.6 1.6 4.8 3.8 2.7 1.7

exp 939 1116 1193 1318 1232 1383 1533 1672


Dibaryon: qqqqqq

Group chain:

[μ]=[33], dim=490

[μ]=[ f ] x [ σ]: [6]x[33], [51]x[42], [42]x[51], [42]x[33]

[411]x[42], [33]x[6], [33]x[42], [321]x[51]

[321]x[42], [222]x[33]

6

(18) (3) ( (6) ( (3) (2) (1)) (2))

[1 ] [222] [ ] [ ]


f I Y J


[f]=[6] dim=28


[f]=[51] dim=35


[f]=[42] dim=27


[f]=[411] dim=10 [f]=[33] dim=10


[f]=[321] dim=8

[f]=[222] dim=1


D01 D10 D03 D30 D12 NΩ ΩΩ H

Y 2 2 2 2 2 -1 -4 0

I 0 1 0 3 1 ½ 0 0

J 1 0 3 0 2 2 0 0

[f] [33] [42] [33] [6] [42] [321] [6] [222]

theo 1873 1884 2355 2420 2173 2652 3072 2093

err 5.6 6.6 6.6 13 7.2 4.0 4.7 2.9

exp 1876 1878? 2357? ? 2148? ? ? ?


Penta-quark (5-quark)

2003, Θ+: B=1, S=+1

minimum quark content: uudds

Roper resonance: N*(1440)


Two steps:1. 4-quark coupling Group chain

[μ]=[31] [f4] x [σ4]=[4]x[31], [31]x[4],[31]x[31],[31]x[22] [22]x[31], [211]x[31],[211]x[22]2. 4q-q coupling: [f]x[σ]=[51]x[41],[51]x[32],[42]x[5],[42]x[41],[42]x[32], [411]x[5],[411]x[41],[411]x[32],[33]x[41], [33]x[32], [321]x[5],[321]x[41],[321]x[32],[222]x[41],[222]x[32]

44 4 4 4

(18) (3) ( (6) ( (3) (2) (1)) (2))

[1 ] [211] [ ] [ ]


f I Y J


[f]=[51] dim=35 J=3/2,1/2


[f]=[42] dim=27 J=5/2, 3/2, 1/2


[f]=[33] dim=10 J=3/2, 1/2


Θ+ Ξ3/2 Θ+ Ω1 Γ Π Θ2 Ω1

Y 2 -1 2 -2 0 -1 2 -2

I 0 3/2 0 1 2 3/2 2 1

J ½ 3/2 5/2 ½ 3/2 5/2 ½ 3/2

[f] [33] [33] [33] [42] [42] [42] [51] [51]

Theo 1540 2287 1926 2433 2360 2710 1862 2652

Err 4.8 4.7 5.7 3.9 6.9 6.1 8.5 5.4

exp ? ? ? ? ? ? ? ?


NN scattering


resonance





deuteron


QDCSM vs ChQM PRC 76(2007) 014001



Hidden color channel effects?

PRC 84 (2011) 064001

Color singlet-color singlet: k=1 Color singlet-color octet: k≠1








Tetra-baryon ： 12-quark system

4He: (nnpp) (u↑u ↑ u ↑ u↓u↓u↓d↑d ↑ d ↑ d↓d↓d↓)

4n: (nnnn) (d↑d ↑ d ↑ d↓d↓d↓--d↑d ↑ d ↑ d↓d↓d↓)

F.M.Marques, et al., PRC65(2002)044006

14Be 10Be + 4n


Hadron level: no tetraneutron multibody interaction -- > bound state ? Quark level: 12-quark system preliminary work: effective potential

V(a) = E (a) - E(∞)


Constructing the wavefunctions

1. 3-quark wavefunctions:


S6 כ S3xS3

coset

decomposition



S12 כ S6 x S6

coset

decomposition

numbers of coset representatives: 12!/(6!6!) = 924


Chiral quark model


Results:




nnΛΛ


Summary QDCSM describes NN scattering, deuteron properties well

QDCSM can explain the similarity between molecular force and nuclear force

Dynamical symmetry analysis predicted the existence of d*

The d* calculation in QDCSM is confirmed by WASA-at-COSY collaboration’s results.

Tetra-baryon will provide an example for extending quark model to multi-hadron molecules.

Thanks!!!

Documents

强作用物质性质研讨会, 遵义, 2014.8 Before and after the discovery of d* dibaryon Hongxia Huang, Jialun Ping Nanjing Normal University Fan Wang Nanjing University