Θ+ mass in flux-tube model

Yi-Bing Ding Graduate School ，

The Chinese Academy of SciecesBeijing

1. Motivation2. Brief Formulation3. Results and discussions4. Conclusions

(In collaboration with Peng-Nian Shen, Hong-Ming Zhao and Xue-Qian Li)

1. Motivation(i)The discovery of Θ+

The first report:

It has baryon number B=+1, stangeness s=+1 and charge Q=+1. But the parity is to be determined

.

Suggestion:

Later, it was confirmed by DIANA, CLAS, SAPHIR, HERMES, ZEUS, and COSY groups

(ii) Negative results:

:

Recently, CLAS claimed that the newest high statistics data do not support their former reported signal.

(iii) There are many theoretical studies on

pentaquark.

Θ+ mass is low? high?

.

What should be the real answer ?

They are still open questions !

If it exists, what can we learn?

multi-quark dynamics that does not exist in

non-exotic hadrons.

complicated color confinement mechanism

(iv) The new results given by LQCD

(a)Alexandrou et al. (PRD71(2005)014504)

Θ+ : 1.603 ± 0.073GeV for negative parity 2.36 ± 0.13GeV for positive parity

(b)N.Mathur et al. (PRD70(2005)074508) K.Holland et al. (hep-lat/0504007)

no evidence for bound pentaquark state

(c) T.T.Takahashi et al. ( hep-ph/0507187)

2.24GeV for positive parity no evidence below 1.75GeV for negative parity

interesting pointdouble Y-shape confining potential for pentaquark R.L.Jaffe & F.Wilczek, Phys.Rev.Lett.91, 232003(2003) T.T.Takahashi et al. Phys.Rev.Lett.94, 192001(2005)

use “OGE coulomb plus double Y-ansatz confinment” potential, to study the mass ofΘ+ with configuration.

qqqqq

2. Brief Formulation

In the framework of the non-relativistic potential model , by using the variational method we solve the eigen-equation

Hamiltonian

OGE Coulomb potential

with

Double Y-ansatz confining potential

with

r0 is the junction point

In CM frame of pentaquark

kinetic energy

Jacobian variables

: mass of u(d) quarkm

qm : mass of anti-strange quark

for negative parity

for positive parity

spatial trial wave function ofΘ+

color wave function of Θ+ with configurationqqqqq

Due to gereralized Pauli principle

Spin-flavor structure for negative parity state

Spin-flavor structure for positive parity state

Coulomb potential

string tension and zero-point energy

other parameters are also obtained from the calculation of baryon with Y-ansatz confining potential

Y-shape confining potential for baryons

r0 is the junction point which makes the length of

flux tube taking the minimal value.

3. Results and discussions

mass of Θ+

is the eigen energy obtained by using the variational method

multi-parameter trial wave function

mass of Θ+ with negative parity is lower than that with positive parity, but is still about 0.36GeV higher than the experimental value of 1.540GeV

mass of Θ+ with positive parity is about 2.217GeV, which is consistent with the lattice QCD result given by T.T.Takahashi et al.

4. Conclusions

(1) Resultant masses of +

are:

(4) Our result does not support Θ+ (1540) as a

pentaquark state

(2) Mass of Θ+ with negative parity is

about 0.36GeV higher than the experimental

value of 1.540GeV (3) Mass of Θ+ with positive parity is

consistent with the lattice QCD result

Thanks!

谢谢