Θ + mass in flux-tube model

Θ+ mass in flux-tube model Yi-Bing Ding Graduate School， The Chinese Academy of Scieces Beijing (In collaboration with Peng-Nian Shen, Hong-Ming Zhao and Xue-Qian Li) • 1. Motivation • 2. Brief Formulation • 3. Results and discussions • 4. Conclusions

1. Motivation • 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:

(ii) Negative results: Recently, CLAS claimed that the newest high statistics data do not support their former reported signal. • Later, it was confirmed by DIANA, CLAS, SAPHIR, HERMES, ZEUS, and COSY groups :

(iii) There are many theoretical studies on pentaquark. Θ+ mass is low? high? What should be the real answer ? If it exists, what can we learn?  multi-quark dynamics that does not exist in non-exotic hadrons.  complicatedcolor confinement mechanism They are still open questions ! .

(iv) The new results given by LQCD • 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

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

Hamiltonian OGE Coulomb potential with • 2. Brief Formulation In the framework of the non-relativistic potential model , by using the variational method we solve the eigen-equation

Double Y-ansatz confining potential with r0 is the junction point

Jacobian variables : mass of u(d) quark : mass of anti-strange quark kinetic energy In CM frame of pentaquark

for negative parity for positive parity color wave function of Θ+ with configuration spatial trial wave function ofΘ+

Spin-flavor structure for negative parity state Spin-flavor structure for positive parity state Due to gereralized Pauli principle

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.

multi-parameter trial wave function mass of Θ+ is the eigen energy obtained by using the variational method 3. Results and discussions

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

Thanks! 谢谢

Θ + mass in flux-tube model