Θ + mass in flux-tube model
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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)
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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:
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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.
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(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
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(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
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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
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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
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Double Y-ansatz confining potential
with
r0 is the junction point
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In CM frame of pentaquark
kinetic energy
Jacobian variables
: mass of u(d) quarkm
qm : mass of anti-strange quark
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for negative parity
for positive parity
spatial trial wave function ofΘ+
color wave function of Θ+ with configurationqqqqq
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Due to gereralized Pauli principle
Spin-flavor structure for negative parity state
Spin-flavor structure for positive parity state
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Coulomb potential
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string tension and zero-point energy
other parameters are also obtained from the calculation of baryon with Y-ansatz confining potential
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Y-shape confining potential for baryons
r0 is the junction point which makes the length of
flux tube taking the minimal value.
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3. Results and discussions
mass of Θ+
is the eigen energy obtained by using the variational method
multi-parameter trial wave function
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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.
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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
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Thanks!
谢谢