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Temperature and Density Effect on the Pentaquark Theta+ Mass and Width. Xuguang Huang Xuewen Hao Pengfei Zhuang Physics Department Tsinghua University. Outline. Motivations Methods Numerical Results Conclusions. Motivations. Known : M=1540 MeV,
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23/4/1923/4/19 11
Temperature and Density Effect on the Pentaquark Theta+ Mass and Width
Xuguang Huang
Xuewen Hao
Pengfei Zhuang
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OutlineOutline
Motivations
Methods Numerical Results
Conclusions
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MotivationsMotivations
Known: M=1540 MeV, <25MeV, B=+1, S=+1, Q=+1
Decay channels:
Unknown: Spin, Isospin, Parity
0or nK pK + + +
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MotivationsMotivations
In medium, the mass and width of a particle would change.
For example. Considering chiral symmetry restoration at finite temperature and density, the effective nucleon mass can be determined through the gap equation of NJL model in the mean field approximation:
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MotivationsMotivations
Temperature dependence and chemical potential dependence of the effective nucleon mass:
Questions: Why so narrow? How to determine its parity? Can it be formed easily in RHIC?
What are the medium effect on the pentaquark characteristics? Can the Temperature and Density Effects help us to solve these questions?
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MethodsMethods
Effective Lagrangians[PLB579(2004)43-51 & hep-ph/0402141]:
Here, P=+1 is assumed. For the case P=-1, there is no i in the Lagrangians. The coupling constants are fixed to reproduce the decay width =15MeV at zero temperature and zero density. At tree level one has:
5
1 0.28 3.8
1 0.16 0.53
A
A
P g g
P g g
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MethodsMethods
The propagator reads:
where , is the
lowest-order self-energy calculated from the following
Feynman diagram
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MethodsMethods
The complex mass is obtained by
In the rest frame of Theta+:
For negative parity, the only difference is
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Numerical ResultsNumerical Results
Temperature dependence of the medium modification to Theta+ mass:
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Numerical ResultsNumerical Results
Chemical potential dependence of the medium modification to Theta+ mass:
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Numerical ResultsNumerical Results
Temperature dependence of the medium modification to Theta+ width:
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Numerical ResultsNumerical Results
Chemical potential dependence of the medium modification to Theta+ width:
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Numerical ResultsNumerical Results The medium modifications to Theta+ mass without
considering effect of chiral symmetry restoration on mucleon mass:
The medium modifications to Theta+ mass including the effect of chiral symmetry restoration on mucleon mass:
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Numerical ResultsNumerical Results The temperature modifications to Theta+ width without
considering effect of chiral symmetry restoration on mucleon mass:
The temperature modifications to Theta+ width including the effect of chiral symmetry restoration on mucleon mass:
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Mumerical ResultsMumerical Results
Temperature and density effect on Theta+ mass and width at RHIC energy region, where T=200MeV and is determined by
/ 0.65p pn n
PV+ PS+ PV- PS-
0 -3 0 0
15 32 5 1
( )M MeV
( )MeV
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Analyses on the numerical Analyses on the numerical resultsresults The mass and width of Theta+ with positive parity are
strongly affected by the medium, but weakly in the case with negative parity.
The density effect is much stonger than the temperature effect.
The width is much more sensitive to the medium effect compared with the mass.
Theta+ becomes light and unstable in the medium.
The effect of chiral phase transition plays an important role. If we neglect the effect of chiral phase transition , namely keeping the mucleon mass as a constant, the medium corrections are very small.
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ConclusionsConclusions
It is more difficult to find Theta+ at RHIC region than to find it at zero temperature and density.
If the mass and width of Theta+ change substantially, one implies the positive parity of Theta+. If the mass and width of Theta+ change slightly, one implies the negative parity of Theta+.
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