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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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