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arXiv 1003.1747hep-phnucl-th
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共形对称性与轻味重子谱

Conformal symmetry and light flavor baryon spectra

M. Kirchbach, C. B. Compean

摘要:

在N和Delta谱中系统地观察到的宇称对间的简并性被解释为暗示了在与AdS_5/CFT_4一致的轻味重子扇区中可能的共形对称实现。这个例子是通过证明,所有观测到的质量低于2500 MeV的N和Delta共振都相当好地分布在共形群的幺正表示的第一级上,该表示覆盖了夸克-双夸克系统的光谱,直接放置在AdS_5锥上,共形紧致化为R^1*S^3。S^3流形上的自由测地线运动可以用那里的标量共形方程来描述,它是克莱因-戈登型的。然后,该方程由具有余切函数形式的“弯曲”库仑势来衡量。共形对称不是精确的,这是因为规范势稍微修改了自由测地线运动的共形离心势垒。由于这一点,来自同一能级的P11-S11对之间的简并被放松,而属于同一能级的其余状态实际上保持简并。该模型通过核子谱描述了P11-S11对的正确质量排序,一方面是上述共形对称破缺的综合效应,另一方面是双夸克从低质量标量到高质量赝标量的宇称变化。波函数的质量通过计算质子、质子P11(1440)和S11(1535)共振的实际均方电荷半径和电荷形状因子来说明。该方案还允许从规范势的傅里叶变换预测有效的瞬时胶子传播子的敷料功能。我们发现一个敷料功能,是有限的红外线和趋于零,在无穷大。

英文摘要:

The degeneracy among parity pairs systematically observed in the N and Delta spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS_5/CFT_4. The case is made by showing that all the observed N and Delta resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on the AdS_5 cone, conformally compactified to R^1*S^3. The free geodesic motion on the S^3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon type. The equation is then gauged by the "curved" Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11-S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11-S11 pairs through the nucleon spectrum as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean-square charge radii and electric charge form-factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.

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