标量玻色子与费米子耦合的谱函数
Spectral function of a scalar boson coupled to fermions
摘要：
本文计算了一个耦合到费米子的不稳定标量玻色子的谱函数，它是由标量粒子自能的单圈图重新表示的结果。我们使用一个大但有限的高能截止：这样，标量场的谱函数总是正确地归一化为1，与截止值无关。我们发现，这种高能量的截止影响的Breit-Wigner宽度的不稳定粒子：越大的截止，较小的是在固定耦合的宽度。因此，高能量截止（别名最小长度）的存在，以及例如可能在该能量标度之外打开新的自由度，原则上可以通过在较低能量标度下测量不稳定标量态的线形来证明。虽然这里考虑的拉格朗日只代表一个玩具模型，我们讨论了我们的工作可能是相关的粒子物理现象学未来可能的扩展。
英文摘要：
We present the calculation of the spectral function of an unstable scalar boson coupled to fermions as resulting from the resummation of the one loop diagrams in the scalar particle self energy. We work with a large but finite high-energy cutoff: in this way, the spectral function of the scalar field is always correctly normalized to unity, independently on the value of the cutoff. We show that this high energy cutoff affects the Breit-Wigner width of the unstable particle: the larger the cutoff, the smaller is the width at fixed coupling. Thus, the existence of a high energy cutoff (alias minimal length), and for instance the possible opening of new degrees of freedom beyond that energy scale, could then be in principle proven by measuring, at lower energy scales, the line shape of the unstable scalar state. Although the Lagrangian here considered represents only a toy-model, we discuss possible future extensions of our work which could be relevant for particle physics phenomenology.
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