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arXiv 1406.2355hep-ph
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驯服戈德斯通贡献的有效潜力

Taming the Goldstone contributions to the effective potential

Stephen P. Martin

摘要:

标准微扰有效势有两个相关的原理问题,涉及依赖于场的戈德斯通玻色子平方质量G。首先,一般来说,G可以是负的,在标准模型中它实际上是负的;这导致了对有效势的虚贡献,而这些虚贡献与物理不稳定性无关,因此是虚假的。第二,在G接近零的极限下,有效势最小化条件在两个回路阶已经在数学上发散,并且在更高的回路阶具有越来越严重的幂律奇异性。我解决这两个问题,通过计算戈德斯通玻色子的贡献的有效潜力。对于所得的简化有效势,给出真空期望值的最小值和最小化条件以完全不涉及G的形式获得。

英文摘要:

The standard perturbative effective potential suffers from two related problems of principle involving the field-dependent Goldstone boson squared mass, G. First, in general G can be negative, and it actually is negative in the Standard Model; this leads to imaginary contributions to the effective potential that are not associated with a physical instability, and therefore spurious. Second, in the limit that G approaches zero, the effective potential minimization condition is logarithmically divergent already at two-loop order, and has increasingly severe power-law singularities at higher loop orders. I resolve both issues by resumming the Goldstone boson contributions to the effective potential. For the resulting resummed effective potential, the minimum value and the minimization condition that gives the vacuum expectation value are obtained in forms that do not involve G at all.

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