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arXiv 0910.5506hep-phhep-th
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稠密介质中标量束缚态的有效拉格朗日量

An effective Lagrangian for scalar bound states in a dense medium

P. Rembiesa

摘要:

最近的分析表明,在TeV尺度,将在大型强子对撞机访问大量的颜色标量部分子的束缚态可能会产生。如果是这样的话,标量将留下足够长的时间来相互作用,这可能会导致新的物理学。这些相互作用可以是直接的,但也可以通过它们传播的致密部分子介质的中介作用来发生。由于必须包括多个过程,后一种情况太复杂,不能用应用于标准模型的微扰方法来处理。我们探讨了一种可能性,描述这种相互作用的非局部拉格朗日量,这是一个无限的多项式的场变量,动量和质量。我们把所有的标量作为相同的,使用O(N)-对称拉格朗日,其中N是数量的标量和讨论的问题在1/N展开。该模型不能用传统的标准进行重正化,只要拉格朗日量中的参数不被看作是一组无限的独立耦合常数,而被看作是拉格朗日量的有限个场变量、质量和动量的幂展开系数,就只需要有限组乘法重正化。对这些系数的相对大小的必要约束可以在单个耦合常数和1/N中的双级数中逐阶确定。

英文摘要:

Recent analyses suggest that in TeV scales that will be made accessible at the LHC copious amounts of color scalar parton bound states may be produced. Would this be the case, the scalars would leave long enough to interact and this could lead to new physics. These interaction could be direct, but also take place with a mediation of the dense parton medium through which they propagate. Since multiple processes would have to be included, the latter case is too convoluted to be treated with perturbative methods applied to the Standard Model. We explore a possibility of describing such interaction by a nonlocal Lagrangian which is an infinite polynomial in the field variables, momentum and mass. We treat all scalars as identical, use a O(N)-symmetric Lagrangian, where N is the number of scalars and discuss the problem in 1/N expansion. Nonrenormalizable by all traditional criteria, such model still requires only a limited set of multiplicative renormalizations, provided that the parameters in the Lagrangian are not treated as an infinite set of independent coupling constants, but as finite expansion coefficients of the Lagrangian in powers of field variables, mass and momenta. The necessary constraints on the relative magnitudes of these coefficients can be determined order by order in a double series in the single coupling constant and 1/N.

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