Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F1 at large Q2
Factorizing the hard and soft spectator scattering contributions for the nucleon form factor F1 at large Q2
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分解大 Q2 处核子形状因子 F1 的硬观察者散射和软观察者散射贡献
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发表时间：
2012
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通讯作者：
N. Kivel
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作者：
N. Kivel
在过去的研究中（Phys.Rev.D83，093005（2011））我们提出了核子形状因子的因式分解公式，该公式由描述硬和软旁观者散射的两个贡献之和组成，并且我们提供了FF F1的软重散射贡献的描述，其根据硬重散射和硬重散射的卷积积分。具有适当的软矩阵元素的共线系数函数。在本文中，我们调查软观众散射的FF F1的贡献。我们把注意力集中在对应于从SCET-I到SCET-II的过渡的硬共线尺度$sim QLambda$的因式分解上。我们计算了首阶喷流函数，发现软分数上的卷积积分是几何发散的。这种发散性是增强不变性的结果，并且不依赖于描述软旁观者夸克的软关联函数模型。作为一个例子，我们使用的两个回路图证明，这样的发散对应的软共线区域的重叠。因此，人们得到一个大的快度对数，必须包括在正确的因式分解形式主义。我们的结论是，F1的因式分解的一致描述意味着在硬和软观众的贡献，即卷积积分相对于共线分数的端点共线发散没有很好地定义。只有当扭曲-3核子分布振幅具有特定的终点行为时，这种情况才能实现，该行为与核子分布振幅演化所预期的行为不同。这种行为导致违反共线分解的硬观众散射的贡献。我们认为，软旁观者散射和手征对称性破缺提供的机制，负责违反共线因式分解的情况下的形状因子F1。尽管SCET分解的复杂性，它可以是非常有用的硬排斥反应的唯象分析。这种方法的基础是由SCET-I形状因素的普遍性提供的，它可以出现在不同的硬过程中。我们表明，在某些情况下，使用所谓的物理减法方案SCET因式分解允许进行系统的分析的强子过程的范围内的适度的值$ Q^{2}sim 5- 20 $GeV^2的硬共线标度$sim QLambda$仍然不是很大。
In a previous paper (Phys. Rev. D 83, 093005 (2011)) we suggested the factorization formula for the nucleon form factors which consists of the sum of two contributions describing the hard and soft spectator scattering, and we provided a description of the soft rescattering contribution for the FF F1 in terms of convolution integrals of the hard and hard-collinear coefficient functions with the appropriate soft matrix elements. In the present paper we investigate the soft spectator scattering contribution for the FF F1. We focus our attention on the factorization of the hard-collinear scale $sim QLambda$ corresponding to transition from SCET-I to SCET-II. We compute the leading-order jet functions and find that the convolution integrals over the soft fractions are logarithmically divergent. This divergency is the consequence of the boost invariance and does not depend on the model of the soft correlation function describing the soft spectator quarks. Using as example a two-loop diagram we demonstrated that such a divergency corresponds to the overlap of the soft and collinear regions. As a result one obtains a large rapidity logarithm which must be included in the correct factorization formalism. We conclude that a consistent description of the factorization for F1 implies the end-point collinear divergencies in the hard and soft spectator contributions, i.e. convolution integrals with respect to collinear fractions are not well defined. Such scenario can only be realized when the twist-3 nucleon distribution amplitude has specific end-point behavior which differs from one expected from the evolution of the nucleon distribution amplitude. Such behavior leads to the violation of the collinear factorization for the hard spectator scattering contribution. We suggest that the soft spectator scattering and chiral symmetry breaking provide the mechanism responsible for the violation of collinear factorization in the case of form factor F1. In spite of complexities of the SCET factorization it can be very useful for a phenomenological analysis of hard exclusive reactions. The basis for such approach is provided by the universality of the SCET-I form factors which can appear in different hard processes. We show that using the so-called physical subtraction scheme SCET factorization in some cases allows to perform the systematical analysis of the hadronic processes in the range of moderate values of $ Q^{2}sim 5--20$ GeV^2 where the hard-collinear scale $sim QLambda$ is still not large.