论文标题
手性扰动理论中的操作员计数和软块
Operator Counting and Soft Blocks in Chiral Perturbation Theory
论文作者
论文摘要
手性扰动理论（CHPT）是QCD的低能量有效场理论，也是基于对称性破坏模式$ {\ rm su}（n_f）（n_f）\ times \ times {\ rm su}（n_f）（n_f）\ to {\ rm su}（\ rm su}（n_f）$的非线性Sigma模型。在无质量$ n_f $ quarks的极限下，我们通过计数和呈现派生式扩展中的每个顺序的软块来列举独立的操作员，而没有外部来源，最多可在派生范围内计数和呈现软块，最高可达$ {\ cal o}（p^{10}）$。鉴于无质量的壳条件和总动量保护，当任何外部动量变得柔软而消失时，柔软的块是运动不变的均匀多项式。此外，软块是用于递归生成的种子，无需求助于CHPT，并与“低能常数”（Wilson系数）一对一地对应。操作员之间的关系，例如由运动方程，逐个组成，墓穴和对称结构产生的关系，以简单的方式在软块中表现出来。我们找到了与NNNLO的现有结果的协议，并在N $^4 $ lo中进行预测。
Chiral perturbation theory (ChPT) is a low-energy effective field theory of QCD and also a nonlinear sigma model based on the symmetry breaking pattern ${\rm SU}(N_f)\times {\rm SU}(N_f)\to {\rm SU}(N_f)$. In the limit of massless $N_f$ quarks, we enumerate the independent operators without external sources in ChPT using an on-shell method, by counting and presenting the soft blocks at each order in the derivative expansion, up to ${\cal O}(p^{10})$. Given the massless on-shell condition and total momentum conservation, soft blocks are homogeneous polynomials of kinematic invariants exhibiting the Adler's zero when any external momentum becomes soft and vanishing. In addition, soft blocks are seeds for recursively generating all tree amplitudes of Nambu-Goldstone bosons without recourse to ChPT, and in one-to-one correspondence with the "low energy constants" which are the Wilson coefficients. Relations among operators, such as those arising from equations of motion, integration-by-parts, hermiticity, and symmetry structure, manifest themselves in the soft blocks in simple ways. We find agreements with the existing results up to NNNLO, and make a prediction at N$^4$LO.
