论文标题
手性扰动理论的振幅/操作员基础
Amplitude/Operator Basis in Chiral Perturbation Theory
论文作者
论文摘要
我们在$ d = 4 $时空维度和任意数量的口味$ n_f $中建立了手性扰动理论（CHPT）的壳振幅/操作员基础的系统构建。对于运动因素，我们采用旋转螺旋变量来构建软块，这些变量是满足Adler零状况的局部幅度，并考虑到由于$ o（p^{10}）$ o（p^{10}）$ n $ n $ n $ n $ n $ n $ n $ n y n y n y y n y n y n y n y y a n y Amply $ n y a n y Ammape $ n y y a n y Ammape $ n $ n $ n y Ammply $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n。对于风味因素，我们包括小$ n_f $，$ n_f \ le n $的群体理论关系，这降低了风味的基础。结果是通过调整年轻的张量方法来构建一般有效场理论的操作员基础的年轻张量方法，以实现非线性实现的对称性。在无数夸克限制下，我们向$ o（p^6）$和$ o（p^8）$（$ n = 6 $和任意$ n_f $）呈现纯粹的中间运算符，并在幅度基础和操作员基础之间建立直接对应关系。此外，由于$ n = 6、8 $和10，以$ o（p^{10}）$研究了由于克决定因素的冗余。
We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in $D=4$ spacetime dimensions and with an arbitrary number of flavors $N_f$. For kinematic factors, we employ spinor-helicity variables to construct the soft blocks, which are local amplitudes satisfying the Adler's zero condition, as well as to take into account the reduction in the kinematic basis due to the Gram determinant, which arises at $O(p^{10})$ when the number of multiplicity $N$ in an amplitude becomes large: $N>D$. For flavor factors, we include group-theoretic relations at small $N_f$, $N_f\le N$, which decreases the flavor basis. The result is obtained by adapting the Young tensor method of constructing the operator basis for generic effective field theories to the case of non-linearly realized symmetries. Working in the massless quark limit, we present purely mesonic operators for both even- and odd-parity at $O(p^6)$ and $O(p^8)$ for $N=6$ and arbitrary $N_f$, and establish a direct correspondence between the amplitude basis and the operator basis. Furthermore, the redundancy due to the Gram determinant is studied at $O(p^{10})$ for $N=6, 8$ and 10.
