Chiral perturbation theory in the two-flavour sector allows one to analyse Green functions in QCD in a limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses. In this framework, the pertinent low-energy constants depend on the value of the heavy quark masses. In a recent article, we have worked out, for the coupling constants which occur at order p^4, the dependence on the strange quark mass at two-loop accuracy. Here, we provide analogous relations for some of the couplings which are relevant at order p^6. To keep the calculations somewhat reasonable in size, we consider only those 28 couplings which enter the Green functions built from vector- and axial-vector quark currents in the chiral limit. This provides the matching for 27 linear combinations of the 28 couplings.
We calculate all neutral vector two-point functions in Chiral Perturbation Theory (ChPT) to two-loop order and use these to estimate the ratio of disconnected to connected contributions as well as contributions involving the strange quark. We extend the ratio of $-1/10$ derived earlier in two flavour ChPT at one-loop order to a large part of the higher order contributions and discuss corrections to it. Our final estimate of the ratio disconnected to connected is negative and a few % in magnitude.
Pions: Experimental Tests of Chiral Symmetry Breaking
基于手征对称性的自发破缺，手征微扰理论（ChPT）被认为是禁闭尺度QCD的近似。专门的和越来越精确的实验和改进的晶格计算正在证实这一信念，我们正在进入一个新的时代，我们可以在一些精心选择的反应中测试限制尺度QCD。这是证明了低能量的实验测试的ChPT预测的$ππ$散射，π介子性质，$π$ N散射和电磁π介子生产的概述。这些预言已经被越来越精确的格子计算证明与介子扇区的QCD是一致的。目前，实验和ChPT计算之间有很好的协议，包括$ππ$和$π$ N s波散射长度和$π^{0}$寿命。最近，精确的π原子数据与手征计算一致，一旦考虑到由于上下夸克的质量差引起的同位旋破缺效应，就像提取$ππ$散射长度所要求的那样。除了测试的理论，比较$ππ$和$π$ N之间的相互作用的基础上一般手性原则进行了讨论。晶格计算现在提供的基本结果，长期和不确定的研究，$π$ N $σ$长期和奇怪的夸克的贡献的质子质量。越来越精确的实验，在电磁π介子生产实验的质子，测试ChPT计算（及其能量区域的有效性）。这些实验也开始测量最终状态的$π$ N相互作用。本文基于2012年8月在Jefferson实验室举行的手性动力学研讨会CD12上的总结发言。
The extended Linear Sigma Model (eLSM) is an effective hadronic model based on the linear realization of chiral symmetry $SU(N_f)_L \times SU(N_f)_R$, with (pseudo)scalar and (axial-)vector mesons as degrees of freedom. In this paper, we study the low-energy limit of the eLSM for $N_f=2$ flavors by integrating out all fields except for the pions, the (pseudo-)Nambu--Goldstone bosons of chiral symmetry breaking. We only keep terms entering at tree level and up to fourth order in powers of derivatives of the pion fields. Up to this order, there are four low-energy coupling constants in the resul…
We calculate the form factors of the $K \to πl ν$ semileptonic decays in three-flavor lattice QCD, and study their chiral behavior as a function of the momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is exactly preserved by using the overlap quark action, which enables us to directly compare the lattice data with chiral perturbation theory (ChPT). We generate gauge ensembles at a lattice spacing of 0.11fm with four pion masses covering 290-540 MeV and a strange quark mass m_s close to its physical value. By using the all-to-all quark propagator, we calculate the vector …
We calculate the light quark condensate, the strange quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($χ$PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $χ$PT effective potential and condensates can be mapped onto two-flavor $χ$PT ones by integrating out mesons with strange quark content (kaons and eta), with renormalized couplings. We compare the results for the light quark and pion condensates at finite pseudoscalar source with ($2+1$)-flavor lattice…
ChPT and the $1/N_c$ expansion provide systematic frameworks for the strong interactions at low energy. A combined framework of both expansions has been developed and applied for baryons with three light-quark-flavors. The small scale expansion of the combined approach is identified as the $ξ$-expansion, in which the power counting of the expansions is linked according to $O(p)=O(1/N_c)=O(ξ)$. The physical baryon masses as well as lattice QCD baryon masses for different quark mass masses are analyzed to $O(ξ^3)$ in that framework. $σ$ terms are addressed using the Feynman Hellmann theorem. For…
Chiral--Maxwell Cavity EFT: Reduced Gauge-Mode Condensation and Quantum-Optics Limits
Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Instituto de Ciencias Básicas, Facultad de Ingeniería y Ciencias, Universidad Diego Portales（迭戈帕托莱斯大学工程与科学学院基础科学研究所）
