γ γ-> π π的罗伊-施泰纳方程
Roy-Steiner equations for gamma gamma -> pi pi
摘要：
从双曲色散关系出发，我们推导出一个系统的罗伊-施泰纳方程的π康普顿散射，尊重解析性，幺正性，规范不变性，交叉对称性。因此，它保持了基础量子场论的所有对称性。为了抑制高能量输入的可观测量的依赖，我们还考虑一次和两次减去版本的方程，并确定与偶极和四极π极化率的减法常数。基于Mandeltmann解析性假设，我们确定了方程有效的运动学范围。作为应用，我们考虑了有限匹配点的Muskhelishvili-Omnès表示对$γγ\toππ$分波的分解.我们发现一个总和规则的同位旋2 $S$波，其中，连同手征约束，产生一个改进的预测带电π四极极化率$(α_2-β_2)^{π^\pm}=(15.3\pm 3.7)\cdot 10^{-4} {\rm fm}^5$。我们研究了我们的$σ$共振$Γ_{σγγ}$的双光子耦合的色散关系的预测。减去两次的版本预测了这个宽度和同位旋零π介子极化率之间的相关性，这在很大程度上独立于方程中使用的高能输入。利用这种关联，手征微扰理论的π极化率的结果，和我们的新的求和规则，我们发现$Γ_{σγγ}=(1.7\pm 0.4)\,{\rm keV}$。
英文摘要：
Starting from hyperbolic dispersion relations, we derive a system of Roy--Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on high-energy input, we also consider once- and twice-subtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equations are valid. As an application, we consider the resolution of the $γγ\toππ$ partial waves by a Muskhelishvili--Omnès representation with finite matching point. We find a sum rule for the isospin-two $S$-wave, which, together with chiral constraints, produces an improved prediction for the charged-pion quadrupole polarizability $(α_2-β_2)^{π^\pm}=(15.3\pm 3.7)\cdot 10^{-4} {\rm fm}^5$. We investigate the prediction of our dispersion relations for the two-photon coupling of the $σ$-resonance $Γ_{σγγ}$. The twice-subtracted version predicts a correlation between this width and the isospin-zero pion polarizabilities, which is largely independent of the high-energy input used in the equations. Using this correlation, the chiral perturbation theory results for pion polarizabilities, and our new sum rule, we find $Γ_{σγγ}=(1.7\pm 0.4)\,{\rm keV}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
