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arXiv 1707.07682hep-phhep-latnucl-th
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色散改进的手征有效场论中的核子形状因子I：标量形状因子

Nucleon form factors in dispersively improved Chiral Effective Field Theory I: Scalar form factor

J. M. Alarcón, C. Weiss

备注：
17 pages and 11 figures
发表信息：
Phys. Rev. C 96, 055206 (2017)
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摘要：

提出了一种结合手征有效场论和色散分析计算$G$宇称偶算符核子形状因子的方法。FF表示为在$t > 4 M_π^2$的2 π介子切割上的色散积分。从弹性么正性条件得到的谱函数表示为复$ππ\rightarrow N\bar N$分波振幅和类时π FF的乘积。$χ$ EFT用于计算分波振幅与π介子FF的比率，π介子FF是实数并且在$t$ -通道中没有$ππ$再散射（$N/D$方法）。再散射效应然后通过乘以经验π介子FF的平方模来合并。该程序的结果在一个显着的改善相比，传统的$χ$ EFT计算的谱函数。我们将此方法应用于核子标量FF，计算了标量谱函数、标量半径、$t$依赖的FF和Cheng-Dashen差异。高阶手征校正估计通过$πN$低能常数。结果与色散理论计算非常吻合。我们阐述了我们的方法的其他几个有趣的方面。由于$χ$ EFT计算包含了$N$和$Δ$中间态，结果在QCD的大$N_c$极限下显示了适当的标度行为.我们的方法所需的类时π FF模的平方可以从格点QCD计算的真空相关函数的运营商在大欧几里德距离。我们的方法可以适用于其他运营商的核子FF的利益，如isovector-vector电流，能量动量张量，扭曲-2 QCD运营商（广义部分子分布的时刻）。

英文摘要：

We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($χ$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t > 4 M_π^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $ππ\rightarrow N\bar N$ partial-wave amplitudes and the timelike pion FF. $χ$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $ππ$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $χ$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $πN$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$N_c$ limit of QCD because the $χ$EFT calculation includes $N$ and $Δ$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).

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