arXiv nucl-th/03010342003-01-10nucl-th

手征微扰理论中两圈级核子的诱导赝标形状因子

Induced pseudoscalar form factor of the nucleon at two-loop order in chiral perturbation theory

N. Kaiser

备注：: 6 pages, 2 figures, accepted for publication in Physical Review C
发表信息：: Phys.Rev. C67 (2003) 027002
DOI：: 10.1103/PhysRevC.67.027002

摘要：

在双圈重子手征微扰理论框架下，计算了核子$G_P(t)$的诱导赝标形状因子的虚部。在普通μ子俘获$μ^-p\to ν_μn$中，计算出的三π介子连续谱对赝标常数$g_P = (m_μ/2M) G_P(t=-0.877m_μ^2)$的影响可以忽略不计。可能的贡献在两个循环的顺序从计数器项的数值小于占主导地位的π介子-核子耦合常数$g_{πN}= 13.2\pm 0.2$成比例的π介子-极点项的不确定性。我们得出的结论是，低动量转移时核子诱导赝标形状因子的足够准确的表示$t$由π极项和阿德勒-多森-沃尔芬斯坦项之和给出：$G_P(t) = 4g_{πN} M f_π/ (m_π^2 -t)- 2g_A M^2 < r_A^2 >/3$，其中$<r_A^2> = (0.44 \pm 0.02)$ fm $^2$是核子的轴向均方半径。

英文摘要：

We calculate the imaginary part of the induced pseudoscalar form factor of the nucleon $G_P(t)$ in the framework of two-loop heavy baryon chiral perturbation theory. The effect of the calculated three-pion continuum on the pseudoscalar constant $g_P = (m_μ/2M) G_P(t=-0.877m_μ^2)$ measurable in ordinary muon capture $μ^-p\to ν_μn$ turns out to be negligibly small. Possible contributions from counterterms at two-loop order are numerically smaller than the uncertainty of the dominant pion-pole term proportional to the pion-nucleon coupling constant $g_{πN}= 13.2\pm 0.2$. We conclude that a sufficiently accurate representation of the induced pseudoscalar form factor of the nucleon at low momentum transfers $t$ is given by the sum of the pion-pole term and the Adler-Dothan-Wolfenstein term: $G_P(t) = 4g_{πN} M f_π/ (m_π^2 -t)- 2g_A M^2 < r_A^2 >/3$, with $<r_A^2> = (0.44 \pm 0.02)$ fm$^2$ the axial mean square radius of the nucleon.

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