论文标题
大动量有效场理论的手性扰动
Chiral Perturbation for Large Momentum Effective Field Theory
论文作者
论文摘要
大动量有效场理论（LAMET）可以通过将计算的准PDF与PDFS的分解定理直接在欧几里得晶格上提取Parton分布函数（PDF）。我们将手性扰动理论（CHPT）应用于叶片上，以进一步分开软尺度，例如光夸克质量和晶格大小，以获得领先的模型独立外推公式，以外推到物理夸克质量和无限体积。我们发现，当核子带有有限动量时，有限体积效应会降低。对于大于$ 1 $ gev的核能动量，晶格尺寸$ l $和pion质量$m_π$满足$m_πl\ geq 3 $，有限体积效应不到$ 1 \％\％$，并且对于当前的晶格计算精确度而言是可忽略的。这可以解释为在$ z $方向上核子大小的洛伦兹收缩，这使得晶格大小在该方向上有效地更大。我们还发现，用非零核子动量计算出的无限体积限制的夸克质量依赖性会如预期的那样重现以零动量计算的先前结果。我们的方法可以概括地将parton的其他可观察物转发。
Large momentum effective field theory (LaMET) enables the extraction of parton distribution functions (PDFs) directly on a Euclidean lattice through a factorization theorem that relates the computed quasi-PDFs to PDFs. We apply chiral perturbation theory (ChPT) to LaMET to further separate soft scales, such as light quark masses and lattice size, to obtain leading model independent extrapolation formulas for extrapolations to physical quark masses and infinite volume. We find that the finite volume effect is reduced when the nucleon carries a finite momentum. For nucleon momentum greater than $1$ GeV and the lattice size $L$ and pion mass $ m_π$ satisfying $m_πL\geq 3$, the finite volume effect is less than $1\%$ and is negligible for the current precision of lattice computations. This can be interpreted as a Lorentz contraction of the nucleon size in the $z$-direction which makes the lattice size effectively larger in that direction. We also find that the quark mass dependence in the infinite volume limit computed with non-zero nucleon momentum reproduces the previous result computed at zero momentum, as expected. Our approach can be generalized to other parton observables in LaMET straight forwardly.
