论文标题
IBP减少系数变得简单
IBP reduction coefficients made simple
论文作者
论文摘要
我们提出了一种有效的方法，可以缩短逐件分析积分（IBP）还原系数的系数。对于我们的方法，我们开发了Leinartas的多元部分分数算法的改进版本，并根据计算机代数系统单数提供了现代实现。此外，我们观察到，在具有统一的先验（UT）权重的整体基础上，相对于UT基础，IBP还原系数的分母是符号字母或纯粹的多项式，纯粹是在空间尺寸$ d $中。在UT的基础上，部分分数算法在其性能和尺寸降低方面都更有效。我们表明，在存在UT基础的复杂示例中，IBP降低系数的大小可以降低到$ \ sim 100 $的一倍。我们观察到，我们的算法对于没有UT基础的设置也很好。
We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas' multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, We observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension $D$. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as $\sim 100$. We observe that our algorithm also works well for settings without a UT basis.
