Analytic structure of all loop banana integrals
Analytic structure of all loop banana integrals
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DOI：
10.1007/jhep05(2021)066
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发表时间：
2020-08
影响因子：
5.4
通讯作者：
Kilian Bönisch;Fabian Fischbach;A. Klemm;Christoph Nega;R. Safari
中科院分区：
文献类型：
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作者：
Kilian Bönisch;Fabian Fischbach;A. Klemm;Christoph Nega;R. Safari
利用Gelfand-Kapranov-Zelevinskirt系统对维数为环阶减1的完全相交Calabi-Yau流形的无穷级数的本原上同调，完全阐明了所有具有任意质量的香蕉积分的解析结构.特别是，我们发现高能区域中对应于最大幂单值点的领先对数结构由镜子周围空间中的新估值确定，而该区域中积分的虚部则由镜子决定。卡拉比-丘流形本身。我们为前者以及Frobenius κ-常数提供了简单的闭环公式，它决定了当动量平方等于质量平方和时积分的行为，以zeta值表示。我们扩展我们以前的工作，从三个到四个循环，为后一种情况下提供了一套完整的（非齐次）皮卡-富克斯微分方程的任意质量。这允许在非常短的时间内对所有物理参数值进行非常高的数值精度的香蕉积分。利用模的周期性质，我们确定的最大切割等质量四圈积分的值在吸引点的模权2和4 Hecke特征形和准周期的亚纯表兄弟。
Using the Gelfand-Kapranov-Zelevinskĭ system for the primitive cohomology of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of all banana integrals with arbitrary masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novelevaluation in the ambient spaces of the mirror, while the imaginary part of the integral in this regime is determined by theof the mirror Calabi-Yau manifold itself. We provide simple closed all loop formulas for the former as well as for the Frobenius κ-constants, which determine the behaviour of the integrals when the momentum square equals the sum of the masses squared, in terms of zeta values. We extend our previous work from three to four loops by providing for the latter case a complete set of (inhomogeneous) Picard-Fuchs differential equations for arbitrary masses. This allows to evaluate the banana integral in very short time to very high numerical precision for all values of the physical parameters. Using modular properties of the periods we determine the value of the maximal cut equal mass four-loop integral at the attractor points in terms of periods of modular weight two and four Hecke eigenforms and the quasiperiods of their meromorphic cousins.