On symbology and differential equations of Feynman integrals from Schubert analysis

We take the first step in generalizing the so-called "Schubert analysis", originally proposed in twistor space for four-dimensional kinematics, to the study of symbol letters and more detailed information on canonical differential equations for Feynman integral families in general dimensions with general masses. The basic idea is to work in embedding space and compute possible cross-ratios built from (Lorentz products of) maximal cut solutions for all integrals in the family. We demonstrate the power of the method using the most general one-loop integrals, as well as various two-loop planar integral families (such as sunrise, double-triangle and double-box) in general dimensions. Not only can we obtain all symbol letters as cross-ratios from maximal-cut solutions, but we also reproduce entries in the canonical differential equations satisfied by a basis of dlog integrals.Comment: 51 pages, many figure

ε\varepsilon-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves

In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain $\varepsilon$-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders.Comment: Journal version. Add the Lambert series for the Y-invarian

ε\varepsilon-forms for non-planar triangles with elliptic curves at two loops

In this talk, we discuss how to generalize ideas developed for Banana integrals to two two-loop non-planar triangle Feynman integrals involving elliptic curves, which have non-trivial sub-sectors and whose Picard-Fuchs operators share less symmetry than Banana integrals, to obtain the canonical differential equations and to solve them with suitable boundary conditions.Comment: RADCOR202

On symbology and differential equations of Feynman integrals from Schubert analysis

Abstract We take the first step in generalizing the so-called “Schubert analysis”, originally proposed in twistor space for four-dimensional kinematics, to the study of symbol letters and more detailed information on canonical differential equations for Feynman integral families in general dimensions with general masses. The basic idea is to work in embedding space and compute possible cross-ratios built from (Lorentz products of) maximal cut solutions for all integrals in the family. We demonstrate the power of the method using the most general one-loop integrals, as well as various two-loop planar integral families (such as sunrise, double-triangle and double-box) in general dimensions. Not only can we obtain all symbol letters as cross-ratios from maximal-cut solutions, but we also reproduce entries in the canonical differential equations satisfied by a basis of d log integrals

ε-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves

Abstract In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain ε-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders

Proof of Principle of the Lunar Soil Volatile Measuring Instrument on Chang’ e-7: In Situ N Isotopic Analysis of Lunar Soil

The nitrogen isotopic compositions of lunar soil have important implications for the sources of lunar volatiles and even the evolution of the moon. At present, the research on the lunar nitrogen isotopic compositions is mainly based on the lunar meteorites and the samples brought back by the Apollo and Luna missions. However, volatiles adsorbed on the surface of the lunar soil may be lost due to changes in temperature and pressure, as well as vibration and shock effects when the sample is returned. At the same time, in the case of low N content in the sample, since N is the main component of the earth’s atmosphere, it is easily affected by the atmosphere during the analysis process. Therefore, in situ nitrogen isotopic analysis of lunar soil on orbit is necessary to avoid the problems mentioned above and is one of the primary science goals for the Lunar Soil Volatile Measuring instrument on Chang’e-7 spacecraft. After the nitrogen purification procedure, the volatiles in lunar soil that are released through single-step or stepped heating techniques diffuse to the quadrupole mass spectrometer to obtain the N contents and isotopic compositions of the lunar soil. This paper introduces the ground test for N isotopic analysis of lunar soil in orbit according to the Lunar Soil Volatile Measuring Instrument. After long-term repeated measurements, the background and CO-corrected Air-STD 14N/15N ratio is 268.986 ± 4.310 (1SD, n = 35), and the overall reproducibility of measurements is 1.6%. The accuracy of N isotopic compositions is calculated to be better than 5%, which can distinguish different sources of N components in lunar soil