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Symbology of Feynman integrals from twistor geometries

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We study the symbology of planar Feynman integrals in dimensional regularization by considering geometric configurations in momentum twistor space corresponding to their leading singularities(LS).Cutting propagators in momentum twistor space amounts to intersecting lines associated with loop and external dual momenta,including the special line associated with the point at infinity,which breaks dual conformal symmetry.We show that cross-ratios of intersection points on these lines,especially those on the infinity line,naturally produce symbol letters for Feynman integrals in D=4-2e,which include and generalize their LS.At one loop,we obtain all symbol letters using intersection points from quadruple cuts for integrals up to pentagon kinematics with two massive comers,which agree perfectly with canonical differential equation(CDE)results.We then obtain all two-loop letters,for up to four-mass box and one-mass pentagon kinematics,by considering more intersections arising from two-loop cuts.Finally we comment on how cluster algebras appear from this construction,and importantly how we may extend the method to non-planar integrals.

Feynman integralssymbol letterstwistor geometry

Song He、Jiahao Liu、Yichao Tang、Qinglin Yang

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School of Fundamental Physics and Mathematical Sciences,Hangzhou Institute for Advanced Study,UCAS,Hangzhou 310024,China

CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China

International Centre for Theoretical Physics Asia-Pacific,Beijing 100049/Hangzhou 310024,China

Peng Huanwu Center for Fundamental Theory,Hefei 230026,China

School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

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New Cornerstone Science Foundation through the XPLORER PRIZE国家自然科学基金国家自然科学基金国家自然科学基金国家自然科学基金

12225510119350131204750312247103

2024

10.1007/s11433-023-2264-8

中国科学:物理学 力学 天文学(英文版)
中国科学院

中国科学:物理学 力学 天文学(英文版)

CSTPCD
影响因子：0.91
ISSN：1674-7348
年,卷(期)：2024.67(3)
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