Planar Double Box Integral for Top Pair Production with a Closed Top Loop to all orders in the Dimensional...

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Computational Physics

Background:

• Top pair production is crucial for understanding the Standard Model.
• Feynman integrals are essential for precise theoretical predictions in particle physics.
• Elliptic multiscale integrals present significant computational challenges.

Purpose of the Study:

• To compute the Laurent expansion of a specific planar double box Feynman integral.
• To develop a systematic method for solving complex Feynman integrals relevant to top quark physics.
• To demonstrate a technique applicable to elliptic multiscale integrals.

Main Methods:

• Systematic computation of the Laurent expansion in the dimensional regularization parameter epsilon.
• Transformation of differential equations to a strictly lower triangular form.
• Order-by-order solution of the simplified system of equations.

Main Results:

• The Laurent expansion in epsilon for the planar double box Feynman integral was systematically computed.
• A method was established to solve systems of differential equations for Feynman integrals by achieving a lower triangular form.
• The computation involved handling elliptic subtopologies within the integral.

Conclusions:

• The developed method provides an efficient way to handle complex Feynman integrals.
• This approach is applicable to a broader class of elliptic multiscale integrals.
• The results contribute to more precise theoretical predictions in high energy physics.