Heavy Quark Form Factors at Three Loops in the Planar Limit

Abstract

We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for all first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.

Figures (4)

• Figure 1: The color-planar topologies
• Figure 2: The $n_l$ topologies
• Figure 3: The $O(\varepsilon^0)$ contribution to the axialvector three-loop form factors $F_{A,1}^{(3)}$ (left) and $F_{A,2}^{(3)}$ (right) as a function of $x$. Dash-dotted line: leading color contribution of the non-singlet form factor; Full line: sum of the complete non-singlet $n_l$-contributions for $n_l =5$ and the color-planar non-singlet form factor; Dashed line: large $x$ expansion; Dotted line: small $x$ expansion.
• Figure 4: The $O(\varepsilon^0)$ contribution to the scalar and pseudoscalar three-loop form factors $F_S^{(3)}$ (left) and $F_P^{(3)}$ (right) as a function of $x$. Dash-dotted line: leading color contribution of the non-singlet form factor; Full line: sum of the complete non-singlet $n_l$-contributions for $n_l =5$ and the color-planar non-singlet form factor; Dashed line: large $x$ expansion; Dotted line: small $x$ expansion.