Heavy Quark Form Factors Research Articles

Three loop QCD corrections to heavy quark form factors

Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated integrals over an alphabet the structure of which is implied by the coefficient matrix of the given system. We apply this method to calculate the master integrals in the color–planar and complete light quark contributions to the three-loop massive form factors.

Asymptotic behavior of the heavy quark form factors at higher order

In the asymptotic limit $Q^2 \gg m^2$, the heavy quark form factors exhibit Sudakov behavior. We study the corresponding renormalization group equations of the heavy quark form factors which do not only govern the structure of infrared divergences, but also control the high energy logarithms. This enables us to obtain the complete logarithmic three--loop and partial four--loop contributions to the heavy quark form factors in perturbative Quantum Chromodynamics.

Heavy quark form factors at three loops in the planar limit

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.

Heavy quark form factors at two loops

We compute the two-loop QCD corrections to the heavy quark form factors in case of the vector, axial-vector, scalar and pseudo-scalar currents up to second order in the dimensional parameter $\epsilon = (4-D)/2$. These terms are required in the renormalization of the higher order corrections to these form factors.

Heavy-quark form factors in the large beta _0 limit

Heavy-quark form factors are calculated at beta _0 alpha _s sim 1 to all orders in alpha _s at the first order in 1/beta _0. Using the inversion relation generalized to vertex functions, we reduce the massive on-shell Feynman integral to the HQET one. This HQET vertex integral can be expressed via a {}_2F_1 function; the nth term of its varepsilon expansion is explicitly known. We confirm existing results for n_l^{L-1} alpha _s^L terms in the form factors (up to L=3), and we present results for higher L.

Heavy-quark Form Factors at Two Loops in Perturbative QCD

We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization parameter. We outline the necessary computational details, ultraviolet renormalization and corresponding universal infrared structure.

Two-loop QCD corrections to the heavy quark form factors: Anomaly contributions

We present closed analytic expressions for the order α s 2 triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark–antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.

Two-loop QCD corrections to the heavy quark form factors: Axial vector contributions

We consider the Z ∗ Q Q ¯ vertex to order α S 2 in the QCD coupling for an on-shell massive quark–antiquark pair and for arbitrary momentum transfer of the Z boson. We present closed analytic expressions for the two parity-violating form factors of that vertex at the two-loop level in QCD, excluding the contributions from triangle diagrams. These form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

Two-loop QCD corrections to the heavy quark form factors: the vector contributions

We present closed analytic expressions of the electromagnetic vertex form factors for heavy quarks at the two-loop level in QCD for arbitrary momentum transfer. The calculation is carried out in dimensional regularization. The electric and magnetic form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.