Twistor-inspired construction of massive quark amplitudes

Abstract

The analog of the Cachazo -Svrček -Witten rules for scattering amplitudes with massive quarks is derived following an approach previously employed for amplitudes with massive scalars. A prescription for the external wave-functions is given that leads to a one-to-one relation between fields in the action and spin-states of massive quarks. Several examples for the application of the rules are given and the structure of some all-multiplicity amplitudes with a pair of massive quarks is discussed. The rules make supersymmetric relations to amplitudes with massive scalars manifest at the level of the action. The formalism is extended to several quark flavors with different masses.

Holonomies of gauge fields in twistor space 6: Incorporation of massive fermions

“…We can check the validity of our definitions (3.3)-(3.6) for the massless fermions as follows. From the study of fermionic extension of the CSW rules, we find that the next-to-UHV (NUHV) vertices, i.e., vertices of an arbitrary number of positive-helicity gluon plus one negative-helicity gluon and a pair of fermions, can be calculated as [12,13]:…”

“…Notation of fermions here is different from the one found in the literature. For example, in [13] light-cone treatment of fermions is used and they are denoted byψ ± , ψ ± ; these are related to our chiral notation by ψ − ⇔ ψ L , ψ + ⇔ ψ R ,ψ − ⇔ψ R and ψ + ⇔ψ L . Carrying out the Grassmann integrals that are analogous to (2.38), we can easily check that the assignments (3.3)-(3.6) indeed lead to the NUHV vertices (3.8) and (3.9) for massless fermions.…”

“…We continue our discussion to include massive fermions. The massive fermion UHV vertices, the fermionic analogs of (2.35), are given by [13]:…”

“…This feature is qualitatively different from the massive scalar amplitudes where the number of involving gluons can be arbitrary.Recent developments on the calculation of scattering amplitudes in gauge theories within a framework of the spinor-helicity formalism are remarkable. Technically and practically these developments can be recapitulated by a field theoretic prescription, either the CSW rules [1] or the BCFW recursion relation [2,3].Incorporation of massive fermions along the lines of these developments, a main subject of the present paper, has been studied in various methods, e.g., by extension of BCFW-like recursion relations [4,5,6,7] (see also recent progress [8,9]), by use of supersymmetric Ward identities [10,11], and by developing massive versions of the CSW rules [12,13]. (The massive CSW rules are initially developed in [14,15] for the incorporation of massive scalars into the original CSW rules.)…”

“…Incorporation of massive fermions along the lines of these developments, a main subject of the present paper, has been studied in various methods, e.g., by extension of BCFW-like recursion relations [4,5,6,7] (see also recent progress [8,9]), by use of supersymmetric Ward identities [10,11], and by developing massive versions of the CSW rules [12,13]. (The massive CSW rules are initially developed in [14,15] for the incorporation of massive scalars into the original CSW rules.)…”