Building blocks for subleading helicity operators

Abstract

On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in the Soft-Collinear Effective Theory (SCET) away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. We also describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.

A complete basis of helicity operators for subleading factorization

“…We focus in particular on the treatment of operators involving ultrasoft fields, and use the BPS field redefinition to define collinear and ultrasoft gauge invariant operator building blocks. Additionally, selection rules on the hard scattering operators due to angular momentum conservation are described [72]. Extensions of the formalism to SCET II as well as SCET with massive collinear quarks are also discussed, as are complications associated with evanescent operators.…”

“…In this section we discuss the extension of the helicity operator approach of [73] to subleading powers. We review the full set of subleading power building block operators introduced in [72], and provide more details about them. In section 3.1 we describe operators involving only collinear fields, and in section 3.2 we describe operators involving insertions of the P ⊥ operator.…”

“…We now look at how to treat the sectors at subleading power that contain multiple collinear fields, as was discussed in [72]. Collinear gluons appear in gauge invariant building blocks of definite helicity, and therefore operators with multiple collinear gluons in the same sector can simply be obtained by multiplying copies of the gluon building blocks, such as B a i+ B b i+ .…”

“…Indeed, the scalar currentχ n i χ n i = 0, vanishes, as do the plus and minus helicity components of the vector currentχ n i γ ± ⊥ χ n i = 0. We therefore define the helicity operators involving two collinear quarks in the same sector as [72] h=0:…”

“…Using the results of ref. [72], we further develop and explore a set of SCET helicity operator building blocks which is valid for constructing operator bases at any order in the power expansion. These operators extend the leading power basis of ref.…”