Abstract
Factorization theorems play a crucial role in our understanding of the strong interaction. For collider processes they are typically formulated at leading power and much less is known about power corrections in the λ ≪ 1 expansion. Here we present a complete basis of power suppressed operators for a scalar quark current at mathcal{O}left({lambda}^2right) in the amplitude level power expansion in the Soft Collinear Effective Theory, demonstrating that helicity selection rules significantly simplify the construction. This basis applies for the production of any color singlet scalar in qoverline{q} annihilation (such as boverline{b}to H ). We also classify all operators which contribute to the cross section at mathcal{O}left({lambda}^2right) and perform matching calculations to determine their tree level Wilson coefficients. These results can be exploited to study power corrections in both resummed and fixed order perturbation theory, and for analyzing the factorization properties of gauge theory amplitudes and cross sections at subleading power.
Highlights
Studying the behavior of observables at all orders in perturbation theory is an important goal towards the understanding of the theory of strong interactions
We present a complete basis of power suppressed operators for a scalar quark current at O(λ2) in the amplitude level power expansion in the Soft Collinear Effective Theory, demonstrating that helicity selection rules significantly simplify the construction
We present a complete operator basis to O(λ2) in the Soft Collinear Effective Theory (SCET) power expansion using operators of definite helicity [17, 19, 25], and discuss how helicity selection rules simplify the structure of the basis
Summary
Studying the behavior of observables at all orders in perturbation theory is an important goal towards the understanding of the theory of strong interactions. We perform the tree level matching onto our operators These results can be used to study subleading power corrections either in fixed order, or resummed perturbation theory, and are intended to compliment recent analyses for the case of vector quark currents [19] and color singlet scalar production in gluon fusion [21]. If the leading power glauber lagrangian, L(G0), is proven to be irrelevant, the Hilbert spaces for the soft and collinear degrees of freedom are factorized, and the cross section can be written as a product of squared matrix elements, each involving only collinear fields or soft fields after a series of algebraic manipulations, such as the application of color and dirac fierz identities This procedure it is used to define each of the functions appearing in eq (1.5) in terms of hard scattering operators and Lagrangian insertions in SCET. Some extensions are included in the appendices, including enumerating operators with an additional Lagrangian mass insertion that causes a helicity flip
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