Spectator interactions in soft-collinear effective theory

Abstract

Soft-collinear effective theory is generalized to include soft massless quarks in addition to collinear fields. This extension is necessary for the treatment of interactions with the soft spectator quark in a heavy meson. The power counting of the relevant fields and the construction of the effective Lagrangian are discussed at leading order in Λ/m b . Several novel effects occur in the matching of full-theory amplitudes onto effective-theory operators containing soft light quarks, such as the appearance of an intermediate mass scale and large non-localities of operators on scales of order 1/Λ. Important examples of effective-theory operators with soft light quarks are studied and their renormalization properties explored. The formalism presented here forms the basis for a systematic analysis of factorization and power corrections for any exclusive B-meson decay into light particles.

Factorization and NNLL Resummation for Higgs production with a jet veto

“…The jet veto then implies an upper bound on the vector sum of the transverse momenta of all particles, which is equivalent to a bound on the transverse momentum of the Higgs boson. Assuming that the formalism of [17] is still valid 1 in the limit of very large R, we can then match the R-dependent two-loop terms obtained in this paper with the ones following from (31) and from the results obtained in our previous work [23,44] for the transverse-momentum spectrum of the Higgs boson. In this way, we obtain…”

“…Up to the order shown in the equations above, the functions F gg and I g←i entering the factorization formulae (30) and (31) are closely related to corresponding quantities entering the resummed cross section for Higgs production at small transverse momentum [23,44]. The only difference is that in that case L ⊥ = ln(x 2 T µ 2 /b 2 0 ) with b 0 = 2e −γ E .…”

“…The formalism of expressing SCET operators in terms of gauge-invariant building blocks is described, e.g., in [21,31]. In the present case, the corresponding matching relation reads [7] G…”

Factorization at subleading power and irreducible uncertainties in $ \bar{B} \to {X_s}\gamma $ decay

“…The quantities Wn and W n are the familiar (anti-)hard-collinear Wilson lines of SCET. Similarly, we define the hard-collinear and anti-hard-collinear gluon fields [58] …”

Effective field theory for large logarithms in radiative corrections to electron proton scattering

“…Here we outline the evaluation of the mixed real-virtual corrections using a decomposition into soft and collinear momentum regions, formalized as soft-collinear effective theory [18][19][20][21][22][23][24][25]. We first review the analysis of vertex corrections.…”