Abstract
We consider matching from ${\mathrm{SCET}}_{\mathrm{I}},$ which includes ultrasoft and collinear particles, onto ${\mathrm{SCET}}_{\mathrm{II}}$ with soft and collinear particles at one loop. Keeping the external fermions off their mass shell does not regulate all IR divergences in both theories. We give a new prescription to regulate infrared divergences in SCET. Using this regulator, we show that soft and collinear modes in ${\mathrm{SCET}}_{\mathrm{II}}$ are sufficient to reproduce all the infrared divergences of ${\mathrm{SCET}}_{\mathrm{I}}.$ We explain the relationship between IR regulators and an additional mode proposed for ${\mathrm{SCET}}_{\mathrm{II}}.$
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