A non-linear representation of general scalar extensions of the Standard Model for HEFT matching - Huayang Song; Xia Wan (Journal of High Energy Physics)
Abstract We introduce a non-linear representation of ultraviolet (UV) complete model, U representation, under which matching HEFT to general scalar extensions of the standard model is straightforward. The main idea is to express a scalar multiplet in its symmetric tensor representation rotated by U matrices, where U matrix is exponential form of Goldstones based on Pauli matrices and meanwhile is a special SU(2) L rotation. All together the doublet is expressed in U matrix multiplying a doublet column (or a bidoublet matrix), which is composed of physical Higgs. Under these forms, in the UV Lagrangian there leave no mass mixing or kinetic mixing among U matrix and physical states, thus the Goldstones could be kept in U matrix throughout HEFT matching, and the matching process under functional method is much simplified. As an example, using U representation we show a complete matching between HEFT and the real triplet extension of Standard Model in a decoupling scenario.