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<p>We introduce a non-linear representation of ultraviolet (UV) complete model, <i>U representation</i>, 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 <i>U</i> matrices, where <i>U</i> matrix is exponential form of Goldstones based on Pauli matrices and meanwhile is a special SU(2)<sub><i>L</i></sub> rotation. All together the doublet is expressed in <i>U</i> 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 <i>U</i> matrix and physical states, thus the Goldstones could be kept in <i>U</i> matrix throughout HEFT matching, and the matching process under functional method is much simplified. As an example, using <i>U representation</i> we show a complete matching between HEFT and the real triplet extension of Standard Model in a decoupling scenario.</p>

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A non-linear representation of general scalar extensions of the Standard Model for HEFT matching

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  • 发表日期：

    2025年6月4日

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  • Huayang Song,
  • Xia Wan

摘要

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.