The flair of Higgsflare: Distinguishing electroweak EFTs with $W_LW_L \to n\times h$

Abstract

The electroweak symmetry-breaking sector is one of the most promising and uncharted parts of the Standard Model; but it seems likely that new electroweak physics may be out of reach of the present accelerator effort and the hope is to observe small deviations from the SM. Given that, Effective Field Theory becomes the logic method to use, and SMEFT has become the standard. However, the most general theory with the known particle content is HEFT, and whether SMEFT suffices should be investigated in future experimental efforts. Building on investigations by other groups that established geometric criteria to distinguish SMEFT from HEFT (useful for theorists examining specific beyond-SM completions), we seek more phenomenological understanding and present an analogous discussion aimed at a broader audience.We discuss various aspects of (multi-) Higgs boson production from longitudinal electroweak gauge bosons WLWL → n × h in the TeV region as the necessary information to characterise the Flare function, F(h), that determines whether SMEFT or HEFT is needed. We also present tree-level amplitudes including contact and exchange channels, as well as a short discussion on accessing F from the statistical limit of many bosons. We also discuss the status of the coefficients of the series expansion of F(h), its validity, whether its complex-h extension can be used to predict or not a tell-tale zero, and how they relate to the dimension-6 and -8 SMEFT operators in the electroweak sector. We derive a set of new correlations among BSM corrections to the HEFT coefficients that help decide, from experimental data, whether we have a viable SMEFT. This analysis can be useful for machines beyond the LHC that could address the challenging final state with several Higgs bosons. CONTENTS 1. Derivation and result at dimension-6 2. Result at dimension-8 III. Geometric and analytic distinction between HEFT and SMEFT A. Flat SM geometry B. Beyond SM: curved φ geometry C. Zero and analyticity of F upon passing from HEFT to SMEFT IV. Generic properties of the flare function F(h) A. Current knowledge of F(h)

Chiral effective theory in the Higgs sector

“…We would like to note the similarities and differences between HEFT and SMEFT [11]: both effective EFT's are based on the gauge symmetry 𝐺; however, SMEFT includes the Higgs ℎ and EW Goldstones 𝜔 𝑎 as a complex doublet Φ, not as separate degrees of freedom. In addition, HEFT is organized according to the chiral counting, while SMEFT is organized according to an expansion in the canonical dimension of the operators.…”

“…An extensive analyses on the SMEFT↔HEFT relation can be found in [11]. Here, we provide a simplified discussion.…”

“…The issue is not whether we write our all-order EFT Lagrangian in the form (26) or (27), the problem is to make sense of the EFT perturbative expansion in that realization [37]. Thus, if one assumes the SMEFT (26) and rewrites it in the L (NL) form, the deviations from the SM in the ℎ𝑊𝑊 and ℎℎ𝑊𝑊 vertices, respectively Δ(𝑎 2 ) = 𝑎 2 − 1 and Δ𝑏 = 𝑏 − 1, have the precise form [11,39] 6…”

“…This EFT is based on the SM symmetries but incorporates both the Higgs and the EW Goldstones all together in a complex doublet Φ. The similarities and differences of both HEFT and SMEFT approaches have been long discussed in the bibliography [11][12][13][14][15][16].…”