Exploring correlations between HEFT Higgs couplings $$\kappa _V$$ and $$\kappa _{2V}$$ via HH production at $$e^+e^-$$ colliders release_saclzy34mfh4nfbux2km6othai

by J. M. Dávila, D. Domenech, M. J. Herrero, Roberto A. Morales

Published in European Physical Journal C: Particles and Fields by Springer Science and Business Media LLC.

2024   Volume 84, Issue 5

Abstract

<jats:title>Abstract</jats:title>In this work we explore the phenomenological implications at future <jats:inline-formula><jats:alternatives><jats:tex-math>$$e^+e^-$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> colliders of assuming anomalous couplings of the Higgs boson to gauge bosons <jats:italic>HVV</jats:italic> and <jats:italic>HHVV</jats:italic><jats:inline-formula><jats:alternatives><jats:tex-math>$$(V=W,Z)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>V</mml:mi> <mml:mo>=</mml:mo> <mml:mi>W</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> given by the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-modifiers with respect to the Standard Model couplings, <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa _V$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mi>V</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa _{2V},$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> respectively. For this study we use the Higgs Effective Field Theory (HEFT) where these two <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> parameters are identified with the two most relevant effective couplings at leading order, concretely <jats:inline-formula><jats:alternatives><jats:tex-math>$$a=\kappa _V$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>κ</mml:mi> <mml:mi>V</mml:mi> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$b=\kappa _{2V}.$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> Our focus is put on these two couplings and their potential correlations which we believe carry interesting information on the underlying ultraviolet theory. The particular studied process is <jats:inline-formula><jats:alternatives><jats:tex-math>$$e^+e^- \rightarrow HH \nu \bar{\nu },$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>H</mml:mi> <mml:mi>H</mml:mi> <mml:mi>ν</mml:mi> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>,</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> where the vector boson scattering subprocess <jats:inline-formula><jats:alternatives><jats:tex-math>$$WW \rightarrow HH$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>W</mml:mi> <mml:mi>W</mml:mi> <mml:mo>→</mml:mo> <mml:mi>H</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> plays a central role, specially at the largest planned energy colliders. Our detailed study of this process as a function of the energy and the angular variables indicates that the produced Higgs bosons in the BSM scenarios will have in general a high transversality as compared to the SM case if <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa _V^2 \ne \kappa _{2V}.$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>κ</mml:mi> <mml:mi>V</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>≠</mml:mo> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> In order to enhance the sensitivity to these HEFT parameters <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa _V$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mi>V</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\kappa _{2V}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and their potential correlations we propose here some selected differential cross sections for the <jats:inline-formula><jats:alternatives><jats:tex-math>$$e^+e^- \rightarrow HH \nu \bar{\nu }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>H</mml:mi> <mml:mi>H</mml:mi> <mml:mi>ν</mml:mi> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> process, where different kinematic properties of the BSM case with respect to the SM are manifested. Finally, we will focus on the dominant Higgs decays to <jats:inline-formula><jats:alternatives><jats:tex-math>$$b {\bar{b}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mover> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> pairs leading to final events with 4 <jats:italic>b</jats:italic>-jets and missing transverse energy from the undetected neutrinos and will provide the expected accessibility to the <jats:inline-formula><jats:alternatives><jats:tex-math>$$(\kappa _V,\kappa _{2V})$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>κ</mml:mi> <mml:mi>V</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> effective couplings and their potential correlations. In our study we will consider the three projected energies for <jats:inline-formula><jats:alternatives><jats:tex-math>$$e^+e^-$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> colliders of 500 GeV, 1000 GeV and 3000 GeV.
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