Determining the spacetime structure of bottom-quark couplings to spin-zero particles

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Determining the spacetime structure of bottom-quark couplings to spin-zero particles

Tathagata Ghosh, Rohini Godbole, and Xerxes Tata

Phys. Rev. D 100, 015026 – Published 18 July 2019

Abstract

We present a general argument that highlights the difficulty of determining the spacetime structure of the renormalizable bottom-quark Yukawa interactions of the Standard Model Higgs boson, or for that matter of any hypothetical spin-zero particle, at high energy colliders. The essence of the argument is that, it is always possible, by chiral rotations, to transform between scalar and pseudoscalar Yukawa interactions without affecting the interactions of bottom quarks with SM gauge bosons. Since these rotations affect only the $b$ -quark mass terms in the Standard Model Lagrangian, any differences in observables for scalar versus pseudoscalar couplings vanish when $m_{b} \to 0$ , and are strongly suppressed in high energy processes involving the heavy spin-zero particle where the $b$ quarks are typically relativistic. We show, however, that the energy dependence of, for instance, $e^{+} e^{-} \to b \bar{b} X$ (here $X$ denotes the spin-zero particle) close to the reaction threshold may serve to provide a distinction between the scalar versus pseudoscalar coupling at electron-positron colliders that are being proposed, provided that the $X b \bar{b}$ coupling is sizeable. We also note that while various kinematic distributions for $t \bar{t} h$ are indeed sensitive to the spacetime structure of the top-Yukawa coupling, for a spin-zero particle $X$ of an arbitrary mass, the said sensitivity is lost if $m_{X} ≫ m_{t}$ .

Received 27 April 2019

DOI:https://doi.org/10.1103/PhysRevD.100.015026

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Extensions of Higgs sector Particle interactions

Particles & Fields

Authors & Affiliations

Tathagata Ghosh^1,*, Rohini Godbole^2,†, and Xerxes Tata^1,‡

¹Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
²Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560012, India

^*tghosh@hawaii.edu
^†rohini@iisc.ac.in
^‡tata@phys.hawaii.edu

Article Text

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Issue

Vol. 100, Iss. 1 — 1 July 2019

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Images

Figure 1
Left panel: The distribution of $p_{T_{h}}$ in $p p \to t \bar{t} h$ production at the LHC with $\sqrt{s} = 14 TeV$ , assuming that the Lagrangian Yukawa coupling is given by its SM value for both $α_{t} = 0$ as well as $α_{t} = π / 2$ . Right panel: The same distribution normalized to unity. The total cross sections for the two cases are 480.6 and 219.6 fb, respectively.
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Figure 2
Left panel: The distribution of $p_{T_{h}}$ in $p p \to b \bar{b} h$ production at the LHC with $\sqrt{s} = 14 TeV$ , assuming that the Lagrangian Yukawa coupling is given by its SM value for both $α_{b} = 0$ as well as $α_{b} = π / 2$ . Right panel: The same distribution normalized to unity. The purely electroweak contribution where the $h$ is radiated off the virtual $Z$ boson is significant in this case. After the $E_{T} (b) > 30 GeV$ and $| η (b) | < 2.5$ cuts, the cross section for the case $\cos α_{b} = 1$ and $y_{b} = 0$ is 37.1 fb while the corresponding total cross section is 51.4 fb. The impact of the $Z Z h$ coupling, which we assume is absent for the $α_{b} = π / 2$ case, is illustrated by the three histograms shown.
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Figure 3
The left panel shows the differential distribution of $p_{T_{h}}$ produced via $e^{+} e^{-} \to b \bar{b} h$ at an electron-positron collider with $\sqrt{s} = 161 GeV$ for $α_{b} = 0$ and $α_{b} = π / 2$ . As in Fig. 2, we show three histograms for $α_{b} = 0$ and one for $α_{b} = π / 2$ . The dot-dashed green histogram for $α_{b} = π / 2$ and the dashed red histogram for $α_{b} = 0$ are to be read on the right-hand scale. The same distributions, but normalized to unity, are shown in the right panel. The total cross sections for $\cos α_{b} = 1$ and $\sin α_{b} = 1$ cases are 17.2 and $9.75 \times 10^{- 3} ab$ , respectively.
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Figure 4
Differential distributions for kinematic variables, $p_{T_{X}}$ (upper left), $E_{X}$ (upper right), $ϕ^{*}$ (lower left), $θ_{b \bar{b}}$ (lower right) for the process $e^{+} e^{-} \to b \bar{b} X$ for (unpolarized initial beams) at a center-of-mass energy $\sqrt{s} = 161 GeV$ , where $X$ is a spin-zero particle. All distributions are normalized to unity. We take $m_{X} = 100 GeV$ and the Yukawa coupling to bottom quarks $y_{b b X} = 0.7$ .
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Figure 5
Cross section for $e^{+} e^{-} \to b \bar{b} X$ process (with unpolarized beams) for $\cos α_{b} = 1$ and $\sin α_{b} = 1$ , taking $m_{X} = 100 GeV$ and $y_{b b X} = 0.7$ versus $x = \sqrt{s} - m_{X} - 2 m_{b}$ , including beamstrahlung effects on a linear scale (left frame). We also show the same cross section using a log scale (right frame) to show the behavior close to the threshold, $x = 0$ , along with straight lines that illustrate quadratic and cubic rise of the cross section. The inset on the left frame shows the same cross section with (solid) and without (dashed) beamstrahlung in linear scale.
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Figure 6
In the top panel we show the invariant mass distributions for $t \bar{t} h$ production at the LHC, for $m_{h} = 125 GeV$ . In the two lower panels we show invariant mass distributions for $m_{h} = 250$ and 400 GeV.
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Physical Review D

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