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Full order alpha electroweak corrections to double Higgs-strahlung at the linear collider

G. Belanger, F. Boudjema, J. Fujimoto, T. Ishikawa, T. Kaneko Y. Kurihara, K. Kato, Y. Shimizu

TL;DR

This work delivers the complete $O(\alpha)$ electroweak corrections to the double Higgs-strahlung process $e^+e^- \to ZHH$ using GRACE-loop, including a careful separation of QED and genuine weak effects. It shows that while initial-state radiation drives large QED corrections near threshold, the genuine weak corrections are small (∼a few percent) at energies where the cross section is largest, with more pronounced negative corrections at higher energies. The study also analyzes how these corrections affect the invariant mass distribution $M_{HH}$, finding that QED effects can distort the distribution via radiative return, whereas weak corrections mostly scale the rate without drastically altering the shape. The results underscore the necessity of ISR resummation for precision Higgs self-coupling measurements at a linear collider and indicate that the triple-Higgs coupling could still be probed effectively with proper radiative corrections included.

Abstract

We present the full order alpha electroweak radiative corrections to the double Higgs-strahlung process e+e- --> ZHH. The computation is performed with the help of GRACE-loop. After subtraction of the initial state QED radiative corrections, we find that the genuine weak corrections in the $α$-scheme are small for Higgs masses and energies where this cross section is largest and is most likely to be studied. These corrections decrease with increasing energies attaining about $\sim -10%$ at $\sqrt{s}=1.5$TeV. The full order alpha correction on the other hand is quite large at threshold but small at energies around the peak. We also study changes in the shape of the invariant mass of the Higgs pair which has been shown to be a good discriminating variable for the measurement of the triple Higgs vertex in this reaction.

Full order alpha electroweak corrections to double Higgs-strahlung at the linear collider

TL;DR

This work delivers the complete electroweak corrections to the double Higgs-strahlung process using GRACE-loop, including a careful separation of QED and genuine weak effects. It shows that while initial-state radiation drives large QED corrections near threshold, the genuine weak corrections are small (∼a few percent) at energies where the cross section is largest, with more pronounced negative corrections at higher energies. The study also analyzes how these corrections affect the invariant mass distribution , finding that QED effects can distort the distribution via radiative return, whereas weak corrections mostly scale the rate without drastically altering the shape. The results underscore the necessity of ISR resummation for precision Higgs self-coupling measurements at a linear collider and indicate that the triple-Higgs coupling could still be probed effectively with proper radiative corrections included.

Abstract

We present the full order alpha electroweak radiative corrections to the double Higgs-strahlung process e+e- --> ZHH. The computation is performed with the help of GRACE-loop. After subtraction of the initial state QED radiative corrections, we find that the genuine weak corrections in the -scheme are small for Higgs masses and energies where this cross section is largest and is most likely to be studied. These corrections decrease with increasing energies attaining about at TeV. The full order alpha correction on the other hand is quite large at threshold but small at energies around the peak. We also study changes in the shape of the invariant mass of the Higgs pair which has been shown to be a good discriminating variable for the measurement of the triple Higgs vertex in this reaction.

Paper Structure

This paper contains 12 sections, 13 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Grace-Loop and the calculation of $e^+ e^- \rightarrow Z H H\;$
  3. Checks on the one-loop result
  4. The five point function
  5. Input parameters
  6. Overview of the Feynman diagrams
  7. Results
  8. Tree-level
  9. QED corrections: Slicing vs subtracting
  10. The genuine weak corrections
  11. Corrections to the $M_{HH}$ distribution
  12. Conclusions

Figures (4)

  • Figure 1: A small selection of different classes of loop diagrams contributing to $e^+ e^- \rightarrow Z H H\;$. We keep the same graph numbering as that produced by the system. The first three graphs represent corrections to the $HHH$ vertex. Graph 720 and Graph 805 are box corrections representing $Z^\star,\gamma^\star \rightarrow HHZ$. Graph 3369 is a $t$-channel induced diagram with $W^+ W^- \rightarrow Z H^\star$ as a subprocess. Graph 3417 is a typical pentagon diagram. Graph 5415 is a two-point function correction. We do not show the QED graphs as they amount to dressing the vertex $e^+ e^- Z^\star$.
  • Figure 2: Total cross section for $e^+ e^- \rightarrow Z H H\;$ as a function of the centre of mass energy for $M_H=120,150,180$GeV.
  • Figure 3: The full ${\cal O}(\alpha)$ relative correction (top panel) and the relative electroweak correction $\delta_W$ (lower panel) as a function of energy for $M_H=120,150,180$GeV. In addition, the genuine weak correction $\delta_W^{G}$ in the $G_\mu$ scheme is presented for $M_H=120$GeV (dotted line). The insert shows $\delta_W$ for $e^+ e^- \rightarrow ZH$ for the same three Higgs masses.
  • Figure 4: $d\sigma/d M_{HH}$ for $M_H=120$GeV at $\sqrt{s}=1$TeV. We show the tree-level (full curve), the effect of including only the genuine weak corrections (dotted curve) and the effect of including the full ${\cal O}(\alpha)\;$ (dashed curve).