Analytic next-to-leading order electroweak corrections to Higgs boson pair production at high energies

Abstract

We compute the complete next-to-leading order electroweak corrections to the form factors entering gluon-induced Higgs boson pair production. We consider the top quark contribution in the limit where the Mandelstam variables are much larger than all other scales involved in the process and compute about a hundred expansion terms in analytic form. They are used to obtain precise numerical results even for fairly low values of the transverse momentum of the Higgs boson. We show that these electroweak corrections at high energies are of the order of $-10\%$. We also discuss the leading logarithmic corrections of the analytic expressions.

Figures (7)

• Figure 1: Sample Feynman diagrams contributing to the NLO electroweak corrections to $gg\to HH$. In the top, middle and bottom row, 1PR, triangle and box diagrams are shown. Note that (c-1) and (c-2) enter the box form factors since there is no Higgs boson propagator.
• Figure 2: Ratio of various $\delta$ and $m_H$ expansion terms normalized to the highest available approximation for $F_{\rm box1}$. Results for the real and imaginary parts are shown as solid and dashed lines, respectively. The expansion depths given in the legend indicate the expansion terms which are are used for the construction of the Padé approximation. Here "$\delta^n, (m_H^{\rm ext})^m$" means that all expansion terms $\delta^k$ and $(m_H^{\rm ext})^l$ with $k\le n$ and $l\le m$ are included. Top row: Fixed expansion depth in $m_H$. Bottom row: Fixed expansion depth in $\delta$.
• Figure 3: $r_{\rm EW}$ for various $\delta$ and $m_H$ expansion terms normalized to highest available approximation for $p_T=400$ GeV. For details concerning the meaning of the legend we refer to the caption of Fig. \ref{['fig::FF_he_ra']}.
• Figure 4: Real and imaginary parts of $F_{\rm box1}^{(0,1)}$ for $p_T=350$ GeV and $p_T=400$ GeV as a function of $\sqrt{s}$ for different expansion depth in $m_t$ used for the Padé approximation, as indicated in the legend: $\{n,m\}$ means that for the construction of the Padé approximation at most expansions up to $(m_t^2)^m$ and at least up to $(m_t^2)^n$ are taken into account.
• Figure 5: $F_{\rm box1}$, $F_{\rm box2}$ and $F_{\rm tri1}$ as a function of $\sqrt{s}$ for fixed $p_T$. Note that the triangle form factor is independent of $p_T$.