Higgs pair production at next-to-next-to-leading logarithmic accuracy at the LHC

TL;DR

The paper develops a threshold resummation of soft-gluon effects for Higgs pair production via gluon fusion in the heavy-top limit, achieving NNLL accuracy and matching to NNLO cross sections. Using Mellin space formalism, the authors exponentiate the Sudakov factor and compute the required coefficients C_gg^(1,2) to NNLL, enabling precise predictions with reduced perturbative uncertainties. Numerical results at the LHC show a modest cross section increase (up to about 7% at 14 TeV) and significantly reduced scale uncertainties (~5-6%), while finite top-mass uncertainties remain ~10%. The study demonstrates the stability of NNLL predictions with respect to central scales and provides improved benchmarks for Higgs self-coupling assessments via HH production.

Abstract

We perform the threshold resummation for Higgs pair production in the dominant gluon fusion channel to next-to-next-to-leading logarithmic (NNLL) accuracy. The calculation includes the matching to the next-to-next-to-leading order (NNLO) cross section obtained in the heavy top-quark limit, and results in an increase of the inclusive cross section up to 7% at the LHC with centre-of-mass energy Ecm=14TeV, for the choice of factorization and renormalization scales $μ_F=μ_R=Q$, being Q the invariant mass of the Higgs pair system. After the resummation is implemented, we estimate the theoretical uncertainty from the perturbative expansion to be reduced to about +-5.5%, plus ~10% from finite top-mass effects. The resummed cross section turns out to be rather independent of the value chosen for the central factorization and renormalization scales in the usual range (Q/2,Q).

Figures (5)

• Figure 1: The Higgs pair invariant mass distribution for $E_{cm}=14\text{ TeV}$ and the central scale $\mu_0=Q$, for the fixed order (left) and resummed (right) predictions. In the left (right) we show the LO (LL), NLO (NLL) and NNLO (NNLL) curves, with blue dotted, red dashed and black solid lines respectively.
• Figure 3: The $K$-factors for the fixed order and resummed cross sections as a function of the Higgs pair invariant mass, for $E_{cm}=14\text{ TeV}$. The left (right) panel shows the results for $\mu_0=Q$ ($\mu_0=Q/2$). The color coding is the same of Figure \ref{['dsdQ_14_mu1']}.
• Figure 4: The ratio between the NNLL and the NNLO predictions as a function of the Higgs pair invariant mass, for the scales $\mu=Q$ (left) and $\mu=Q/2$ (right). Results are shown for center of mass energies of $8\text{ TeV}$ (orange solid), $14\text{ TeV}$ (magenta dashed), $33\text{ TeV}$ (purple dot-dashed) and $100\text{ TeV}$ (black dotted).
• Figure 5: The scale dependence of the total cross section at $E_{cm}=14\text{ TeV}$, for the fixed order (upper) and resummed (lower) predictions. The color coding is the same of Figure \ref{['dsdQ_14_mu1']}.
• Figure 6: The total fixed order (FO) and resummed (RES) cross sections at leading (blue circle), next-to-leading (red square) and next-to-next-to-leading (black triangle) accuracy, for $E_{cm}=8\text{ TeV}$ (left) and $14\text{ TeV}$ (right), for both central scales $\mu_0=Q$ and $\mu_0=Q/2$. The vertical solid lines indicate the scale uncertainty. The horizontal dotted lines indicate in each case the best prediction (NNLL).