Joint Resummation for Higgs Production

TL;DR

This work applies the joint resummation formalism to Higgs production via gluon fusion, unifying threshold and recoil resummation at NLL accuracy in a heavy-top effective theory. The cross section is computed through a double inverse transform in Mellin-N and impact-parameter space, with an interpolating function χ(bQ,N) that blends large-N and large-b limits and a Sudakov exponent that incorporates known NNLL terms. Numerical results show that threshold effects are modest at small to moderate Higgs transverse momentum, while the inclusive cross section is notably reduced relative to pure threshold resummation due to non-threshold small-x contributions; adjustments to coefficient functions can alter the total rate and high-Q_T behavior. The study highlights the importance of non-threshold effects and motivates extending the joint resummation framework to NNLL to achieve more precise predictions for LHC Higgs phenomenology.

Abstract

We study the application of the joint resummation formalism to Higgs production via gluon-gluon fusion at the LHC, defining inverse transforms by analytic continuation. We work at next-to-leading logarithmic accuracy. We find that at low Q_T the resummed Higgs Q_T distributions are comparable in the joint and pure-Q_T formalisms, with relatively small influence from threshold enhancement in this range. We find a modest (about ten percent) decrease in the inclusive cross section, relative to pure threshold resummation.

Figures (5)

• Figure 1: Choice of contour for $b$ integration (thick solid lines) for $\eta=1$. The straight sections of the contour from $0$ to $b_c$ are to be interpreted as on the positive real axis. The remaining curves represent lines of singularity discussed in KSV.
• Figure 2: Transverse momentum distribution for Higgs production at the LHC in the framework of joint resummation and of "pure-$Q_T$" resummation.
• Figure 3: Dependence of the jointly resummed transverse momentum distribution for Higgs production at the LHC on the value of the parameter $\eta$.
• Figure 4: Fractional deviation $\Delta$ (as defined in Eq. (\ref{['frdev']})) between the "exact" ${\cal O} (\alpha s{$α_s${ }})$ result and the ${\cal O} (\alpha s{$α_s${ }})$ expansion of the jointly and the pure-$Q_T$ resummed cross sections.
• Figure 5: Effect of introducing extra terms in the $C$ coefficients, as shown in Eq. (\ref{['ccoeff1']}) and discussed in the text, on the transverse momentum distribution for Higgs production at the LHC in the framework of joint resummation.