Associated Higgs production with top quarks at the Large Hadron Collider: NLO QCD corrections

TL;DR

The paper delivers a full next-to-leading order QCD calculation for the associated production of a Higgs boson with a top-quark pair at the LHC, including all relevant partonic channels ($gg$, $q\bar{q}$, and $(q,\bar{q})g$). It tackles the computational challenges of pentagon loop integrals and infrared/ultraviolet divergences via rigorous renormalization and two independent phase-space slicing schemes, confirming cutoff independence and cross-checks between methods. The results show a significantly reduced renormalization/factorization scale dependence and a net increase in the cross section across a broad Higgs-mass range, yielding a theoretical uncertainty around 15–20% and providing a robust prediction for top-Yukawa coupling studies at the LHC. The methodology and insights extend to related Higgs production processes, reinforcing the ttH channel as a key probe of the Higgs sector and the top quark Yukawa coupling.

Abstract

We present in detail the calculation of the O(alpha_s^3) inclusive total cross section for the process pp -> t-tbar-h, in the Standard Model, at the CERN Large Hadron Collider with center-of-mass energy sqrt(s_H)=14 TeV. The calculation is based on the complete set of virtual and real O(alpha_s) corrections to the parton level processes q-qbar -> t-tbar-h and gg -> t-tbar-h, as well as the tree level processes (q,qbar)g -> t-tbar-h-(q,qbar). The virtual corrections involve the computation of pentagon diagrams with several internal and external massive particles, first encountered in this process. The real corrections are computed using both the single and the two cutoff phase space slicing method. The next-to-leading order QCD corrections significantly reduce the renormalization and factorization scale dependence of the Born cross section and moderately increase the Born cross section for values of the renormalization and factorization scales above m_t.

Figures (12)

• Figure 1: Feynman diagrams contributing to the tree level process $gg\to t\bar{t}h$. The circled crosses indicate all possible insertions of the final state Higgs boson leg, each insertion corresponding to a different diagram.
• Figure 2: ${\cal O}(\alpha_s)$ virtual corrections to $gg\to t\bar{t}h$: self-energy diagrams. The shaded blobs denote standard one-loop QCD corrections to the gluon and top quark propagators respectively. The circled crosses denote all possible insertions of the final state Higgs boson leg, each insertion corresponding to a different diagram. All $t$-channel diagrams (labeled as $S_{i,t}^{(j)}$) have corresponding $u$-channel diagrams.
• Figure 3: ${\cal O}(\alpha_s)$ virtual corrections to $gg\to t\bar{t}h$: vertex diagrams. The shaded blobs denote standard one-loop QCD corrections to the $ggg$, $gt\bar{t}$, or $ht\bar{t}$ vertices respectively. The circled crosses denote all possible insertions of the final Higgs boson leg, each insertion corresponding to a different diagram. Diagrams with a closed fermion loop have to be counted twice, once for each orientation of the loop fermion line. All $t$-channel diagrams (labeled as $V_{i,t}^{(j)}$) have corresponding $u$-channel diagrams.
• Figure 4: ${\cal O}(\alpha_s)$ virtual corrections to $gg\to t\bar{t}h$: box diagrams. The circled crosses denote all possible insertions of the final Higgs boson leg, each insertion corresponding to a different diagram. Diagrams with a closed fermion loop have to be counted twice, once for each orientation of the loop fermion line. All $t$-channel diagrams (labeled as $B_{i,t}^{(j)}$) have corresponding $u$-channel diagrams.
• Figure 5: ${\cal O}(\alpha_s)$ virtual corrections to $gg\to t\bar{t}h$: pentagon diagrams. The circled crosses denote all possible insertions of the final Higgs boson leg, each insertion corresponding to a different diagram. All $t$-channel diagrams (labeled as $P_{i,t}$) have corresponding $u$-channel diagrams.