Higgs Production at the LHC

The Higgs boson is produced at the LHC through various processes. To understand their relative importance, we need to carefully consider the partonic cross sections and parton distribution functions (PDFs). The convolution of partonic cross sections is given by

$\sigma (pp\to hX)={\sum }_{a,b}\int d{x}_{a}d{x}_b{f}_a(x_a)f_b(x_b)\hat{\sigma }(a(x_a)b(x_b)\to hX)$.

Here, $f_a(x_a)$ and $f_b(x_b)$ are the parton distribution functions for the partons $a$ and $b$ in the proton, and $\hat{\sigma }(ab\to hX)$ is the partonic cross section.

Despite being loop-induced, the dominant production mechanism for the Higgs boson at the LHC is gluon-gluon fusion, $gg\to h$. The next-to-leading order QCD corrections to the partonic cross section are substantial, leading to an enhancement by a factor of about 2. This dominance is due to the abundance of gluons in the initial state protons, i.e., large contributions from the gluon PDFs. (~85%)

Vector boson fusion is the second most important production mechanism. It is characterised by two high-energy “forward jets” in the final state, i.e., those that align closely with the beam axis with one each either half of the detector. They are produced by the t-channel exchange of vector bosons. By artificially selecting such events, we can have a combination of $hZZ$ and $hWW$ couplings, which are only indirectly accessible through $h$ decay to cascaded final states, e.g., $h\to Z{Z}^{\ast }(\to {\ell }^{+}{\ell }^{-})$ or $h\to W{W}^{\ast }\to t\bar{t}b\bar{b}$.

Higgsstrahlung or associated production $q\bar{q}\to Vh$ is the third most important production mechanism. Its contribution is small due to the suppression of antiquark PDFs. (~5%)

Associated production with top quarks $gg\to t\bar{t}h$ is the least important production mechanism. It test the top Yukawa coupling, which is inaccessible through $h$ decay. (~1%)

(diagrams)

• Gluon Fusion