Constraining the Higgs boson valence contribution in the proton

Nonperturbative gauge invariance under the strong and the weak interactions dictates that the proton contains a nonvanishing valence contribution from the Higgs particle. By introducing an additional parton distribution function (PDF), we investigate the experimental consequences of this prediction. The herwig7 event generator and a parameterized CMS detector simulation are used to obtain predictions for a scenario amounting to the LHC run-II dataset. We use those to assess the impact of the Higgs PDF on the $pp\to t\overline{t}$ process in the single-lepton final state. Comparing to nominal simulation we derive expected limits as a function of the shape of the valence Higgs PDF. We also investigate the process $pp\to t\overline{t}Z$ at the parton level to add further constraints.

Figure 1

Impact of the Higgs-induced subprocesses on the transverse momentum (left) and the rapidity (right) of the final state top quarks in $pp\to t\overline{t}$. We have used an example PDF of $0.01\times (1-x)\exp (-43x^2)/x$ without any rescaling taken into account for sum rules and a distribution of the intermediate virtuality according to the massive version of the propagator term. We separately show the parton-induced production (“$q\overline{q}/gg$”) and then the cross sections from the gluon-Higgs ($gH$) and Higgs-Higgs ($HH$) induced subprocesses. Notice that the $gH$ and $Hg$ subprocesses are mirror symmetric in the rapidity distribution but identical in the $p_{\perp }$ distribution.

Figure 2

The allowed band (13) as a function of $c$ for $t\overline{t}$ (left panel) and $t\overline{t}Z$ (right panel) for the PDF (7) for varying values $c_t$. The horizontal lines represent $e_l^X$ and $e_u^X$.

Figure 3

The top-left panel shows five different version of the PDF, with parameters fixed to allow for maximal Higgs content of the proton. The other five panels show how the optimal parameter is obtained from constraints due to the total cross sections for the processes $pp\to t\overline{t}$ and $pp\to t\overline{t}Z$.

Figure 4

The differential cross section for the $p_T$ distribution of the top for the final state $t\overline{t}$ (left panel) and $t\overline{t}Z$ (right panel). The top panels show the comparison between the initial state without and with a valence Higgs boson. The latter is shown also broken down into its different contributions of partonic initial states. The bottom panels show the ratio of the differential cross sections for both initial states. This is PDF 2 with tuning parameter $c_t=40$ and Higgs content $c=0.0608$. Errors are herwig errors for 10000 events.

Figure 5

Simulated distribution of $E_{\mathrm{T}}^{\mathrm{miss}}$ (left) and the $p_T$ of the leading jet (right) for Higgs PDF 2 in the event selection described in the text.

Figure 6

The left-hand side shows the upper limits at 68% and 95% confidence level as a function of the tuning parameter from the analysis with delphes for Higgs PDF 2 at $c_t=35$. The right panel shows the resulting optimal Higgs PDF overall size as a function of the Higgs PDF 2 tuning value.

Figure 7

The Higgs PDF 2 corresponding to the upper limit at 95% confidence level for a tuning parameter $c_t=100$ in comparison to the remaining PDFs for the MMHT’14 set at a $Q^2$ corresponding approximately to the Higgs mass.