Usefulness of effective field theory for boosted Higgs production

The $\text{Higgs}+\text{jet}$ channel at the LHC is sensitive to the effects of new physics both in the total rate and in the transverse momentum distribution at high $p_T$. We examine the production process using an effective field theory (EFT) language and discussing the possibility of determining the nature of the underlying high-scale physics from boosted Higgs production. The effects of heavy color triplet scalars and top partner fermions with TeV scale masses are considered as examples and Higgs-gluon couplings of dimension five and dimension seven are included in the EFT. As a byproduct of our study, we examine the region of validity of the EFT. Dimension-seven contributions in realistic new physics models give effects in the high $p_T$ tail of the Higgs signal which are so tiny that they are likely to be unobservable.

Figure 1

Allowed values of the EFT coefficients when the total gluon fusion rate, $gg\to h$, is within $\pm 10\%(\pm 5\%)$ of the SM prediction, (${\kappa }_g\equiv 12\pi v{C}_1/{\alpha }_s$).

Figure 2

The evolution of the dimension-five and dimension-seven EFT coefficients from the scale of new physics, $\sim \mathrm{\Lambda }$, to the electroweak scale.

Figure 3

Contribution of a 500 GeV color triplet scalar (lhs) and a 1 TeV scalar (rhs), relative to the SM Higgs $p_T$ distribution. The $gg$ and $qg$ partonic channels, and the sum of all partonic channels (which also includes $q\overline{q}$), are shown separately. Both the SM top and the scalar contributions are included exactly at LO.

Figure 4

Contribution of a 500 GeV color triplet scalar and a 1 TeV scalar, relative to the SM cross section, with a cut $p_{T_{\text{cut}}}$. The $gg$ and $qg$ partonic channels, and the sum of all partonic channels (which also include $q\overline{q}$), are shown separately. Both the SM top and the scalar contributions are included exactly at LO.

Figure 5

Accuracy of the effective field theory calculation of $d\sigma /d{p}_T$ relative to the exact calculation when including 500 GeV (lhs) and 1 TeV (rhs) color triplet scalars including all partonic initial states. The dashed lines contain only the dimension-five contributions, while the dotted lines contain both the dimension-five and dimension-seven contributions. The SM top quark contribution is always included exactly.

Figure 6

Accuracy of the effective field theory calculation of the total cross section subject to a $p_{T_{\text{cut}}}$, relative to the exact calculation when including 500 GeV (LHS) and 1 TeV (RHS) color triplet scalars including all partonic initial states. The dashed lines contain only the dimension-five contributions, while the dotted lines contain both the dimension-five and dimension-seven contributions. The SM top quark contribution is included exactly.

Figure 7

Accuracy of the effective field theory calculation of $d\sigma /d{p}_T$ relative to the exact calculation when including 500 GeV (lhs) 1 TeV (rhs) color triplet scalars and including only the $gg$ initial state. The dashed lines contain only the dimension-five contributions, while the dotted lines contain both the dimension-five and dimension-seven contributions. The SM top quark contribution is included exactly.

Figure 8

Accuracy of the effective field theory calculation of $d\sigma /d{p}_T$ relative to the exact calculation when including 500 GeV (lhs) and 1 TeV (rhs) color triplet scalars and including only the $qg$ initial state. The dashed lines contain only the dimension-five contributions, while the dotted lines contain both the dimension-five and dimension-seven contributions. The SM top quark contribution is included exactly.

Figure 9

The BSM contribution, relative to the SM contribution, to the differential (LHS) and integrated Higgs $p_T$ distribution (RHS). The $gg$ and $qg$ partonic channels, and the sum of all partonic channels (which also include $q\overline{q}$), are shown separately. Both the top partner and top quark contributions are included exactly at LO.

Figure 10

Accuracy of the effective field theory calculation of the differential (lhs) and integrated (rhs) $p_T$ distribution, relative to the exact calculation, for a 500 GeV fermionic top partner with $\theta =\pi /12$.

Figure 11

Cross sections including the SM result and a 500 GeV color triplet scalar, the SM result and a 500 GeV top partner, compared with the SM predictions.

Figure 12

Inclusive cross section with a $p_T$ cut at $\sqrt{s}=14\mathrm{TeV}$, normalized to the SM rate. In our parametrization of BSM effects, the SM rate is rescaled by ${\kappa }_t$, while $C_1$, $C_3$, and $C_5$ are rescaled by ${\kappa }_g$, ${\kappa }_3$, and ${\kappa }_5$, respectively, with the model in Sec. 4a corresponding to $|{\kappa }_g|/{\kappa }_{g0}={\kappa }_3={\kappa }_5=1$, ${\kappa }_{g0}\approx 0.0337$. We have fixed ${\kappa }_t+{\kappa }_g=1$ to approximately conserve the total cross section. ${\kappa }_3$ is fixed to zero in this plot to highlight the effects of ${\kappa }_g$ and ${\kappa }_5$.

Figure 13

Inclusive cross section with a $p_T$ cut at $\sqrt{s}=14\mathrm{TeV}$, normalized to the SM rate. In our parametrization of BSM effects, the SM rate is rescaled by ${\kappa }_t$, while $C_1$, $C_3$, and $C_5$ are rescaled by ${\kappa }_g$, ${\kappa }_3$, and ${\kappa }_5$, respectively, with the model in Sec. 4a corresponding to $|{\kappa }_g|/{\kappa }_{g0}={\kappa }_3={\kappa }_5=1$, ${\kappa }_{g0}\approx 0.0337$. We have fixed ${\kappa }_t+{\kappa }_g=1$ to approximately conserve the total cross section. ${\kappa }_5$ is fixed to zero in this plot to highlight the effects of ${\kappa }_g$ and ${\kappa }_3$. The effect of ${\kappa }_3$ can be seen to be extremely small.