Inclusive production of Higgs boson in the two-photon channel at the LHC within ${\kappa }_t$-factorization approach and with the standard model couplings

We calculate differential cross sections for the Higgs boson and/or two-photon production from the intermediate (virtual) Higgs boson within the formalism of $k_t$ factorization. The off-shell $g^{*}{g}^{*}\to H$ matrix elements are used. We compare results obtained with infinite top fermion (quark) mass and with finite mass taken into account. The latter effect is rather small. We compare the results with different unintegrated gluon distributions from the literature. Two methods are used. In the first method first Higgs boson is produced in the $2\to 1$ $gg\to H$ $k_t$-factorization approach and then isotropic decay with the Standard Model branching fraction is performed. In the second method we calculate directly two photons coupled to the virtual Higgs boson. The results of the two methods are compared and differences are discussed. The results for the two photons from the Higgs boson are compared with recent ATLAS Collaboration data. The leading-order $gg\to H$ contribution is rather small compared to the ATLAS experimental data ($\gamma \gamma$ transverse momentum and rapidity distributions) for all unintegrated gluon distributions from the literature. We include also the higher-order contribution $gg\to H(\to \gamma \gamma )g$, $gg\to gHg$ and the contribution of the $W^{+}{W}^{-}$ and $Z^0{Z}^0$. The $gg\to Hg$ mechanism gives a similar cross section as the $gg\to H$ mechanism. We argue that there is almost no double counting when adding $gg\to H$ and $gg\to Hg$ contributions due to the different topology of Feynman diagrams. The final sum is comparable with the ATLAS two-photon data. We discuss uncertainties related to both the theoretical approach and existing unintegrated gluon distribution functions.

Figure 1

Dominant leading-order diagram for inclusive Higgs boson production in the two-photon channel.

Figure 2

Typical diagrams for QCD NLO contributions to the Higgs boson production.

Figure 3

The $2\to 3$ diagrams which are used in order to make reference to the $2\to 1$ $k_t$-factorization calculation.

Figure 4

Diagrams for the $WW$ fusion.

Figure 5

Typical diagram for the $ZZ$ fusion.

Figure 6

Distribution in ${\log }_{10}(x_1)$ or ${\log }_{10}(x_2)$ for $gg\to H$ and for different UGDFs used in the present analysis.

Figure 7

Distribution in $q_{1t}$ and $q_{2t}$ for $gg\to H$ and for different UGDFs: KMR, Jung CCFM ($\mathrm{set}A0$), Kutak-Staśto and Kutak-Sapeta.

Figure 8

Distributions in photon transverse momenta $p_{1t}$ and $p_{2t}$ for the $gg\to H$ and for the KMR, Jung CCFM ($\mathrm{set}A0$), Kutak-Staśto and Kutak-Sapeta UGDFs.

Figure 9

Distributions in photon transverse momenta $p_{1t}$ and $p_{2t}$ for $gg\to H$ and for the KMR and Jung CCFM ($\mathrm{set}A0$) UGDFs for the contour representation.

Figure 10

Transverse momentum distribution of the Higgs boson produced in the $gg\to H$ subprocess in the $\gamma \gamma$ channels for different UGDFs from the literature.

Figure 11

Distribution in ${\log }_{10}{x}_i$ for the KMR UGDF and ${\mu }^2=m_H^2$ for the first (on-shell Higgs boson, long-dashed line) and second (off-shell Higgs boson, solid line) method.

Figure 12

Distribution in $p_{it}$ ($\mathrm{i}=1,2$) for the KMR UGDF and ${\mu }^2=m_H^2$ for the first (long-dashed line) and second (solid line) method.

Figure 13

Distribution in $p_{t,\mathrm{sum}}$ for the KMR UGDF and ${\mu }^2=m_H^2$ for the first (long-dashed line) and second (solid line) method.

Figure 14

Distribution of the photon transverse momentum for the KMR (solid line) and the Jung CCFM ($\mathrm{set}A0$) (long-dashed line) UGDF, for ${\mu }^2=m_H^2$.

Figure 15

Distribution of diphoton invariant mass for the KMR (solid line) and the Jung CCFM ($\mathrm{set}A0$) (long-dashed line) UGDF, for ${\mu }^2=m_H^2$.

Figure 16

Distribution of diphoton transverse momentum for the KMR (solid line) and the Jung CCFM ($\mathrm{set}A0$) (long-dashed line) UGDF, for ${\mu }^2=m_H^2$.

Figure 17

Distribution of the azimuthal angle between photons for the KMR (solid line) and the Jung CCFM ($\mathrm{set}A0$) (long-dashed line) UGDF, for ${\mu }^2=m_H^2$.

Figure 18

Two-dimensional distribution in $(q_{1t},q_{2t})$ for the KMR (left panel) and for the Jung CCFM ($\mathrm{set}A0$) (right panel) UGDF and for ${\mu }^2=m_H^2$.

Figure 19

Two-dimensional distribution in photon transverse momenta $(p_{1t},p_{2t})$ for the KMR (left panel) and for the Jung CCFM ($\mathrm{set}A0$) (right panel) UGDF and for ${\mu }^2=m_H^2$.

Figure 20

Two-dimensional distribution in $(q_{1t},q_{2t})$ for the $gg\to Hg$ process for the four different UGDFs used previously also for the $gg\to H$ calculation: KMR UGDF and ${\mu }_F^2=m_H^2$ (left top panel) and Jung CCFM $\mathrm{set}A0$ (right top panel), Kutak-Staśto (left bottom panel) and Kutak-Sapeta (right bottom panel).

Figure 21

Comparison of the standard collinear NLO result (dashed line) with our $k_t$-factorization result (solid line).

Figure 22

Transverse momentum distribution of the Higgs boson in the $\gamma \gamma$ channel produced in the $gg\to Hg$ subprocess for the different UGDFs from the literature.

Figure 23

Transverse momentum distribution of the Higgs boson in the $\gamma \gamma$ channel produced in the $gg\to H$ and in the $gg\to Hg$ subprocesses for the different UGDFs from the literature.

Figure 24

Two-dimensional distribution in jet transverse momenta $(p_{3t},p_{4t})$ for the $2\to 3$ process $gg\to gHg$ (left) and $ij\to iHj$ (right). In this calculation ${\mu }_F^2=m_H^2$ and ${\mu }_{r,1}^2=p_{3t}^2$, ${\mu }_{r,2}^2=p_{4t}^2$. A cut on $p_{3t},p_{4t}>10\mathrm{GeV}$ has been assumed in addition.

Figure 25

${\log }_{10}(x_i)$ distribution for the $k_t$-factorization approach for $gg\to H$ (upper dashed line, red online) and for $gg\to gHg$ (lower dashed line) and $ij\to iHj$ (solid line) for $q_{1t},q_{2t}>10\mathrm{GeV}$.

Figure 26

Transverse momentum distribution of the Higgs boson in the $\gamma \gamma$ channels for different mechanisms: $gg\to H$ (solid line), $gg\to Hg$ (dashed line) and $WW\to H$ (dash-dotted line).