Prompt photon production in proton collisions as a probe of parton scattering in high energy limit

We study the prompt photon hadroproduction at the LHC with the $k_T$-factorization approach and the $q{g}^{*}\to q\gamma$ and $g^{*}{g}^{*}\to q\overline{q}\gamma$ partonic channels, using three unintegrated gluon distributions which depend on gluon transverse momentum. They represent three different theoretical schemes which are usually considered in the $k_T$-factorization approach, known under the acronyms: KMR, CCFM, and GBW gluon distributions. We find sensitivity of the calculated prompt photon transverse momentum distribution to the gluon transverse momentum distribution. The predictions obtained with the three approaches are compared to data, that allows to differentiate between them. We also discuss the significance of the two partonic channels, confronted with the expectations which are based on the applicability of the $k_T$-factorization scheme in the high energy approximation.

Figure 1

Prompt photon production in proton-proton collisions. The dashed lines represent the photon isolation cone.

Figure 2

Partonic channels in $\gamma$ hadroproduction: (a) the $q_{\mathrm{val}}{g}^{*}\to q\gamma$ channel and (b) the $g^{*}{g}^{*}\to q\overline{q}\gamma$ channel. The crossed blobs represent channel dependent hard scattering amplitudes.

Figure 3

Eight Feynman diagrams that contribute to the $g^{*}{g}^{*}\to q\overline{q}\gamma$ partonic channel corresponding to the amplitudes ${\mathcal{M}}^{(i)}$ for $i=1,2,\dots ,8$, respectively. The black blobs denote the effective triple gluon vertex $V_{\mathrm{eff}}$, see Appendix of Ref. [5] for its definition.

Figure 4

Four unintegrated gluon distributions $F_g(x,k_T,\mu )$ (see the text) as a function of gluon transverse momentum $k_T$ for two indicated values of gluon $x$ and factorization scales ${\mu }_F$. In the computation of the GBW gluon distribution, the leading order running ${\alpha }_s={\alpha }_s({\mu }_F)$ was used.

Figure 5

The “collinear integral” (23) computed for the four indicated unintegrated gluon distributions and two factorization scales ${\mu }_F$ as a function of $x$, compared to the collinear gluon distribution CT10 at the NLO.

Figure 6

Prompt photon production cross section computed in the $q{g}^{*}$ (top) and $g^{*}{g}^{*}$ (bottom) schemes with the indicated unintegrated gluon distributions, compared to the ATLAS@8 TeV data [34] for the central rapidity bin.

Figure 7

Theory to experiment ratios for the prompt photon production at ATLAS@8 TeV obtained from the JH and JH-2013 unintegrated gluon distributions within the $q{g}^{*}$ (right) and $g^{*}{g}^{*}$ (left) schemes for the central rapidity bin.

Figure 8

Theory to experiment ratios for the prompt photon production within the $q{g}^{*}$ scheme for the ATLAS@7 TeV [32] (left column), CMS@7 TeV [33] (central column) and ATLAS@8 TeV [34] (right column) data and the KMR-AO (green shaded bands), JH (red hatched bands) and GBW (blue curves) unintegrated gluon distributions. The theory uncertainties are due to the variation of the factorization scale ${\mu }_F={\mu }_R$ between $q_T/2$ and $2q_T$.

Figure 9

Theory to experiment ratios for the prompt photon production within the $g^{*}{g}^{*}$ scheme for the ATLAS@7 TeV [32] (left column), CMS@7 TeV [33] (central column) and ATLAS@8 TeV [34] (right column) data and the KMR-AO (green shaded bands), JH (red hatched bands) and GBW (blue curves) unintegrated gluon distributions. The theory uncertainties are due to the variation of the factorization scale ${\mu }_F={\mu }_R$ between $q_T/2$ and $2q_T$.

Figure 10

Decomposition of the prompt photon production cross section into partonic channels in $q{g}^{*}$ and $g^{*}{g}^{*}$ schemes. Plotted ratios of the partonic cross sections: $\sigma (q_{\mathrm{val}}{g}^{*})/\sigma (q{g}^{*})$, $\sigma (q_{\mathrm{sea}}{g}^{*})/\sigma (q{g}^{*})$, and $\sigma (g^{*}{g}^{*})/\sigma (q{g}^{*})$.