Two-photon dilepton production in proton-proton collisions: Two alternative approaches

We investigate different methods to incorporate the effect of photons in hard processes. We compare the two different approaches used for calculating cross sections for the two-photon $pp\to l^{+}{l}^{-}X$ process. In one of the approaches the photon is treated as a collinear parton in the proton. In the second approach the recently proposed $k_T$ factorization method is used. We discuss how results of the collinear parton model depend on the initial condition for the QCD evolution and discuss an approximate treatment where the photon is excluded from the combined QCD-QED evolution. We demonstrate that it is not necessary to put the photon into the evolution equation as is often done, but it is sufficient to use a simplified approach in which the photon couples to quarks and antiquarks, which by themselves undergo DGLAP evolution equations. We discuss the sensitivity of the results to the choice of structure function parametrization and experimental cuts in the $k_T$ factorization approach. We explicitly display regions of $x$ and $Q^2$ (arguments of structure functions) relevant for different experiments. We compare the results of our calculations with recent experimental data for dilepton production and find that in most cases the contribution of the photon-photon mechanism is rather small. We discuss how to enhance the photon-photon contribution. We also compare our results to those of recent measurements of exclusive and semiexclusive $e^{+}{e}^{-}$ pair production with certain experimental data by the CMS Collaboration.

Figure 1

Different mechanisms of the two-photon production of dileptons.

Figure 2

Collinear photon distributions for different scales. The left panel is for the standard MRST2004(QED) parton distribution, while the right panel is for the case when the initial input at ${\mu }^2=2{\mathrm{GeV}}^2$ is set to zero, i.e., completely neglected. In both panels, the uppermost curve corresponds to ${\mu }^2={10}^4{\mathrm{GeV}}^2$ and ${\mu }^2$ drops monotonically from the top to the bottom curves.

Figure 3

The proton structure function $F_2(x,Q^2)$ as a function of $x$ for $Q^2=0.225{\mathrm{GeV}}^2$ (top left), $Q^2=1.25{\mathrm{GeV}}^2$ (top right), $Q^2=2.5{\mathrm{GeV}}^2$ (bottom left), and $Q^2=4.5{\mathrm{GeV}}^2$ (bottom right). Shown are different parmetrizations available in the literature.

Figure 4

The proton structure function $F_2(x,Q^2)$ as a function of $x$ at $Q^2=2.5{\mathrm{GeV}}^2$ shown with a logarithmic $x$-axis to make visible the small $x$ behavior of different parametrizations. Here, also HERA data are included.

Figure 5

The inelastic-inelastic contribution to dilepton invariant mass distributions for the ISR (upper left), PHENIX (upper right), ATLAS (lower left), and LHCb (lower right) experiments for different structure functions.

Figure 6

The $(\text{elastic-inelastic})+(\text{inelastic-elastic})$ contribution to dilepton invariant mass distributions for the ISR (upper left), PHENIX (upper right), ATLAS (lower left), and LHCb (lower right) experiments for different structure functions.

Figure 7

The inelastic-inelastic and $(\text{elastic-inelastic})+(\text{inelastic-elastic})$ contributions to dilepton invariant mass distributions for the ATLAS (upper panels) and LHCb (lower panels) experiments for the MRST2004 QED photon distributions (black), NNPDF2.3 QED photon distributions (red), and for $k_t$ factorization with the ALLM structure function.

Figure 8

Missing mass distributions for ineleastic-inelastic photon-photon contributions for different experiments (ISR, PHENIX, ATLAS, LHCb) and different parametrizations of the structure functions as explained inside the figures.

Figure 9

Distributions for $M_X\times M_Y$ for different structure functions: Szczurek-Uleshchenko (upper left), Fiore et al. (upper right), Suri-Yennie (lower right), and ALLM (lower left) for $\sqrt{s}=200\mathrm{GeV}$ and $p_{T1}$, $p_{T2}>0.2\mathrm{GeV}$.

Figure 10

Distributions for $Q_1^2\times Q_2^2$ for different experiments: ISR (upper left), PHENIX (upper right), ATLAS (lower right), and LHCb (lower left) for the ALLM structure function. Here, $-t_i=Q_i^2/(1{\mathrm{GeV}}^2)$.

Figure 11

Number of events per invariant mass interval for the CMS experimental cuts for SY (left) and ALLM (right) structure functions. The experimental data points are from Ref. [8].

Figure 12

Number of events per pair transverse momentum interval for the CMS experimental cuts for SY (left) and ALLM (right) structure functions. The experimental data points are from Ref. [8].

Figure 13

Number of events per pair relative azimuthal angle interval for the CMS experimental cut for SY (left) and ALLM (right) structure functions. The experimental data points are from Ref. [8].

Figure 14

Number of events per invariant mass interval for the CMS experimental cuts for collinear factorization approach. The results when initial MRST2004(QED) input is included [thick (red on line) lines] is compared with those when it is discarded [thin (blue on line) lines]. The experimental data points are from Ref. [8].

Figure 15

Distributions for $Q_2^2\times x_{\mathrm{Bj}2}$ for different experiments: ISR (upper left), PHENIX (upper right), ATLAS (lower left), and LHCb (lower right) for the ALLM structure function for elastic-inelastic photon-photon contributions. Here, $-t_i=Q_i^2/(1{\mathrm{GeV}}^2)$.

Figure 16

Distributions for $Q_2^2\times x_{\mathrm{Bj}2}$ for different experiments: ISR (upper left), PHENIX (upper right), ATLAS (lower left), and LHCb (lower right) for the ALLM structure function for inelastic-inelastic photon-photon contributions. Here, $-t_i=Q_i^2/(1{\mathrm{GeV}}^2)$.

Figure 17

Distributions for $x_{\mathrm{Bj}1}\times x_{\mathrm{Bj}2}$ for different experiments: ISR (upper left), PHENIX (upper right), ATLAS (lower left), and LHCb (lower right) for the ALLM structure function for inelastic-inelastic photon-photon contributions. Here $-t_i=Q_i^2/(1{\mathrm{GeV}}^2)$.

Figure 18

Distributions for $x_{\text{Bj}}$ for the ATLAS experiment. The left panel is for elastic-inelastic components, and the right panel is for inelastic-inelastic components.