$pp\to pp{K}^{+}{K}^{-}$ reaction at high energies

We evaluate differential distributions for the four-body $pp\to pp{K}^{+}{K}^{-}$ reaction at high energies, which constitutes an irreducible background to three-body processes $pp\to ppM$, where $M=\varphi ,f_2(1275),f_0(1500),f_2^{\prime }(1525),{\chi }_{c0}$. We consider the central diffractive contribution mediated by Pomeron and Reggeon exchanges as well as a completely new mechanism of emission of kaons from the proton lines. We include absorption effects due to proton-proton interaction and kaon-kaon rescattering. We compare our results with measured cross sections for the CERN Intersecting Storage Rings experiment. We make predictions for future experiments at RHIC, Tevatron, and LHC. Differential distributions in invariant two-kaon mass, kaon rapidities, and transverse momenta of kaons are presented. Two-dimensional distribution in $(y_{K^{+}},y_{K^{-}})$ is particularly interesting. The higher the incident energy, the higher preference for the same-hemisphere emission of kaons. We find that the kaons from the new mechanism of emission directly from proton lines are produced rather forward and backward but the corresponding cross section is rather small. The processes considered here constitute a sizeable contribution to the total proton-proton cross section as well as to the kaon inclusive cross section. We consider a measurement of exclusive production of a scalar ${\chi }_{c0}$ meson in the proton-proton collisions via ${\chi }_{c0}\to K^{+}{K}^{-}$ decay. The corresponding amplitude for exclusive central diffractive ${\chi }_{c0}$ meson production is calculated within the $k_t$-factorization approach. The influence of kinematical cuts on the signal-to-background ratio is discussed.

Figure 1

Differential distributions for $K^{+}p$ (left) and $K^{-}p$ (right) elastic scattering for three incident-beam momenta of $P_{lab}=5,50,200\mathrm{GeV}$. The experimental data are taken from Refs. 32 and the names of first authors are given explicitly in the figure.

Figure 2

The integrated cross section for the $KN$ total and elastic scattering. The experimental data are taken from particle data book [20]. The lines are explained in the main text.

Figure 3

The central diffractive mechanism of exclusive production of $K^{+}{K}^{-}$ pairs including the absorptive corrections due to proton-proton interactions as well as kaon-kaon rescattering. $S_{eik}$ ($S$ matrix for eikonal approach).

Figure 4

The central diffractive mechanism of exclusive production of $K^{+}{K}^{-}$ pairs via the $K^{*}(892)$ meson exchanges. $f$ means a specific isoscalar meson.

Figure 5

Other diffractive contributions leading to the $pp\to pp{K}^{+}{K}^{-}$ channel.

Figure 6

The $\pi \pi \to KK$ subprocess leading to the $pp\to pp{K}^{+}{K}^{-}$ reaction.

Figure 7

Differential cross section $d\sigma /d{M}_{KK}$ for the $pp\to pp{K}^{+}{K}^{-}$ reaction at $\sqrt{s}=62\mathrm{GeV}$ with experimental cuts relevant for the CERN ISR experimental data from Ref. 12. The right panel shows the same in the logarithmic scale. Results without (dotted line) and with (solid line) absorption effects are shown. Here ${\Lambda }_{\mathrm{off}}^2=2{\mathrm{GeV}}^2$ and ${\Lambda }_{\mathrm{int}}=2\mathrm{GeV}$. In the right panel the central diffractive mechanism with $K^{*}(892)$ meson exchanges corresponding to diagrams in Fig. 4 without (dashed line) and with (solid line) a $K^{*}$ Reggezaition are shown in addition.

Figure 8

Differential cross sections for the $pp\to pp{K}^{+}{K}^{-}$ reaction at $\sqrt{s}=7\mathrm{TeV}$ without (dotted line) and with (solid line) the absorption effects. These calculations were done with the cutoff parameter ${\Lambda }_{\mathrm{off}}^2=2{\mathrm{GeV}}^2$ and ${\Lambda }_{\mathrm{int}}=2\mathrm{GeV}$.

Figure 9

Differential cross section $d\sigma /d{y}_K$ for the $pp\to pp{K}^{+}{K}^{-}$ reaction at $\sqrt{s}=0.5,1.96,7\mathrm{TeV}$ with ${\Lambda }_{\mathrm{off}}^2=2{\mathrm{GeV}}^2$. The results without (upper lines) and with (bottom lines) absorption effects due to the $pp$ interaction and $KK$-rescattering are shown too.

Figure 10

Differential cross section $d\sigma /d{y}_K$ for the $pp\to pp{K}^{+}{K}^{-}$ reaction at $\sqrt{s}=7\mathrm{TeV}$ with ${\Lambda }_{\mathrm{off}}^2=2{\mathrm{GeV}}^2$. The different lines corresponds to the situation when all and only some components in the amplitude are included. The details are explained in the main text.

Figure 11

Differential cross section in $(y_3,y_4)$ for the central diffractive contribution for three incident energies $\sqrt{s}=0.5,1.96,7\mathrm{TeV}$. We show a standard lego plot as well as a map with standard map color coding above the lego plot. The absorption effects were included here.

Figure 12

Differential cross section in $(p_{t,K},M_{KK})$ for the central diffractive contribution for two incident energies $\sqrt{s}=0.5,7\mathrm{TeV}$. The absorption effects were included here.

Figure 13

The $K^{+}{K}^{-}$ invariant mass distribution at $\sqrt{s}=0.5,1.96,7\mathrm{TeV}$ integrated over the full phase space (upper row) and with the detector limitations in kaon pseudorapidities (lower rows). The solid lines present the $KK$ continuum with the cutoff parameters ${\Lambda }_{\mathrm{off}}^2=2{\mathrm{GeV}}^2$. The ${\chi }_{c0}$ contribution is calculated with the GRV94 NLO (dotted lines) and GJR08 NLO (filled areas) collinear gluon distributions. The cross section for $\varphi$ contribution at $\sqrt{s}=7\mathrm{TeV}$ is calculated as in 29. The absorption effects were included in the calculations. A clear ${\chi }_{c0}$ signal with a relatively small background can be observed.

Figure 14

Differential cross section $d\sigma /d{p}_{t,K}$ at $\sqrt{s}=0.5,1.96,7\mathrm{TeV}$ with cuts on the kaon pseudorapidities. The diffractive background was calculated with the cutoff parameter ${\Lambda }_{\mathrm{off}}^2=2{\mathrm{GeV}}^2$. Results for the kaons from the decay of the ${\chi }_{c0}$ meson including the $K^{+}{K}^{-}$ branching ratio, for the GRV94 NLO (upper lines) and GJR08 NLO (bottom lines) UGDFs, are shown. In the right panel $\varphi$ meson contribution is shown in addition. The absorption effects were included here.

Figure 15

Differential cross sections $d\sigma /d{y}_{K^{+}}$ (left panel) and $d\sigma /d{y}_{K^{-}}$ (right panel) for the $pp\to pp{K}^{+}{K}^{-}$ reaction at $\sqrt{s}=7\mathrm{TeV}$. The solid line represents the coherent sum of all amplitudes. The dotted, dashed, dash-dotted, long-dashed, long-dash-dotted lines correspond to contributions from diagrams (a)–(e) in Fig. 5. The Reggeization of the particle exchange was included here.

Figure 16

A schematic localization of different mechanisms for the $pp\to pp{K}^{+}{K}^{-}$ reaction at high energies.