We discuss the exclusive photoproduction of π+π− pairs in photon-proton and in proton-proton collisions at high energies. The ρ0, ω, f2(1270), and non-resonant (Drell-Söding) contributions are considered. The calculation is based on the tensor-pomeron model that includes not only the dominant pomeron exchange but also reggeon and odderon exchanges. In the Drell-Söding contribution we have different subenergies for the π+p and π−p systems. In the method which we propose now we take this into account. Respecting the gauge-invariance constraints is then a nontrivial problem for which, however, we present a solution here. In the present paper we give in this way a substantial improvement of the calculations for real photoproduction of π+π− from JHEP 01, 151 (2015), and we extend the calculations to low Q2 electroproduction, 0 ⩽ Q2 ⩽ 0.5 GeV2. The photo- and electroproduction amplitudes are then the basis for the calculation of central exclusive production (CEP) of π+π− pairs in proton-proton collisions, where at least one proton participates in the CEP via a virtual-photon emission. The revised model leads to enhanced cross sections and gives an increased skewing of the ρ0 spectral shape. For the pp → ppπ+π− reaction, we calculate differential cross sections as function of the two-pion invariant mass, pion transverse momentum and pion pseudorapidity. Predictions of proton-pion and proton-pion-pion invariant mass distributions and the distribution in the proton-proton four-momentum transfer squared are also presented. This research is relevant in the context of ALICE, ATLAS, CMS, and LHCb measurements in pp collisions, even when the leading protons are not detected and instead only rapidity-gap conditions are checked experimentally. Our results can also serve as basis for the description of coherent π+π− production in ultra-peripheral pA and AA collisions at the LHC. The formulas given in our paper can directly be used for the analysis of photoproduction and small-Q2 electroproduction in ep collisions at high energies. Such data exist from the HERA experiments and will be obtained in the future at the electron-ion colliders.

Production of π⁺π⁻ pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution

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2026年6月1日

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Piotr Lebiedowicz,
Otto Nachtmann,
Antoni Szczurek

摘要

We discuss the exclusive photoproduction of π⁺π⁻ pairs in photon-proton and in proton-proton collisions at high energies. The ρ⁰, ω, f₂(1270), and non-resonant (Drell-Söding) contributions are considered. The calculation is based on the tensor-pomeron model that includes not only the dominant pomeron exchange but also reggeon and odderon exchanges. In the Drell-Söding contribution we have different subenergies for the π⁺p and π⁻p systems. In the method which we propose now we take this into account. Respecting the gauge-invariance constraints is then a nontrivial problem for which, however, we present a solution here. In the present paper we give in this way a substantial improvement of the calculations for real photoproduction of π⁺π⁻ from JHEP 01, 151 (2015), and we extend the calculations to low Q² electroproduction, 0 ⩽ Q² ⩽ 0.5 GeV². The photo- and electroproduction amplitudes are then the basis for the calculation of central exclusive production (CEP) of π⁺π⁻ pairs in proton-proton collisions, where at least one proton participates in the CEP via a virtual-photon emission. The revised model leads to enhanced cross sections and gives an increased skewing of the ρ⁰ spectral shape. For the pp → ppπ⁺π⁻ reaction, we calculate differential cross sections as function of the two-pion invariant mass, pion transverse momentum and pion pseudorapidity. Predictions of proton-pion and proton-pion-pion invariant mass distributions and the distribution in the proton-proton four-momentum transfer squared are also presented. This research is relevant in the context of ALICE, ATLAS, CMS, and LHCb measurements in pp collisions, even when the leading protons are not detected and instead only rapidity-gap conditions are checked experimentally. Our results can also serve as basis for the description of coherent π⁺π⁻ production in ultra-peripheral pA and AA collisions at the LHC. The formulas given in our paper can directly be used for the analysis of photoproduction and small-Q² electroproduction in ep collisions at high energies. Such data exist from the HERA experiments and will be obtained in the future at the electron-ion colliders.

Production of π+π− pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution

摘要

Production of π⁺π⁻ pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution