Exclusive diffractive photon bremsstrahlung at the LHC

We calculate differential distributions for the $pp\to pp\gamma$ reaction at the LHC energy $\sqrt{s}=14\mathrm{TeV}$. We consider diffractive classical bremsstrahlung mechanisms including effects of the non-point-like nature of protons. In addition, we take into account (vector meson)-pomeron, photon-pion, and photon-pomeron exchange processes for the first time in the literature. Predictions for the total cross section and several observables related to these processes, e.g., differential distributions in pseudorapidities and transverse momenta of photons or protons are shown and discussed. The integrated diffractive bremsstrahlung cross section ($E_{\gamma }>100\mathrm{GeV}$) is only of the order of $\mu \mathrm{b}$. We try to identify regions of the phase space where one of the mechanisms dominates. The classical bremsstrahlung dominates at large forward/backward photon pseudorapidities, close to the pseudorapidities of scattered protons. In contrast, the photon-pomeron (pomeron-photon) mechanism dominates at midrapidities but the related cross section is rather small. In comparison the virtual-omega–rescattering mechanism contributes at smaller angles of photons (larger photon rapidities). Photons in the forward/backward region can be measured by the Zero Degree Calorimeters installed in experiments at the LHC while the midrapidity photons are difficult to measure (small cross section, small photon transverse momenta). Protons could be measured by the ALFA detector (ATLAS) or TOTEM detector at CMS. The exclusivity could be checked with the help of main central detectors.

Figure 1

Diagrams of the bremsstrahlung amplitudes driven by the pomeron exchange.

Figure 2

Diagrams of the bremsstrahlung amplitudes with the virtual $\omega$ meson (Reggeon) and its transformation to a final-state photon.

Figure 3

Diagrams with the $\gamma {\pi }^0$ and ${\pi }^0\gamma$ exchanges in the $pp\to pp\gamma$ reaction.

Figure 4

Diagrams with the $\gamma \mathbb{P}$ and $\mathbb{P}\gamma$ exchanges for the $pp\to pp\gamma$ reaction.

Figure 5

Energy spectrum of photons (left panel) and distribution in transverse momentum of photons (right panel) for all processes considered here at $\sqrt{s}=14\mathrm{TeV}$ and for ${\eta }_{\gamma }>0$. For classical bremsstrahlung we have imposed $E_{\gamma }>100\mathrm{GeV}$ and used two values of ${\Lambda }_N=0.8$, 1 GeV in the proton off-shell form factors [Eq. (2.9)] (see the lower and upper solid line, respectively).

Figure 6

Distribution in ${\xi }_1={log}_{10}(p_{1\perp }/1\mathrm{GeV})$ (left panel) and ${\xi }_2={log}_{10}(p_{2\perp }/1\mathrm{GeV})$ (right panel) at $\sqrt{s}=14\mathrm{TeV}$ and for ${\eta }_{\gamma }>0$. For classical bremsstrahlung $E_{\gamma }>100\mathrm{GeV}$ and we have used two values of ${\Lambda }_N=0.8$, 1 GeV (see the lower and upper solid line, respectively).

Figure 7

Distribution in $({\xi }_1,{\xi }_2)=({log}_{10}(p_{1\perp }/1\mathrm{GeV}),{log}_{10}(p_{2\perp }/1\mathrm{GeV}))$ for the classical bremsstrahlung (a), the $\omega$-rescattering (b), the pion-cloud (c), and the $\gamma$-rescattering (d) mechanisms at $\sqrt{s}=14\mathrm{TeV}$. In addition, for the classical bremsstrahlung we have imposed $E_{\gamma }>100\mathrm{GeV}$ and used ${\Lambda }_N=1\mathrm{GeV}$ in the proton off-shell form factors.

Figure 8

Distribution in (pseudo)rapidity of emitted photons (left panel) and in pseudorapidity of outgoing protons (right panel) at $\sqrt{s}=14\mathrm{TeV}$. For classical bremsstrahlung we have imposed $E_{\gamma }>100\mathrm{GeV}$ and used two values of ${\Lambda }_N=0.8$, 1 GeV (see the lower and upper solid line, respectively). A large cancellation between the initial- (2.3) and final-state radiation (2.1) is shown (see the blue short-dashed and the blue long-dashed lines, respectively). The lower-pseudorapidity limit for the CMS ZDC detector (${\eta }_{\gamma }>8.5$) is shown by the vertical line.

Figure 9

Distribution in four-momentum squared $t_1$ (left panel) and $t_2$ (right panel) at $\sqrt{s}=14\mathrm{TeV}$ and for ${\eta }_{\gamma }>0$. For classical bremsstrahlung we have imposed $E_{\gamma }>100\mathrm{GeV}$ and used two values of ${\Lambda }_N=0.8$, 1 GeV (see the lower and upper solid line, respectively).

Figure 10

Distribution in $(t_1,t_2)$ for the classical bremsstrahlung (a) ($E_{\gamma }>100\mathrm{GeV}$ and ${\Lambda }_N=1\mathrm{GeV}$), the $\omega$-rescattering (b), the pion-cloud (c), and the $\gamma$-rescattering (d) contributions at $\sqrt{s}=14\mathrm{TeV}$ and for ${\eta }_{\gamma }>0$.

Figure 11

Distribution in the $\gamma p$ subsystem energy $W_{13}$ for all processes considered here at $\sqrt{s}=14\mathrm{TeV}$ and for ${\eta }_{\gamma }>0$. For classical bremsstrahlung we have imposed $E_{\gamma }>100\mathrm{GeV}$ and used two values of ${\Lambda }_N=0.8$, 1 GeV (see the lower and upper solid line, respectively).

Figure 12

Distribution in relative azimuthal angle between outgoing protons for different mechanisms at $\sqrt{s}=14\mathrm{TeV}$ and for ${\eta }_{\gamma }>0$. For classical bremsstrahlung we have imposed $E_{\gamma }>100\mathrm{GeV}$ and used two values of ${\Lambda }_N=0.8$, 1 GeV (see the lower and upper solid line, respectively).