Equivalent Photon Approximation Research Articles

Exclusive production of heavy charged Higgs boson pairs in thepp→ppH+H−reaction at the LHC and a future circular collider

We calculate differential cross sections for exclusive production of heavy charged scalar, weakly interacting particles (charged Higgs bosons, charged technipions, etc.) via photon-photon exchanges in the $pp\ensuremath{\rightarrow}pp{H}^{+}{H}^{\ensuremath{-}}$ reaction with exact $2\ensuremath{\rightarrow}4$ kinematics. We present distributions in rapidities, transverse momenta, and correlations in azimuthal angles between the protons and between the charged Higgs bosons. As an example, the integrated cross section for $\sqrt{s}=14\text{ }\text{ }\mathrm{TeV}$ (LHC) is about 0.1 fb and about 0.9 fb at the Future Circular Collider (FCC) for $\sqrt{s}=100\text{ }\text{ }\mathrm{TeV}$ when assuming ${m}_{{H}^{\ifmmode\pm\else\textpm\fi{}}}=150\text{ }\text{ }\mathrm{GeV}$. The results are compared with results obtained within standard equivalent-photon approximation known from the literature. We discuss the role of the Dirac and Pauli electromagnetic form factors of the proton. We have also performed first calculations of cross sections for the exclusive diffractive Khoze-Martin-Ryskin mechanism. We have estimated limits on the ${g}_{h{H}^{+}{H}^{\ensuremath{-}}}$ coupling constant within the two-Higgs doublet model based on recent experimental data from the LHC. The diffractive contribution is, however, much smaller than the $\ensuremath{\gamma}\ensuremath{\gamma}$ one. The $Z\ensuremath{\gamma}$, $\ensuremath{\gamma}Z$, and $ZZ$ exchanges give even smaller contributions. Absorption corrections are calculated for the first time differentially for various distributions. In general, they lead to a damping of the cross section. The damping depends on the ${M}_{{H}^{+}{H}^{\ensuremath{-}}}$ invariant mass and on $t$ four-momentum transfers squared. In contrast to diffractive processes, the larger the collision energy, the smaller the effect of absorption. We discuss a possibility to measure the exclusive production of two charged Higgs bosons with the help of so-called ``forward proton detectors'' at the LHC experiments.

Double Scattering Production of Two $\rho ^0$ Mesons in UPC

We review our recent results for double-scattering mechanism in the exclusive $AA \to AA \rho^0\rho^0$ reaction in ultrarelativistic ultraperipheral heavy ion collisions. The cross section for single and double-$\rho^0$ production is calculated in the impact parameter space equivalent photon approximation. We compare the results of our calculation with the STAR and ALICE Collaboration results on one $\rho^0(770)$ meson and four-charged-pion production.

Double lepton pair production with electron capture in relativistic heavy-ion collisions

We present a theoretical study of a double lepton pair production in ultra--relativistic collision between two bare ions. Special emphasis is placed to processes in which creation of (at least one) $e^+ e^-$ pair is accompanied by the capture of an electron into a bound ionic state. To evaluate the probability and cross section of these processes we employ two approaches based on (i) the first--order perturbation theory and multipole expansion of Dirac wavefunctions, and (ii) the equivalent photon approximation. With the help of such approaches, detailed calculations are made for the creation of two bound--free $e^+ e^-$ pairs as well as of bound--free $e^+ e^-$ and free--free $\mu^+ \mu^-$ pairs in collisions of bare lead ions Pb$^{82+}$. The results of the calculations indicate that observation of the double lepton processes may become feasible at the LHC facility.

Peripheral, Ultrarelativistic Production of Particles in Heavy Ion Collisions

The cross sections for the production of two-pions in ultraperipheral ultrarelativistic heavy ion collisions, calculated in the impact parameter Equivalent Photon Approximation (EPA), are presented. Differential distributions in impact parameter, dipion invariant mass, single pion and dipion rapidity, pion transverse momentum and pion pseudorapidity are shown. The $\gamma \gamma \to \pi^+ \pi^-$ subprocess constitutes a background to the $A A \to A \rho^0 (\to \pi^+ \pi^-) A$ process, initiated by emission of a photon by one of colliding nuclei. Only a part of the dipion invariant mass distribution associated with the $\gamma\gamma$-collisions can be visible as the cross section for the $A A \to A \rho^0 A$ reaction is very large. Differential distributions for two $\rho^0$ meson production in exclusive ultraperipheral, ultrarelativistic collisions via a double scattering mechanism are presented. The cross section for $\gamma A \to \rho^0 A$ is parametrized based on a calculation from the literature. Smearing of $\rho^0$ masses is taken into account. The results of calculations are compared to experimental data obtained at RHIC and to the contribution of the two-photon mechanism. The double scattering mechanism populates larger $\rho^0 \rho^0$ invariant masses and larger rapidity distances between the two $\rho^0$ mesons compared to the $\gamma \gamma$ fusion. It gives a significant contribution to the $A A \to A A \pi^+ \pi^- \pi^+ \pi^-$ reaction. Some observables related to charged pions are presented. The results of our calculation are compared with the STAR collaboration results for four charged pion production. While the shape in invariant mass of the four-pion system is very similar to the measured one, the predicted cross section constitutes only 20 \% of the measured one. \end{abstract}

Exclusive electromagnetic production of pion pairs in lead-lead collisions at LHC

The cross section for π+ π− and π 0 π 0 meson pairs production in peripheral ultrarelativistic heavy-ion collisions is calculated in the impact parameter space equivalent photon approximation. The cross section is calculated at the energy available at the CERN Large Hadron Collider, √s NN = 3.5 TeV. For the first time the world data for γ γ → ππ are described, both for the total cross section and for the angular distribution. This is obtained simultaneously for γ γ → π+ π− and γ γ → π 0 π 0 at all experimentally available energies.

Probe of extra dimensions inγq→γqat the LHC

We have examined TeV scale effects of extra spatial dimensions through the processes gamma q-> gamma q where q=u,d,c,s,b, anti-u, anti-d, anti-c, anti-s, anti-b. These processes have been treated in a photon-proton collision via the main reaction pp-> p gamma p-> p gamma qX at the LHC. We have employed equivalent photon approximation for incoming photon beams and performed statistical analysis for various forward detector acceptances.

π+π−andπ0π0pair production in photon-photon scattering and ultraperipheral ultrarelativistic heavy-ion collisions

We discuss ${\gamma}{\gamma}\to {\pi}{\pi}$ reactions, starting from the two-pion threshold up to about $\sqrt{s_{{\gamma}{\gamma}}}$ = 6 GeV. We include the dipion continuum due to pion exchange (for ${\pi}^+{\pi}^-$) and ${\rho}^\pm$ exchange (for ${\pi}^0{\pi}^0$) as well as the dipion ${\sigma}(600)$, $f_0(980)$ and $f_2(1270)$ s-channel resonances. We discuss also a possible contribution of less pronounced scalar resonances $f_0(1500)$ and $f_0(1710)$ as well as the tensor resonances $f'_2(1525)$, $f_2(1565)$ and $f_2(1950)$. We find that the inclusion of the spin-four $f_4(2050)$ resonant state improves the situation at $\sqrt{s_{{\gamma}{\gamma}}} \approx$ 2 GeV. We estimate the relevant diphoton partial decay width to be ${\Gamma}_{f_4 \to {\gamma}{\gamma}} \approx$ 0.7 keV. At higher energies, Brodsky-Lepage and hand-bag mechanisms are included in addition. We nicely describe the world data for ${\gamma}{\gamma}\to {\pi}{\pi}$ for the first time both for the total cross section and angular distributions. The cross section for the production of two-pions in ultraperipheral ultrarelativistic heavy ion collisions is calculated in the impact parameter space Equivalent Photon Approximation (EPA). We obtain the nuclear cross section of 46.7 mb for ${\pi}^+{\pi}^-$ and 8.7 mb for ${\pi}^0{\pi}^0$ at the LHC energy $\sqrt{s_{NN}} =$ 3.5 TeV and minimal cut on pion transverse momentum $p_t>$ 0.2 GeV. Differential distributions in impact parameter, dipion invariant mass, single pion and dipion rapidity, pion transverse momentum as well as pion pseudorapidity are shown. The ${\gamma}{\gamma}\to {\pi}^+ {\pi}^-$ subprocess constitutes a background to $A A \to A {\rho}^0 (\to {\pi}^+ {\pi}^-) A$ process.

The γγ→J/ψJ/ψ reaction and the J/ψJ/ψ pair production in exclusive ultraperipheral ultrarelativistic heavy ion collisions

We calculate the cross section for the γγ→J/ψJ/ψ process. Two mechanisms are considered: box (two-loop) diagrams of the order of $O(\alpha_{\mathrm{em}}^{2} \alpha_{s}^{2})$ and two-gluon exchange of the order of $O(\alpha_{\mathrm{em}}^{2} \alpha_{s}^{4})$ . The first mechanism is calculated in the heavy-quark non-relativistic approximation while in the second case we also include the effects of quantum motion of quarks in the bound state. The box contribution dominates at energies close to the threshold (W< 15 GeV) while the two-gluon mechanism takes over at W> 15 GeV. Including the bound-state wave function effects for the two-gluon exchange mechanism gives a cross section 0.1–0.4 pb, substantially smaller than that in the non-relativistic limit (0.4–1.6 pb). We also find a strong infrared sensitivity which manifests itself in a rather strong dependence on the mass for the t-channel gluons. The elementary cross section is then used in the Equivalent Photon Approximation (EPA) in the impact parameter space to calculate the cross section for 208Pb+208Pb→208Pb+J/ψJ/ψ+208Pb reaction. Distributions in rapidity of the J/ψJ/ψ pair and invariant mass of the pair are shown. It is shown that in heavy ion collisions the box mechanism significantly dominates over the two-gluon exchange mechanism.

Bound–free pair production in ultra–relativistic ion collisions at the LHC collider: analytic approach to the total and differential cross sections

A theoretical investigation of the bound-free electron-positron pair production in relativistic heavy ion collisions is presented. Special attention is paid to the positrons emitted under large angles with respect to the beam direction. The measurement of these positrons in coincidence with the down--charged ions is in principle feasible by LHC experiments. In order to provide reliable estimates for such measurements, we employ the equivalent photon approximation together with the Sauter approach and derive simple analytic expressions for the differential pair--production cross section, which compare favorably to the results of available numerical calculations. Based on the analytic expressions, detailed calculations are performed for collisions of bare Pb$^{82+}$ ions, taking typical experimental conditions of the LHC experiments into account. We find that the expected count rate strongly depends on the experimental parameters and may be significantly enhanced by increasing the positron-detector acceptance cone.

Subdominant terms in the production ofcc¯pairs in proton-proton collisions

At high-energies the gluon-gluon fusion is the dominant mechanism of $c \bar c$ production. This process was calculated in the NLO collinear as well as in the k$_t$-factorization approaches in the past. We show that the present knowledge of gluon distributions does not allow to make a precise predictions for $c \bar c$ production at LHC, in particular at forward rapidities. In this paper we study production of $c \bar c$ pairs including several subleading mechanisms. This includes: $gg \to Q \bar Q$, $\gamma g \to Q \bar Q$, $g \gamma \to Q \bar Q$, $\gamma \gamma \to Q \bar Q$. In this context we use MRST-QED parton distributions which include photon as a parton in the proton as well as elastic photon distributions calculated in the equivalent photon approximation. We present distributions in the $c$ quark ($\bar c$ antiquark) rapidity and transverse momenta and compare them to the dominant gluon-gluon fusion contribution. We discuss also inclusive single and central diffractive processes using diffractive parton distribution found from the analysis of HERA diffractive data. As in the previous case we present distribution in $c$ ($\bar c$) rapidity and transverse momentum. Finally we present results for exclusive central diffractive mechanism discussed recently in the literature. We show corresponding differential distributions and compare them with corresponding distributions for single and central diffractive components.

Formula omitted] pair production in proton-proton collisions including subdominant terms

For the c c ¯ production at high-energies the gluon-gluon fusion is the dominant mechanism. This process was calculated in the NLO collinear as well as in the k t -factorisation approaches in the past. We show that the present knowledge of gluon distributions does not allow to make precise predictions for c c ¯ production at LHC. Next, we study production of c c ¯ pairs including following subprocesses: g g → Q Q ¯ , γ g → Q Q ¯ , g γ → Q Q ¯ , γ γ → Q Q ¯ . In this context we use MRST-QED (Martin, Roberts, Stirling, Thorne) parton distributions which include photon as a parton in the proton. We include also elastic contributions (single proton in the final state) within the equivalent photon approximation. We present distributions in c ( c ¯ ) rapidity and transverse momenta and compare them with the dominant gluon-gluon fusion contribution. We discuss also single and central diffractive processes using diffractive parton distribution found from the analysis of HERA data. As in the previous case we present distribution in c ( c ¯ ) rapidity and transverse momentum.

Exclusive production of lepton, quark and meson pairs in peripheral ultrarelativistic heavy ion collisions

We discuss exclusive production of lepton-antilepton, quark-antiquark, $\pi \pi$ and $\rho^0 \rho^0$ pairs in ultraperipheral, ultrarelativistic heavy-ion collisions. The cross sections for exclusive production of pairs of particles is calculated in Equivalent Photon Approximation (EPA). Realistic (Fourier transform of charge density) charge form factors of nuclei are used and the corresponding results are compared with the cross sections calculated with monopole form factor used in the literature. Absorption effects are discussed and quantified. The cross sections obtained with realistic form factors are significantly smaller than those obtained with the monopole form factors.

Exclusive production of large invariant mass pion pairs in ultraperipheral ultrarelativistic heavy ion collisions

The cross section for exclusive production of π+π− and π0π0 meson pairs in ultrarelativistic heavy ion collisions is calculated for LHC energy sNN=3.5 TeV taking into account photon–photon mechanism. We concentrate on the production of large two-pion invariant masses where the mechanism of the elementary γγ→ππ process is not fully understood. In order to include a size of nuclei we perform calculation in the impact-parameter equivalent photon approximation (EPA). Realistic charge densities are used to calculate charged form factor of 208Pb nucleus and to generate photon fluxes associated with ultrarelativistic heavy ions. Sizeable cross sections are obtained that can be measured at LHC. The cross section for elementary γγ→ππ process is calculated in the framework of pQCD Brodsky–Lepage (BL) mechanism with the distribution amplitude used to describe recent data of the BaBar Collaboration on pion transition form factor, using hand-bag mechanism advocated to describe recent Belle data as well as t- and u-channel meson/reggeon exchanges. We present distributions in two-pion invariant mass as well as the pion pair rapidity for the nuclear process.

EXCLUSIVE PRODUCTION OF ρ0ρ0 PAIRS IN ULTRARELATIVISTIC HEAVY ION COLLISIONS

We disuss exclusive electromagnetic production of two neutral ρ0 mesons and show the predictions for the AA → AAρ0ρ0 reactions for gold-gold collisions at the energy of [Formula: see text] and for lead-lead collisions at the energy of [Formula: see text]. The elementary cross section is calculated with the help of the vector-dominance-model (VDM)-Regge approach which usually very well describes the experimental data at large γγ energy. The low-energy γγ → ρ0ρ0 cross section is parametrized. The cross section for nuclear process is calculated by means of the equivalent photon approximation (EPA). We compare the results with realistic charge density with the results for monopole form factor.

Double-photon exclusive processes with heavy-quark–heavy-antiquark pairs in high-energy Pb-Pb collisions at energies available at the CERN Large Hadron Collider

The cross section for exclusive heavy-quark and heavy-antiquark pair ($Q\mathrm{Q\ifmmode \bar{}\else \={}\fi{}}$) production in peripheral ultrarelativistic heavy-ion collisions is calculated at an energy available at the CERN Large Hadron Collider, i.e., $\sqrt{{s}_{\mathit{NN}}}$ = 5.5 TeV. Here we consider only processes with photon-photon interactions and omit diffractive contributions. We present results in the impact parameter equivalent photon approximation and compare some of them with results obtained by exact calculations of the Feynman diagrams in the momentum space. We include $Q\mathrm{Q\ifmmode \bar{}\else \={}\fi{}}$, $Q\mathrm{Q\ifmmode \bar{}\else \={}\fi{}}g$, and $Q\mathrm{Q\ifmmode \bar{}\else \={}\fi{}}q\mathrm{q\ifmmode \bar{}\else \={}\fi{}}$ final states as well as photon single-resolved components. Realistic charge densities in nuclei were taken in the calculation. The different components give contributions of the same order of magnitude to the nuclear cross section. The cross sections found here are smaller than those for the diffractive photon-Pomeron mechanism and larger than the diffractive Pomeron-Pomeron discussed in the literature.

Nuclear form factor, validity of the equivalent photon approximation and Coulomb corrections to muon pair production in photon–nucleus and nucleus–nucleus collisions

We study in detail the influence of the nuclear form factor both on the Born cross section and on the Coulomb corrections to the photo-production of muon pairs off heavy nuclei (γ Z→μ + μ − Z) and in heavy-ion collisions (ZZ→ZZ μ + μ −). Our findings indicate a number of issues which have not been sufficiently described as yet in the literature: (i) the use of a realistic form factor, based on the Fermi charge distribution for the nucleus, is absolutely indispensable for reliable theoretical predictions; (ii) we checked quantitatively that the equivalent photon approximation has a very good accuracy for the discussed processes; and (iii) we present a leading logarithmic calculation of the Coulomb corrections which correspond to multi-photon exchange of the produced μ ± with the nuclei. These corrections are found to be small (on the percent level). Our result justifies using the Born approximation for numerical simulations of the discussed process at the RHIC and LHC colliders. Finally, we calculate the total cross section for muon pair production at RHIC and LHC.

Two-photon production of vector resonance in e + e − collisions

A parameterization of the amplitude of the two-photon production of 1++ and 1−+ vector resonances V in the e + e − → e + e − V reaction has been obtained. The differential (in momentum transfer) scattering cross section dσ/dQ 2 has been found for this reaction in the equivalent-photon approximation. The result obtained is model-independent.

Exclusive production of [formula omitted] pairs in γγ collisions at RHIC

We discuss exclusive electromagnetic production of two neutral ρ mesons in coherent photon–photon processes in ultrarelativistic heavy-ion collisions. The cross section is calculated in the equivalent photon approximation (EPA). Both uncertainties of the flux factors and photon–photon cross sections are discussed in detail. We show that inclusion of precise charge densities in nuclei is essential for realistic evaluations of the nuclear photon–photon cross sections. We find that the cross section, especially with realistic flux factors, is sensitive to low energy in the subsystem γγ→ρ0ρ0. The experimental data for the γγ→ρ0ρ0 cross section extracted from e+e− collisions are parametrized and used to estimate the nucleus–nucleus cross section. In addition, we include vector-dominance-model (VDM)–Regge contribution which becomes important at large photon–photon energy. Large nuclear cross sections are obtained. We discuss a possibility of focusing on the large-energy component. We find that both ρ0 mesons are produced predominantly at midrapidities and could be measured by the STAR Collaboration at RHIC.

Exclusive photoproduction at the Fermilab Tevatron and CERN LHC within the dipole picture

We provide predictions for the rapidity distributions of exclusive photoproduced J/{psi} and {upsilon} mesons, and Z{sup 0} bosons, at the Tevatron and Large Hadron Collider. We use the equivalent-photon approximation with the photon-proton cross sections given by the impact parameter dependent dipole saturation model, which has already been shown to give a good description of a wide variety of HERA data. We derive the quark-antiquark light-cone wave functions of timelike neutral electroweak bosons. An essential difference is pointed out between the amplitude for timelike heavy boson photoproduction and the amplitude for deeply virtual Compton scattering.

Exclusive and inclusive muon pair production in collisions of relativistic nuclei

The exclusive production of one ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair in collisions of two ultrarelativistic nuclei is considered. We present a simple method for the calculation of the Born cross section for this process based on an improved equivalent photon approximation. We find that the Coulomb corrections to this cross section (corresponding to multiphoton exchange of the produced ${\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}$ with the nuclei) are small, whereas the unitarity corrections (corresponding to the exchange of light-by-light blocks between nuclei) are large. This is in sharp contrast to the exclusive ${e}^{+}{e}^{\ensuremath{-}}$ pair production where the Coulomb corrections to the Born cross section are large, whereas the unitarity corrections are small. We calculate also the cross section for the production of one ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair and several ${e}^{+}{e}^{\ensuremath{-}}$ pairs in the leading logarithmic approximation. Using this cross section we find that the inclusive production of ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair coincides in this approximation with its Born value.