Two-photon Collisions Research Articles

Status and Prospects of Exotic Hadrons at Belle II

In the past 20 years, many new hadrons that are difficult to explain within the conventional quark model have been discovered in the quarkonium region; these are called exotic hadrons. The Belle II experiment, as the next-generation B factory, provides a good platform for exploring them. The charmonium-like states can be produced at Belle II in several ways, such as B meson decays, initial-state radiation processes, two-photon collisions and double charmonium production. Bottomonium-like states can be produced directly in e + e − colliding energies at Belle II with low continuum backgrounds. Belle II plans to perform a high-statistics energy scan from the threshold up to the highest possible energy of 11.24 GeV to search for new Yb states with J PC = 1−−, Xb [the bottom counterpart of χ c1(3872), also known as X(3872)] and partners of Zb states. We give a mini-review on the status and prospects of exotic hadrons at Belle II.

Radiative decays of the spin-2 partner of X(3872)

It has been generally expected that the X(3872) has a spin-2 partner, X2, with quantum numbers JPC=2++. In the hadronic molecular model, its mass was predicted to be below the D⁎D¯⁎ threshold, and the new structure reported in the γψ(2S) invariant mass distribution by the Belle Collaboration with mass M=(4014.3±4.0±1.5) MeV and decay width Γ=(4±11±6) MeV, with a global significance of 2.8 σ, is a nice candidate for it. We consider the radiative decay widths for the X2→γψ with ψ=J/ψ,ψ(2S) treating the X2 as a D⁎D¯⁎ shallow bound state, and estimate the events of X2 in two-photon collisions that can be collected in the γJ/ψ→γℓ+ℓ− (ℓ=e,μ) final states at Belle. Based on the upper limit for the ratio of decay widths of X(3872)→γψ(2S) and X(3872)→γJ/ψ measured by BESIII, we predict the similar ratio Γ(X2→γψ(2S))/Γ(X2→γJ/ψ) to be smaller than 1.0. We suggest searching for the X2 signal in the γJ/ψ invariant mass distribution via two-photon fusions. The results will lead to insights into both the X(3872) and the new structure observed by Belle.

Two-photon physics at future electron-positron colliders* *The work of V.V.B. was supported in part by the Heisenberg-Landau Program

Two photon collisions offer a variety of physics phenomena that can be studied at future electron-positron colliders. Using the planned CEPC parameters as a benchmark, we consider several topics within two-photon collisions. With the full integrated luminosity, Higgs boson photoproduction can be reliably observed, and large statistics on various quarkonium states can be collected. The LEP results for the photon structure function and tau lepton anomalous magnetic moment can be improved by 1-2 orders of magnitude.

Power Scaling for Collimated γ -Ray Beams Generated by Structured Laser-Irradiated Targets and Its Application to Two-Photon Pair Production

Using three-dimensional kinetic simulations, we examine the emission of collimated gamma-ray beams from structured laser-irradiated targets with a pre-filled cylindrical channel. The channel guides the incident laser pulse, enabling generation of a slowly evolving azimuthal plasma magnetic field that serves two key functions: to enhance laser-driven electron acceleration and to induce emission of gamma-rays by the energetic electrons. Our main finding is that the conversion efficiency of the laser energy into a beam of gamma-rays ($5^{\circ}$ opening angle) can be significantly increased without increasing the laser intensity by utilizing channels with an optimal density. The conversion efficiency into multi-MeV photons increases roughly linearly with the incident laser power $P$, as we increase $P$ from 1 PW to 4 PW while keeping the laser peak intensity fixed at $5 \times 10^{22}$ W/cm$^2$. This scaling is achieved by using an optimal range of plasma densities in the channel between 10 and $20 n_{cr}$, where $n_{cr}$ is the classical cutoff density for electromagnetic waves. The corresponding number of photons scales as $P^2$. One application that directly benefits from such a strong scaling is the pair production via two-photon collisions, with the number of generated pairs increasing as $P^4$ at fixed laser intensity.

Photonuclear and Two-Photon Interactions at High-Energy Nuclear Colliders

Ultraperipheral collisions (UPCs) of heavy ions and protons are the energy frontier for electromagnetic interactions. Both photonuclear and two-photon collisions are studied at collision energies that are far higher than those available elsewhere. In this review, we discuss physics topics that can be addressed with UPCs, including nuclear shadowing, nuclear structure, and searches for physics beyond the Standard Model.

Numerical method of electron-positron pairs generation in photon-photon collider

The creation of positron and electron pairs through photon-photon collision, named Breit-Wheeler process, has been well understood in the theories of quantum electrodynamics for nearly 100 years. The photon-photon collision, which is one of the most basic processes of matter generation in the universe, has not been observed yet. The study on photon-photon collision can promote the development of two-photon physics, quantum electrodynamics theories and high energy physics. To observe photon-photon collision in the laboratory, one needs to collimate a huge number of energetic γ-ray photons into a very small spot. Recently, the development of highly collomated source generated by 10 PW laser makes photon-photon collider much more possible than before. In photon-photon collider, the study of numerical simulation plays a critical role since no experiment has achieved such a process. In this paper, a new numerical method is developed to handle the two-photon Breit-Wheeler process. This method is based on the exact two-photon collision dynamic principle, including energy threshold condition, cross-section condition, Lorentz transformation, etc. In the method, the photons are divided into quantitative photon blocks based on the spatial coordinates. Firstly, one needs to find the collision blocks according to the spatial motion law. Secondly, the ergodic method is used to look up the photons that satisfy the energy threshold condition and the cross-section condition from the blocks. Then, one can calculate the electron yield of the photon collision, and the kinetic parameters of the positrons and electrons. This method rigorously follows the physical principle so it has high precision. On the other hand, this method determines the collision of the block in advance, which can reduce the computational requirement a lot. A series of tests is carried out to confirm the accuracy and feasibility of this numerical method by calculating the collision between mono-energetic photon beams. In the tests, the collision angle is assumed to 180° and 60° separately, the results of pair momentum distribution are discussed. We also simulate the collision of the γ-ray beams generated through the interaction between ultra-intense laser and narrow tube targets. In the simulations, the collision angle is changed from 170° to 30° to see its effect on pair production. It is found that the yield of electron-positron pairs decreases with collision angle increasing, which has also been reported in previous work. Therefore, this numerical method can be efficiently used for modeling photon-photon collider, and provide theoretical reference and suggestion to the future experimental design of γ-ray collision.

Measurement of transition form factors in two-photon collisions at BESIII

The two-photon physics program of the BESIII Collaboration is mainly motivated by the need of new measurements of transition form factors as input for the Standard Model calculations of $ \mathop a\nolimits_\mu ^{HLbL} $, the hadronic light-by-light scattering contribution to the anomalous magentic moment of the muon. The large data sets acquired at BESIII allow to study the transition form factors of pseudoscalar mesons in the relevant region of momentum transfer for $ \mathop a\nolimits_\mu ^{HLbL} $. In this presentation the status of the respective measurements for π0,η and η’ mesons are discussed, and prospects for studies of multi-meson systems as well as of doubly-virtual transition form factors are given.

Measurements of Hadronic and Transition Form Factors at BESIII

Motivated by the need of experimental input to improve the Standard Model prediction of the anomalous magnetic moment of the muon aµ, the BESIII Collaboration started a dedicated program to measure hadronic cross sections as well as transition form factors (TFF) with high accuracy. The large data sets acquired by the BESIII Collaboration allow to exploit initial state radiation in order to study hadron production over a wide energy range, as well as two-photon collisions to study the momentum dependence of TFFs in the space like regime. The current status and ongoing investigations in both endeavors are discussed.

Measurement of ηc(1S) , ηc(2S) , and nonresonant η′π+π− production via two-photon collisions

We report the measurement of gamma gamma to eta_c(1S), eta_c(2S) to eta' pi+ pi- with eta' decays to gamma rho and eta pi+ pi- using 941 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. The eta_c(1S) mass and width are measured to be M = [2984.6\pm0.7 (stat.)\pm2.2 (syst.)] MeV/c^{2} and \Gamma = [30.8^{+2.3}_{-2.2}~(stat.) \pm 2.5~(syst.)] MeV, respectively. First observation of eta_c(2S) to eta' pi+ pi- with a significance of 5.5sigma including systematic error is obtained, and the eta_c(2S) mass is measured to be M = [3635.1\pm3.7~(stat.)\pm2.9~(syst.)] MeV/c^{2}. The products of the two-photon decay width and branching fraction (B) of decays to eta'pi+ pi- are determined to be \Gamma_{gamma gamma}B = [65.4\pm2.6~(stat.)\pm6.9~(syst.)] eV for eta_c(1S) and [5.6^{+1.2}_{-1.1}~(stat.)\pm1.1~(syst.)] eV for eta_c(2S). A new decay mode for the eta_c(1S) to eta'f_0(2080) with f_0(2080) to pi+ pi- is observed with a statistical significance of 20sigma. The f_0(2080) mass and width are determined to be M = [2083^{+63}_{-66}~(stat.)\pm 32~(syst.)] MeV/c^{2} and \Gamma = [178^{+60}_{-178}~(stat.) \pm 55~(syst.)] MeV. The cross sections for gamma gamma to eta' pi+ pi- and eta'f_{2}(1270) are measured for the first time.

Study of KS0 pair production in single-tag two-photon collisions

We report a measurement of the cross section for $K^0_S$ pair production in single-tag two-photon collisions, $\gamma^* \gamma \to K^0_S K^0_S$, for $Q^2$ up to 30 GeV$^2$, where $Q^2$ is the negative of the invariant mass squared of the tagged photon. The measurement covers the kinematic range 1.0 GeV < W < 2.6 GeV and $|\cos \theta^*| < 1.0$ for the total energy and kaon scattering angle, respectively, in the $\gamma^* \gamma$ center-of-mass system. These results are based on a data sample of 759 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. For the first time, the transition form factor of the $f_2'(1525)$ meson is measured separately for the helicity-0, -1, and -2 components and also compared with theoretical calculations. Finally, the partial decay widths of the $\chi_{c0}$ and $\chi_{c2}$ mesons are measured as a function of $Q^2$.

Luminosity of synchrotron radiation from pulsar magnetospheres

We calculate the maximum luminosity of the synchrotron radiation in X-ray and optical bands, which is originated from the electromagnetic cascade in the magnetosphere of rotation-powered pulsars. We find that for pulsars with spin-down luminosity Lsd ≤ 1035 erg s−1, even if the full allowed energy range of the γ-ray photon emitted by the accelerated particles is taken into account, the observed non-thermal luminosities are higher than the maximum luminosity of synchrotron radiation from pairs created by two-photon collision. The synchrotron radiation from the inner region could explain the observed non-thermal luminosities, so that the γ-ray pulsars with Lsd ≤ 1035 erg s−1 would have multiple particle accelerators in the magnetosphere.

Searching for High-energy, Horizon-scale Emissions from Galactic Black Hole Transients during Quiescence

Abstract We search for the gamma-ray counterparts of stellar-mass black holes using the long-term Fermi archive to investigate the electrostatic acceleration of electrons and positrons in the vicinity of the event horizon. We achieve this by applying the pulsar outer-gap model to their magnetospheres. When a black hole transient (BHT) is in a low-hard or quiescent state, the radiatively inefficient accretion flow cannot emit enough MeV photons that are required to sustain the force-free magnetosphere in the polar funnel via two-photon collisions. In this charge-starved gap region, an electric field arises along the magnetic field lines to accelerate electrons and positrons into ultra-relativistic energies. These relativistic leptons emit copious Gamma-rays via the curvature and inverse-Compton (IC) processes. It is found that these gamma-ray emissions exhibit a flaring activity when the plasma accretion rate typically stays between 0.01% and 0.005% of the Eddington value for rapidly rotating, stellar-mass black holes. By analyzing the detection limit determined from archival Fermi/Large Area Telescope data, we find that the 7-year averaged duty cycle of such flaring activities should be less than 5% and 10% for XTE J1118+480 and 1A 0620-00, respectively, and that the detection limit is comparable to the theoretical prediction for V404 Cyg. It is predicted that the gap emission can be discriminated from the jet emission if we investigate the high-energy spectral behavior or observe nearby BHTs during deep quiescence simultaneously in infrared wavelength and very-high energies.

Analysis of γγ → J/ψγ

Many models to describe the nature of heavy quarkonia have been proposed and one of the ways to test them is to analyze charmonium states produced in two-photon collisions through measuring their two-photon decay width(Γγγ) and the angular distribution since they provide information on properties and internal structure of charmonium states. In this analysis, we use the decay channel γγ→X→J/ψγ, J/ψ→ℓ+ℓ−(ℓ=eorμ) based on the 980.4 fb−1 Belle data sample, where X is a charmonium state. Previously, Belle and CLEO collaborations have reported measurements of γγ→χc2(1P)→J/ψγ, J/ψ→ℓ+ℓ− using 32.6 fb−1 and 14.4 fb−1 samples, respectively. By analyzing an about 30 times larger data sample, we can make a more precise measurement of χc2(1P) and other rare charmonium states including a new charmonium(-like) state. In this paper, we discuss the proposal and method of the analysis and show the result of the feasibility study using Monte Carlo (MC) samples of γγ→χc2(1P)→J/ψγ.

Efficiency of Synchrotron Radiation from Rotation-powered Pulsars

Abstract Synchrotron radiation is widely considered to be the origin of the pulsed non-thermal emissions from rotation-powered pulsars in optical and X-ray bands. In this paper, we study the synchrotron radiation emitted by the created electron and positron pairs in the pulsar magnetosphere to constrain the energy conversion efficiency from the Poynting flux to the particle energy flux. We model two pair creation processes, two-photon collision, which efficiently works in young γ-ray pulsars (≲106 year), and magnetic pair creation, which is the dominant process to supply pairs in old pulsars (≳106 year). Using the analytical model, we derive the maximum synchrotron luminosity as a function of the energy conversion efficiency. From the comparison with observations, we find that the energy conversion efficiency to the accelerated particles should be an order of unity in the magnetosphere, even though we make a number of the optimistic assumptions to enlarge the synchrotron luminosity. In order to explain the luminosity of the non-thermal X-ray/optical emission from pulsars with low spin-down luminosity L sd ≲ 1034 erg s−1, non-dipole magnetic field components should be dominant at the emission region. For the γ-ray pulsars with L sd ≲ 1035 erg s−1, observed γ-ray to X-ray and optical flux ratios are much higher than the flux ratio between curvature and the synchrotron radiations. We discuss some possibilities such as the coexistence of multiple accelerators in the magnetosphere as suggested from the recent numerical simulation results. The obtained maximum luminosity would be useful to select observational targets in X-ray and optical bands.

LEPTON ACCELERATION IN THE VICINITY OF THE EVENT HORIZON: HIGH-ENERGY AND VERY-HIGH-ENERGY EMISSIONS FROM ROTATING BLACK HOLES WITH VARIOUS MASSES

ABSTRACT We investigate the electrostatic acceleration of electrons and positrons in the vicinity of the event horizon, applying the pulsar outer-gap model to black hole (BH) magnetospheres. During a low accretion phase, the radiatively inefficient accretion flow (RIAF) cannot emit enough MeV photons that are needed to sustain the force-free magnetosphere via two-photon collisions. In such a charge-starved region (or a gap), an electric field arises along the magnetic field lines to accelerate electrons and positrons into ultra-relativistic energies. These relativistic leptons emit copious gamma rays via curvature and inverse-Compton (IC) processes. Some of such gamma rays collide with the submillimeter-IR photons emitted from the RIAF to materialize as pairs, which polarize to partially screen the original acceleration electric field. It is found that the gap gamma-ray luminosity increases with decreasing accretion rate. However, if the accretion rate decreases too much, the diminished RIAF soft photon field can no longer sustain a stationary pair production within the gap. As long as a stationary gap is formed, the magnetosphere becomes force-free outside the gap by the cascaded pairs, irrespective of the BH mass. If a nearby stellar-mass BH is in quiescence, or if a galactic intermediate-mass BH is in a very low accretion state, its curvature and IC emissions are found to be detectable with Fermi/LAT and imaging atmospheric Cherenkov telescopes (IACT). If a low-luminosity active galactic nucleus is located within about 30 Mpc, the IC emission from its supermassive BH is marginally detectable with IACT.

Study ofπ0pair production in single-tag two-photon collisions

We report a measurement of the differential cross section of $\pi^0$ pair production in single-tag two-photon collisions, $\gamma^* \gamma \to \pi^0 \pi^0$, in $e^+ e^-$ scattering. The cross section is measured for $Q^2$ up to 30 GeV$^2$, where $Q^2$ is the negative of the invariant mass squared of the tagged photon, in the kinematic range 0.5 GeV < W < 2.1 GeV and $|\cos \theta^*|$ < 1.0 for the total energy and pion scattering angle, respectively, in the $\gamma^* \gamma$ center-of-mass system. The results are based on a data sample of 759 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The transition form factor of the $f_0(980)$ and that of the $f_2(1270)$ with the helicity-0, -1, and -2 components separately are measured for the first time and are compared with theoretical calculations.

Pair creation in collision of γ-ray beams produced with high-intensity lasers.

Direct production of electron-positron pairs in two-photon collisions, the Breit-Wheeler process, is one of the basic processes in the universe. However, it has never been directly observed in the laboratory because of the absence of the intense γ-ray sources. Laser-induced synchrotron sources emission may open a way to observe this process. The feasibility of an experimental setup using a MeV photon source is studied in this paper. We compare several γ-ray sources and estimate the expected number of electron-positron pairs and competing processes by using numerical simulations including quantum electrodynamic effects.

Comprehensive amplitude analysis ofγγ→π+π−,π0π0andK¯Kbelow 1.5 GeV

In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two-photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the $\ensuremath{\gamma}\ensuremath{\gamma}$ to meson pair amplitudes as possible. Having data with limited angular coverage, typically $|\mathrm{cos}\ensuremath{\theta}|&lt;0.6--0.8$, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing symmetry makes up for the experimentally missing information. Above 1.5 GeV multimeson production channels become important, and we have too little information to resolve the amplitudes. Nevertheless, below 1.5 GeV the two-photon production of hadron pairs serves as a paradigm for the application of $S$-matrix techniques. Final state interactions among the meson pairs are critical to this analysis. To fix these, we include the latest $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$, $\overline{K}K$ scattering amplitudes given by dispersive analyses, supplemented in the $\overline{K}K$ threshold region by the recent precision Dalitz plot analysis from BABAR. With these hadronic amplitudes built into unitarity, we can constrain the overall description of $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\overline{K}K$ data sets, both integrated and differential cross sections, including the high statistics charged and neutral pion, as well as ${K}_{s}{K}_{s}$, data from Belle. Since this analysis invokes coupled hadronic channels, having data on both $\ensuremath{\pi}\ensuremath{\pi}$ and $\overline{K}K$ reduces the solution space to essentially a single form in the region where these channels saturate unitarity. For the $\ensuremath{\pi}\ensuremath{\pi}$ channel, the separation of isospin-0 and -2 and helicity-0 and -2 components is complete. We present the partial wave amplitudes, show how well they fit all the available data, and give the two-photon couplings of scalar and tensor resonances that appear. These partial waves are important inputs into forthcoming dispersive calculations of hadronic light-by-light scattering.

High-statistics study of KFormula pair production in two-photon collisions

We report a high-statistics measurement of the differential cross section of the process gamma gamma --> K^0_S K^0_S in the range 1.05 GeV <= W <= 4.00 GeV, where W is the center-of-mass energy of the colliding photons, using 972 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e^+ e^- collider operated at and near the Upsilon-resonance region. The differential cross section is fitted by parameterized S-, D_0-, D_2-, G_0- and G_2-wave amplitudes. In the D_2 wave, the f_2(1270), a_2(1320) and f_2'(1525) are dominant and a resonance, the f_2(2200), is also present. The f_0(1710) and possibly the f_0(2500) are seen in the S wave. The mass, total width and product of the two-photon partial decay width and decay branching fraction to the K bar{K} state Gamma_{gamma gamma}B(K bar{K}) are extracted for the f_2'(1525), f_0(1710), f_2(2200) and f_0(2500). The destructive interference between the f_2(1270) and a_2(1320) is confirmed by measuring their relative phase. The parameters of the charmonium states chi_{c0} and chi_{c2} are updated. Possible contributions from the chi_{c0}(2P) and chi_{c2}(2P) states are discussed. A new upper limit for the branching fraction of the P- and CP-violating decay channel eta_c --> K^0_S K^0_S is reported. The detailed behavior of the cross section is updated and compared with QCD-based calculations.

Study ofX(3915)→J/ψωin two-photon collisions

We study the process γγ→J/ψω using a data sample of 519.2 fb−1 recorded by the BABAR detector at SLAC at the PEP-II asymmetric-energy e+e− collider at center-of-mass energies near the Υ(nS) (n=2,3,4) resonances. We confirm the existence of the charmoniumlike resonance X(3915) decaying to J/ψω with a significance of 7.6 standard deviations, including systematic uncertainties, and measure its mass (3919.4±2.2±1.6) MeV/c2 and width (13±6±3) MeV, where the first uncertainty is statistical and the second systematic. A spin-parity analysis supports the assignment JP=0+ and therefore the identification of the signal as due to the χc0(2P) resonance. In this hypothesis we determine the product between the two-photon width and the final state branching fraction to be (52±10±3) eV.1 MoreReceived 12 July 2012DOI:https://doi.org/10.1103/PhysRevD.86.072002© 2012 American Physical Society