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Two-photon physics
Two-photon physics
Two-photon physics
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A Feynman diagram (box diagram) for photon–photon scattering: one photon scatters from the transient vacuum charge fluctuations of the other

Two-photon physics, also called gamma–gamma physics, is a branch of particle physics that describes the interactions between two photons. Normally, beams of light pass through each other unperturbed. Inside an optical material, and if the intensity of the beams is high enough, the beams may affect each other through a variety of non-linear optical effects. In pure vacuum, some weak scattering of light by light exists as well. Also, above some threshold of this center-of-mass energy of the system of the two photons, matter can be created.

Astronomy

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Cosmological/intergalactic gamma rays

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Photon–photon interactions limit the spectrum of observed gamma-ray photons at moderate cosmological distances to a photon energy below around 20 GeV, that is, to a wavelength of greater than approximately 6.2×10−11 m. This limit reaches up to around 20 TeV at merely intergalactic distances. [1] An analogy would be light traveling through a fog: at near distances a light source is more clearly visible than at long distances due to the scattering of light by fog particles. Similarly, the further a gamma-ray travels through the universe, the more likely it is to be scattered by an interaction with a low energy photon from the extragalactic background light.

At those energies and distances, very high energy gamma-ray photons have a significant probability of a photon-photon interaction with a low energy background photon from the extragalactic background light resulting in either the creation of particle-antiparticle pairs via direct pair production or (less often) by photon-photon scattering events that lower the incident photon energies. This renders the universe effectively opaque to very high energy photons at intergalactic to cosmological distances.

Experiments

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Two-photon physics can be studied with high-energy particle accelerators, where the accelerated particles are not the photons themselves but charged particles that will radiate photons. The most significant studies so far were performed at the Large Electron–Positron Collider (LEP) at CERN. If the transverse momentum transfer and thus the deflection is large, one or both electrons can be detected; this is called tagging. The other particles that are created in the interaction are tracked by large detectors to reconstruct the physics of the interaction.

Frequently, photon-photon interactions will be studied via ultraperipheral collisions (UPCs)[2] of heavy ions, such as gold or lead. These are collisions in which the colliding nuclei do not touch each other; i.e., the impact parameter is larger than the sum of the radii of the nuclei. The strong interaction between the quarks composing the nuclei is thus greatly suppressed, making the weaker electromagnetic interaction much more visible. In UPCs, because the ions are heavily charged, it is possible to have two independent interactions between a single ion pair, such as production of two electron-positron pairs. UPCs are studied with the STARlight simulation code.

Light-by-light scattering, as predicted in,[3] can be studied using the strong electromagnetic fields of the hadrons collided at the LHC,[4][5] it has first been seen in 2016 by the ATLAS collaboration[6][7] and was then confirmed by the CMS collaboration.,[8] including at high two-photon energies.[9] The best previous constraint on the elastic photon–photon scattering cross section was set by PVLAS, which reported an upper limit far above the level predicted by the Standard Model.[10] Observation of a cross section larger than that predicted by the Standard Model could signify new physics such as axions, the search of which is the primary goal of PVLAS and several similar experiments.

Processes

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From quantum electrodynamics it can be found that photons cannot couple directly to each other and a fermionic field according to the Landau-Yang theorem[11] since they carry no charge and no 2 fermion + 2 boson vertex exists due to requirements of renormalizability, but they can interact through higher-order processes or couple directly to each other in a vertex with an additional two W bosons: a photon can, within the bounds of the uncertainty principle, fluctuate into a virtual charged fermion–antifermion pair, to either of which the other photon can couple. This fermion pair can be leptons or quarks. Thus, two-photon physics experiments can be used as ways to study the photon structure, or, somewhat metaphorically, what is "inside" the photon.

The photon fluctuates into a fermion–antifermion pair.
Creation of a fermion–antifermion pair through the direct two-photon interaction. These drawings are Feynman diagrams.

There are three interaction processes:

  • Direct or pointlike: The photon couples directly to a quark inside the target photon.[12] If a lepton–antilepton pair is created, this process involves only quantum electrodynamics (QED), but if a quark–antiquark pair is created, it involves both QED and perturbative quantum chromodynamics (QCD).[13][14][15]

The intrinsic quark content of the photon is described by the photon structure function, experimentally analyzed in deep-inelastic electron–photon scattering.[16][17]

  • Single resolved: The quark pair of the target photon form a vector meson. The probing photon couples to a constituent of this meson.
  • Double resolved: Both target and probe photon have formed a vector meson. This results in an interaction between two hadrons.

For the latter two cases, the scale of the interaction is such as the strong coupling constant is large. This is called vector meson dominance (VMD) and has to be modelled in non-perturbative QCD.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Two-photon physics

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Two-photon physics, also known as gamma-gamma physics, is a branch of that investigates the interactions and reactions occurring when two photons—either real or virtual—collide to produce particles or probe fundamental structures. These processes are characterized by their clean quantum electrodynamic (QED) environment, allowing precise tests of perturbative and insights into hadron dynamics without the complications of strong initial-state interactions. The field originated theoretically in with early discussions of photon-pair production, but experimental exploration began in the 1960s and 1970s using electron-positron (e⁺e⁻) colliders, where quasi-real photons are emitted by the beams via , enabling the equivalent photon approximation to model the effective photon fluxes. Key early experiments at facilities like (VEPP-2) and (ADONE) confirmed high cross-sections for two-photon events, sparking dedicated workshops in the late 1970s and 1980s. Subsequent lepton colliders, such as TRISTAN, LEP, and Belle, amassed large datasets—approximately 650 pb⁻¹ per experiment at LEP2—revealing phenomena like production (e.g., η and η' mesons) and charm pair creation, with cross-sections reaching several nanobarns at center-of-mass energies around 10-100 GeV. Central to two-photon physics are exclusive and inclusive processes: exclusive channels, such as , provide access to form factors and decay constants via QCD factorization, while inclusive events like reveal the photon's partonic structure, including its and content, with pointlike and hadronic components. Jet production in two-photon collisions tests higher-order QCD predictions, with observables like the two-jet cross-section ratio (R ≈ 34/27 for light ) confirming perturbative calculations. Additionally, two-photon interactions occur in ultraperipheral heavy-ion collisions at RHIC and the LHC, scaling with squared (Z⁴) due to enhanced photon fluxes, facilitating studies of photoproduction and , including its first observation. These measurements have constrained anomalies in QED, such as the pion's triangle anomaly, and provided bounds on exotic states like glueballs or the in early searches. Looking forward, proposed future e⁺e⁻ colliders like the (CEPC) and (ILC), operating at 240-500 GeV with luminosities up to ab⁻¹ scale, promise to elevate two-photon physics by an in precision for photon structure functions, tau lepton magnetic moments (potentially to 1-2 permille), and Higgs photoproduction, while exploring new . Advances in Monte Carlo simulations (e.g., , Phojet) and next-to-leading-order QCD calculations continue to refine event reconstruction and theoretical interpretations, ensuring two-photon processes remain a vital tool for precision .

Theoretical Foundations

Quantum Electrodynamics Basics

Two-photon physics, also known as gamma-gamma physics, is a branch of that describes the interactions between two , focusing on quantum processes at high energies. This field is distinct from , which involves photon interactions mediated by atomic or molecular media rather than quantum effects. Quantum electrodynamics (QED) is the fundamental governing electromagnetic interactions, combining and to describe how photons mediate forces between charged particles. In QED, photons are neutral, massless gauge bosons that do not carry , prohibiting direct photon-photon interactions at the tree level of . Such interactions only emerge at higher orders, typically through quantum loops involving charged particles. The primary mechanism for photon-photon scattering in QED is captured by the one-loop Feynman box diagram, in which two incoming photons exchange virtual electron-positron pairs, resulting in scattered outgoing photons. For low-energy regimes where photon energies are much smaller than the , this process is approximated by the Euler-Heisenberg effective Lagrangian, which treats the as a nonlinear medium: L=2α245me4[(FμνFμν)2+74(FμνF~μν)2],\mathcal{L} = \frac{2\alpha^2}{45m_e^4} \left[ (F_{\mu\nu}F^{\mu\nu})^2 + \frac{7}{4} (F_{\mu\nu}\tilde{F}^{\mu\nu})^2 \right], where α\alpha is the , mem_e is the , FμνF_{\mu\nu} is the electromagnetic field strength tensor, and F~μν\tilde{F}^{\mu\nu} is its dual. This effective description originated from the 1936 prediction by and , who calculated light-by-light scattering as a nonlinear effect arising from in Dirac's theory of the and . In extensions to perturbative (QCD), photons can be viewed as composite objects with internal structure, characterized by photon structure functions that encode the probability distributions of quarks and gluons within the photon at high resolution scales. These functions evolve according to QCD equations, revealing the photon's hadronic content analogous to that of hadrons.

Light-by-Light Scattering Mechanism

Light-by-light scattering refers to the elastic process γγ→γγ\gamma \gamma \to \gamma \gamma, in which two photons collide and emerge as two photons, a phenomenon arising solely from quantum electrodynamic (QED) effects at leading order through virtual electron-positron pairs in the vacuum. This interaction is forbidden in classical electrodynamics but permitted in QED due to the nonlinear nature of the theory, where photons indirectly couple via loops. The originates from the one-loop box diagram, consisting of four photon vertices connected by electron propagators in a closed fermion loop. The calculation requires evaluating the Feynman integral over the loop momentum, employing techniques such as to handle ultraviolet divergences, which cancel due to the ward identities of QED. In the low-energy limit, where photon energies E≪meE \ll m_e (with mem_e the ), the differential cross section simplifies to dσdΩ∝α4me8(E4sin⁡4θ)\frac{d\sigma}{d\Omega} \propto \frac{\alpha^4}{m_e^8} (E^4 \sin^4\theta), where α\alpha is the and θ\theta the scattering angle in the ; this form corresponds to specific polarization configurations, such as initial photons with parallel polarizations perpendicular to the plane. The total cross section in this regime scales as σ∼α4ω6me8\sigma \sim \frac{\alpha^4 \omega^6}{m_e^8}, with ω\omega the , reflecting the sixth-power energy dependence characteristic of the effective Euler-Heisenberg Lagrangian description of nonlinear QED at low energies. Higher-order corrections to the leading-order result include two-loop contributions from additional photon exchanges or fermion loops, which modify the amplitude by factors of order α2\alpha^2 and become relevant at higher energies. effects, arising from virtual electron-positron pairs screening the propagator, alter the effective and thus the coupling strength in the process, particularly influencing the running of α\alpha for photon energies approaching or exceeding mem_e. The foundational theoretical computation of the light-by-light scattering amplitude for arbitrary kinematics was performed by Karplus and Neuman in 1950, who evaluated the box diagram explicitly and provided numerical results for the cross section as a function of energy and angle.

Physical Processes

Direct Interactions

Direct processes in two-photon physics are characterized by point-like, perturbative interactions in which both photons couple directly to quarks or leptons through their elementary quantum electrodynamics (QED) or quantum chromodynamics (QCD) vertices, without the photons resolving into hadronic structure, leading to final states such as lepton pairs or quark jets. These interactions contrast with resolved photon processes, which involve the hadronic content of quasi-real photons. The point-like nature arises from the fundamental coupling of photons to charged fermions, allowing clean tests of perturbative theory at short distances. The of such two-photon collisions are typically analyzed within the equivalent photon approximation, where the nearly real emitted by the incoming electrons or positrons are treated as a flux surrounding the beams. The differential for the subprocess is given by dLγγdW∝ln⁡2(sme2),\frac{dL_{\gamma\gamma}}{dW} \propto \ln^2 \left( \frac{s}{m_e^2} \right), where WW is the (center-of-mass energy) of the γγ\gamma\gamma system, ss is the center-of-mass energy squared of the e+e−e^+e^- collision, and mem_e is the . This logarithmic enhancement reflects the increasing photon flux with energy, enabling access to high-WW regimes up to s\sqrt{s}
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