Quantum electrodynamics (QED) predicts the interaction between two real photons, which leads to the linear Breit-Wheeler (LBW) electron-positron (e±) pair production [1] and photon-photon elastic scattering [2]. Although both the processes are observed in the collision of two virtual photons by means of the equivalent photon approximation of ultrarelativistic heavy-ion beams [3,4], the validation via real photon-photon collisions has never been realized due to the lack of high-brilliance γ-photon beams. One of the most important physical projects in the planned γγ collider is to search for higher-order photon-photon scattering, which is solid evidence of the vacuum polarization and is of interest as a search for new physics [5–8]. Because the cross section of the lowest-order LBW process is several orders of magnitude larger than that of the photon-photon scattering [9], it produces useful signatures for diagnostics, feedback, and luminosity optimization in a γγ collider [10,11]. Therefore, it is necessary to investigate the comprehensive physics of the LBW process, especially with polarized photons and energy distribution. Moreover, despite the significance in validating basic QED theory, the LBW process is one of the most elemental ingredients of pair plasma production in high-energy astrophysical environment [12], such as γ-ray bursts [13], black hole accretion [14,15], and active galactic nuclei [16].

Thanks to the developments of γ-photon sources driven by the electron beams of laser wakefield acceleration [17], high-brilliance γ-photon beams with MeV energy can be produced experimentally through bremsstrahlung [18,19], nonlinear Thomson scattering [20,21], and inverse Compton scattering [22–24], which open the way to investigate the real photon-photon interaction. Recently, numerous theoretical proposals on the γγ collider were put forward to validate the LBW process [9,25–33]. Among those proposals, the γγ collider is designed either with GeV-energy photons from bremsstrahlung inside a high-Z target and keV-energy partner photon from laser-target radiation or x-ray free electron laser [25,31,33], or with two same MeV γ-photon sources from a laser-driven synchrotron or nonlinear Compton scattering [9,26–28,30]. Moreover, the dominated LBW process is studied in laser-driven plasmas [34,35], and the quasiparticle-hole pair production in gapped graphene monolayers can be analogous to the LBW process [36]. However, the above proposals mainly focus attention on the large pair yield, but generally ignore the inherent spin effects of scattering particles. The polarization transfer (i.e., helicity transfer) between initial photons and final e± pairs is associated with their spin angular momentum. Based on the production of high-brilliance photons with highly-circular polarization [37–42], the LBW process can be investigated in a polarized γγ collider. The fundamental physics of helicity in the LBW process has been analyzed qualitatively from the perspective of angular momentum conservation [43]. The latest experiment confirms that the linearly-polarized photons can induce the azimuthal-angle distribution of the LBW pairs [4], since the linear polarization is related to the azimuthal angle of pair momenta. In addition, the impact of energy distribution of γ-photon beam on the LBW pair yield is analyzed in a semianalytical model [32]. However, considering realistic polarization and energy distribution into laser-driven γ-photon beams, the spin-associated momentum and polarization characteristics of the LBW process have not been uncovered and are still great challenges.

In this paper, we investigate the complete polarization effects in the LBW process by virtue of our newly developed spin-resolved Monte Carlo (MC) simulation method, which is applicable for general binary collisions of leptons and photons (see the interaction scenario in Fig. 1). We find that the circular polarization of γ-photons can modify the kinematics of scattering particles and induces a correlated energy-angle shift of the LBW pairs [see Fig. 1 (top) and more details in Fig. 2], and the polarization characteristic of the LBW pairs depends on the helicity configures of scattering particles [see Fig. 1 (bottom) and more details in Fig. 3]. Our method confirms that the polarized γγ collider with an asymmetric setup can be performed with currently achievable laser facilities (see Table I), and the considered polarization effects may have significant applications in high-energy astrophysics.

Let us first summarize our simulation method for calculating the production and polarization of the LBW pairs. Employing the standard treatment of particle density matrixes in the scattering amplitude of incoherent binary collisions [43–48], the polarized LBW cross section in center of mass (c.m.) frame is obtained as dσdΩ=σ0[F+∑i=13(Gi+ζi++Gi-ζi-)+∑i,j=13Hi,jζi+ζj-],(1)where σ0=re2me2|pe|/16ϵ3, Ω is the solid angle, pe the c.m. momentum of electron, ϵ the c.m. energy of photon, electron and positron (they are equal in the c.m. frame), me and re the electron mass and classical radius, respectively, ζi± the spin components of electron (“-”) and positron (“+”), and the factors F, Gi±, and Hi,j include the photon Stokes parameters ξi [44] and are given in [49]. Summing over ζi± and integrating over Ω, one obtains σ¯tot=re2me4π4ϵ4s˜-4s˜(-s˜-4+2ξ1(1)ξ1(2)+3s˜ξ2(1)ξ2(2)-2ξ3(1)ξ3(2))+16πs˜tanh-1s˜-4s˜(2s˜2+8s˜-16+8ξ1(1)ξ1(2)-2s˜2ξ2(1)ξ2(2)-8ξ3(1)ξ3(2)),(2)where s˜=4ϵ2/me2. Relativistic units with c=ℏ=1 are used throughout.

In our considered collision scenario, a γ-photon beam is initialized with a specific energy distribution and divergence angle in laboratory frame. During the beam-beam collision, the colliding region is meshed into solid cells at every time step, and the probable colliding photons inside a cell are sampled by the Thomson cross section and paired by no-time-count method [50], as illustrated in Fig. 1 (top). By the Lorentz boost along the c.m. frame velocity βcm [51–53], every set of paired photons with s˜>4 are permitted for the single BW process in Eq. (1) by using the acceptance-rejection method. For each BW event, the c.m. momentum pe is determined in the defined momentum configure (see Fig. 1 in [49]) where the scattering angle θs is defined as the angle between pe and k. Here θs is calculated by solving σ¯θ/σ¯tot=R1∈(-1,1), where R1 is an uniform random number and σ¯θ=s˜(s˜-4)/4∫-|cosθs||cosθs|dσ¯. Moreover, the energy and momenta of e± in the laboratory frame are obtained by the inverse Lorentz boost acting on ϵ and pe.

The mean spin polarization vectors of electron and positron ζ±¯ are determined by the defined three-vector basis [45,49] and their components can be analytically calculated via ζ±¯i=Gi±/F [44]. With the determined pe, the mean helicities of a pair are expressed as λ±=∓ζ±¯pe/2|pe|, and the corresponding helicity configure is illustrated in Fig. 1 (bottom). In our MC method, the projections of ζ±¯ onto the defined spin states D± (unit vectors) of a detector are calculated with transition probabilities, and the latter determine the sign of components Di±=ζ±¯i/|ζ±¯|. Consequently, the total beam polarization is calculated by Ptot=(D1±¯)2+(D2±¯)2+(D3±¯)2 with the averaged components Di±¯ over the particle number [54]. Aligning D± to the parallel or perpendicular direction of the momenta can further obtain the longitudinal polarization PL or transverse polarization PT for e± beams. (More details of our simulation method are clarified in the Supplemental Material [49].)

Impact of the γ-photon polarization on the energy and polar angle distributions of the LBW pairs is shown in Fig. 2. σ¯tot of the γR(1)γR(2) case increases about 33% at the peak energy and narrows the spectrum, compared with that of the nonpolarized case [see Fig. 2(a)], while the linear polarization only modifies the amplitude because it has no impact on θs [49]. A definite shaped Pθ(θs) implies that the produced electron (positron) is scattered into a certain range of dθs with a corresponding probability of dPθ [see Fig. 2(b)]. The reactions within θs≲π/6 in the γR(1)γL(2) collision near the threshold energy are almost forbidden due to the approximate zero probabilities. By contrast, the dominated reactions occur within θs≲π/6 in the γR(1)γR(2) collision at the energy far beyond the threshold. Therefore, the distinct energy-angle spectra can be produced by the quasimonoenergetic beams in two collision schemes, and the γR(1)γL(2) (γR(1)γR(2)) collision with a Gaussian energy spectrum, an average energy of 0.6 (1.8) MeV and a 30% energy spread produces the dipole (quadrupole) angular spectrum, which distributes perpendicular to (parallel with) the z-axis, as shown in Fig. 1 (top). The distinct energy-correlated θs in these two interaction schemes causes the energy-angle correlation of the pairs, whereby the γR(1)γL(2) collision results in the larger kinetic energy E¯k than that of the γR(1)γR(2) collision [see Fig. 2(c)]. As the initial circular polarization (PCP) of γ-photons increases, in the γR(1)γL(2) collision the average kinetic energy E¯k and the divergence angle θrms of positrons both increase as well, while in the γR(1)γR(2) collision the tendency is inverse [see Fig. 2(d)]. Thus, θrms is positively correlated to E¯k. The influence of the energy and divergence-angle fluctuations of the γ-photon beams on θrms and E¯k is estimated, and the results indicate that the polarization-induced signatures of the energy-angle shift can be resolved as the fluctuations of the divergence angle and the average energy are less than 50% and 5%, respectively (see [49]). Note that the correlated polar angle and energy distributions of the LBW pairs can be resolved precisely in experiments by the single particle detector [33].

Particularly, the spin-polarization of the LBW pairs is derived from the circular polarization of parent γ-photons. For the γR(1)γR(2) collision, the partial polarization is produced near the threshold energy of the pair production [see Fig. 3(a)], while for the γR(1)γL(2) collision, the partial polarization is produced around θs=π/2 [see Fig. 3(b)]. It is nontrivial to reveal the variation of the positron polarization with respect to the γ-photon polarization. For the γR(1)γR(2) collision, PL dominates the polarization and increases linearly, and PT [attributed to the dσ+-±∓ channel; see Fig. 4(e)] is less than 0.2 as PCP varies [see Fig. 3(c)], since the produced pairs possess sole negative helicities [see Fig. 4(a)]. While, for the γR(1)γL(2) collision PT dominates the polarization [see Fig. 3(d)], since the produced pairs possess the mixed helicity states [55] around θs=π/2 and the magnitude of PT is affected by the extracted polar angle range [see Fig. 4(b)]. Thus, one could observe the signatures of polarization in the LBW process either via detecting PL in the γR(1)γR(2) collision around the colliding axis or via detecting PT in the γR(1)γL(2) collision around the perpendicular direction of the colliding axis.

The physical mechanism of the helicity transfer in the LBW process is analyzed in Fig. 4. The polarization is derived from the mean helicity distribution, and the γR(1)γR(2) collision leads to the energy-dependent negative helicities, while the γR(1)γL(2) collision leads to the angle-dependent alternating helicities (vary between −0.5 and 0.5) [see Figs. 4(a) and (b)]. The positron helicity originates from the superposition of various helicity eigenstates with different weights determined by the differential cross section. There are only three nonvanished helicity channels dσ++--, dσ+++-, and dσ++-+ for the γR(1)γR(2) collision [see Figs. 4(d) and 4(e)]. Here, dσ++±∓ dominate the reaction near the threshold energy, produce the positrons at the helicity states |+⟩ or |-⟩ with the same weights, and consequently, cancel each other (i.e., PL vanishes and PT maximizes). Thus, only the channel of dσ++-- contributes to the state |-⟩, i.e., dσ++-- solely induces PL. These helicity channels finally result in the mean helicity distribution in Fig. 4(a) and the corresponding positron polarization in Fig. 3(a). Similarly, in the γR(1)γL(2) collision, there are four helicity channels dσ+-±± and dσ+-±∓ (note that here dσ+--+ is symmetric about θs=π/2 with dσ+-+- and thus is not shown) [see Figs. 4(g) and (h)]. dσ+-±± only contribute to PT and dσ+-±∓ mainly to PL [see Figs. 4(b) and 3(b)].

For the experimental feasibility, the symmetric and asymmetric setups are considered to design the polarized γγ collider, as shown in Table I. The symmetric setup reveals the polarization-associated signatures in both of momentum and spin (see Figs. 2 and 3), and the required minimal brilliance of the γ-photon beam is rather high in order to produce a resolvable mA current for the polarimetry. In the asymmetric setup, the RCP γ-photon beam injects into a nonpolarized x-ray bath with an uniform energy distribution between 1 keV–3 keV and an isotropic angular distribution, produce a strongly collimated positron (electron) beam with moderate PL and PT. Because the asymmetric setup utilizes the dense x-ray bath generated by laser-heated hohlraum [25] or laser-irradiated target [33], it can significantly reduce the required minimal brilliance of the γ-photon beam as the density of x-rays reaches above 1020  cm-3. The experimentally feasible γ-photon sources with brilliance ∼1022 can be generated through the Compton scattering [22,56], and the polarized one is also available by the bremsstrahlung radiation with a photon number of ∼108 [25,40]. Furthermore, the stabilities of the pair yield and polarization in the asymmetric setup are estimated by varying the divergence angle and polarization of the γ-photon beam, the results (see [49]) indicate that both the variations of the initial polarization and divergence angle have slight influence on the current of produced electrons (positrons), and the longitudinal polarization can reach the maximum 50% as the divergence and polarization of γ-photon beam increase. In terms of the polarization detection, the e± polarimetry technology has achieved a high precision ≲1%, e.g., Compton transmission polarimetry [38–40] and Mott polarimetry [57–59], which are both applicable at the energy of 0.1 MeV–10 MeV and can response the current as low as ≲100  μA [57,58].

Furthermore, we underline that the LBW process is also widely involved in high-energy astrophysical phenonema. The measured γ-ray spectra of those intense compact astrophysical objects (such as GRBs, blazars, pulsar, and etc) are supposed to be attenuated at the high-energy end by the low-energy radiation therein via this process [60–65]. Both the low-energy radiation and the γ-ray radiation, which generally arise from the synchrotron radiation and the inverse Compton scattering respectively, can be polarized in the presence of magnetic field. Taking into account the polarized LBW process would enhance the opacity of γ-photons of those sources and consequently exacerbate the inconsistency between some observations and standard models, which may challenge the current understanding on the astrophysical objects.

In conclusion, we develop a fully spin-resolved simulation method for general binary collisions to investigate the complete polarization effects of the LBW process in polarized γγ collision. Qualitative signatures of polarized LBW process are imprinted on momentum and spin of produced pairs. Our results of polarized LBW processes are effective in calibrating and monitor the upcoming polarized γγ collider, and pave the way for proceeding the elusive photon-photon scattering. Moreover, the polarization-induced fluctuations of the e± density in high-energy astrophysical objects possibly associate with certain of significant observations, which calls for the further investigation.