Strong field processes in beam-beam interactions at the Compact Linear Collider

The demand for high luminosity in the next generation of linear $e^{+}{e}^{-}$ colliders necessitates extremely dense beams, giving rise to strong fields at the collision point, and therefore the impact of the field on the physical processes occurring at the interaction point must be considered. These processes are well described by the interaction of the individual lepton with the field of the oncoming bunch, and they depend strongly on the beamstrahlung parameter $\mathrm{\Upsilon }$ which expresses the field experienced by the lepton in units of the critical field. In this paper, we describe calculations and simulations of strong field processes—also of higher order—at the interaction point.

Figure 1

Energy distributions of the disrupted particles produced at the IP as functions of angular cut. The muons shown here do not include the effect of disruption.

Figure 2

Comparison between spectra of coherent pairs produced by CAIN and GUINEA-PIG++. The sign of the energy corresponds to the sign of the charge.

Figure 3

Distribution of same-charge (defocused) coherent pairs after one bunch crossing using the 3 TeV CLIC baseline design parameters. On the $z$ axis is the number of particles in each bin, per bunch crossing.

Figure 4

Distribution of opposite-charge (focused) coherent pairs after one bunch crossing using the 3 TeV CLIC baseline design parameters. On the $z$ axis is the number of particles in each bin, per bunch crossing.

Figure 5

Feynman diagram for the direct trident process used for the Weizsäcker-Williams calculation. The incoming wavy line represents the coherent interaction of many particles—described as a homogeneous field—with the electron.

Figure 6

Feynman diagrams for incoherent pairs and incoherent muons. From left to right: the Breit-Wheeler, Bethe-Heitler, and Landau-Lifshitz processes. For each of these $u$-channel diagrams, there is a corresponding $t$-channel diagram (which means connecting each photon to the opposite virtual fermion vertex).

Figure 7

Spectrum of virtual photons used for generating direct tridents, $x=\hslash \omega /E_0$. The expression (11) (“analytical”) exhibits a cutoff in the maximum energy, which is clearly more physical than the semiclassical spectrum (“Erber”) from [14].

Figure 8

Total yield of direct tridents at a primary energy of 250 GeV. Red: Monte Carlo simulation, this paper. Blue dashed: approximate expression by Chen [15]. Green dotted: Erber [14]. Note that the Chen and Erber curves are shown outside of their respective regions of validity.

Figure 9

Spectrum of the various pair production mechanisms after full beam crossing simulation.

Figure 10

Bunch length dependence of the yield of the coherent pair production mechanisms. The bunch charge is kept constant.

Figure 11

Distribution of same-charge (defocused) direct tridents after one bunch crossing using the 3 TeV CLIC baseline design parameters. On the $z$ axis is the number of particles in each bin, per bunch crossing. May be compared with the distribution of coherent pairs shown in Figs. 3 and 4.

Figure 12

Same as Fig. 11 but for opposite-charge (focused) particles.

Figure 13

CLIC nominal luminosity spectrum at ideal conditions; the spectrum includes contributions from coherent pairs and initial state radiation.

Figure 14

Dependence of various relative yields on vertical offset between colliding bunches normalized to production at perfect conditions. The average strong field increases with this offset, increasing the yield of strong field processes. Peak luminosity refers to the amount of luminosity within 1% of the nominal collision energy. $\gamma \gamma \to \text{hadrons}$ refers to the amount of hadronic events from collisions between real or virtual photons.

Figure 15

The strong field dependence (16) of the anomalous magnetic moment of the electron.

Figure 16

The CLIC depolarization as function of a cut in the lower CM energy.

Figure 17

Depolarization as function of vertical offset using Gaussian input beams. Top: total depolarization. Bottom: depolarization within 1% of the nominal CM energy.

Figure 18

Comparison of the transverse momentum of incoherent electrons and muons. Cross sections have been scaled up by $10^4$ to decrease simulation time. At production time, the cut $p_t>m_{\mu }c$ has been employed. Red dashed line indicates incoherent electrons. Black solid line indicates incoherent muons.

Figure 19

Spectrum of incoherent muons at the time of production. The sign of the energy corresponds to the muon charge sign. The muon cross section is scaled up by a factor $10^4$, taking $(m_{\mu }/m_e{)}^2=4\times {10}^4$ into account, to decrease simulation time.

Figure 20

Spatial distribution of energy deposited by the tertiary photons at a transverse plane 3 m from the IP. Only photons with production angles above 20 mrad are displayed here.

Figure 21

Low-energy part of the tertiary photon spectrum.

Figure 22

Correlation between luminosity and number of tertiary photons (per 10 bunch crossings) when the size of one beam is varied. Each color in the optical region corresponds to an energy bin of 0.5 eV width.