<p>This study examines the production of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\tau $</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> lepton pairs (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$e^+ + e^- \rightarrow Z \rightarrow \tau ^+ + \tau ^-$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <mo>+</mo> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo stretchy="false">→</mo> <mi>Z</mi> <mo stretchy="false">→</mo> <msup> <mi>τ</mi> <mo>+</mo> </msup> <mo>+</mo> <msup> <mi>τ</mi> <mo>-</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>) through the collision of electrons and positrons. This process is important for understanding the generation of fermion pairs and confirming the accuracy of the Standard Model at high energy levels. We used data from the LEP program to investigate <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\tau $</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> lepton production in resonance with the Z boson, both with and without a circularly polarized monochromatic laser field. In our theoretical model, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\tau $</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation> leptons are considered free Dirac states, while electrons and positrons are described by Dirac–Volkov states altered by the laser field. Our analysis involved using Mathematica to calculate the differential cross-section (DCS) and total cross-section (TCS). Our findings indicate that the TCS increases with laser frequency and stabilizes at specific thresholds, revealing significant effects of the laser field on the interaction dynamics. To validate our theoretical approach, we compared it with data from OPAL and Muijs (2001) and found excellent agreement in the absence of laser effects. Additionally, we examined how various laser parameters, such as the strength of the electric field and the number of exchanged photons, impact the scattering process.</p>

Laser-assisted electron–positron annihilation into tau pairs with associated Z-boson production

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发表日期：

2026年3月10日

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Hrour Elmostafa,
Abaragh Mouloud

摘要

This study examines the production of $\tau $ $τ$ lepton pairs ( $e^+ + e^- \rightarrow Z \rightarrow \tau ^+ + \tau ^-$ $e^{+} + e^{-} \to Z \to τ^{+} + τ^{-}$ ) through the collision of electrons and positrons. This process is important for understanding the generation of fermion pairs and confirming the accuracy of the Standard Model at high energy levels. We used data from the LEP program to investigate $\tau $ $τ$ lepton production in resonance with the Z boson, both with and without a circularly polarized monochromatic laser field. In our theoretical model, $\tau $ $τ$ leptons are considered free Dirac states, while electrons and positrons are described by Dirac–Volkov states altered by the laser field. Our analysis involved using Mathematica to calculate the differential cross-section (DCS) and total cross-section (TCS). Our findings indicate that the TCS increases with laser frequency and stabilizes at specific thresholds, revealing significant effects of the laser field on the interaction dynamics. To validate our theoretical approach, we compared it with data from OPAL and Muijs (2001) and found excellent agreement in the absence of laser effects. Additionally, we examined how various laser parameters, such as the strength of the electric field and the number of exchanged photons, impact the scattering process.