Electroweak radiative corrections in high energy processes

TL;DR

This work analyzes electroweak radiative corrections in high-energy SM and MSSM processes, focusing on Sudakov-type logarithms that grow with energy in TeV-scale collisions. It develops and applies the infrared evolution equation (IREE) framework to resum both double and subleading logarithms, including renormalization-group improvements and matching across the weak scale, and extends the approach to broken gauge theories by leveraging the Goldstone boson equivalence theorem. The results show that higher-order Sudakov corrections can amount to several percent in cross sections at TeV energies, with angular-dependent and Yukawa-enhanced terms (notably in the third generation and MSSM) playing a substantial role, thereby underscoring their necessity for precision predictions at future linear colliders. The paper also validates the IREE approach against fixed-order calculations and applies it to SM and MSSM processes such as gauge boson and Higgs production, heavy quark production, and charged Higgs processes, illustrating the impact on cross sections and the potential to probe MSSM parameters like tanβ. Overall, the framework provides a systematic, gauge-invariant method to incorporate higher-order electroweak radiative corrections in high-energy collider phenomenology, with clear implications for precision tests and new-physics searches at TeV energies.

Abstract

Experiments at future colliders will attempt to unveil the origin of electroweak symmetry breaking in the TeV range. At these energies the Standard Model (SM) predictions have to be known precisely in order to disentangle various viable scenarios such as supersymmetry and its manifestations. In particular, large logarithmic corrections of the scale ratio $\sqrt{s}/M$, where $M$ denotes the gauge boson masses, contribute significantly up to and including the two loop level. In this paper we review recent progress in the theoretical understanding of the electroweak Sudakov corrections at high energies up to subleading accuracy in the SM and the minimal supersymmetric SM (MSSM). We discuss the symmetric part of the SM Lagrangian at high energies yielding the effective theory employed in the framework of the infrared evolution equation (IREE) method. Applications are presented for important SM and MSSM processes relevant for the physics program of future linear colliders including higher order purely electroweak angular dependent corrections. The size of the higher order subleading electroweak corrections is found to change cross sections in the several percent regime at TeV energies and their inclusion is thus mandatory for predictions of high energy processes at future colliders.

Figures (34)

• Figure 1: The schematic depiction of the effective high energy regimes ($\sqrt{s} \gg M \gg \lambda$) in the framework of the infrared evolution equation method. In region I), the high energy corrections are obtained effectively in the unbroken $SU_L(2)\times U_Y(1)$ theory described by ${\cal L}_{\mathrm{symm}}$ in Eq. (\ref{['eq:lsym']}) where all terms connected to the v.e.v. can be neglected to SL accuracy. For external fermions and transverse gauge bosons this picture contains at the subleading level Yukawa interactions and contributions from Higgs doublets to the anomalous scaling violations. For external longitudinal gauge bosons ($\phi = \{ \phi^+, \phi^-, \chi \}$) the equivalence theorem (E.T.) is employed yielding effectively a scalar theory charged under the unbroken gauge group. Again this scenario contains at the subleading level Yukawa terms introduced by the spontaneous symmetry breaking. For all charged particles, the soft photon effects, regulated here by a fictitious photon mass $\lambda$, are included by integrating in region II) which incorporates pure QED effects including mass terms. In the calculation $\lambda$ is replaced by a cutoff $\mu$ on the exchanged $|{\hbox{\boldmath $k$}_{\perp}}|$. The matching condition is given by the requirement that the high energy solution in region I) is obtained if the infrared cutoff $\mu$ is chosen to be the gauge boson mass $M$.
• Figure 2: The virtual Sudakov DL-phase space in massive QED for the function $R$ in the $\{ u,v \}$ representation. The cutoff $\mu$ plays the role of $\lambda$ for $\mu \ll m$. The shaded area is the region of integration and is symmetric with respect to $u$ and $v$. For $\mu \geq m$ the relevant phase space is mass independent.
• Figure 3: The virtual Sudakov DL-phase space in massive QED for the function $R$ in the $\{ {\hbox{\boldmath $k$}_{\perp }^2}, v \}$ representation. The shaded area is the region of integration. For $\mu \ll m$ the cufoff plays the role of $\lambda$ in the text. For $\mu \geq m$ the relevant phase space is mass independent as in the $\{u,v\}$ representation of Fig. \ref{['fig:suv']}.
• Figure 4: Bremsstrahlung in a process involving charged fermions. At high energies only the external legs contribute to DL accuracy.
• Figure 5: Higher order splittings determining the imaginary part of the scattering amplitude. At high energies, Gribov proofed that the pole terms in the variables $2p_ik$ do not dominate the amplitude and that the large terms factorize with respect to $1/|{\hbox{\boldmath $k$}_{\perp }}|$.