⚛️ phenomenology

Bhabha scattering at future colliders with BHLUMI/BHWIDE

This paper introduces the Monte Carlo event generators BHLUMI and BHWIDE for simulating small and large angle Bhabha scattering, respectively, and outlines potential improvements to meet the precision requirements of future electron-positron colliders.

Original authors: Wiesław Płaczek, Maciej Skrzypek, Bennie F. L. Ward, Scott A. Yost

Published 2026-01-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Wiesław Płaczek, Maciej Skrzypek, Bennie F. L. Ward, Scott A. Yost

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of particle physics as a massive, high-stakes photography contest. Scientists are trying to take the perfect picture of the universe's smallest building blocks. To do this, they use giant machines called colliders (like the future FCC-ee) that smash electrons and positrons together at incredible speeds.

However, taking a photo isn't enough; you need to know exactly how bright the flash was and how many photos you took to make sense of the image. In physics, this "brightness" and "count" is called luminosity. If you don't know your luminosity perfectly, you can't calculate the true size of the particles you are studying.

This is where Bhabha scattering comes in. Think of Bhabha scattering as the "calibration shot." It's a process where an electron and a positron bounce off each other. Because we understand the rules of this bounce (the laws of physics) so well, scientists can use it as a ruler to measure the luminosity of the collider.

The paper discusses two specific computer programs, BHLUMI and BHWIDE, which act as the "mathematical calculators" for these calibration shots. The authors explain that while these programs worked perfectly for the old machines (LEP), the new, super-precise future machines will need them to be upgraded.

Here is the breakdown of the two programs and the upgrade plan, using simple analogies:

1. The Two Types of "Bounces"

The paper splits the calibration shots into two categories based on how sharply the particles bounce:

Small-Angle (SABS): The particles barely glance off each other, like two cars passing on a highway and just brushing their mirrors. This happens at very shallow angles.
Large-Angle (LABS): The particles bounce back hard, like two cars colliding head-on and ricocheting in opposite directions. This happens at wide angles.

2. The Old Calculators: BHLUMI and BHWIDE

BHLUMI (The Small-Angle Specialist): This program calculates the math for the "glancing blow" collisions. It has been the gold standard for years. It uses a clever trick called YFS exponentiation, which is like a super-efficient accounting method that handles millions of tiny, invisible energy packets (photons) all at once, rather than counting them one by one.
BHWIDE (The Large-Angle Specialist): This program handles the "head-on" collisions. These are much more complicated because the particles interact in more complex ways (swapping different types of force carriers). BHWIDE currently calculates these interactions with a high degree of accuracy, but not quite enough for the future.

3. The Problem: The "Future" Needs Better Precision

The old machines (LEP) were like standard-definition cameras. The new machines (FCC-ee) will be like 8K, high-definition cameras.

The Issue: The current math in BHLUMI and BHWIDE is good enough for standard definition, but for 8K, even the tiniest rounding errors in the math will ruin the picture.
The Goal: The authors want to upgrade these programs so their mathematical predictions are accurate to within one part in ten thousand (or even better). If the math isn't this precise, the "ruler" used to measure the collider's performance will be slightly off, and scientists might miss new discoveries or misinterpret the data.

4. The Upgrade Plan: A Three-Stage Renovation

The authors propose a step-by-step plan to renovate these calculators:

For BHLUMI (Small-Angle):

Stage 1: They will add missing "ingredients" to the recipe. Currently, the math stops at a certain level of complexity. They need to add more complex terms (specifically involving higher powers of a number called $\alpha$ and a "big log" factor) to get the precision right. They will also combine BHLUMI with two other programs (BHWIDE and KoralW) to handle all the different ways the particles can interact.
Stage 2: They will merge all these different calculation methods into a single, unified program so everything is in one place.
Stage 3: They will apply a new, even more powerful mathematical framework called CEEX. Think of this as upgrading from a manual calculator to a quantum computer for this specific task, ensuring the highest possible precision.

For BHWIDE (Large-Angle):

This one is trickier because the "head-on" collisions involve more complex physics.
The authors plan to add two-loop corrections. Imagine calculating the path of a ball; currently, they calculate the path and the wind. The upgrade will calculate the path, the wind, the humidity, the air pressure, and how the ball's spin changes the air around it.
They will use new software tools (like OpenLoops and Recola) to automate these incredibly complex calculations, which were previously too hard to do by hand.

5. The Bottom Line

The paper is essentially a blueprint for upgrading the software that runs the world's most advanced particle physics experiments.

The authors argue that to make the next generation of particle colliders (like the FCC-ee) work as intended, we cannot just build better hardware; we must also build better "mathematical lenses." By upgrading BHLUMI and BHWIDE through these three stages, they aim to ensure that when scientists look at the data from these future machines, the numbers are sharp enough to reveal the deepest secrets of the universe, or at least confirm that our current understanding of physics is perfect.

The paper concludes by honoring the late Staszek Jadach, a mentor who was instrumental in developing these original tools, acknowledging that this future work stands on the foundation he helped build.

Technical Summary: Bhabha Scattering at Future Colliders with BHLUMI/BHWIDE

Problem Statement
The paper addresses the critical need for high-precision theoretical predictions for Bhabha scattering ( $e^+e^- \to e^+e^-$ ) to support the next generation of electron–positron colliders (e.g., FCC-ee, ILC, CLIC, CEPC). As the High Energy Physics community moves toward the post-LHC era, these colliders aim to perform precision measurements of the Higgs boson and search for deviations from the Standard Model (SM). The experimental precision expected at these facilities—particularly at the Z-boson peak, where luminosity measurements could reach relative precisions of $\lesssim 10^{-4}$ —demands that theoretical uncertainties match or exceed this level. Currently, the theoretical tools used at LEP, while sufficient for that era, are insufficient for the sub-permil precision required by future machines.

Bhabha scattering is divided into two regimes based on the scattering angle ( $\theta_e$ ):

Small-Angle Bhabha Scattering (SABS): $\theta_e \lesssim 100$ mrad. This process is the primary reference for luminosity measurement due to its dominance by $t$ -channel photon exchange and high event statistics.
Large-Angle Bhabha Scattering (LABS): $\theta_e \gtrsim 100$ mrad. This process is used for measuring the electron partial decay width of the Z boson ( $\Gamma_e$ ) and serves as a background for other processes at higher energies.

Methodology and Current Tools
The authors focus on two Monte Carlo Event Generators (MCEGs) originally developed for LEP:

BHLUMI: Designed for SABS. It utilizes the Yennie–Frautschi–Suura (YFS) exclusive exponentiation (EEX) method, which sums infrared (IR) singularities to infinite order. The current version (4.04) employs a "pragmatic" QED expansion, including terms up to $O(\alpha^2 L^2)$ (where $L$ is a large logarithm).
BHWIDE: Designed for LABS. It also uses YFS EEX but includes $O(\alpha)$ electroweak (EW) radiative corrections. It interfaces with libraries like BABAMC and ALIBABA to handle one-loop virtual corrections and Dyson resummation of light-fermion contributions to boson self-energies.

The paper argues that to achieve the required precision for future colliders, the perturbative series must be reordered. Specifically, for SABS, the expansion must move from the traditional $O(\alpha^2)$ to an $O(\alpha^3)_{\text{prag}}$ level, incorporating higher-order logarithmic terms ( $\alpha^2 L$ and $\alpha^3 L^3$ ).

Key Contributions and Proposed Improvements
The paper outlines a three-stage plan to upgrade BHLUMI and BHWIDE to meet future precision goals:

1. Upgrades for SABS (BHLUMI):

Stage 1: Immediate implementation of available photonic corrections ( $O(\alpha^2 L)$ and $O(\alpha^3 L^3)$ ) into BHLUMI. This stage involves a combined approach using three generators: BHLUMI (for the dominant $t$ -channel), BHWIDE (for $s$ -channel and $Z$ -exchange interferences), and KoralW (for light-fermion pair corrections).
Stage 2: Integration of matrix elements from BHWIDE (covering all $\gamma$ and $Z$ exchanges and light-fermion pairs) directly into a single, unified BHLUMI instance, creating an $O(\alpha^3)_{\text{prag}}$ YFS EEX generator.
Stage 3: Application of the Coherent Exclusive Exponentiation (CEEX) formalism to SABS, mirroring the approach used in the KKMC generator for other processes. This aims to produce an $O(\alpha^3)_{\text{prag}}$ YFS CEEX BHLUMI that satisfies the theoretical precision needs for luminosity measurements.
Validation: The authors note that testing tools (LUMLOG and OLDBIS) must be upgraded to $O(\alpha^4 L^4)$ and fixed-order $O(\alpha^2)$ , respectively, to cross-check the new generators. External validation with generators like BabaYaga is also proposed.

2. Upgrades for LABS (BHWIDE):

The paper identifies that LABS is more complex due to interference between $s$ and $t$ channels for both $\gamma$ and $Z$ exchanges.
To reach the necessary precision ( $\lesssim 1\%$ at high energies, sub-permil at the Z peak), BHWIDE requires the inclusion of Next-to-Next-to-Leading Order (NNLO) QED corrections and, at the Z peak, NNLO EW corrections.
Implementation Strategy:
- Two-loop corrections with massive leptons (recently calculated).
- One-loop corrections to single bremsstrahlung (computable via automated tools like OpenLoops or Recola).
- Tree-level double-bremsstrahlung matrix elements (calculable via spin amplitudes or automated packages).
- NNLO EW corrections at the Z peak (computable via the GRIFFIN library).

Results and Feasibility
The authors do not present new numerical results for the upgraded generators but rather a roadmap for their development. They assert that:

The theoretical error for LEP at the Z pole has been reassessed to 0.037%.
Forecasts for FCC-ee suggest a theoretical precision of $0.7 \times 10^{-4}$ at the Z pole is achievable.
The necessary components for these upgrades (e.g., two-loop QED calculations with massive leptons, specific matrix elements) have recently become available or are computable with existing software.
While the effort required is considerable, reaching the precision levels of future $e^+e^-$ colliders for both SABS and LABS is deemed feasible.

Significance and Claims
The paper claims that the proposed upgrades to BHLUMI and BHWIDE are essential for the success of future electron–positron colliders. Without these improvements, theoretical uncertainties would become the limiting factor in luminosity measurements and precision tests of the Standard Model, potentially obscuring signals of new physics. The authors emphasize that the YFS resummation method, particularly when enhanced with collinearly-enhanced terms, provides a robust framework for achieving these goals. The work serves as a technical proposal for the theoretical community to align its tools with the experimental capabilities of the next generation of colliders.