Addendum to multiplicities of charged pions, kaons and unidentified charged hadrons on an isoscalar target measured by COMPASS Collaboration

This paper presents an updated set of isoscalar multiplicities for charged pions, kaons, and unidentified hadrons measured by the COMPASS Collaboration, incorporating improved QED radiative corrections via the DJANGOH Monte Carlo generator to ensure consistency with recent proton-target results and superseding previous 2017 publications.

The Gist

Imagine you are a detective trying to figure out how often a specific type of car (a "charged pion" or "kaon") is produced when a high-speed bullet (a muon) smashes into a target. You want to count these cars to understand how the universe builds matter.

However, there's a problem: your camera lens is slightly dirty. Every time you take a picture, the lens distorts the image a little bit. In the world of particle physics, this "dirty lens" is called radiative correction. It's a mathematical adjustment needed to account for extra energy that gets lost or gained during the crash, which can make your counts look wrong.

The Old vs. The New Lens

For years, the COMPASS team (a group of scientists at CERN) used an old, somewhat blurry lens (a computer program called TERAD) to clean up their photos. They used this to publish their counts of these particles back in 2017.

Recently, the team realized they had a brand new, crystal-clear lens called DJANGOH. This new tool is much better at simulating exactly what happens when particles crash, including the messy "debris" (hadronic final states) that the old tool couldn't handle well.

The Big Discovery

When the scientists swapped the old lens for the new one, they found that their previous counts were off by quite a bit in certain areas.

• The Analogy: Imagine you were counting apples in a basket. With the old lens, you thought you saw 100 apples. With the new, sharper lens, you realized you were actually seeing 112 apples because the old lens was hiding some of them in the shadows.
• The Scale: In the most difficult-to-see areas (where the particles are moving in specific, tricky ways), the new lens revealed that the numbers needed to be adjusted by up to 12%. That's a huge difference in science!

Why This Paper Exists

This document is an Addendum, which is basically a "Correction Notice." The scientists are saying:

1. "We recently published a paper about proton targets using this new, super-accurate lens."
2. "To make sure our data is consistent, we need to go back and fix our older data about isoscalar targets (a different type of target material) using the same new lens."
3. "We are officially replacing the 2017 numbers with these new, corrected numbers."

What Changed?

The scientists took their old results, stripped away the old "blurry" corrections, and applied the new "sharp" corrections.

• For pions (the most common particles they study), the numbers changed significantly, especially in the "low-x, high-z" region (a fancy way of saying specific angles and speeds where the old lens was most confused).
• For kaons (a heavier, rarer particle), the changes were smaller. Why? Because when they published the kaon data in 2017, they were already being very cautious and conservative, guessing that the old lens might be wrong. So, the new lens didn't have to change their numbers as drastically.

The Bottom Line

This paper doesn't discover a new particle or a new law of physics. Instead, it's a quality control update. It ensures that all the COMPASS data—whether from proton targets or isoscalar targets—is now calculated using the same, most accurate method available today.

Think of it as the scientists saying, "We found a better ruler. We measured our table with the old ruler last year, but now we've re-measured it with the new one. Here are the correct dimensions, and please use these for any future work."

The new numbers are now the official standard, replacing the old ones, ensuring that anyone studying how particles break apart and form new matter has the most accurate map possible.

Technical Summary

Technical Summary: Addendum to Multiplicities of Charged Pions, Kaons, and Unidentified Charged Hadrons on an Isoscalar Target

Problem Statement
The COMPASS Collaboration previously published measurements of hadron multiplicities (pions, kaons, and unidentified hadrons) from deep-inelastic scattering (DIS) of muons off isoscalar targets (Phys. Lett. B 764 (2017) 1 and Phys. Lett. B 767 (2017) 133). These measurements rely on radiative corrections to convert observed cross-sections to one-photon exchange cross-sections. In the earlier publications, the correction factor for hadron production ($r_{chad}$) was estimated using the TERAD program, which was designed for inclusive DIS cross-sections. This approach involved subtracting elastic and quasi-elastic contributions as an approximation. While this method yielded corrections of less than 2% in the low-$x$, middle-$y$ region, the Collaboration recognized it as an approximate method. Furthermore, a subsequent publication on proton target multiplicities (Phys. Rev. D 112 (2025) 012002) employed a more robust method using the DJANGOH Monte Carlo generator, which includes the simulation of hadronic final states. To ensure a consistent theoretical treatment of data obtained from both isoscalar and proton targets, the isoscalar multiplicity results required re-evaluation using the improved radiative correction methodology.

Methodology
The primary methodological advancement in this addendum is the replacement of the TERAD-based radiative corrections with those derived from the DJANGOH Monte Carlo generator (DJANGOH-MC). The DJANGOH-MC has been previously verified by COMPASS to provide a satisfactory description of SIDIS data.

The radiative correction factor, denoted as $R_C$, is defined as the ratio of the hadron production correction to the inclusive DIS correction ($R_C = r_{chad}/r_{cDIS}$).

• Previous Approach: Used $R_C^{TERAD}$, where $r_{cDIS}$ was taken from TERAD and $r_{chad}$ was estimated via an approximate subtraction method or, in the case of kaons, a conservative average of hadron and inclusive corrections.
• New Approach: Uses $R_C^{DJANGOH}$. The values are derived using a two-step procedure described in Ref. [3]: $r_{cDIS}$ is taken from TERAD, while $r_{chad}$ is obtained directly from DJANGOH-MC simulations.

The new multiplicity values ($dM_{new}/dz$) are calculated by removing the previously applied corrections and applying the new DJANGOH-derived factors according to the following relation:
$$\frac{dM_{new}}{dz} = \frac{dM_{previous}}{dz} \times \left( \frac{r_{cDIS}}{r_{chad}} \right)_{TERAD} \times R_C^{DJANGOH}$$

Statistical uncertainties are propagated with the multiplicity values, while systematic uncertainties remain unchanged. The new correction factors are provided in a three-dimensional binning of the Bjorken variable $x$, the lepton energy fraction $y$, and the hadron energy fraction $z$.

Key Results

• Magnitude of Corrections: The application of DJANGOH-derived corrections results in significant changes to the multiplicity values, particularly in the kinematic region of low $x$, high $y$, and high $z$. The corrections are up to 12% larger in these regions compared to the previously applied TERAD-based corrections.
• Particle Dependence: The differences between the old and new results are most pronounced for pions. For kaons, the differences are smaller because the original analysis (Ref. [2]) had already adopted a conservative correction strategy that averaged the TERAD-based hadron and inclusive corrections.
• Target Dependence: Comparisons between isoscalar and proton targets show that the $R_C^{DJANGOH}$ values are consistent across target types, with only small differences observed.
• Data Availability: The new multiplicity results and the $R_C^{DJANGOH}$ correction factors are made available on the HEPData repository. Bins in the corners of the kinematic region where $R_C^{DJANGOH}$ could not be obtained are omitted from the new tables.

Significance and Claims
The paper presents this work as an addendum to supersede the previous isoscalar multiplicity results published in Phys. Lett. B 764 (2017) 1 and Phys. Lett. B 767 (2017) 133. The primary significance of this update is the establishment of a consistent treatment of COMPASS data sets obtained using both isoscalar and proton targets. By aligning the isoscalar results with the methodology used in the recent proton target publication (Phys. Rev. D 112 (2025) 012002), the Collaboration ensures that theoretical and phenomenological studies extracting fragmentation functions from COMPASS data are based on a uniform and theoretically robust treatment of QED radiative corrections. The authors explicitly state that the new results supersede the previous ones.