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Charged kaon and proton multiplicities in semi-inclusive deep-inelastic scattering with 11 GeV electrons

This paper reports measurements of charged kaon and proton multiplicities in semi-inclusive deep-inelastic scattering at Jefferson Lab, revealing that while kaon data aligns with DSS fragmentation functions for $K^+$ but underpredicts $K^-$ , proton-to-pion ratios significantly exceed TMD predictions at low $W^2$ yet decrease at higher $W^2$ in agreement with Lund Monte Carlo models, with no significant differences observed between proton and deuteron targets.

Original authors: P. Bosted, W. Armstrong, H. Bhatt, D. Dutta, R. Ent, D. Gaskell, S. Jia, E. Kinney, H. Mkrtchyan, S. Ali, R. Ambrose, D. Androic, C. Ayerbe Gayoso, A. Bandari, V. Berdnikov, D. Bhetuwal, D. Biswas, M.

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: P. Bosted, W. Armstrong, H. Bhatt, D. Dutta, R. Ent, D. Gaskell, S. Jia, E. Kinney, H. Mkrtchyan, S. Ali, R. Ambrose, D. Androic, C. Ayerbe Gayoso, A. Bandari, V. Berdnikov, D. Bhetuwal, D. Biswas, M. Boer, E. Brash, A. Camsonne, M. Cardona, J. P. Chen, J. Chen, M. Chen, E. M. Christy, S. Covrig, S. Danagoulian, M. Diefenthaler, B. Duran, C. Elliot, H. Fenker, E. Fuchey, J. O. Hansen, F. Hauenstein, T. Horn, G. M. Huber, M. K. Jones, M. L. Kabir, A. Karki, B. Karki, S. J. D. Kay, C. Keppel, V. Kumar, N. Lashley-Colthirst, W. B. Li, D. Mack, S. Malace, P. Markowitz, M. McCaughan, E. McClellan, D. Meekins, R. Michaels, A. Mkrtchyan, C. Morean, G. Niculescu, I. Niculescu, B. Pandey, S. Park, E. Pooser, B. Sawatzky, G. R. Smith, H. Szumila-Vance, A. S. Tadepalli, V. Tadevosyan, R. Trotta, H. Voskanyan, S. A. Wood, Z. Ye, C. Yerom, X. Zheng

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 inside of a proton (a tiny particle found in the center of every atom) as a bustling, chaotic city. Inside this city, tiny messengers called quarks zoom around. When scientists want to understand the layout of this city, they don't just look at it; they throw a high-speed "probe" (an electron) at it to see how the messengers react.

This paper is a report from a team of scientists at Jefferson Lab who threw these electron probes at two different targets: a bottle of liquid hydrogen (pure protons) and liquid deuterium (protons mixed with neutrons). They wanted to see what kind of "debris" flew out after the crash. Specifically, they were looking for two types of debris: Kaons (a type of particle) and Protons (the same type of particle they started with, but knocked loose).

Here is the story of what they found, explained simply:

1. The Setup: A High-Speed Collision

Think of the experiment like a high-speed billiard game.

The Cue Ball: A beam of electrons traveling at nearly the speed of light (10.2 to 10.6 GeV).
The Target: A tank of liquid hydrogen or deuterium.
The Collision: When the electron hits a quark inside a proton, it knocks the quark loose.
The Debris: As the quark flies away, it doesn't stay alone. It instantly grabs other particles to form new, stable "packages" called hadrons. The scientists caught these packages in giant, high-tech cameras (spectrometers) to see what they were made of.

2. The Mystery of the "Soft" Zone

The scientists were trying to figure out where in the collision these new particles were born. They divided the collision zone into three neighborhoods:

The "Current" Neighborhood: Where the quark was knocked out. This is a well-understood area where the rules of physics (called TMD factorization) work perfectly.
The "Target" Neighborhood: Where the leftover pieces of the proton hang out.
The "Soft" Central Zone: A messy middle ground where the rules are fuzzy and hard to predict.

The Kaon Story (The "In-Between" Traveler):
The Kaons they caught were like travelers who spent some time in the well-understood "Current" neighborhood and some time in the messy "Soft" zone.

Positive Kaons ( $K^+$ ): These behaved exactly as the scientists' maps predicted. They were like tourists following a well-marked guidebook.
Negative Kaons ( $K^-$ ): These were the troublemakers. The scientists found far fewer of them than the maps predicted. It's as if the guidebook said, "You will see 100 of these," but they only found 20. This suggests our current maps of how these particles are made are missing something important.

The Proton Story (The "Messy" Zone Resident):
The protons they found were like people who never left the messy "Soft" Central Zone.

The Surprise: The scientists found a huge number of protons—way more than the standard maps predicted. At the lowest energy levels, they found ten times more protons than expected. Even at the highest energies, they still found twice as many.
The Explanation: Because these protons were born in the messy "Soft" zone, the standard rules (which work for the "Current" zone) didn't apply. The scientists found that a different kind of simulation (called the "Lund Monte Carlo," which is like a very detailed video game engine for particle physics) did a much better job of predicting these numbers.

3. The Wiggles (Azimuthal Modulations)

When particles fly out, they don't just go straight; they sometimes wobble or spin in specific patterns. The scientists looked for these "wiggles" (mathematically described as $A$ and $B$ ).

For Kaons: The wiggles were so tiny they were basically zero. The particles flew out evenly, like rain falling straight down.
For Protons: The wiggles were also mostly zero, but there was a tiny hint of a pattern in one direction. It's like a gentle breeze that pushes the particles slightly to the left, but not enough to be a strong storm.

4. The Takeaway

This paper is essentially a "field report" saying:

We have new data: We measured exactly how many Kaons and Protons come out of these collisions across a wide range of speeds and angles.
The Maps are Incomplete: Our current theories (fragmentation functions) work great for positive Kaons and high-energy protons, but they fail to predict the number of negative Kaons and low-energy protons.
The "Soft" Zone is Real: The fact that we found so many protons confirms that there is a messy, central region in these collisions where our current mathematical rules don't fully work yet.
Video Games Help: The computer simulations that treat these collisions like a complex game (Lund Monte Carlo) seem to understand this messy zone better than our current math does.

In short, the scientists threw electrons at protons, caught the resulting debris, and discovered that while some particles behave exactly as predicted, others (especially the negative Kaons and low-energy protons) are much more common than we thought, hinting that there is still a lot to learn about the messy middle ground of particle physics.

Technical Summary: Charged Kaon and Proton Multiplicities in Semi-Inclusive Deep-Inelastic Scattering with 11 GeV Electrons

Problem and Motivation
Semi-inclusive deep-inelastic scattering (SIDIS) serves as a primary tool for probing the three-dimensional internal structure of the nucleon, linking quark parton distribution functions (PDFs) with fragmentation functions (FFs). While pion production in SIDIS is well-studied and often amenable to transverse-momentum-dependent (TMD) factorization, the behavior of identified kaons and protons remains less explored, particularly at the kinematics accessible at Jefferson Lab (JLab). Previous kaon data from HERMES and COMPASS were obtained at significantly higher energies and invariant masses ( $W^2$ ). Furthermore, no existing publications reported cross sections or multiplicities for identified protons in SIDIS kinematics. A critical theoretical challenge is defining the kinematic boundaries where TMD factorization is valid versus regions dominated by "soft" central processes or target fragmentation, where factorization theorems are not yet established. This experiment addresses these gaps by measuring charged kaon and proton multiplicities in a kinematic regime that spans the transition from the soft central region to the TMD-affinity region.

Methodology
The experiment was conducted in 2018–2019 at the Thomas Jefferson National Accelerator Facility (JLab) Hall C. Data were collected using 10.2 and 10.6 GeV electron beams impinging on 10-cm-long liquid hydrogen (proton) and deuterium targets. The experimental setup utilized the High Momentum Spectrometer (HMS) for electron detection and the Super High Momentum Spectrometer (SHMS) for hadron detection.

Kinematics: The analysis focused on the range $0.3 < x < 0.6$ , $3 < Q^2 < 6$ GeV $^2$ , $0.3 < z < 0.7$ , and transverse momentum $P_t < 0.6$ GeV. This corresponds to a final-state invariant mass squared $4 < W^2 < 10.9$ GeV $^2$ .
Particle Identification (PID):
- Kaons: Identification relied on a combination of the SHMS aerogel Cherenkov detector, Heavy Gas Cherenkov (HGC) detector, time-of-flight (TOF), and calorimeter energy deposition. Cuts were optimized to suppress pion and proton contamination, achieving efficiencies of ~94–97% for kaons while maintaining contamination below 10%.
- Protons: Identification utilized similar detectors but leveraged the significantly longer time-of-flight of protons compared to lighter particles. Contamination from positrons, pions, and kaons was kept below 1%.
Analysis: Experimental yields were normalized by beam charge and corrected for detector efficiencies, trigger/live-time effects, and radiative corrections. Multiplicities were extracted by comparing experimental yields to Monte Carlo simulations (SIMC). The azimuthal distributions were fitted to the functional form $M_0[1 + A \cos(\phi^*) + B \cos(2\phi^*)]$ to extract the multiplicity $M_0$ and modulation parameters $A$ and $B$ .
Theoretical Context: The kinematic coverage was analyzed using the Boglione et al. framework, which divides SIDIS into current fragmentation (TMD valid), target fragmentation, and a "soft" central region based on hadron rapidity ( $y_h$ ).

Key Results

Kaon Multiplicities ( $K^+$ and $K^-$ ):
- The kinematic range for kaons spans both the soft central region and the region where TMD factorization is applicable.
- $K^+$ : Multiplicities for the deuteron target agree remarkably well with predictions using CTEQ5 PDFs and DSS fragmentation functions. However, $K^+$ multiplicities on the proton target are noticeably larger than on the deuteron, a discrepancy not captured by the CTEQ/DSS predictions.
- $K^-$ : Measured $K^-$ multiplicities are significantly lower than predicted by DSS fragmentation functions across most of the kinematic range, except at the highest $W^2$ values where TMD affinity is highest.
- Azimuthal Modulations: The modulation parameters $A$ and $B$ for kaons are small and consistent with zero, showing no dependence on $W^2$ .
- Ratios: The $K^+/ \pi^+$ ratio increases with $z$ and $W^2$ , consistent with Lund Monte Carlo (LEPTO/JETSET) and CTEQ/DSS trends. Conversely, the $K^-/ \pi^-$ ratio is very small and lies well below both Lund and DSS predictions.
Proton Multiplicities:
- The kinematic range for protons lies almost entirely within the "soft" central region ( $-1 < y_h < 1$ ), where no factorization theorems currently exist.
- Magnitude: Observed proton multiplicities are orders of magnitude larger than predictions based on DSS fragmentation functions at low $W^2$ . As $W^2$ increases, the ratio of observed to predicted values decreases, approaching within a factor of two at the highest $W^2$ , but remaining significantly higher than TMD-based predictions.
- Target Dependence: No significant difference was observed between proton and deuteron targets.
- Azimuthal Modulations: The parameter $A$ is consistently positive with an average value of approximately 0.01, while $B$ is consistent with zero.
Model Comparisons:
- Standard TMD-based predictions (CTEQ/DSS) fail to describe the magnitude of proton multiplicities and the $K^-/ \pi^-$ ratios in this kinematic regime.
- The Lund Monte Carlo event generator (LEPTO/JETSET), tuned with HERMES data, provides a qualitative description of the observed trends for both kaons and protons, particularly the strong decrease in proton-to-pion ratios with increasing $W^2$ .

Significance and Claims
The paper claims that the measured kinematic range for protons is situated squarely in the "soft" central rapidity region, providing a physical explanation for why observed proton multiplicities exceed TMD-based predictions by factors of two to ten. For kaons, the results highlight a discrepancy in $K^-$ production that is not accounted for by current fragmentation functions, even at higher $W^2$ .

The authors assert that while TMD factorization is a powerful framework for pions, its application to kaons is marginal in this experiment, and for protons, it is not applicable due to the dominance of soft processes. The paper concludes that the HERMES-tuned LEPTO/JETSET generator offers a useful practical tool for understanding non-perturbative contributions to SIDIS in these kinematic regimes, though it is not a perfect description. The work provides the first reported multiplicities for identified protons in SIDIS and establishes a baseline for future global fits and theoretical developments regarding fragmentation in the soft central region.

1. The Setup: A High-Speed Collision

2. The Mystery of the "Soft" Zone

3. The Wiggles (Azimuthal Modulations)

4. The Takeaway

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