First measurements of deuteron production spectra in p+p collisions at beam momentum of 158 GeV/c at NA61/SHINE

This paper presents the first differential measurements of deuteron production spectra in inelastic p+p collisions at 158 GeV/c by the NA61/SHINE experiment, providing essential data to refine models of cosmic antinuclei production for dark matter searches.

The Gist

Imagine the universe as a giant, chaotic construction site. High-energy particles (like protons) are speeding around like tiny, invisible race cars, crashing into each other constantly. When they crash, they sometimes create new, heavier "vehicles" called deuterons (which are basically a proton and a neutron glued together).

Scientists want to understand exactly how these "vehicles" are built during these crashes. Why? Because if we can understand how normal matter is made in these crashes, we might be able to spot a very special, rare "ghost vehicle" called an antideuteron. Finding these ghosts could be the smoking gun that proves the existence of Dark Matter, the invisible stuff that holds the universe together.

Here is a simple breakdown of what the scientists at the NA61/SHINE experiment did, using some everyday analogies.

1. The Goal: Hunting for Cosmic Ghosts

Think of the universe as a busy highway. Most of the time, cars (protons) crash into each other and create debris. Sometimes, this debris includes "anti-cars" (antimatter).

• The Problem: It's very hard to tell if an "anti-car" came from a Dark Matter crash or just a normal traffic accident.
• The Solution: To know what a "normal traffic accident" looks like, we need to study it in a controlled lab. This paper is about studying how deuterons (the normal version of the anti-car) are made when protons smash into other protons. Once we know the "normal" recipe perfectly, any "anti-car" that doesn't fit the recipe might be a Dark Matter ghost!

2. The Experiment: The Giant Particle Slingshot

The scientists used a massive machine at CERN (the European particle physics lab) called the NA61/SHINE spectrometer.

• The Setup: Imagine a giant cannon firing a beam of protons (the "projectiles") at a target made of liquid hydrogen (the "target").
• The Speed: They fired these protons at 158 GeV/c. To put that in perspective, that's like a proton moving at 99.999999% the speed of light.
• The Catch: Deuterons are very rare in these crashes. It's like trying to find a specific, rare type of seashell on a beach where millions of regular rocks are being thrown. The scientists had to sift through 60 million collisions to find just a few hundred deuterons.

3. The Detective Work: Finding the Needle in the Haystack

How do you find a deuteron when it looks almost exactly like a proton or a pion (another particle)?

• The "ID Card" Method: The scientists used two main clues to identify the particles:
  1. How heavy they are (Mass): They measured how much energy the particle lost as it passed through a gas detector (like a car slowing down in mud).
  2. How fast they are (Time): They measured how long it took the particle to travel a specific distance.
• The Analogy: Imagine you are at a crowded party. You want to find a specific person (the deuteron). You can't just look at their face because everyone looks similar. Instead, you check their height (mass) and walking speed (time of flight). By combining these two clues, you can separate the deuterons from the crowd of protons and pions.

4. The Results: Testing the Recipes

The scientists compared their findings to two famous "recipes" (theories) for how deuterons are made:

1. The Thermal Model: This is like baking a cake in an oven. It assumes the particles are just hot and jiggling around until they stick together.
2. The Coalescence Model: This is like a dance floor. It assumes that if a proton and a neutron are dancing close enough to each other at the right moment, they will grab hands and stick together.

The Verdict: The data from the experiment fit both recipes pretty well! This is great news because it means our current understanding of how these particles form is on the right track.

5. What's Next? The Upgrade

The scientists are just getting started.

• The Current Limit: They found about 200 deuterons. This is a good start, but it's like trying to guess the rules of a game by watching only a few seconds of it.
• The Future: They are upgrading their detectors (making them faster and clearer) and planning to run the experiment at even higher energies. They hope to find 3,000 deuterons and, crucially, about 100 antideuterons.
• The Big Dream: If they find those 100 antideuterons and they don't match the "normal" recipes, it could be the first direct evidence that Dark Matter exists and is decaying into these particles.

Summary

In short, this paper is a "practice run." The scientists built a super-sensitive camera to take a picture of how normal matter is created in high-speed crashes. By mastering the art of finding the "normal" deuterons, they are preparing the ground to spot the "ghostly" antideuterons that could finally reveal the secret identity of Dark Matter. It's a bit like learning to perfectly identify a regular coin so that you can instantly spot a counterfeit one that might be worth a million dollars.

Technical Summary

1. Problem Statement and Motivation

The detection of cosmic antinuclei (specifically antideuterons and antihelium) is considered a potential breakthrough method for identifying dark matter. However, the primary background for these signals arises from the interaction of cosmic-ray protons with interstellar hydrogen gas. To distinguish a dark matter signal from this astrophysical background, precise modeling of cosmic antinuclei production is required.

• The Gap: While deuteron production in cosmic rays is well-studied, the production of antideuterons is extremely rare and difficult to measure. Existing data on deuteron production in proton-proton ($p+p$) collisions within the momentum range relevant to cosmic antideuterons (100–400 GeV/$c$) is limited and suffers from large uncertainties.
• The Goal: This paper presents the first differential production measurements of deuterons in inelastic $p+p$ interactions at a beam momentum of 158 GeV/$c$ ($\sqrt{s} = 17.3$ GeV). These measurements serve as a critical benchmark for validating theoretical models (thermal and coalescence) used to predict cosmic antinuclei yields.

2. Methodology and Experimental Setup

Experimental Facility:
The data was collected using the NA61/SHINE spectrometer at the CERN Super Proton Synchrotron (SPS).

• Beam: Proton beam at 158 GeV/$c$.
• Target: Liquid Hydrogen Target (LHT).
• Detectors: The setup includes two Vertex Time Projection Chambers (VTPC-1/2) inside superconducting magnets, a small GAP TPC, two large Main TPCs (MTPC-L/R), and downstream Time-of-Flight (ToF) detectors (ToF-L/R).
• Dataset: The analysis utilizes high-statistics data recorded between 2009 and 2011, comprising 60.6 million recorded $p+p$ collisions, yielding approximately 35.3 million selected inelastic events and 750 million reconstructed tracks.

Analysis Strategy:

1. Event and Track Selection:
   • Events were selected based on inelastic $p+p$ criteria: valid beam proton trajectory, a reconstructed interaction vertex within $\pm 20$ cm of the target center, and rejection of elastic scattering (events with only one positive track matching beam momentum).
   • Tracks were required to originate from the primary vertex, satisfy a positive rigidity cut ($p_{lab,x}/q > 0$), and have sufficient cluster reconstruction (min. 30 clusters, 15 in VTPCs).
2. Particle Identification (PID):
   • Method: A combined $t_{of} - dE/dx$ approach was used.
   • Challenge: Deuterons have a mass ($m \approx 1.87$ GeV/$c^2$) close to protons ($m \approx 0.938$ GeV/$c^2$), making them difficult to separate from the high-mass tail of the proton distribution in standard 2D fits ($m^2$ vs. $dE/dx$).
   • Innovation: A new data-driven template fitting method was developed.
     • Pions and positrons were separated using $dE/dx$ cuts.
     • For the remaining heavy particles (Kaons, Protons, Deuterons), a 1D $m^2$ template fit was performed.
     • Templates for Kaons, Protons, and Deuterons were constructed by modifying the pion mass distribution to account for detector resolution and specific particle masses.
     • A probability method was applied to assign each track a probability ($P_i$) of being a specific particle type based on the fitted $m^2$ distributions.
3. Background Subtraction:
   • Off-target backgrounds were quantified using runs with the liquid hydrogen target removed.
   • Secondary interactions within the target were estimated to be negligible ($<2\%$).
4. Correction and Uncertainty:
   • Raw counts were corrected for detector geometry, acceptance, and ToF efficiency using Monte Carlo simulations.
   • Systematic Uncertainties: Dominated by the modeling of the proton tail under the deuteron peak ($\sim 20\%$) and the choice of phase-space binning ($\sim 15\%$), resulting in a total systematic uncertainty of $\approx 25\%$.
   • Statistical Uncertainties: Ranged from 30% to 60% due to the rarity of deuteron production (only $\sim 200$ identified tracks).

3. Key Contributions

• First Measurement: This is the first differential measurement of deuteron production spectra in $p+p$ collisions at 158 GeV/$c$, filling a critical gap in the momentum range relevant for cosmic-ray physics.
• Novel PID Technique: The development and validation of a data-driven template fitting method for $m^2$ distributions, which successfully isolates the deuteron signal from the overwhelming proton background where standard 2D fits fail.
• Model Validation: The data provides a rigorous testbed for two competing theoretical frameworks: the Thermal Model and the Coalescence Model.

4. Results

• Spectra: The paper presents double-differential production spectra of deuterons as functions of rapidity ($y$) and transverse momentum ($p_T$).
• Model Comparison:
  • Thermal Model: The data shows good agreement with a thermal model (fixed temperature $T=150$ MeV) where only the amplitude was fitted.
  • Coalescence Model: The data also aligns well with predictions from the coalescence model (using parameters from previous literature).
• Conclusion on Models: Within the current level of statistical and systematic uncertainties, both the thermal and coalescence models describe the experimental data equally well. This implies that current data cannot yet discriminate between these two formation mechanisms for deuterons in this energy regime.

5. Significance and Outlook

• Cosmic Ray Physics: These measurements are a foundational step for modeling the production of secondary cosmic antinuclei. Understanding the deuteron production mechanism in $p+p$ collisions is essential for accurately predicting the background of cosmic antideuterons, which is crucial for dark matter searches.
• Future Prospects:
  • Antideuteron Search: The analysis framework was successfully applied to negatively charged tracks, identifying $\sim 50,000$ antiprotons and a few antideuteron candidates in the existing dataset.
  • Upgrades: The NA61/SHINE detector has been upgraded (new TPC electronics, improved ToF) to reduce noise and increase data rates by $\sim 20\times$.
  • Next Steps: In October 2025, NA61/SHINE will collect 600 million $p+p$ collisions at 300 GeV/$c$. This 10-fold increase in statistics is expected to identify $\sim 3,000$ deuterons and $\sim 100$ antideuterons, significantly reducing uncertainties and enabling the discrimination between thermal and coalescence models, potentially leading to a breakthrough in dark matter identification.