Modification of heavy quark hadronization in high-multiplicity collisions at LHCb

This paper presents recent LHCb results showing that the significantly enhanced production ratios of heavy flavor hadrons (such as $D_{s}^{+}/D^{+}$ and $\Lambda_{b}^{0}/B^{0}$) in high-multiplicity collisions suggest a modification of the hadronization mechanisms in these events.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as a giant, high-speed particle racetrack. Physicists from the LHCb collaboration are like race commentators trying to understand what happens when heavy "cars" (heavy quarks) crash into each other and break apart into smaller vehicles (hadrons).

Usually, scientists have a standard rulebook for how these heavy cars break apart. They assume the process is the same whether the crash happens in a quiet, empty parking lot (low-multiplicity collisions) or in a massive, chaotic mosh pit (high-multiplicity collisions). This rulebook was written based on data from simpler, cleaner crashes.

However, this paper reports that the rulebook might be wrong when the crash gets crowded. Here is what they found, explained simply:

1. The "Crowded Room" Effect

The researchers looked at what happens when heavy quarks turn into specific types of particles (like $D_s$ mesons or $\Lambda_b$ baryons) in two different scenarios:

• The Quiet Room: Few particles are created in the crash.
• The Mosh Pit: A huge number of particles are created in the crash (high multiplicity).

The Finding: When the "Mosh Pit" gets bigger, the heavy quarks don't just break apart randomly. They seem to prefer forming specific, heavier, or stranger combinations of particles much more often than they do in the quiet room.

2. The Three Main Experiments

The paper details three specific "races" to prove this point:

• Race A: The $D_s$ vs. $D$ Showdown (in pPb collisions)
  They compared two types of particles, $D_s$ and $D$. In a crowded collision, the $D_s$ particles (which contain a "strange" ingredient) became much more common relative to the $D$ particles.

  • The Analogy: Imagine a bakery. In a quiet morning, they bake mostly plain donuts ($D$). But when the bakery is swarmed by a huge crowd ($D_s$), they suddenly start baking a lot more "strange-flavored" donuts ($D_s$). The ratio of strange donuts to plain donuts skyrockets.
  • The Twist: This change happened even for particles moving very fast (high momentum), suggesting it's not just a slow, lazy effect but a fundamental change in how they are made.

• Race B: The Baryon vs. Meson Tally (in pPb collisions)
  They looked at the ratio of strange baryons ($\Xi_c$) to non-strange ones ($\Lambda_c$) and to mesons ($D^0$).

  • The Finding: The data showed that in these collisions, the production of these strange particles didn't change much based on how fast they were moving. However, the current computer simulations (the "rulebooks" physicists use) failed to predict these numbers correctly. The simulations underestimated how many strange particles were actually being made.

• Race C: The $\Lambda_b$ vs. $B^0$ Sprint (in pp collisions)
  They compared a heavy baryon ($\Lambda_b$) to a heavy meson ($B^0$) in proton-proton collisions.

  • The Finding: In high-multiplicity events (the mosh pit), the $\Lambda_b$ particles were produced much more frequently than in low-multiplicity events.
  • The Speed Limit: Interestingly, this "crowded room" advantage disappears as the particles get faster. At very high speeds, the ratio drops back down to match what we see in the quiet, empty collisions (like those in electron-positron colliders). It's as if the "crowd effect" only works on the slower, heavier traffic.

3. What Does This Mean?

The authors suggest that the standard "rulebook" for how heavy quarks turn into particles is incomplete.

• The Old View: Heavy quarks turn into particles in a vacuum, independent of how many other particles are around.
• The New Reality: In high-multiplicity collisions, the environment matters. The "crowd" of other particles seems to help heavy quarks stick together in specific ways (a process called coalescence) or creates more "strange" ingredients.

They also offer a second possibility: maybe the heavy quarks are forming "excited states" (like a car with its trunk full of extra luggage) that we haven't fully accounted for. These extra states might decay into the particles we see, making it look like there are more of them than there actually are.

Summary

In short, LHCb found that when heavy quarks collide in a crowded environment, they don't follow the old, quiet rules. They change their behavior, producing more specific types of particles than expected. This suggests that the "glue" holding these particles together (hadronization) is sensitive to the size of the collision, hinting at new physics that depends on how crowded the crash site is.

Technical Summary

Technical Summary: Modification of Heavy Quark Hadronization in High-Multiplicity Collisions at LHCb

Problem Statement
In high-energy hadron colliders, heavy quarks are primarily generated through hard parton-parton interactions during the initial stages of collisions, a process well-described by perturbative QCD and the factorization theorem. Under this framework, the production cross-sections of heavy-flavor hadrons depend on parton distribution functions, hard scattering cross-sections, and fragmentation functions. Traditionally, hadronization is assumed to be a universal process independent of the colliding system, with fragmentation functions parameterized using data from $ee$ or $ep$ collisions. However, recent observations suggest that this universality may break down in high-multiplicity environments. The central problem addressed in this work is whether the hadronization mechanisms of heavy quarks are modified in high-multiplicity collisions compared to low-multiplicity events, as evidenced by deviations in heavy-flavor hadron production ratios.

Methodology
The LHCb collaboration analyzed data from proton-lead ($p$Pb) collisions at $\sqrt{s_{NN}} = 8.16$ TeV and proton-proton ($pp$) collisions at $\sqrt{s} = 13$ TeV. The study focused on measuring cross-section ratios of specific heavy-flavor hadrons as a function of event multiplicity and transverse momentum ($p_T$).

• Multiplicity Definition: Event multiplicity was characterized using the number of tracks associated with the primary vertex (PV) in $p$Pb collisions, and specific track counts in the VELO detector ($N^{\text{tracks}}_{\text{VELO}}$) and backward tracks ($N^{\text{tracks}}_{\text{back}}$) in $pp$ collisions.
• Ratios Measured: The analysis targeted three key ratios:
  1. $D^+_s / D^+$: A probe of strange meson production.
  2. $\Xi^+_c / \Lambda^+_c$: A ratio of strange to non-strange baryons.
  3. $\Lambda^0_b / B^0$: A ratio of bottom baryons to bottom mesons.
• Comparative Analysis: Results were compared across different rapidity regions (forward vs. backward), $p_T$ ranges, and collision systems. The data were benchmarked against theoretical calculations, including EPPS16, Pythia 8.3 with color reconnection, EPOS4HQ, and statistical hadronization models (SHM) incorporating feeddown contributions from the Particle Data Group (PDG) and the Relativistic Quark Model (RQM).

Key Contributions and Results

1. $D^+_s / D^+$ Ratio in $p$Pb Collisions:
   Measurements of the $D^+_s / D^+$ cross-section ratio as a function of normalized event multiplicity revealed a significant enhancement in high-multiplicity events. This enhancement was observed across various $p_T$ ranges (up to 12 GeV/c) and was more pronounced in the backward rapidity region compared to forward rapidity and $pp$ collisions. The data indicates that the ratio increases with multiplicity, a trend not predicted by standard fragmentation models based on $ee$ collisions. The enhancement persists even at high $p_T$ ($6 < p_T < 12$ GeV/c).

2. $\Xi^+_c / \Lambda^+_c$ and $\Xi^+_c / D^0$ in $p$Pb Collisions:
   The production ratios of strange baryons to non-strange baryons ($\Xi^+_c / \Lambda^+_c$) and strange baryons to non-strange mesons ($\Xi^+_c / D^0$) were measured in $p$Pb collisions. These ratios showed no significant dependence on $p_T$. While the $\Xi^+_c / \Lambda^+_c$ ratio was slightly higher in backward rapidity than in forward rapidity, the values were generally consistent within uncertainties. Notably, theoretical calculations (EPPS16, Pythia 8.3, EPOS4HQ) tended to overestimate these ratios compared to the experimental data.

3. $\Lambda^0_b / B^0$ Ratio in High-Multiplicity $pp$ Collisions:
   In $pp$ collisions at 13 TeV, the $\Lambda^0_b / B^0$ cross-section ratio exhibited a strong dependence on event multiplicity. A clear enhancement was observed in high-multiplicity bins compared to low-multiplicity bins. At low $p_T$, the ratio in high-multiplicity events was significantly higher than values observed in $e^+e^-$ collisions. As $p_T$ increased, the ratio tended to converge toward the $e^+e^-$ results. The data was compared to statistical hadronization models; the model including feeddown from an expanded set of $b$-baryons (SHM+RQM) provided a better description of the enhancement than the model using only PDG-listed states, though the predicted lack of weakening of this feeddown contribution with increasing $p_T$ contrasts with the observed convergence at high $p_T$.

Significance and Claims
The paper concludes that the significant enhancement of the $D^+_s / D^+$ and $\Lambda^0_b / B^0$ ratios with increasing event multiplicity implies that hadronization mechanisms are likely modified in high-multiplicity events. The results challenge the assumption of universal fragmentation functions independent of the collision system.

The authors propose two potential explanations for these observations:

1. The existence of alternative hadronization mechanisms dependent on collision size, potentially involving coalescence mechanisms and strangeness enhancement.
2. A larger contribution from excited state feeddown in high-multiplicity collisions, which could artificially inflate the observed cross-section ratios.

The work underscores that standard fragmentation models parameterized from $ee$ or $ep$ data may be insufficient to describe heavy-flavor production in the high-multiplicity environment of LHC collisions, suggesting a need to incorporate multiplicity-dependent effects into theoretical frameworks.