Nonperturbative effects in triple-differential dijet and Z+jet production at the LHC

This paper investigates the impact of nonperturbative effects on triple-differential dijet and Z+jet production using Monte Carlo event generators, revealing significant process-dependent differences that motivate a proposed triple-differential measurement of the underlying event in Z+jet production to resolve whether this non-universal behavior exists in nature.

The Gist

Imagine you are trying to bake the perfect cake (a particle collision) based on a very precise recipe (the laws of physics). You know the ingredients and the steps, but when you actually bake it, the cake rises differently than the recipe predicts. Why? Because of "non-perturbative effects"—the messy, unpredictable things that happen when the batter is hot and bubbling, like how the oven heat spreads unevenly or how the ingredients stick to the pan.

In the world of particle physics at the Large Hadron Collider (LHC), scientists are trying to measure the "recipe" of the universe with extreme precision. To do this, they need to understand the difference between the "perfect theoretical cake" (what the math says should happen) and the "real cake" (what the detectors actually see).

This paper investigates two specific types of "cakes":

1. Dijet Production: Two jets of particles flying out in opposite directions.
2. Z+Jet Production: A Z boson (a heavy particle that decays into two muons) and one jet flying out.

The scientists wanted to see if the "messy" effects (like the cake sticking to the pan) affected both types of cakes in the same way. They used powerful computer simulations (called Monte Carlo generators) to model these events.

The Surprise: Two Different Kitchens

The researchers expected that the "messy" effects would behave similarly for both processes, just like how oven heat affects all cakes the same way. However, they found a strange difference:

• The Dijet Cake: The messy effects were consistent. No matter how you looked at the cake, the "mess" behaved predictably.
• The Z+Jet Cake: The messy effects changed dramatically depending on the angle at which the particles were flying. It was as if the oven heat suddenly got hotter or colder just because the cake was tilted slightly differently.

This is like walking into a kitchen where the oven behaves normally for a sponge cake but acts completely unpredictably for a soufflé, even though they are baked at the same temperature. The paper calls this "non-universal behavior," meaning the rules for the messiness aren't the same for every process.

The Detective Work: Who is the Culprit?

The scientists then asked: "What is causing this weird behavior in the Z+Jet cake?"

They broke down the "mess" into two main suspects:

1. Hadronisation: This is like the moment the batter solidifies into a cake.
2. The Underlying Event (MPI): This is like the background noise in the kitchen—other people cooking, the door opening, the lights flickering. It's extra activity happening at the same time as the main event.

When they turned off the "background noise" (MPI) in their simulations, the weird behavior didn't go away. In fact, the weird behavior was still there even when they removed the messy "cake solidifying" part.

The Big Reveal: The "mess" they thought was purely "non-perturbative" (unpredictable physics) actually contained a lot of "perturbative" (predictable math) parts that they hadn't accounted for. Specifically, the computer models were missing some extra "ingredients" (additional jets) that should have been included in the recipe. Because the recipe was incomplete, the computer blamed the missing ingredients on the "messy oven" instead of realizing the recipe was just too simple.

The Conclusion

The paper concludes that we cannot simply apply a single "correction factor" (a fix) to all particle collisions. The "mess" depends heavily on the specific type of collision and the angle of the particles.

To get the right answer, scientists need to:

1. Stop assuming the "mess" is the same for everything.
2. Update their recipes to include more complex scenarios (like adding extra jets to the simulation).
3. Measure the "background noise" (the underlying event) in a very specific, three-dimensional way to understand exactly what is happening.

In short, the universe is more like a chaotic kitchen where every dish has its own unique set of rules for how it gets messy, rather than a kitchen where the oven behaves the same way for every single cake.

Technical Summary

Technical Summary: Nonperturbative effects in triple-differential dijet and Z+jet production at the LHC

Problem Statement
Precision measurements at the Large Hadron Collider (LHC) require theoretical predictions at least at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics (pQCD). However, experimental data are recorded at the particle level, whereas high-order pQCD calculations typically provide results at the parton level. Bridging this gap requires correcting for nonperturbative (NP) effects, specifically hadronisation and the Underlying Event (UE), usually estimated via Monte Carlo (MC) event generators.

This study investigates the universality of these NP corrections. Specifically, it compares the impact of NP effects on two processes critical for determining the strong coupling constant ($\alpha_s$) and the proton gluon parton distribution function (PDF): inclusive dijet production ($p+p \to \text{jet}+\text{jet}+X$) and $Z$+jet production ($p+p \to Z/\gamma^* + \text{jet} + X$, with $Z \to \mu^+\mu^-$). The authors aim to determine if NP corrections are process-independent (universal) or if they exhibit process-specific behaviors that could bias precision extractions of fundamental parameters.

Methodology
The analysis employs a triple-differential measurement framework, defining the cross section as a function of:

1. $y_b$: The longitudinal boost of the center-of-mass system relative to the laboratory frame.
2. $y^*$: The rapidity of the two back-to-back final-state objects in the center-of-mass frame.
3. $X$: An energy-scale variable, defined as the average transverse momentum $\langle p_T \rangle_{1,2}$ for dijets and the transverse momentum of the $Z$ boson ($p_{T,Z}$) for $Z$+jet events.

The phase space is constrained by detector acceptance ($|y| < 3.0$ for jets, $|y| < 2.4$ for muons) and binned into 15 regions in the $(y_b, y^*)$ plane.

NP correction factors ($C_{NP}$) are derived by comparing MC event generators at the particle level (including Matrix Element (ME), Parton Shower (PS), Hadronisation (Had), and Multiple Parton Interactions (MPI)) against the same generators with Had and MPI switched off (parton level only). The correction is defined as:
$$C_{NP} = \frac{\sigma_{ME+PS+Had+MPI}}{\sigma_{ME+PS}}$$

The study utilizes two independent MC generators, HERWIG7 (v7.2.3) and SHERPA (v2.2.15), at both Leading Order (LO) and Next-to-Leading Order (NLO) accuracy. To disentangle the contributions of hadronisation and MPI, the authors compute separate correction factors for each effect. Furthermore, "Rick-Field-type" Underlying Event observables (activity in "towards," "away," and "transverse" azimuthal regions relative to the leading object) are analyzed to investigate the source of observed trends.

Key Results

1. Dijet Production: The NP correction factors for dijet production are close to unity at high transverse momentum and decrease at lower scales, as expected. Crucially, these corrections show no significant dependence on the perturbative order (LO vs. NLO) or the kinematic variables $y_b$ and $y^*$.
2. Z+jet Production: In stark contrast to dijets, NP correction factors for $Z$+jet production exhibit a strong dependence on $y^*$. The corrections increase significantly as $y^*$ increases (i.e., as the scattering angle in the center-of-mass frame becomes more central), particularly at lower $p_{T,Z}$. This trend is observed in both HERWIG7 and SHERPA.
3. Perturbative Order Dependence: For $Z$+jet, the magnitude of the NP corrections decreases when moving from LO to NLO matrix elements. This suggests that a portion of the "nonperturbative" correction is actually driven by missing higher-order perturbative radiation (unobserved jets) rather than true nonperturbative physics.
4. Decomposition of Effects:
   • Hadronisation: Corrections are largely independent of $y_b$ and $y^*$ and approach unity at high $p_T$.
   • MPI: The MPI correction factors reproduce the $y^*$ dependence and the reduction at NLO seen in the total $C_{NP}$.
5. Underlying Event Analysis: The analysis of UE activity (sum of transverse momenta in the transverse region) reveals that the activity strongly depends on $y^*$ but not on $y_b$. This dependence persists even when MPI is switched off in the simulation, indicating that the observed activity is not solely due to the MPI model but is linked to the hard process topology and perturbative radiation.

Significance and Claims
The paper concludes that the conventional definition of NP corrections (the ratio of particle-level to parton-level cross sections) may not be entirely of nonperturbative origin. Specifically for $Z$+jet production, the observed corrections are non-universal; they depend on the scattering angle ($y^*$) and the perturbative order of the hard process.

The authors argue that attributing these $y^*$-dependent corrections solely to nonperturbative models (like MPI or hadronisation) is misleading. Instead, a significant portion of the effect arises from perturbative modeling, specifically the presence of additional unobserved jets in the final state. Consequently, the paper proposes that to obtain appropriate correction factors for $Z$+jet precision measurements, one must include additional jets via multijet merging (potentially at NLO) in the simulation, rather than relying on standard NP tuning alone.

Finally, the authors propose a triple-differential measurement of the Underlying Event in $Z$+jet production to experimentally verify the observed $y^*$ dependence, which remains an open question regarding whether this non-universal behavior is realized in nature.