In the zippy world of particle physics, charm quarks are like cameo appearances in a grand, never-ending stage play. They flicker into existence for a moment, then vanish, leaving behind clues about how matter holds itself together at the smallest scales. A new study led by Antoni Szczurek of the Institute of Nuclear Physics, Polish Academy of Sciences in Kraków, with Anna Cisek and Rafał Maciuła of the University of Rzeszów, turns a fixed-target twist of the LHCb experiment into a magnifying glass for those clues. The team asks a precise, almost detective-like question: how are open charm mesons (the D mesons) and hidden charm (quarkonia like J/ψ) produced when a proton collides with a nucleus at relatively modest energies? Their answer is a chorus of mechanisms that must all sing together to fit the data, revealing new constraints on the proton’s inner weather map and on how charm can hide inside the proton’s quantum cloud.
The work, presented by Szczurek at a Cracow Epiphany Conference in 2025, is a reminder that modern physics thrives on tests that are patient and nuanced. It is not enough to say “gluon fusion creates charm.” The researchers show that, at the energies and kinematics accessible to the SMOG fixed-target setup inside LHCb, you need three players: ordinary gluon-gluon fusion, a pinch of intrinsic charm tucked into the proton’s wavefunction, and a recombination mechanism that handily reshapes how charm ends up in observed D mesons. The result is more than just a better fit to numbers. It’s a sharper lens on how the proton seeds charm and how the strong force sculpts what we finally detect in detectors around the world.
A spectrum of charm: open and hidden
Open charm refers to charm quarks that end up in D mesons, meting out their presence in a final state you can actually observe. Hidden charm, by contrast, hides its quark content inside bound states like J/ψ, a particle that behaves like a tiny beacon for how charm quarks can bind together. The LHCb fixed-target data, gathered with the SMOG device at a collision energy around 68.5 GeV in the proton–neon system, live in a regime where the momentum fraction x carried by gluons in the proton is relatively large. It’s a rare vantage point: high enough energy to produce charm, but low enough that the proton’s inner structure at larger x still matters in tangible ways.
The authors insist that you cannot explain what LHCb sees with a single production channel. Gluon–gluon fusion—the familiar workhorse of charm production at the LHC—must be joined by two additional threads: an intrinsic charm component to the nucleon, and a recombination mechanism that stitches quarks into D mesons during the collision’s aftermath. The framework they favor, kt-factorization, is a way to fold in the transverse momentum of gluons inside the proton. It’s not just a technical flourish; it’s a practical move that captures higher-order effects in a regime where fully fixed-order calculations become unwieldy. In this picture, the differential cross sections depend on unintegrated gluon distributions, functions that tell you not only how likely a gluon carries a certain fraction of momentum but also how likely it is to have a given transverse kick. The headline takeaway is simple and profound: forward charm production in these fixed-target conditions only looks right when all three mechanisms are allowed to contribute.
Mechanisms that must dance together
The first mechanism is gluon–gluon fusion: g + g → c + c̄. In the high-energy limit this process is straightforward, but at the energies of the SMOG setup, including the transverse momenta of the incoming gluons is essential. The kt-factorization approach blends the off-shell matrix elements with unintegrated gluon distributions Fg(x, kt, μ2). The result is a more faithful rendering of how charm pops into existence in this particular energy window, but it’s not enough on its own to match the data. The data demand a richer cast—hence the other two mechanisms.
The second mechanism is intrinsic charm. The proton’s wavefunction can, with a small probability, contain a c c̄ pair in a nontrivial configuration. This intrinsic charm component contributes especially at large x and in kinematic corners where the ordinary, perturbative production would be too feeble. The authors describe this via a cg* → cg channel that multiplies a collinear charm quark distribution by a gluon distribution evaluated at small x. The upshot is a subtle, non-negligible addition to charm production that helps the theory bend toward the data in the backward direction and at higher transverse momentum, where pure gluon fusion tends to undershoot.
The third mechanism is recombination, inspired by a perturbative Braaten–Jia–Mechen picture. Here a light quark and a gluon create a (¯cq)n intermediate state, which can hadronize into a D meson with a probability encoded in ρ. This recombination process acts like a bridge between the quark-level chaos and the hadron-level observables. It is particularly powerful in generating asymmetries between D0 and D̄0 production, and it helps explain how the observed D mesons populate the backward region with modest transverse momentum. Taken together, the three mechanisms do more than fit the numbers; they reveal a coherent narrative for how charm is produced, transported, and finally observed in fixed-target experiments.
Fixed-target LHCb as a probe of large-x gluons
Why study charm production at fixed-target energies rather than in the collider’s standard proton–proton mode? The answer lies in x. In fixed-target collisions at SMOG, researchers access gluons carrying a relatively large fraction of the proton’s momentum. This regime has proven difficult to pin down with precision in global fits, and it’s exactly where different models of the gluon distribution disagree most. Szczurek and colleagues therefore use a suite of unintegrated gluon distributions—KMR, JH2013, a Gaussian ansatz with a modest width, KL, KS, and MP/M-P-M variants—to see which ones can track the LHCb measurements of D mesons and J/ψ yields. The result is not a slam dunk for any single distribution, but a landscape in which some are closer to the data than others, and in which the dramatic differences between models start to shrink as the measurements pin down the behavior of gluons at larger x.
The practical message is more nuanced than “this model is right.” Some UGDFs, like KMR and JH2013, land reasonably close to the data for several observables. Others overshoot or undershoot depending on the observable and the kinematic region. The exercise matters because it uses real, fixed-target data to carve away at the uncertainties that plague predictions for collider energies too. If you want reliable predictions for charm production in a wide range of experiments—neutrino scattering, cosmic-ray interactions in the atmosphere, or future colliders—you need better guidance on how gluons behave when they carry a sizable slice of the proton’s momentum. This study uses the fixed-target laboratory to sharpen that guidance.
Crucially, the paper makes a concrete set of claims about the relative weight of the three mechanisms. The intrinsic charm probability sits at a fractional percent level, with an upper bound around half a percent to about one percent depending on the specific fit and model, such as CT18-based formulations. The recombination probability, ρ, emerges around ten percent, a value that explains the D and D̄ production asymmetry observed by LHCb in backward kinematics and low pT. The nearly one-percent ceiling on intrinsic charm is small, but it is precisely the kind of tiny, systematic feature that shifts the whole dataset’s shape and thereby informs our understanding of proton structure at large x.
What the results say about proton structure
One of the study’s most striking messages is that a proton is not a simple bag of three valence quarks plus a cloud of sea quarks and gluons. It is a dynamic, probabilistic ensemble in which even a heavy quark pair can flicker into existence as part of the proton’s quantum fluctuations. The intrinsic charm component—if it exists at all in the percent range—serves as a persistent whisper in the proton’s partonic orchestra. The fixed-target analysis provides an upper bound that aligns with similar constraints from other phenomena, reinforcing the idea that the proton’s charm content is real but very small. It’s a reminder that the proton’s interior isn’t static; it’s a fluctuating, context-dependent sea whose exact composition depends on the energy and the measurement you perform.
The D0 vs D̄0 asymmetry is another diagnostic tool. The fact that recombination can reproduce this asymmetry, especially in the backward region and at modest pT, shows that how charm hadronizes—how quarks turn into observable mesons—matters. It’s not enough to know how likely a charm quark is produced; you also need to know how likely it is to partner with a light quark to form a D meson in the very moment and place the collision creates those quarks. This is a vivid reminder that hadronization is not an afterthought but a central piece of the physics you’re trying to describe when you compare theory to data.
In the J/ψ sector, the kt-factorization framework—with its nonrelativistic treatment and a spectrum of UGDFs—manages to describe the data reasonably well at these energies. The spread in predictions across different UGDFs teaches an important lesson: the same physical process probes different corners of the proton’s gluon dynamics depending on the chosen distribution. The fixed-target measurements therefore become a valuable cross-check on how we model gluons in a regime that global fits have struggled to pin down with high certainty.
Why this matters beyond the lab
At its core, the paper maps the proton’s inner weather report. The proton is not a dull, static object; it is a jittery, probabilistic system where heavy quarks like charm can appear briefly in the quantum soup. Pinning down how often intrinsic charm shows up, and how recombination sculpts the final-state particles we observe, helps tighten the three pillars of quantum chromodynamics calculations: the parton distributions, the hard scattering matrix elements, and the hadronization process. The LHCb fixed-target program, modest in energy but rich in kinematic reach, provides a rare laboratory for testing large-x physics that global analyses often struggle to constrain. In this sense, the study doesn’t just explain a data point; it contributes a critical datapoint to the broader effort to map the proton’s inner geography.
On a human scale, the work is a testament to cross-border science in action. The Kraków-based team led by Szczurek, with Cisek and Maciuła from Rzeszów, demonstrates how international collaborations can produce precise, physics-rich insights from focused datasets. The fixed-target measurements are not a backwater; they are a focused lens that complements the high-energy frontier. Collectively, they help calibrate gluon behavior at large x, guiding global fits that feed into predictions across the scientific ecosystem—from detector design to astrophysical modeling and beyond.
And then there is the lingering question that will keep theorists and experimentalists talking: if intrinsic charm exists at the level of a fraction of a percent, what does that imply for the proton’s history and for how we model strong interactions in the wild? The authors’ careful upper bounds, together with their demonstration of the recombination mechanism’s role, point toward a coherent, testable picture. The fixed-target LHCb data, in harmony with kt-factorization and a suite of UGDFs, suggest a world where charm’s presence inside the proton is real, measurable, and essential for understanding hadronization at moderate energies. The path forward may involve more fixed-target experiments, different targets, and a continued dialogue between theory and data to tighten those percent-level constraints into a clearer map of the proton’s innards.
In the end, Szczurek and colleagues remind us that the simplest questions—how is charm produced? where is it coming from inside the proton?—can still surprise us when explored with the right instrument and the right patience. The study is not just a technical achievement; it’s a narrative about how nature stores information in tiny quantum bits and how human ingenuity decodes that information, one carefully analyzed collision at a time.
Institution and authors: The work is conducted by a team led by Antoni Szczurek at the Institute of Nuclear Physics, Polish Academy of Sciences in Kraków, Poland, with Anna Cisek and Rafał Maciuła from the University of Rzeszów. The study was presented at the XXXI Cracow Epiphany Conference on the Recent LHC Results, Kraków, January 2025.
