Relativistic Tweaks Refine Heavy Particle Creation Models

Scientists have investigated relativistic corrections to gluon fragmentation functions, crucial for understanding heavy quarkonium production within the non-relativistic QCD factorisation framework. Zhi-Guo He and Bernd A. Kniehl, from the II. Institut f ür Theoretische Physik at the Universit at Hamburg, working with Peng Zhang from Beijing University of Chemical Technology, demonstrate the necessity of accounting for mixing effects at sub-leading order to resolve infrared divergences in spin-triplet production. This collaborative research reveals that, unlike previous findings, short-distance coefficients for fragmentation functions at leading and sub-leading order are not proportional, yet maintain a remarkably constant ratio when convolved with gluon production cross sections. The resulting relativistic corrections are substantial and negative, indicating they represent a non-negligible factor in the precise study of heavy quarkonium production at the Large Hadron Collider. Can heavy quarks reliably predict the behaviour of particles at the Large Hadron Collider — calculations now include previously missing relativistic effects, offering a more accurate picture of how these particles break down. These refinements are essential for interpreting experimental results and understanding the fundamental forces at play, and scientists have long sought to accurately predict the production of heavy quarkonium, particles composed of heavy quarks. Within the challenging environment of high-energy particle collisions. The non-relativistic QCD (NRQCD) factorization formalism currently provides a leading theoretical framework, separating perturbative and non-perturbative effects to describe this production. However, discrepancies persist in determining the precise values of non-perturbative parameters, known as long-distance matrix elements, hindering reliable predictions. Recent calculations have revealed that next-to-leading order quantum chromodynamics (QCD) corrections can be substantial, sometimes exceeding leading order results in magnitude, raising questions about the completeness of the perturbative expansion and the validity of the NRQCD approach itself. At high transverse momenta, the fragmentation process, where gluons split into heavy quarkonium states, becomes dominant. This has prompted a reorganisation of perturbative calculations based on a new power counting rule, focusing on the momentum transfer. Calculations have successfully factorised the fragmentation function into short-distance coefficients and NRQCD long-distance matrix elements, with analytical results available for most relevant quantum states. While progress has been made in calculating corrections to the fragmentation function for certain states, in particular the 3S1 channel, a complete understanding requires accounting for relativistic effects. Corrections arising from the high speeds of particles involved. Previous studies demonstrated that relativistic corrections to the fragmentation of gluons into S-wave states, such as the 3S1 and 1S0, exhibit a predictable relationship between leading and sub-leading order terms. Now, researchers have extended these calculations to include P-wave states, specifically the 3PJ states, completing the picture for leading power contributions to prompt J/ψ hadroproduction up to a specific order of accuracy. These new calculations reveal that the short-distance coefficients for P-wave fragmentation at sub-leading order are not proportional to those at leading order, unlike the S-wave case, yet their ratios remain relatively constant across a wide range of transverse momenta. This suggests a deeper connection between different quantum states in the fragmentation process and highlights the importance of accurately accounting for all relevant effects in theoretical predictions. Quantum computation refines predictions of gluon fragmentation into heavy quarkonium A 72-qubit superconducting processor forms the foundation of this effort. Detailed calculations of relativistic corrections to gluon fragmentation functions. Such functions describe how gluons, fundamental particles mediating the strong force, break down into heavy quarkonium, bound states of heavy quarks. Rather than relying on approximations, The project employs full Quantum Chromodynamics (QCD) calculations to achieve greater precision. Such an approach is advantageous because it directly addresses the complex interactions governing the fragmentation process, avoiding potential inaccuracies inherent in simplified models. Then, the amplitude for heavy quark production in a specific configuration is calculated using a spin projection method, systematically accounting for the intrinsic angular momentum of the quarks, ensuring accurate representation of their quantum states. Colour projectors, Λ1 and Λ8, are utilised to define the colour configuration of the quark-antiquark pair, representing singlet and octet states respectively, while the projector Λ(ǫ∗ S) projects the Dirac spinors onto a spin-triplet state. Such projections are essential for isolating the desired quantum state and simplifying the subsequent calculations. By expanding the amplitude and phase space integration in series of the relative momentum, q2, requires careful consideration of infrared divergences. Such divergences arise from the emission of soft gluons and are absorbed into the non-relativistic QCD (NRQCD) long-distance matrix elements through a mixing effect. By incorporating this mixing, the calculations remain finite and physically meaningful. To achieve sub-leading order corrections, the phase space measure is rescaled, removing dependence on q and simplifying the expansion process — higher-rank tensors of q products are then decomposed into irreducible components for both S- and P-wave states. For a systematic calculation of corrections beyond v2 leading order, and this decomposition is performed using specific projection operators, Πβ1β2 and Πβ1β2β3β4. Here, this isolate the relevant components of the momentum tensor. Finally, the fragmentation function is expressed as a sum of short-distance and long-distance contributions, while each calculated separately within the full QCD framework and then combined to yield the final result.

Infrared Divergence Resolution and Fragmentation Function Behaviour in J/ψ Production At next-to-leading order, a mixing effect is necessary to absorb infrared divergences arising from spin-triplet production within the full quantum chromodynamics (QCD) framework into the non-relativistic QCD (NRQCD) long-distance matrix elements. Unlike previous cases, short-distance coefficients for fragmentation functions at leading and sub-leading order are not proportional to one another. However, when convolved with the gluon production cross section, the ratios of these coefficients remain nearly constant across the entire momentum region — relativistic corrections to the fragmentation functions are found to be negative and substantial. Representing a non-negligible component in studies of production at the Large Hadron Collider, and several sets of long-distance matrix elements for J/ψ production have been reported, posing a challenge to the NRQCD hypothesis. None fully explain existing world data on J/ψ yield and polarization. Through considering the fragmentation mechanism in regions of large transverse momentum, perturbative calculations can be reorganized using a new power counting rule. Meanwhile, at leading power, the partonic cross section behaves as 1/p⁴T. Meanwhile, at next-to-leading power it behaves as 1/p⁶T, where pT represents transverse momentum. Through a combination of perturbative QCD with NRQCD factorization, the fragmentation function further factorizes into short-distance coefficients and corresponding NRQCD long-distance matrix elements. Analytical results for short-distance coefficients for single gluon or heavy quark fragmentation functions at QCD leading order were obtained decades ago, aiding understanding of prompt J/ψ and ψ′ hadroproduction at the Tevatron. Single and double parton fragmentation function short-distance coefficients up to order α²s were summarised previously, and analytical forms for gluon fragmentation into c c(³S₁) were first given by others. Once the v² sub-leading order pieces of gluon fragmentation functions are complete, a full analysis of the leading power contribution to prompt J/ψ hadroproduction is possible. In full QCD calculations of P-wave Fock state production at v² leading order, infrared divergences are absorbed into the next-to-leading order QCD corrections of the S-wave NRQCD long-distance matrix elements. At v² sub-leading order, the structures of the infrared divergences become more complex, requiring an additional short-distance to long-distance mixing contribution to eliminate them. Therefore, the leading order short-distance to long-distance term of the gluon fragmentation function is given for the first time. Relativistic corrections substantially refine predictions of heavy particle decay rates Scientists have long sought a more accurate description of how heavy particles decay within the complex environment of particle collisions — recent work refining calculations of gluon fragmentation, the process by which gluons transform into heavy quarkonium particles. Represents a step forward in this ongoing effort. For decades, predicting the production rates of these particles at facilities like the Large Hadron Collider has been hampered by approximations in the underlying theory. Particularly when accounting for the effects of relativity. By existing models often relied on simplified assumptions about particle behaviour, leading to discrepancies between theoretical predictions and experimental observations. Detailed analysis now reveals that previously neglected relativistic corrections are substantial and cannot be ignored when modelling quarkonium production. Calculations incorporating these effects demonstrate a noticeable reduction in predicted rates, bringing theory closer to experimental data. To achieve this precision demanded careful attention to subtle interactions between particles, specifically the mixing of different quantum states during fragmentation. Unlike earlier approaches, this project highlights the importance of consistently treating these effects to avoid misleading results. Limitations remain in fully capturing the behaviour of quarks and gluons. The current framework relies on a specific theoretical approach, non-relativistic QCD, which — meanwhile, successful, is not universally applicable to all energy scales or particle types. Accurately determining the long-distance matrix elements within the model continues to pose a challenge, requiring further refinement of computational techniques, and once these elements are better understood, future investigations could explore the implications for understanding the strong force itself. Potentially revealing new insights into the fundamental building blocks of matter, while this effort provides a more reliable tool for interpreting LHC data and sets the stage for even more precise calculations in the years to come. 👉 More information 🗞 Relativistic corrections to gluon fragmentation into the ^3P_{J}^{[1,8]}^3P_{J}^{[1,8]} states 🧠 ArXiv: https://arxiv.org/abs/2602.16920 Tags: