We explore the impact of subleading logs on PDFs for muon colliders and present a rigorous comparison between NLL and LL approximations without resummation. Our analysis shows solid evidence that leading-log PDFs are sufficient for most high-energy predictions.
Subleading logs represent smaller but potentially relevant corrections in certain regimes. By comparing unresummed NLL with LL, we evaluate their effect on momentum distributions in cross sections and on theoretical uncertainties, identifying where differences may be marginal or significant.
Methodology: we calculate corrections with different factorization schemes, apply typical experimental cuts for a muon collider, and estimate the impact on key observables. We find that differences between unresummed NLL and LL rarely exceed the expected theoretical uncertainty range for high-momentum predictions, suggesting that LL approximations offer a robust description in most relevant scenarios.
Results: for processes dominated by high-scale dynamics, subleading corrections are subdominant. In most cases, leading-log PDFs accurately reproduce the cross sections and distribution shapes needed for physics studies and experimental design. Only in situations with sensitivity to intermediate scales or at phase-space edges is it advisable to review unresummed NLL or apply more refined resummation techniques.
Practical implications: using leading-log PDFs reduces computational complexity and accelerates exploratory studies while maintaining sufficient precision for most high-energy predictions. We recommend using them as a standard for quick estimates and reserving unresummed NLL for precision analyses or observables with specific sensitivity to subleading corrections.
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Why choose us: we combine expertise in computational physics and machine learning to provide practical recommendations on PDFs and simulations, and we develop optimized pipelines for intensive computing. If you need advice on theoretical models, simulation optimization, or integration with custom software solutions and AWS and Azure cloud services, Q2BSTUDIO brings expertise in artificial intelligence and cybersecurity to deploy secure and scalable solutions.
Contact and next steps: contact Q2BSTUDIO for a technical audit, to test leading-log PDF implementations in your workflows, or to develop custom AI agents that automate uncertainty analyses. Leverage our capabilities in custom applications and artificial intelligence for companies and improve your results with integrated and secure solutions.
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