Vector Boson Fusion: Unlocking New Physics in High-Energy Muon Colliders

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11 Jul 2025

Abstract and 1. Introduction

2 Muons vs. Protons

2.1 Muon annihilation

2.2 Vector boson fusion

2.3 Annihilation vs. VBF

2.4 Signal vs. background

3 Muon Colliders Are Gauge Boson Colliders

3.1 From the effective vector approximation to PDFs

3.2 PDFs with broken electroweak symmetry

3.3 Impact of subleading logs

3.4 Finite mass effects

4 Physics

4.1 Electroweak symmetry breaking

4.2 Dark matter

4.3 Naturalness

5 Complementarity

5.1 EDMs

5.2 Flavor

5.3 Gravitational waves

6 Summary and Future Directions

Acknowledgments

A. Simplified Models

A.1 Standard Model

A.2 Supersymmetry

A.3 Vector-like quarks

A.4 Higgs portal

A.5 Hidden valleys

A.6 Axion-like particles

References

2.2 Vector boson fusion

For collisions well above the production threshold, the virtual electroweak gauge boson content of high-energy muon beams becomes increasingly relevant, akin to the virtual gluon content of high-energy proton beams. VBF becomes a correspondingly important channel for the production of SM and BSM particles alike, with cross sections typically scaling with c.m. energy as ∼ log(s) far above threshold. The practical aspects of VBF at high-energy muon colliders have recently been studied in detail in [32], while the treatment of VBF in terms of electroweak parton distribution functions (PDFs) has been initiated in [25]. Here we summarize the qualitative features of VBF production, reserving a detailed discussion of electroweak PDFs for Sec. 3.

Authors:

(1) Hind Al Ali, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(2) Nima Arkani-Hamed, School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA;

(3) Ian Banta, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(4) Sean Benevedes, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(5) Dario Buttazzo, INFN, Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy;

(6) Tianji Cai, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(7) Junyi Cheng, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(8) Timothy Cohen, Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;

(9) Nathaniel Craig, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(10) Majid Ekhterachian, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA;

(11) JiJi Fan, Department of Physics, Brown University, Providence, RI 02912, USA;

(12) Matthew Forslund, C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794, USA;

(13) Isabel Garcia Garcia, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA;

(14) Samuel Homiller, Department of Physics, Harvard University, Cambridge, MA 02138, USA;

(15) Seth Koren, Department of Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA;

(16) Giacomo Koszegi, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(17) Zhen Liu, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA and School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA;

(18) Qianshu Lu, Department of Physics, Harvard University, Cambridge, MA 02138, USA;

(19) Kun-Feng Lyu, Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., P.R.C;

(20) Alberto Mariotti, Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel, and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels, Belgium;

(21) Amara McCune, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(22) Patrick Meade, C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794, USA;

(23) Isobel Ojalvo, Princeton University, Princeton, NJ 08540, USA;

(24) Umut Oktem, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(25) Diego Redigolo, CERN, Theoretical Physics Department, Geneva, Switzerland and INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy;

(26) Matthew Reece, Department of Physics, Harvard University, Cambridge, MA 02138, USA;

(27) Filippo Sala, LPTHE, CNRS & Sorbonne Universite, 4 Place Jussieu, F-75252 Paris, France

(28) Raman Sundrum, Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA;

(29) Dave Sutherland, INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy;

(30) Andrea Tesi, INFN Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino, Italy and Department of Physics and Astronomy, University of Florence, Italy;

(31) Timothy Trott, Department of Physics, University of California, Santa Barbara, CA 93106, USA;

(32) Chris Tully, Princeton University, Princeton, NJ 08540, USA;

(33) Lian-Tao Wang, Department of Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA;

(34) Menghang Wang, Department of Physics, University of California, Santa Barbara, CA 93106, USA.


This paper is available on arxiv under CC BY 4.0 DEED license.