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Probing a Specific Extension of the Standard Model at Future Muon Colliders


Core Concepts
This article proposes a method to search for a specific extension of the Standard Model of particle physics, characterized by the addition of a scalar triplet and a scalar singlet, at future muon colliders with center-of-mass energies of 3 TeV and 10 TeV.
Abstract
  • Bibliographic Information: Bandyopadhyay, P., & Parashar, S. (2024). Probing a scalar singlet-triplet extension of the Standard Model via VBF at the Muon Collider. arXiv preprint arXiv:2410.06298v1.

  • Research Objective: This research paper investigates the potential of future muon colliders to discover a specific extension of the Standard Model of particle physics. This extension involves the addition of a scalar triplet and a scalar singlet, where the singlet acts as a dark matter candidate.

  • Methodology: The authors utilize Monte Carlo simulations to study the production and decay of the new particles at muon colliders with center-of-mass energies of 3 TeV and 10 TeV. They focus on the vector boson fusion (VBF) production mechanism and analyze three distinct final states characterized by specific combinations of leptons, jets, and missing transverse energy (MET). To enhance the sensitivity to the signal, they employ both traditional cut-based analysis techniques and a boosted decision tree (BDT) classifier.

  • Key Findings: The study demonstrates that a 3 TeV muon collider with 1 ab−1 of integrated luminosity could potentially probe triplet scalar masses up to 450 GeV using the BDT classifier. Furthermore, a 10 TeV muon collider with 10 ab−1 of integrated luminosity could extend the reach up to 800 GeV for certain decay channels. The presence of Forward muons in VBF processes is identified as a crucial element for triggering and background reduction.

  • Main Conclusions: The authors conclude that future muon colliders offer a promising avenue for exploring this specific extension of the Standard Model. The combination of high energy, clean collision environment, and the unique features of VBF production provide a powerful tool for discovering new physics beyond the Standard Model.

  • Significance: This research contributes to the ongoing effort in particle physics to search for new particles and understand the nature of dark matter. The findings highlight the potential of muon colliders as discovery machines for new physics, complementing the research conducted at other colliders like the LHC.

  • Limitations and Future Research: The study primarily focuses on a limited set of benchmark points in the model parameter space. A more comprehensive exploration of the parameter space, considering various mass hierarchies and coupling strengths, would be beneficial. Additionally, incorporating detector effects and more realistic background estimations would further refine the analysis and projections.

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Stats
The MuC is projected to operate at a center-of-mass energy of 3 TeV with 1 ab−1 of target luminosity. An upgrade of the MuC with a 10 TeV of center-of-mass energy is also in the cards, with 10 ab−1 of target luminosity. The 3 TeV MuC is projected to probe triplet scalar masses of 450 GeV with the BDT classifier. The 10 TeV MuC can pinpoint the custodial symmetry breaking T ± →ZW ± →3-lepton decay up to 800 GeV of triplet scalar mass from cut-based analysis, with λst as low as 1.5 being adequate.
Quotes
"A future multi-TeV muon collider (MuC) can come to the rescue as a cleaner, more precise alternative [61–64]." "With the salient feature of producing particles with the full energy of the beams as the centre-of-mass energy, combined with suppressed QCD-born backgrounds, the MuC stands as a beacon of hope for BSM searches [35, 65–84]." "At higher energies, the MuC essentially becomes a vector boson fusion (VBF) machine, suitable for producing triplet scalars via the large TTVV-type vertices [49, 85]."

Deeper Inquiries

How do the experimental challenges and costs of a muon collider compare to those of other proposed future colliders, such as the FCC-hh?

Answer: Muon colliders and hadron colliders like the FCC-hh present distinct experimental challenges and cost considerations. Let's delve into a comparative analysis: Muon Collider: Challenges: Muon Production and Cooling: Generating and cooling muons to sufficiently low temperatures for collisions is a major hurdle. Muons are short-lived particles, decaying rapidly, which necessitates efficient production and rapid cooling techniques. Beam-Induced Background (BIB): The decay of muons in the beam pipe produces a substantial background of particles, termed BIB, posing challenges for detector design and data analysis. Neutrino Radiation: Muon decay also generates neutrinos, leading to significant radiation levels that demand robust shielding and detector materials. Machine Protection: The high-energy muon beams require sophisticated systems to protect the collider components from potential damage. Costs: R&D Intensive: Muon collider technology is less mature compared to hadron colliders, requiring substantial investment in research and development. Cooling Systems: The complex and large-scale cooling infrastructure contributes significantly to the overall cost. Shielding and Detector: Addressing the challenges posed by BIB and neutrino radiation necessitates specialized and expensive shielding and detector components. FCC-hh (Hadron Collider): Challenges: Pile-up Events: High luminosity at hadron colliders leads to multiple proton-proton interactions per bunch crossing (pile-up), complicating event reconstruction. Radiation Hardness: The intense radiation environment at hadron colliders demands radiation-hard detectors and electronics. Synchrotron Radiation: High-energy protons in circular colliders emit synchrotron radiation, which can lead to energy loss and heat load on the accelerator components. Costs: Large Circumference: Achieving high energies in circular hadron colliders requires a large circumference, increasing construction costs. High-Field Magnets: Guiding and focusing the proton beams necessitate powerful and expensive high-field magnets. Comparison: Energy Efficiency: Muon colliders offer higher energy efficiency as muons, being fundamental particles, lose less energy to synchrotron radiation compared to protons in circular colliders. Precision: The cleaner collision environment at muon colliders, with reduced pile-up and background, potentially enables higher precision measurements. Cost and Timescale: Currently, hadron collider technology is more mature, and FCC-hh is projected to be less expensive and achievable on a shorter timescale compared to a muon collider. Conclusion: Both muon colliders and hadron colliders present unique challenges and cost considerations. While muon colliders offer advantages in energy efficiency and precision, their technological maturity and cost-effectiveness remain to be fully demonstrated. The choice between these collider options involves a careful evaluation of scientific goals, technical feasibility, and financial constraints.

Could the presence of additional new particles beyond the scalar triplet and singlet, as suggested by some theoretical models, affect the proposed search strategy and results?

Answer: Yes, the presence of additional new particles beyond the scalar triplet and singlet, as predicted by various theoretical extensions of the Standard Model, could significantly impact the proposed search strategy and results at a muon collider. Here's a breakdown of the potential implications: Altered Production Cross-Sections: New particles could introduce additional Feynman diagrams contributing to the production of the scalar triplet and singlet. This could either enhance or suppress the production cross-sections of the final states under consideration (FS1, FS2, FS3), depending on the couplings and masses of the new particles involved. Modified Decay Channels: The scalar triplet and singlet might decay into these new particles if kinematically allowed. This would lead to a reduction in the branching ratios of the decay channels crucial for the proposed search strategy (e.g., H± → ZW±, H0 → SS). Consequently, the signal event rates in the targeted final states would decrease, potentially making the signal less statistically significant. Novel Final States: The decays of the new particles themselves could introduce entirely new final states that might be interesting to explore. These new signatures could provide complementary information about the underlying physics model and potentially offer alternative discovery channels. Increased Backgrounds: Some decays of the new particles could mimic the targeted final states (FS1, FS2, FS3), leading to an increase in the background rates. This would necessitate a more sophisticated analysis strategy, potentially involving additional kinematic cuts or multivariate techniques like Boosted Decision Trees (BDT) to effectively discriminate the signal from the background. Constraints from Other Experiments: The presence of new particles could be constrained by existing experimental data from other searches, such as those at the LHC or from dark matter direct and indirect detection experiments. These constraints would need to be taken into account when interpreting the results of the muon collider searches. Examples: Supersymmetry (SUSY): In supersymmetric extensions, the scalar triplet and singlet could be part of a larger Higgs sector with additional Higgs bosons and their superpartners. These new particles could modify the production and decay patterns of the triplet and singlet, impacting the search strategy. Extra Dimensions: Models with extra spatial dimensions often predict Kaluza-Klein (KK) excitations of the Standard Model particles, including the Higgs boson. These KK states could mix with the scalar triplet and singlet, altering their properties and leading to modifications in the search strategy. Conclusion: The presence of new particles beyond the scalar triplet and singlet could significantly influence the search strategy and results at a muon collider. A comprehensive analysis considering various theoretical possibilities and their experimental constraints is crucial for maximizing the discovery potential of such a future collider.

What are the broader implications for our understanding of the universe if a signal consistent with this specific extension of the Standard Model is observed at a future muon collider?

Answer: Observing a signal consistent with the specific scalar singlet-triplet extension of the Standard Model at a future muon collider would have profound implications for our understanding of the universe, ushering in a new era in particle physics and cosmology. Here's an exploration of the potential ramifications: Confirmation of New Physics Beyond the Standard Model: Such a discovery would provide definitive evidence for physics beyond the Standard Model, confirming that our current understanding of fundamental particles and forces is incomplete. It would mark a paradigm shift, opening up avenues for exploring new theoretical frameworks and experimental possibilities. Insights into Electroweak Symmetry Breaking: The presence of a scalar triplet participating in electroweak symmetry breaking would deepen our understanding of this fundamental mechanism responsible for generating masses of elementary particles. It could shed light on the hierarchy problem, which questions why the Higgs boson mass is so much smaller than the Planck scale. Elucidating the Nature of Dark Matter: The discovery of the scalar singlet as a dark matter candidate would be a groundbreaking achievement. It would provide direct evidence for the particle nature of dark matter, a mysterious substance constituting a significant portion of the universe's mass-energy content. Studying its properties at the muon collider could unveil crucial information about its interactions with other particles and its role in the evolution of the cosmos. Probing the Early Universe: The properties of the scalar singlet and triplet, such as their masses and couplings, could offer valuable insights into the conditions of the early universe. For instance, the scalar singlet's relic abundance could provide clues about the thermal history of the universe, while the triplet's role in electroweak symmetry breaking could have implications for baryogenesis, the process that generated the matter-antimatter asymmetry we observe today. New Theoretical Frameworks: A confirmed signal would necessitate the development of new theoretical frameworks to accommodate the scalar singlet-triplet extension and explain its implications for cosmology and particle physics. This could lead to a more unified understanding of fundamental forces and the fundamental constituents of matter. Technological Advancements: The construction and operation of a muon collider itself would drive significant technological advancements in areas such as high-energy particle beams, high-field magnets, and particle detectors. These advancements could have spin-offs in other fields, including medicine, materials science, and computing. Conclusion: The observation of a signal consistent with the scalar singlet-triplet extension of the Standard Model at a future muon collider would be a momentous event, revolutionizing our understanding of the universe and paving the way for a new era of discovery in particle physics and cosmology.
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