${\mu}$LHC: Antimuon Ring and HL-LHC based ${\mu}^+p$ Collider

This paper presents the conceptual design and performance evaluation of the ${\mu}$LHC, a feasible HL-LHC-based antimuon-proton collider utilizing ultra-cold ${\mu}^{+}$ beam technology to achieve 5.3 TeV center-of-mass energy and high luminosity for exploring QCD, Higgs physics, and beyond-Standard-Model phenomena.

The Gist

Imagine the world of particle physics as a massive, high-stakes game of billiards. Scientists want to smash tiny particles together at incredible speeds to see what they are made of and how they stick together. For decades, the best way to do this has been to crash electrons into protons. But there's a problem: electrons are too light. When they hit a proton, they bounce off too easily, like a ping-pong ball hitting a bowling ball. They can't reach the deep, heavy "insides" of the proton where the real secrets of the universe are hidden.

This paper proposes a clever new way to play the game: swap the ping-pong ball for a heavy, fast-moving "anti-muon."

Here is the breakdown of their idea, the "μLHC" (Muon-LHC), using simple analogies:

1. The Big Idea: A New Kind of Hammer

The authors suggest building a machine that smashes antimuons (a heavy cousin of the electron) into the protons already speeding around the Large Hadron Collider (LHC) at CERN.

• The Analogy: Imagine the LHC is a giant circular racetrack where protons are racing like Formula 1 cars. The new plan is to build a side-track that shoots heavy, fast "anti-muon bullets" tangentially into the racetrack.
• The Result: Because antimuons are much heavier than electrons, they hit the protons with much more force. This allows scientists to reach energy levels of 5.3 TeV (tera-electronvolts). To put that in perspective, the current best electron-proton proposal (LHeC) only reaches about 1.2 TeV. The new machine is like upgrading from a slingshot to a cannon.

2. The Secret Sauce: "Ultra-Cold" Muons

The biggest hurdle in building muon machines has always been that muons are "fussy." They decay (fall apart) very quickly, and making a tight, focused beam of them is incredibly hard.

• The Innovation: The paper relies on a technology developed in Japan (J-PARC) that creates "ultra-cold" positive muons (antimuons).
• The Analogy: Think of regular muons like a swarm of angry bees buzzing everywhere; they are hard to catch and organize. The "ultra-cold" muons are like bees that have been put in a freezer—they slow down, calm down, and can be lined up in a neat, orderly row.
• Why it matters: Because this technology for positive muons already exists and works well, the authors argue we can build this machine much sooner than a full muon collider (which requires cooling negative muons, a technology that doesn't exist yet).

3. Two Ways to Build the Accelerator

The paper explores two different ways to speed up these calm muons before they hit the protons:

• Option A (The Custom Track): Build a brand-new, specialized racetrack based on a Japanese design called "μTRISTAN." It's a long, straight track with curves, designed specifically to accelerate these muons to 1 TeV.
• Option B (The Remodel): Take the existing plans for a different project (the LHeC electron accelerator) and "repurpose" the tunnel. Instead of accelerating electrons, they would use the same tunnel to accelerate muons. It's like buying a house built for a family of four and remodeling the kitchen to fit a family of six.

4. What Will We Learn? (The Physics)

Once the machine is running, it acts like a super-powerful microscope.

• Peering Deeper: It can see parts of the proton that have never been seen before, specifically in areas called "small-x" and "high-Q2."
  • Analogy: If the proton is a city, previous machines could only see the suburbs. This new machine can zoom in to see the tiny, crowded alleyways in the city center where the "glue" (Quantum Chromodynamics or QCD) that holds everything together is working.
• The Higgs Boson: It will produce Higgs bosons (the particle that gives things mass) much more frequently than current plans, allowing scientists to study them in detail.
• New Physics (BSM): It might find "exotic" particles that don't exist in our current rulebook.
  • The "Color-Octet" Muon: The paper specifically looks for a hypothetical particle called a "color-octet muon." Think of this as a muon that has a secret "color" charge (like a hidden superpower) that makes it interact with the strong force. The new machine is so sensitive it could find this particle at masses up to 4,100 GeV, whereas the current LHC might only find it up to 2,300 GeV. It's like having a metal detector that can find gold buried twice as deep as the old one.

5. The Detector: A High-Tech Shield

Because muons decay into other particles (creating a lot of "noise" or background radiation), the detector needs special protection.

• The Analogy: Imagine trying to listen to a whisper in a room where a jet engine is roaring nearby. The paper proposes a "shielding nozzle" (a thick, cone-shaped wall made of tungsten) placed right in front of the detector. This blocks the roar of the jet engine (the decay products) so the detector can hear the whisper (the actual collision data).

Summary

The paper argues that by using existing, mature technology for "ultra-cold" antimuons, we can build a 5.3 TeV muon-proton collider attached to the LHC. This machine would be a "super-microscope" capable of seeing deeper into the structure of matter than ever before, potentially solving mysteries about how the universe gets its mass and finding entirely new types of particles, all while being feasible to build sooner than other proposed muon machines.

Technical Summary

Technical Summary: $\mu$LHC: Antimuon Ring and HL-LHC based $\mu$+p Collider

Problem Statement
The paper addresses the limitations of current and proposed lepton-hadron colliders in probing the internal structure of matter at the energy frontier. While the HERA collider provided foundational data on proton structure, it failed to cover the critical kinematic region of small Bjorken-$x$ ($<10^{-4}$) at high $Q^2$ ($>10$ GeV$^2$), which is essential for understanding Quantum Chromodynamics (QCD) basics, confinement, and hadronization. Furthermore, the Standard Model's QCD sector remains incomplete, and the Higgs mechanism accounts for less than 2% of the visible Universe's mass. Existing proposals like the Large Hadron-electron Collider (LHeC) offer center-of-mass energies ($\sqrt{s}$) up to 1.2 TeV, which is insufficient for the next generation of physics goals. Conversely, muon colliders ($\mu^+\mu^-$) face significant technical hurdles regarding beam cooling and acceleration, with demonstrators not scheduled until 2035. The paper identifies a gap for a high-energy lepton-hadron collider that can achieve multi-TeV energies sooner than a full muon collider, leveraging established ultra-cold antimuon ($\mu^+$) technology.

Methodology
The authors propose the conceptual design of a $\mu$p collider ($\mu$LHC) utilizing the High-Luminosity Large Hadron Collider (HL-LHC) proton beam (7 TeV) colliding tangentially with an accelerated antimuon beam (1 TeV). The study evaluates two distinct acceleration schemes for the $\mu^+$ beam:

1. $\mu$TRISTAN-based Booster Ring: This option adapts the design from the KEK $\mu$TRISTAN concept, utilizing ultra-cold $\mu^+$ production technology developed at J-PARC. It employs a race-track booster ring with 3 km linear accelerator sections and 1 km radius arcs. The design accelerates $\mu^+$ from 212 MeV to 1 TeV over 16 turns. The authors recalculate muon survival rates, finding 82% survival to 960 GeV (requiring a slight adjustment to reach 1 TeV).
2. LHeC ERL-based Booster Ring: This option proposes repurposing the Energy Recovery Linac (ERL) tunnel of the LHeC project. It utilizes a "race-track" layout with two 1 km linacs and recirculation arcs. The study adapts this infrastructure to accelerate $\mu^+$ over 50 turns to 1 TeV, calculating a survival rate of approximately 67%.

The methodology includes:

• Beam Dynamics: Calculation of muon population reduction due to decay in both booster and main rings (3 km circumference).
• Luminosity Optimization: Use of the AloHEP software to simulate interaction regions, accounting for pinch effects, particle decay, and hourglass effects to determine achievable luminosities.
• Detector Design: Proposal of a general-purpose detector with a superconducting solenoid magnet, featuring a shielding tungsten nozzle (cladded with borated polyethylene) to mitigate beam-induced backgrounds (BIB) from muon decays.
• Physics Simulation: Monte Carlo simulations using MadGraph5, Pythia8, and MadAnalysis5 to evaluate Higgs production cross-sections and the search potential for color-octet muons ($\mu^8$).

Key Contributions

• Conceptual Design: The paper presents the first detailed conceptual design for an HL-LHC based $\mu^+$p collider, achieving a center-of-mass energy of 5.3 TeV, significantly surpassing the LHeC (1.2 TeV) and EIC.
• Feasibility Analysis: It demonstrates that $\mu^+$p colliders are technically more feasible in the near term than $\mu^+\mu^-$ colliders because ultra-cold $\mu^+$ beam technology (J-PARC) is established, whereas $\mu^-$ cooling remains a challenge.
• Performance Metrics: The study calculates achievable luminosities exceeding $10^{33}$ cm$^{-2}$s$^{-1}$ for both booster options (8.8 $\times$ 10$^{33}$ for $\mu$TRISTAN-based and 7.2 $\times$ 10$^{33}$ for ERL-based).
• Kinematic Coverage: The design offers a kinematic plane coverage extending to $x \approx 3.6 \times 10^{-7}$ and $Q^2 \approx 2800$ GeV$^2$, far exceeding HERA, EIC, and LHeC capabilities.

Results

• Luminosity and Energy: Both configurations achieve $\sqrt{s} = 5.3$ TeV. The $\mu$TRISTAN-based option yields a luminosity of $8.8 \times 10^{33}$ cm$^{-2}$s$^{-1}$, while the ERL-based option yields $7.2 \times 10^{33}$ cm$^{-2}$s$^{-1}$.
• Higgs Production: The $\mu$LHC is projected to produce significantly more Higgs bosons via W and Z fusion compared to the LHeC. For a 5.3 TeV collider, the annual yield is estimated at ~33,900 (W-fusion) and ~6,600 (Z-fusion) for the $\mu$TRISTAN option, compared to ~1,260 and ~200 respectively for the LHeC (ERL 20).
• BSM Physics (Color-Octet Muons): Simulations for the search of color-octet muons ($\mu^8$) indicate that the $\mu$LHC can probe masses up to ~4100 GeV at 5$\sigma$ significance with 100 fb$^{-1}$ of integrated luminosity. This exceeds the HL-LHC's reach (approx. 2300 GeV) and demonstrates that $\mu$LHC can achieve the same statistical significance as the HL-LHC with only 100 nb$^{-1}$ of data.
• Detector Performance: Simulations of the shielding nozzle indicate that 81% of 1 TeV muons pass through the tungsten cone with minimal energy loss, while 19% deposit energy, necessitating careful optimization to balance background suppression with angular acceptance.

Significance and Claims
The paper claims that the $\mu$LHC represents a critical, feasible pathway for high-energy physics that can be realized earlier than a full muon collider. By leveraging existing ultra-cold $\mu^+$ technology, it offers a unique tool to:

1. Clarify QCD Basics: Provide essential data in the small-$x$, high-$Q^2$ region to test confinement hypotheses and improve Parton Distribution Functions (PDFs) for future hadron colliders (HL-LHC, FCC, SppC).
2. Enhance Higgs Physics: Offer a high-statistics environment for studying Higgs boson properties through vector boson fusion.
3. Explore BSM Physics: Provide superior sensitivity to muon-related Beyond Standard Model phenomena, specifically excited muons, leptoquarks, and color-octet muons, surpassing the discovery potential of the HL-LHC for specific channels.

The authors conclude that systematic studies of the accelerator, detector, and physics aspects of the $\mu$LHC are necessary for long-term planning, positioning it as a potential "second most effective tool" after proton colliders for constituent-level exploration at the multi-TeV scale.