Exploring Scalar Leptoquarks at Muon Collider via Indirect Signatures and Right-Handed Neutrino-Assisted Decays

This paper investigates the discovery potential of a scalar leptoquark doublet coupling to light quarks and right-handed neutrinos at a muon collider, demonstrating that indirect probes and direct production channels (both pair and single) offer robust sensitivity to masses up to 7 TeV, significantly surpassing the projected capabilities of the High-Luminosity LHC.

The Gist

Imagine the universe is a giant, bustling kitchen where particles are the ingredients. For decades, physicists have been cooking with a standard recipe called the Standard Model. But recently, they've noticed some strange flavors in their dishes—experimental results that don't quite match the recipe. They suspect there are secret ingredients they haven't found yet.

One of the most promising "secret ingredients" is a particle called a Leptoquark.

The Mystery Ingredient: The Leptoquark

Think of a Leptoquark as a universal translator or a chameleon.

• Quarks are the building blocks of heavy things (like protons and neutrons).
• Leptons are the building blocks of light things (like electrons and muons).
• In the Standard Model, these two groups rarely talk to each other.
• A Leptoquark is a magical bridge that can turn a heavy quark into a light lepton, and vice versa. It's like a chef who can instantly turn a steak into a fish, or a potato into a carrot.

The Problem: The "Heavy" Ingredient

The scientists in this paper are looking for a specific type of Leptoquark called a Scalar Leptoquark. They suspect these particles are very heavy—so heavy that the world's current biggest particle collider (the Large Hadron Collider, or LHC) might not be strong enough to find them. It's like trying to find a specific needle in a haystack using a weak magnet; if the needle is buried too deep or is made of a different material, you might miss it.

Also, these Leptoquarks might have a secret partner: a Right-Handed Neutrino (RHN). This is a ghostly, invisible particle that doesn't interact with normal matter easily. If the Leptoquark decays into this ghost, it becomes even harder to spot because the ghost disappears without leaving a clear trace.

The Solution: The Muon Collider

The authors propose a new kitchen tool: a Muon Collider.

• The LHC is like smashing two trucks together. It's powerful, but the crash is messy, full of debris (background noise) that makes it hard to see the specific new particle.
• The Muon Collider is like smashing two billiard balls together. Muons are elementary particles (like electrons, but heavier). Because they are clean and precise, the collision is much less messy. Plus, because muons are heavier, they don't lose energy as quickly as electrons, allowing the collider to reach much higher energies.

This new machine acts like a high-powered, precision spotlight that can cut through the noise to find these heavy, elusive Leptoquarks.

The Two Ways to Find the Ghost

The paper describes two main strategies to catch these particles, using a clever mix of direct and indirect detective work.

1. The Indirect Search: Feeling the Ripples

Imagine you are in a dark room and you can't see a large elephant, but you can feel the floor vibrating when it walks by.

• The Method: Even if the Leptoquark is too heavy to be created directly, its presence can still "tug" on the particles colliding in the machine.
• The Analogy: It's like throwing a stone into a pond. You don't need to see the fish to know it's there; you just watch how the water ripples. The scientists look at the "ripples" in the energy of the jets (sprays of particles) coming out of the collision. If the ripples are weird, it means a heavy Leptoquark is influencing the process from the shadows.
• The Result: This method is incredibly robust. It can detect the Leptoquark even if it's too heavy to be made directly, reaching masses up to 7 TeV (which is about 7,000 times heavier than a proton).

2. The Direct Search: Catching the Fish

This is the more obvious approach: smash the particles hard enough to actually create the Leptoquark and watch it fall apart.

• The Challenge: If the Leptoquark is very heavy, you need a lot of energy to make it.
• The Trick: The paper introduces a "cheat code." Instead of just smashing two particles together to make a pair of Leptoquarks (which is hard at high energies), they look for Single Production.
• The Analogy: Imagine you want to find a rare bird.
  • Pair Production: You try to catch two birds at once by throwing a net. Hard to do if the birds are fast and far apart.
  • Single Production: You use a specific bait (the Right-Handed Neutrino) that attracts just one bird. It's much easier to catch one bird than two.
• The Result: By using this "bait" (the interaction with the Right-Handed Neutrino), they can find Leptoquarks up to 6 TeV at a 10 TeV collider. This is a huge leap beyond what the LHC can do.

Why This Matters

The paper concludes that the Muon Collider is a game-changer.

• The LHC is like a sledgehammer: it hits hard but creates a lot of mess, and it might miss the heavy, subtle particles.
• The Muon Collider is like a scalpel: it's precise, clean, and can reach energies the LHC can't touch.

If these Leptoquarks exist, the Muon Collider is the only tool we have that can definitively find them, especially if they are hiding behind the "ghost" of the Right-Handed Neutrino. This discovery would rewrite the recipe of the universe, explaining why neutrinos have mass and potentially solving other cosmic mysteries like dark matter.

In short: The authors are saying, "Stop looking for the needle with a weak magnet in a messy haystack. Let's build a laser scanner (the Muon Collider) that can find the needle even if it's hiding in a different dimension."

Technical Summary

Here is a detailed technical summary of the paper "Exploring Scalar Leptoquarks at Muon Collider via Indirect Signatures and Right-Handed Neutrino-Assisted Decays."

1. Problem Statement

Scalar Leptoquarks (sLQs) are hypothetical particles that couple quarks and leptons, appearing in various Beyond-the-Standard-Model (BSM) theories such as Grand Unified Theories (GUTs) and supersymmetry. While the Large Hadron Collider (LHC) has placed stringent limits on sLQs decaying into charged leptons and jets, a significant portion of the parameter space remains unconstrained. Specifically:

• Right-Handed Neutrinos (RHNs): If sLQs couple to RHNs (which are well-motivated candidates for neutrino mass generation via the seesaw mechanism), the sLQ can decay into an RHN and a jet ($LQ \to N + j$). If the RHN is lighter than the sLQ, this decay mode can dominate, suppressing the conventional charged-lepton signatures ($LQ \to \ell j$) that LHC searches rely on.
• LHC Limitations: In scenarios where RHN decays dominate, LHC direct search limits weaken significantly. Furthermore, conventional RHN production at colliders is suppressed by small active-sterile mixing angles ($V_{\mu N} \sim 10^{-6}$).
• The Gap: There is a need for a high-energy, clean environment to probe sLQs in the multi-TeV regime and simultaneously discover RHNs, particularly in regions where direct pair production is kinematically suppressed or where RHN-assisted decays dominate.

2. Methodology

The authors investigate the discovery potential of a specific sLQ doublet, $\tilde{R}_2(3, 2, 1/6)$, at a future Muon Collider with center-of-mass energies $\sqrt{s} = 5$ TeV and $10$ TeV.

Model Setup:

• Particle Content: The model extends the Standard Model (SM) with an sLQ doublet $\tilde{R}_2$ and a single Majorana RHN ($N$) with mass $M_N > \mathcal{O}(10)$ GeV.
• Couplings: The analysis focuses on two Yukawa couplings:
  • $Y_{12}$: Coupling between the sLQ, a first-generation quark ($d$), and a second-generation lepton ($\mu$).
  • $Z_{11}$: Coupling between the sLQ, a first-generation quark ($u$), and the RHN ($N$).
• Mixing: The RHN mixes with the muon neutrino via an active-sterile mixing angle $V_{\mu N} \approx 10^{-6}$ (consistent with Type-I seesaw).

Search Strategies:
The study employs two complementary approaches:

1. Indirect Search (t-channel exchange):
   • Analyzes the process $\mu^+ \mu^- \to j j$ (dijet production) mediated by the t-channel exchange of the sLQ component $\tilde{R}_2^{2/3}$.
   • This process scales as $\sigma \propto Y_{12}^4$ and is sensitive to the sLQ mass even when direct production is kinematically forbidden.
2. Direct Search (Pair and Single Production):
   • Pair Production: $\mu^+ \mu^- \to \tilde{R}_2 \tilde{R}_2^*$.
   • Single Production: $\mu^+ \mu^- \to \tilde{R}_2 j N$ or $\tilde{R}_2 \mu j$.
   • Decay Topologies: The sLQ decays into $N j$ or $\mu j$. The RHN subsequently decays (promptly) into $\mu j j$ (via off-shell sLQ or $W$ boson).
   • Signal Signatures: The study focuses on final states with dimuons ($\mu\mu$) and high jet multiplicity ($N_{jet} \ge 4$). Both symmetric (both sLQs decay similarly) and asymmetric (one decays to $N$, one to $\mu$) modes are considered.

Simulation and Analysis:

• Tools: Events generated using FeynRules (model implementation), MadGraph5_aMC@NLO (LO generation), Pythia8 (showering/hadronization), and Delphes3 (detector simulation with ILD card).
• Backgrounds: Dominant SM backgrounds include $V+X$ (gauge boson + jets), diboson production ($VV$), top-quark pairs ($t\bar{t}$), and pure QCD dijet production.
• Selection Cuts:
  • Indirect: High $p_T$ jets ($p_T > 3.5$ TeV for 10 TeV collider), $N_{jet} \ge 2$, lepton veto, and $b$-veto.
  • Direct: $N_{\mu} \ge 2$, $N_{jet} \ge 4$, and specific high-$p_T$ jet requirements to suppress backgrounds.
• Statistical Significance: Calculated using the asymptotic formula for $Z$-score (Eq. 12) with integrated luminosities of $3 \text{ ab}^{-1}$(5 TeV) and$10 \text{ ab}^{-1}$ (10 TeV).

3. Key Contributions

• Unified Exploration of RHNs and sLQs: The paper demonstrates that sLQs serve as a powerful portal to produce RHNs at muon colliders, bypassing the severe suppression caused by small active-sterile mixing in direct RHN production.
• Indirect Probe Robustness: It establishes that indirect searches via t-channel dijet production offer a mass-independent sensitivity to the coupling $Y_{12}$, allowing probes of sLQ masses far beyond the kinematic threshold of the collider.
• Single Production Dominance: The study highlights that single production channels become the dominant discovery mode for sLQ masses approaching or exceeding $\sqrt{s}/2$, a regime where pair production is phase-space suppressed.
• Comprehensive Sensitivity Maps: The authors provide detailed sensitivity contours in the $(M_{\tilde{R}_2}, Y_{12})$ and $(M_{\tilde{R}_2}, Z_{11})$ planes, accounting for various RHN masses ($50$GeV,$500$GeV,$2$ TeV) and both symmetric/asymmetric decay modes.

4. Results

Indirect Search Sensitivity:

• Indirect probes are remarkably robust. For $\sqrt{s} = 5$ TeV ($3 \text{ ab}^{-1}$) and$10$TeV ($10 \text{ ab}^{-1}$), the muon collider can achieve **$5\sigma$sensitivity** to sLQ masses up to **4.0 TeV** and **7.0 TeV**, respectively, assuming$Y_{12} \sim \mathcal{O}(1)$.
• The sensitivity extends to couplings as low as $Y_{12} \sim 0.1$, significantly improving upon current LHC indirect limits.

Direct Search Sensitivity:

• Pair Production: Dominates at lower masses ($M_{\tilde{R}_2} < \sqrt{s}/2$).
• Single Production: Decisively extends the reach into the multi-TeV regime.
  • At $\sqrt{s} = 5$ TeV, single production can probe sLQ masses up to 3.0 TeV with $5\sigma$significance for$\mathcal{O}(1)$ couplings.
  • At $\sqrt{s} = 10$ TeV, the reach extends to 6.0 TeV.
• RHN Mass Dependence: The sensitivity contours show distinct features near the kinematic threshold $M_{\tilde{R}_2} \approx M_N$. When $M_{\tilde{R}_2} < M_N$, the decay to RHN is forbidden, drastically reducing sensitivity. However, for $M_{\tilde{R}_2} > M_N$, the single production channel remains effective even for heavy RHNs.
• Comparison with HL-LHC: The muon collider significantly outperforms the High-Luminosity LHC (HL-LHC). For example, to discover a 3.0 TeV sLQ, the HL-LHC requires Yukawa couplings $Y > 3.5$, whereas a 5 TeV muon collider requires $Y \approx 1.5$, and a 10 TeV collider requires $Y < 10^{-2}$.

Background Suppression:

• The dimuon + multi-jet signature, combined with high $p_T$ cuts and $b$-vetoing, reduces SM backgrounds to negligible levels (effective background cross-sections $\sim 0.026$ fb for direct searches), enabling high signal significance even for small couplings.

5. Significance

This work underscores the indispensable role of future muon colliders in the search for heavy BSM physics.

• Beyond Kinematic Limits: Unlike hadron colliders, where parton distribution functions suppress high-mass production, muon colliders utilize the full center-of-mass energy, allowing single production to probe masses well beyond the pair-production threshold.
• Clean Environment: The absence of underlying event activity and the ability to trigger on clean dimuon signatures allow for the exploration of parameter spaces (specifically those involving RHNs and suppressed charged-lepton decays) that are currently inaccessible to the LHC.
• Theoretical Motivation: The study validates the muon collider as a primary facility for testing neutrino mass generation mechanisms (via RHNs) and Grand Unified Theories (via sLQs) simultaneously, offering a unique window into the TeV-scale physics landscape.

In conclusion, the paper demonstrates that a 10 TeV muon collider can discover scalar leptoquarks with masses up to 6.0 TeV and right-handed neutrinos, covering regions of parameter space that are completely unconstrained by current or projected LHC data.