Updated Bounds on the Minimal Left-Right Symmetric Model from LHC Dilepton Resonance Searches

Using 13 TeV LHC dilepton resonance data, this study establishes new lower mass bounds for the $Z_R$ boson in the Minimal Left-Right Symmetric Model across a range of gauge couplings, thereby constraining an unexplored parameter space where the right-handed neutrino is heavier than the $W_R$ boson.

The Gist

Imagine the universe is built on a set of invisible rules, like the laws of physics in a video game. For decades, we've known the "Standard Model," which is the rulebook we use to explain how particles interact. But there's a glitch in this rulebook: it treats "left" and "right" differently, breaking a beautiful symmetry.

Physicists have proposed an upgrade to this rulebook called the Left-Right Symmetric Model (LRSM). Think of it as adding a "mirror world" to our universe. In this mirror world, there are new, heavy particles that act like twins to the ones we already know, but they only interact with the "right-handed" versions of particles.

The New Characters: $W_R$ and $Z_R$

In this mirror world, two new heavy characters appear:

1. The $W_R$ Boson: A charged particle (like a heavy version of the electron's cousin).
2. The $Z_R$ Boson: A neutral particle (like a heavy version of the photon).

Usually, scientists hunting for this new physics focus on the $W_R$ boson. It's the "star of the show" because it's easier to spot in certain scenarios. However, this paper argues that we've been ignoring the $Z_R$ boson, which is like looking for a needle in a haystack while ignoring the magnet that might be holding it.

The Detective Work at the LHC

The authors of this paper acted like detectives at the Large Hadron Collider (LHC), the world's biggest particle smasher in Switzerland. They didn't look for the usual suspects ($W_R$); instead, they looked for the "ghost" of the $Z_R$ boson.

Here is how they did it:

• The Setup: They took data from smashing protons together at incredibly high speeds (13 TeV).
• The Clue: They looked for a specific "signature": two leptons (like electrons or muons) appearing out of nowhere. In the language of the paper, this is the process $pp \to Z_R \to \ell^+ \ell^-$.
• The Analogy: Imagine two cars crashing. Usually, they just crumple. But if a hidden, heavy boulder ($Z_R$) was involved, it would explode into two distinct, high-speed fragments flying in opposite directions. The scientists looked for these specific "explosions" in the data.

The Big Discovery: Raising the Bar

The researchers checked the data to see if these "explosions" actually happened. They didn't find any evidence of the $Z_R$ boson. But in science, not finding something is also a discovery.

It means the $Z_R$ boson must be heavier than we thought. If it were lighter, we would have seen it by now.

• The Old Limit: Previous studies (using less data) said the $Z_R$ must be heavier than about 3 to 4 TeV (a unit of mass).
• The New Limit: With the massive amount of new data (139 times more than some previous studies), the authors pushed this limit up significantly. They found that the $Z_R$ must be heavier than 5.4 TeV (if the forces are balanced) or even 6.1 TeV (if the forces are stronger).

Think of it like a fishing net. The old net had big holes, so small fish could escape. The new net has much smaller holes. Since no fish ($Z_R$) was caught, we now know the fish must be huge—bigger than the holes in our new, tighter net.

Why This Matters (The "Mirror" Twist)

The paper highlights a clever trick. In this model, the mass of the $W_R$ (the star we usually look for) and the $Z_R$ (the ghost we just looked for) are tied together. If you know how heavy one is, you know how heavy the other must be.

The authors found a special "blind spot" in previous searches. Sometimes, the "right-handed neutrino" (another new particle) is heavier than the $W_R$ boson. In this scenario, the $W_R$ becomes very hard to see because it doesn't produce the usual clear signals. It's like trying to hear a whisper in a storm.

However, the $Z_R$ doesn't care about this storm. By hunting for the $Z_R$, the authors found a way to rule out these "heavy neutrino" scenarios. They showed that even if the $W_R$ is hiding, the $Z_R$ would still have been caught if it were light enough. Since they didn't catch the $Z_R$, they proved that this specific "heavy neutrino" region of the universe is likely empty.

The Bottom Line

This paper is a "sweeping of the floor" for a specific type of physics. By using the latest, most powerful data from the LHC, the authors have:

1. Ruled out lighter versions of the $Z_R$ boson, pushing the possible mass limit up by about 2 TeV.
2. Covered a blind spot where previous searches for the $W_R$ boson failed.
3. Proved that if this "Left-Right Symmetry" exists, the new particles are much heavier than we hoped, making them even harder to find in the future.

In short: The universe is still hiding its mirror world, but we now know exactly where not to look, and we know the hidden particles are heavier than ever before.

Technical Summary

Technical Summary: Updated Bounds on the Minimal Left-Right Symmetric Model from LHC Dilepton Resonance Searches

Problem Statement
The Left-Right Symmetric Model (LRSM) extends the Standard Model (SM) to restore parity symmetry at high energies, introducing new gauge bosons: the charged $W_R^\pm$ and the neutral $Z_R$. While collider searches for LRSM signatures have historically focused on the charged current process $pp \to W_R \to N_R \ell \to \ell \ell jj$ (assuming $M_{W_R} > M_{N_R}$), this approach faces limitations when the right-handed neutrino ($N_R$) is heavier than the $W_R$ boson. In such scenarios, the final state leptons possess soft transverse momentum, reducing LHC sensitivity. Furthermore, previous analyses often relied on the assumption of gauge coupling equality ($g_R = g_L$) or utilized limited datasets (e.g., 8 TeV or early 13 TeV runs). This work addresses the need to constrain the LRSM parameter space using the neutral current channel $pp \to Z_R \to \ell^+\ell^-$, specifically exploring the regime where $g_R \neq g_L$ and $M_{N_R} > M_{W_R}$.

Methodology
The authors perform a phenomenological analysis using LHC Run II data with a center-of-mass energy of $\sqrt{s} = 13$ TeV and an integrated luminosity of $139 \text{ fb}^{-1}$.

• Theoretical Framework: The study utilizes the minimal LRSM based on the gauge symmetry $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. The scalar sector involves a bidoublet $\Phi$ and triplets $\Delta_{L,R}$, with symmetry breaking scales satisfying $v_R \gg v \gg v_L$. The masses of the physical bosons are derived via diagonalization of the charged and neutral gauge boson mass matrices, accounting for mixing angles $\theta_1, \theta_2, \theta_3$.
• Simulation and Calculation: The production cross-section for $pp \to Z_R \to \ell^+\ell^- + X$ is computed at leading order (LO) using MadGraph, with the model implemented via FeynRules. The analysis incorporates parton distribution functions (NNPDF40 nlo) and applies kinematic cuts consistent with ATLAS experimental selections ($|\eta| < 2.5$, $p_T > 30$ GeV).
• Parameter Variation: Unlike previous studies that fixed $g_R = g_L$, this work varies the $SU(2)_R$ gauge coupling $g_R$ across the range $0.4 \leq g_R \leq 1.0$. The analysis accounts for the pole in the cross-section arising from the $Z_R$ coupling structure and the kinematic constraint that $v_R$ becomes imaginary if $g_R < g_L \tan(\theta_W) \approx 0.35$.
• Data Comparison: Theoretical predictions are compared against the 95% Confidence Level (C.L.) exclusion limits on the dilepton cross-section provided by the ATLAS collaboration.

Key Contributions

1. Updated Mass Bounds: The paper provides the first updated lower mass bounds on the $Z_R$ boson using the full Run II dataset ($139 \text{ fb}^{-1}$), significantly improving upon previous limits derived from $3.2 \text{ fb}^{-1}$ data.
2. Coupling Dependence: The analysis explicitly maps the exclusion limits as a function of the gauge coupling $g_R$, demonstrating that the mass bound is not a single value but varies with the coupling strength.
3. Complementarity to $W_R$ Searches: The study establishes a direct relationship between $Z_R$ and $W_R$ masses ($M_{W_R} \approx 0.58 M_{Z_R}$ for $g_R=g_L$) and demonstrates that $Z_R$ searches provide orthogonal constraints. Crucially, these constraints remain valid even in the parameter space where $M_{N_R} > M_{W_R}$, a region where direct $W_R$ searches lose sensitivity.
4. Exclusion of $g_R < g_L$ Scenarios: The work highlights the theoretical consistency requirement that $g_R$ must be greater than $\approx 0.35$ to ensure a real symmetry breaking scale $v_R$.

Results
Using the ATLAS dilepton resonance data, the authors derive the following lower mass limits for the $Z_R$ boson at 95% C.L.:

• For the benchmark point $g_R = g_L = 0.65$: $M_{Z_R} > 5.4$ TeV.
• For the benchmark point $g_R = 1.0$: $M_{Z_R} > 6.1$ TeV.
• The exclusion limit varies between $M_{Z_R} > 4.9$ TeV and $M_{Z_R} > 6.1$ TeV depending on the specific value of $g_R$ within the allowed range.

These limits represent an increase of approximately 2 TeV compared to results derived from the $3.2 \text{ fb}^{-1}$ dataset. Consequently, the derived lower bound on the $W_R$ mass (assuming $g_R = g_L$) is updated to $M_{W_R} > 3.2$ TeV.

The authors also overlay these $Z_R$-derived limits onto the $M_{W_R} \times M_{N_R}$ parameter space. They show that the dilepton constraints cover the region where $M_{N_R} > M_{W_R}$, which is currently unexplored by direct $W_R$ searches (typically $pp \to W_R \to \ell \ell jj$). Additionally, the paper compares these collider limits with constraints from neutrinoless double beta decay ($0\nu\beta\beta$), noting that while $0\nu\beta\beta$ provides strong constraints, the collider bounds offer an independent and orthogonal probe of the model.

Significance
The paper argues that the search for the $Z_R$ boson is essential for a comprehensive test of the Left-Right Symmetric Model. While the observation of a right-handed charged current ($W_R$) is a primary signature, the sensitivity of such searches degrades significantly if the right-handed neutrino is heavy. By utilizing the dilepton channel ($Z_R \to \ell^+\ell^-$), which is insensitive to the $N_R$ mass hierarchy, the authors demonstrate that LHC data can effectively probe and exclude regions of the LRSM parameter space that are inaccessible to charged current searches. The updated bounds significantly tighten the constraints on the symmetry breaking scale $v_R$ and the gauge coupling $g_R$, providing a more robust foundation for future LRSM phenomenology.