Phenomenology of electroweak spin-1 resonances

This paper investigates the LHC phenomenology of composite Higgs models with an SU(2)$_L\times$SU(2)$_R$ global symmetry, demonstrating that viable scenarios exist where two neutral and one charged spin-1 resonances, which mix with Standard Model vector bosons, could be singly produced with masses as low as approximately 1.5 TeV.

The Gist

Imagine the universe as a giant, complex machine. For decades, physicists have had a very good manual for how this machine works, called the Standard Model. It explains most of the particles and forces we see. But there's a nagging problem: the manual feels a bit "tuned" or "fine-tuned" in a way that doesn't feel natural. It's like finding a watch where the gears are perfectly balanced, but you have no idea why they are balanced that way.

To fix this, physicists propose a new theory called Composite Higgs Models. Think of this as suggesting that the "Higgs boson" (the particle that gives other particles mass) isn't a fundamental, indivisible brick. Instead, it's like a molecule made of smaller, invisible particles glued together by a new, super-strong force. This is similar to how protons in our everyday world are made of quarks held together by the strong nuclear force.

The New "Heavy" Particles

In this new theory, if you have a strong force holding things together, you expect to see "bound states"—particles that are stuck together. Just as the strong force in our world creates heavy particles like the rho-meson, this new force predicts the existence of heavy, new particles.

The paper focuses on a specific type of these new particles: Spin-1 Resonances.

• The Analogy: Imagine the Standard Model has a set of "delivery trucks" (the W and Z bosons) that carry forces. The new theory predicts there are heavier, faster, and more powerful trucks (the new resonances) that also carry forces but are made of the new "glue."
• The Mix: These new heavy trucks aren't totally separate; they "mix" with the old Standard Model trucks. It's like if a new, super-fast delivery van occasionally swapped its engine with an old pickup truck. Because of this mixing, we might be able to spot the new trucks at the Large Hadron Collider (LHC), the giant particle smasher in Switzerland.

The Search for the "Ghost" Trucks

The authors of this paper asked a simple question: How heavy can these new trucks be before we would have already seen them?

They looked at the data from the LHC, which has been smashing protons together for years. They checked for signs of these new trucks in several ways:

1. Direct Sighting: Did the trucks decay into pairs of electrons or muons (like a truck exploding into two shiny balls)?
2. Top Quark Trails: Did they decay into heavy "top quarks" (the heaviest known particles)?
3. Hidden Passengers: Did they decay into pairs of the new "molecules" (the pNGBs) mentioned earlier?

The Results: They Might Be Hiding in Plain Sight

The researchers ran simulations for many different scenarios (different strengths of the new force, different ways the trucks mix with the old ones).

• The Bad News: If these new trucks are very weak and don't interact much with the heavy top quarks, the LHC data has already ruled them out if they are lighter than about 3 to 4.5 TeV (a unit of mass, roughly 3,000 to 4,500 times the mass of a proton).
• The Good News (The "Loophole"): If these new trucks have a specific "personality"—specifically, if they interact strongly with the new "molecules" (pNGBs) or have a specific mix with the top quark—they can be much lighter.
  • The paper concludes that these new particles could be as light as 1.5 TeV (about 1,500 times a proton's mass) and we still wouldn't have seen them yet. They are hiding because they are decaying into different things than the experiments were originally looking for.

The "Fermiophilic" vs. "Fermiophobic" Analogy

The paper discusses two main ways these new particles might behave regarding matter:

• Fermiophilic (Matter-Loving): The new trucks love to decay into heavy matter (like top quarks). This makes them harder to spot in some channels but easier in others.
• Fermiophobic (Matter-Avoiding): The new trucks avoid heavy matter and prefer to decay into force carriers (like photons or W/Z bosons). This makes them easier to spot in some ways, but the data shows they are more tightly constrained in this scenario.

The Bottom Line

The paper is essentially a "Where's Waldo?" for new physics. The authors have mapped out the landscape of possible new heavy particles. They found that while we have ruled out many possibilities, there is still a viable hiding spot where these new particles could exist with a mass as low as 1.5 TeV.

They are not saying these particles definitely exist, but rather that if they do exist, they could be this light, and we haven't ruled them out yet. The authors suggest that future runs of the LHC, or even a bigger future collider, will need to look specifically for these "hiding" patterns to find them.

Technical Summary

Technical Summary: Phenomenology of Electroweak Spin-1 Resonances

Problem and Motivation
Composite Higgs models (CHMs) propose a solution to the hierarchy problem by postulating a new strong interaction that becomes strong in the multi-TeV range, leading to the spontaneous breaking of global symmetries. In this framework, the Higgs boson emerges as a pseudo-Nambu-Goldstone boson (pNGB). While previous studies have extensively covered the phenomenology of pNGBs and top partners, the phenomenology of electroweak spin-1 resonances—specifically those mixing with Standard Model (SM) vector bosons—requires systematic investigation. This paper focuses on models with a fermionic ultraviolet (UV) completion, utilizing a gauge-fermion description that allows for the systematic classification of resonance properties. The authors investigate models containing $SU(2)_L \times SU(2)_R$ as part of the unbroken global subgroup, predicting the existence of two neutral and one charged spin-1 resonances that mix significantly with SM vector bosons.

Methodology
The study is based on a set of twelve minimal models (M1-M12) derived from three specific cosets: $SU(5)/SO(5)$, $SU(4)/Sp(4)$, and $SU(4)^2/SU(4)$. The authors focus primarily on the first two cosets, as they exhibit identical mixing patterns with SM vector bosons.

1. Model Setup: The spin-1 resonances emerge as bound states of new fermions. The spectrum includes vector ($V_\mu$) and axial-vector ($A_\mu$) states. The mixing between these resonances and SM vector bosons ($W^\pm, Z, \gamma$) is governed by the vacuum misalignment angle $\theta$, defined by $f_\pi \sin \theta = v_{SM}$. The mass eigenstates are obtained via orthogonal rotation matrices ($C$ for charged, $N$ for neutral sectors).
2. Parameters: The phenomenology is characterized by four key parameters: the vector mass parameter $M_V$, the axial-to-vector mass ratio $\xi = M_A/M_V$ (fixed to 1.4 based on lattice and holographic results), the coupling scale of vectors to two pNGBs ($g_{V\pi\pi}$), and the decay constant $f_\pi$ (fixed to 1 TeV). The strong coupling $\tilde{g}$ of the new sector is treated as a free parameter.
3. Scenarios: To explore the impact of unknown couplings, four exemplary scenarios are defined based on couplings to top quarks and pNGBs:
   • Top Couplings: "SM $t$" (SM-like couplings) and "PC $t$" (Partial Compositeness with enhanced top Yukawa couplings).
   • pNGB Couplings: "Weak $\pi$" ($g_{V\pi\pi} = 0$) and "Strong $\pi$" ($g_{V\pi\pi} = 4$).
   • Decay Modes: The study considers decays into SM fermions ($q\bar{q}, \ell^+\ell^-, t\bar{t}, t\bar{b}$), pNGBs ($\pi\pi$), and mixed channels ($HZ, WZ, WW, WH$). Cascade decays via intermediate pNGBs are analyzed under "fermiophilic" (decaying to third-generation quarks) and "fermiophobic" (decaying to gauge bosons via WZW terms) assumptions.
4. Simulation and Constraints:
   • Production: Single production of resonances ($V^0, V^\pm$) via Drell-Yan processes at $\sqrt{s} = 13$ TeV is simulated using MadGraph5_aMC@NLO with NNPDF 2.3 PDFs.
   • Event Generation: Events are showered and hadronized using Pythia8.
   • Analysis: Detector simulation is performed using Delphes 3. Signal regions are analyzed using MadAnalysis5 and CheckMATE.
   • Exclusion Limits: The authors recast existing ATLAS searches for $Z' \to \ell^+\ell^-$, $Z' \to t\bar{t}$, $W' \to \ell\nu$, and $W' \to t\bar{b}$ (using 139 fb$^{-1}$ data). Additionally, searches for final states with two bosons (pNGBs or SM vectors) are recast from literature [70–86]. Exclusion contours are derived at 95% CL using the $CL_s$ method.

Key Results

• Mass Degeneracy: For strong couplings ($\tilde{g} \gtrsim 4$), the charged resonance $V^+_1$ and the neutral resonances $V^0_1, V^0_2$ are nearly mass-degenerate.
• Decay Patterns:
  • In scenarios with strong pNGB couplings and large top couplings (PC $t$, strong $\pi$), resonances decay dominantly into additional pNGBs and $t\bar{t}$.
  • In scenarios with weak pNGB couplings, the $t\bar{t}$ channel dominates if top couplings are enhanced, while decays resemble SM $W/Z$ bosons (plus $t\bar{t}$) if all additional couplings are small.
  • The $W^\pm \to t\bar{b}$ channel provides significantly stronger constraints than neutral $Z' \to t\bar{t}$ due to higher production cross-sections.
• Exclusion Limits:
  • Weak Coupling Scenarios: Scenarios with weak couplings to both top quarks and pNGBs are strongly constrained, requiring $M_V > 3$ TeV – 4.5 TeV depending on $\tilde{g}$.
  • Strong Coupling Scenarios: In scenarios with sizeable couplings to pNGBs (particularly the fermiophilic case with SM-like top couplings), the constraints are significantly weaker.
  • Viability: The authors demonstrate that viable scenarios exist where the masses of these spin-1 resonances can be as low as 1.5 TeV, consistent with all existing LHC data. This lower mass bound is achievable specifically when the resonances have significant branching ratios into pNGBs, reducing the sensitivity of standard dilepton or dijet searches.
• Coset Differences: The bounds for the $SU(4)/Sp(4)$ coset are similar to $SU(5)/SO(5)$, differing mainly in the pNGB sector where fewer states exist.

Significance and Conclusion
The paper concludes that while direct searches for heavy resonances in dilepton and dijet channels impose strict limits on models with SM-like decay patterns, these limits are relaxed in models where spin-1 resonances decay significantly into pNGBs. Consequently, the parameter space for electroweak spin-1 resonances in composite Higgs models is not yet excluded down to masses of approximately 1.5 TeV. The authors note that future constraints or discoveries could arise from processes involving associated production (e.g., $gg \to b\bar{b}V^0$) or pair production at future circular colliders. The work emphasizes the necessity of considering cascade decays and specific coupling scenarios when interpreting LHC data in the context of composite Higgs models.