Hunting the Light Charged Higgs: Muon Colliders Lead the Way

Hey there, fellow universe enthusiasts! So, you know how we found that awesome Higgs boson thing at the LHC? It felt like we’d finally completed the puzzle, right? But honestly, that was just the beginning. There are still tons of head-scratchers out there – why is gravity so weak? What’s dark matter? Why do particles have the masses they do?

This is where the hunt for physics beyond the Standard Model (BSM) comes in, and high-energy colliders are our absolute best tools for this. They let us peek at the fundamental building blocks of everything in a really controlled way. And one of the coolest possibilities for BSM physics is the idea of a light charged Higgs boson, basically a cousin of the Higgs we found, but with an electric charge and a mass *below* the top quark mass.

Current theories, like the Type-I two-Higgs-doublet model (2HDM), still totally allow for this light charged Higgs. While folks have looked for it decaying in other ways, like into a tau lepton and a neutrino ((H^pm rightarrow tau ^pm nu)), there’s another decay channel that’s been a bit overlooked: decaying into an off-shell top quark and a bottom quark ((H^pm rightarrow t^*b)). This mode is actually super important, even leading or subleading, for charged Higgs masses between 130 and 170 GeV.

Why Look at (H^pm rightarrow t^*b)?

In certain BSM models, like the Type-I 2HDM, the way the charged Higgs interacts with other particles means its decay preference is mostly decided by the masses of the particles it can decay into. If it’s heavy enough, it really wants to decay into the heaviest stuff possible. For a light charged Higgs in the 130-170 GeV range, decaying into an off-shell top quark and a bottom quark ((H^pm rightarrow t^*b)) turns out to be a really significant, sometimes even dominant, decay mode. This makes it a prime target for discovery!

Previous studies on this specific decay were pretty limited, often just looking at branching ratios or only considering older colliders. We really needed a deep dive into whether future colliders could actually *find* this signal. And that’s exactly what we set out to do.

How Do We Spot It? Pair Production is Key!

To search for this light charged Higgs, we need to produce it first. We decided to focus on producing them in pairs ((H^+H^-)). Why? Because this process is nice and clean; its rate depends mostly just on the mass of the charged Higgs itself, not on other potentially uncertain parameters of the BSM model like (tan beta). Other ways to produce the charged Higgs, like through top quark decay ((t rightarrow b H^+)), become really inefficient if (tan beta) is large, which current data actually suggests is likely.

So, we looked at the scenario where a pair of charged Higgs bosons is produced, and one decays via (H^pm rightarrow t^*b) and the other via (H^pm rightarrow tau nu). The off-shell top quark then quickly decays into a bottom quark and two light quarks (which show up as jets). The tau lepton also often decays into hadrons and a neutrino. Putting it all together, the signal we’re hunting for looks like this:

• Charged Higgs pair production: (H^+H^-)
• Decay chain: (H^+H^-rightarrow t^*btau nu)
• Final state particles we look for: Two bottom jets, two light quark jets, one hadronic tau lepton, and missing energy from neutrinos. In detector language: (bbjjtau nu).

This specific final state is promising because it combines the interesting (t^*b) decay with the well-studied (tau nu) decay, giving us a distinct signature to look for.

The Challenge at Hadron Colliders (LHC e 100 TeV pp)

Our first thought was, naturally, to see if the current and planned future proton-proton colliders could find this signal. We looked at the High-Luminosity LHC (HL-LHC) and a hypothetical future 100 TeV proton-proton collider. We did detailed simulations, trying out different strategies:

• Cut-flow analysis: Applying a series of filters (cuts) on the data based on kinematic properties like particle energies, angles, and missing energy.
• Boosted Decision Trees (BDT): Using machine learning to try and distinguish signal events from the overwhelming background noise.

We focused on the (bbjjtau nu) final state and the main background, which comes from standard top quark pair production ((tbar{t})). We calculated cross sections, simulated how the particles would look in a detector, and applied our analysis techniques.

The results, honestly, were a bit disappointing. Even with sophisticated methods, the signal significance at both the HL-LHC and the 100 TeV proton-proton collider remained well below the level needed for a discovery. Why?

The main culprit turned out to be the bottom jets coming from the (H^pm rightarrow t^*b) decay. Because the charged Higgs mass is close to the top quark mass, the particles produced in this decay don’t get a huge energy kick. The bottom jets are often too “soft” – they have low transverse momentum ((p_T)). Our detectors have thresholds for identifying jets, and a large fraction of these crucial b-jets just didn’t make the cut. It’s like trying to spot faint stars in a brightly lit city.

Even at the 100 TeV collider, where you’d expect particles to be more energetic, the way protons collide means only a fraction of that energy is available for producing heavy particles like the charged Higgs pair. The b-jets from this decay still weren’t boosted enough to be reliably detected above the background.

Enter the Muon Collider: Our Golden Ticket?

Since hadron colliders struggled, we turned our attention to a different kind of future machine: a multi-TeV Muon Collider (MuC). These are exciting prospects because, unlike protons (which are bags of quarks and gluons), muons are fundamental particles. When you collide muons and anti-muons, the *entire* beam energy is available for the collision, giving a much bigger punch and potentially boosting the decay products of new heavy particles.

We looked at two possible scenarios for a MuC:

• A 3 TeV MuC with 1 ab(^{-1}) of integrated luminosity.
• A 10 TeV MuC with 10 ab(^{-1}) of integrated luminosity.

At a MuC, charged Higgs pairs can be produced in a few ways:

• Directly, like in the Drell–Yan process ((mu^+mu^- rightarrow H^+H^-)).
• With extra neutrinos ((mu^+mu^- rightarrow H^+H^-nubar{nu})).
• With muons that go forward along the beam pipe ((mu^+mu^- rightarrow H^+H^-mu_f^+mu_f^-)).

We found that while the processes with extra particles depend a bit on the specific 2HDM parameters, the direct Drell–Yan production is very robust and depends only on the charged Higgs mass. At 3 TeV, the Drell–Yan process is the dominant production mode, which is great for a model-independent search.

Finding the Signal at the MuC

We performed a detailed signal-to-background analysis for the (bbjjtau nu) final state at the MuC, focusing on the main background from Standard Model (W^+W^-bbar{b}) production. We used a detector simulation tailored for a MuC and employed jet clustering algorithms that work well in this environment.

Crucially, at the MuC, the particles from the charged Higgs decay are much more energetic and boosted. This means the b-jets are much easier to detect! We identified several key variables that help separate the signal from the background:

• Angular separation ((Delta R)): The b-jets from the signal tend to be very close together, originating from the same charged Higgs. The jets in the background are typically further apart. Cuts on (Delta R(b_1, b_2)) and (Delta R(j_i, b_{i’})) were very effective.
• Missing Transverse Energy ((E_T^textrm{miss})): The neutrino from the signal’s (tau nu) decay carries away a lot of energy, resulting in significantly higher (E_T^textrm{miss}) compared to the background. A strong cut on (E_T^textrm{miss}) was a powerful discriminator.
• Invariant Mass ((M(j_1 j_2 b_1 b_2))): The mass of the system formed by the two light jets and two b-jets should cluster around the charged Higgs mass for signal events, providing a resonant peak.

By applying a series of cuts based on these variables, we achieved fantastic results! At the 3 TeV MuC with 1 ab(^{-1}) of luminosity, we found that the signal significance easily surpassed the 5(sigma) threshold required for a discovery. For charged Higgs masses of 130, 150, and 170 GeV, the significances were 13.7, 13.5, and 6.06, respectively. That’s well into discovery territory!

Interestingly, while the 10 TeV MuC also showed good significance (14.8, 14.4, and 6.26 for the same masses), it required a much higher integrated luminosity (10 ab(^{-1})) to get there. This suggests the 3 TeV MuC is particularly efficient for this specific search.

We also briefly considered the potential of CLIC, another future electron-positron collider. With its planned 3 TeV energy and ability to detect particles over a wider range than a MuC (which has limitations due to beam backgrounds), it would likely also have excellent sensitivity to this decay mode. A dedicated study there would be really valuable.

The Bottom Line

So, here’s the scoop: searching for the light charged Higgs boson decaying into an off-shell top quark and a bottom quark ((H^pm rightarrow t^*b)) is a really important way to look for new physics beyond the Standard Model. While current and near-future hadron colliders like the HL-LHC and a 100 TeV proton-proton machine face tough challenges, mainly because the resulting b-jets aren’t energetic enough, the picture changes dramatically at a multi-TeV Muon Collider.

Our analysis shows that a 3 TeV MuC, even with a relatively modest amount of data (1 ab(^{-1})), offers incredible potential for discovering this signal, easily clearing the discovery bar across the relevant mass range. This highlights just how crucial a Muon Collider could be for unlocking the next big secrets of particle physics.

Source: Springer