Status of G2HDM with right handed neutrino coupling in the light of $b\to c τν$ anomalies

This paper demonstrates that the High Luminosity LHC has sufficient sensitivity to exclude the remaining allowed parameter space of a generic Two Higgs Doublet Model with right-handed neutrino couplings, which was proposed to explain the observed $b \to c \tau \nu$ anomalies via a charged Higgs boson.

The Gist

Imagine the Standard Model of particle physics as a massive, incredibly detailed instruction manual for how the universe works. For decades, this manual has explained almost everything we see in particle experiments. But recently, scientists have noticed a few pages that seem to have typos or missing instructions. These "typos" are called anomalies.

This paper is like a team of detectives trying to solve a mystery: Why are certain heavy particles (B mesons) decaying into tau particles and neutrinos more often than the manual predicts?

Here is a breakdown of their investigation using simple analogies:

1. The Mystery: The "Leaky" Recipe

In the world of particle physics, particles decay (break apart) in specific ways. The "recipe" in the Standard Model says that when a specific heavy particle (a B meson) breaks down, it should produce a tau particle (a heavy cousin of the electron) and a neutrino a certain number of times.

However, experiments at the LHCb and other labs have found that this happens more often than the recipe predicts. It's like baking a cake and finding that, statistically, you are getting 30% more chocolate chips than the recipe says you should. This suggests there is a "secret ingredient" missing from the manual.

2. The Suspect: A New Particle and a New Neighbor

The authors propose a new theory to fix the recipe. They suggest adding a Charged Higgs boson (a new type of particle) to the mix.

But here is the twist: In previous theories, this new particle was thought to interact with "left-handed" neutrinos (like a left-handed glove). This paper asks: What if it interacts with "right-handed" neutrinos instead?

Think of neutrinos as people wearing either left-handed or right-handed gloves. The Standard Model only knows about the left-handed ones. The authors are testing a scenario where the new Charged Higgs particle is a "right-handed glove" specialist. They want to see if this specific combination can explain the extra chocolate chips (the anomalies) without breaking the rest of the cake.

3. The Investigation: Fitting the Puzzle Pieces

First, the team did a mathematical "fit." They took all the experimental data (the extra chocolate chips) and tried to find the perfect size and shape for their new "right-handed" theory.

• The Result: They found a specific setting for their theory that fits the current data very well. It explains the anomalies without contradicting other known rules of physics.

4. The Trap: Catching the Suspect at the LHC

Knowing the theory fits the data is only half the battle. Now they need to prove the "Charged Higgs" particle actually exists. They looked at the High-Luminosity Large Hadron Collider (HL-LHC), which is like a super-powered particle microscope that will run in the future.

They simulated two ways to catch this particle:

• Scenario A (The "No-Tag" Search): Looking for the Charged Higgs decaying into a tau and a neutrino, but ignoring any other heavy particles nearby. This is like looking for a specific car in a parking lot without checking its license plate. They found this is hard because the background noise (other cars) is very loud.
• Scenario B (The "B-Tag" Search): Looking for the Charged Higgs produced alongside a bottom quark (a "b-tag"). This is like looking for a specific car that is always parked next to a specific type of truck. Because the truck is rare, it's much easier to spot the car.

The Finding: The "B-Tag" search (Scenario B) is much more powerful. It can filter out the noise much better. The authors calculated that with the future HL-LHC data, this method is sensitive enough to either find this new particle or rule it out completely if it doesn't exist in the mass range they tested.

5. The Verdict: The Map of Possibility

The authors drew a map (a graph) showing where this new particle could hide based on its strength of interaction (Yukawa couplings).

• The Good News: Their theory fits the current "typos" in the data.
• The Bad News (for the theory): The future HL-LHC is so sensitive that it will likely be able to exclude (rule out) the remaining safe zones where this particle could hide.

Summary

In short, this paper says:

1. There are weird glitches in how heavy particles decay.
2. A theory involving a Charged Higgs and Right-Handed Neutrinos could fix these glitches.
3. However, the future HL-LHC is powerful enough to check this theory thoroughly.
4. If the HL-LHC runs its experiments and doesn't find this particle, this specific "Right-Handed" theory will likely be proven wrong, forcing scientists to look for a different explanation for the glitches.

The paper concludes that while the theory is a good fit for today's data, the next generation of experiments will likely have the final say, potentially closing the book on this specific idea.

Technical Summary

Technical Summary: Status of G2HDM with Right-Handed Neutrino Coupling in the Light of $b \to c\tau\nu$ Anomalies

Problem Statement
Recent experimental measurements in semileptonic $B$ meson decays have revealed significant deviations from Standard Model (SM) predictions. Specifically, the LHCb collaboration and others have reported tensions exceeding $3\sigma$ in the ratios $R(D)$ and $R(D^*)$, alongside deviations in other observables such as $R_{J/\psi}$, $P_{D^*}^\tau$, $F_L^{D^*}$, and $R_{\Lambda_c}$. While previous studies have explored explanations using charged Higgs bosons ($H^\pm$) within Type-III Two Higgs Doublet Models (2HDM) coupled to left-handed neutrinos, this paper investigates the viability of a Generic Two Higgs Doublet Model (G2HDM) where the charged Higgs couples to right-handed neutrinos. The authors aim to determine if this specific New Physics (NP) scenario can consistently explain the observed flavor anomalies while satisfying current constraints, and to assess the discovery potential of the High Luminosity Large Hadron Collider (HL-LHC) in this context.

Methodology
The study employs a multi-stage approach combining phenomenological fitting, effective field theory, and collider simulation:

1. Model-Independent Fit: The authors first perform a $\chi^2$ fit using an effective Lagrangian for the $b \to c\ell\nu$ transition. They incorporate scalar Wilson coefficients ($C_{RR}^S$ and $C_{LR}^S$) corresponding to right-handed neutrino couplings. The fit utilizes six experimental observables: $R(D)$, $R(D^*)$, $P_{D^*}^\tau$, $F_L^{D^*}$, $R_{J/\psi}$, and $R_{\Lambda_c}$, while accounting for the correlation between $R(D)$ and $R(D^*)$ and the constraint on the branching fraction $B(B_c \to \tau\nu) \leq 63\%$.
2. Theoretical Framework (G2HDM): The analysis is embedded within a G2HDM framework. The charged Higgs interaction is parameterized by Yukawa couplings $\tilde{y}_{bc}$ (up-type) and $\tilde{y}_{\tau\nu}$ (lepton). The scalar coupling $C_{RR}^S$ is derived from these Yukawa couplings and the charged Higgs mass ($m_{H^\pm}$), with Renormalization Group Equation (RGE) running applied from the $m_{H^\pm}$ scale to the bottom quark mass scale ($m_b$).
3. Collider Analysis: The authors simulate the production of charged Higgs bosons at the HL-LHC ($\sqrt{s} = 14$ TeV, $\mathcal{L} = 3 \text{ ab}^{-1}$) using two distinct channels:
   • $\tau_h\nu$ channel (b-veto): $pp \to H^\pm \to \tau\nu$.
   • $b\tau_h\nu$ channel (b-tag): $pp \to bH^\pm \to b\tau\nu$.
     Simulations are performed using MadGraph5_aMC@NLO for signal and background generation, Pythia8 for showering/hadronization, and Delphes for detector simulation. Backgrounds include $W$+jets, Drell-Yan, top-pair ($t\bar{t}$), and single-top processes.
4. Optimization: A cut-based analysis is performed. Kinematic observables such as transverse momentum ($p_T$), transverse mass ($m_T$), missing transverse energy ($E_T^{miss}$), and azimuthal angle separation ($\Delta\phi$) are optimized to maximize signal significance ($S/\sqrt{B}$).

Key Contributions and Results

• Best-Fit Coupling: The model-independent fit yields a best-fit value for the ratio of scalar couplings $C_{RR}^S / C_{LR}^S = -0.48 \pm 0.08$. This solution successfully accommodates the experimental central values of the flavor observables within the $1\sigma$ to $2\sigma$ range and satisfies the $B(B_c \to \tau\nu)$ constraint.
• Yukawa Coupling Constraints: In the G2HDM context, the product of Yukawa couplings $|\tilde{y}_{bc}| \times |\tilde{y}_{\tau\nu}|$ is constrained by flavor data, $B_c$ decay limits, and $B_s-\bar{B}_s$ mixing. The analysis shows that the allowed parameter space is significantly reduced for lower charged Higgs masses due to $B_s-\bar{B}_s$ mixing constraints.
• Collider Sensitivity:
  • The $b$-tag channel ($pp \to bH^\pm \to b\tau\nu$) proves more effective than the $b$-veto channel. The requirement of a $b$-tagged jet significantly suppresses the dominant $W$+jets background, leading to a higher signal-to-background ratio and more stringent upper limits on the production cross-section.
  • The study derives projected 95% Confidence Level (CL) upper limits on the production cross-section for charged Higgs masses ranging from 180 to 400 GeV.
• Exclusion Potential: By mapping the collider exclusion limits onto the $|\tilde{y}_{bc}| - |\tilde{y}_{\tau\nu}|$ parameter plane, the authors demonstrate that the HL-LHC has the sensitivity to exclude the remaining allowed regions of the G2HDM model that explain the flavor anomalies. Specifically, the $b$-tag analysis can probe the parameter space for higher charged Higgs masses where the $b$-veto channel is less sensitive.

Significance and Claims
The paper claims that the G2HDM with right-handed neutrino couplings provides a consistent explanation for the $b \to c\tau\nu$ anomalies, with the best-fit parameters lying within the $2\sigma$ experimental contours. However, the primary significance of the work lies in its demonstration of the HL-LHC's capability to test this specific New Physics scenario.

The authors conclude that while current flavor data allows for a viable region in the model's parameter space, the HL-LHC has the potential to exclude these remaining allowed regions. The study emphasizes that the $b$-tagged channel is crucial for this exclusion, offering superior sensitivity compared to the inclusive $\tau\nu$ channel due to better background suppression. The work does not claim to have discovered new physics but rather defines the specific experimental reach required to either confirm or rule out the charged Higgs with right-handed neutrino couplings as the solution to the current flavor anomalies.