Connecting DUNE to UV models through an EFT pipeline

This paper proposes a pipeline to connect DUNE-motivated signals in the Standard Model Effective Field Theory (SMEFT) to specific ultraviolet completions with extra isosinglet and/or isodoublet fields, finding that current flavor constraints limit the viable Wilson coefficient for lepton-flavour-violating semileptonic interactions to approximately one order of magnitude below the DUNE benchmark.

The Gist

Imagine the universe as a giant, incredibly complex puzzle. Scientists have a picture of how most of the pieces fit together, called the "Standard Model." But they know there are missing pieces—tiny gaps where the picture doesn't quite make sense, especially regarding neutrinos (ghostly particles that barely interact with anything).

The DUNE experiment is like a new, super-powerful magnifying glass designed to look at these gaps. If DUNE finds a weird signal, it suggests there's a hidden piece of the puzzle we haven't seen yet.

This paper is essentially a "detective manual" for figuring out what that hidden piece might look like. Here is the story of the investigation, broken down simply:

1. The Clue: A Specific "Fingerprint"

The researchers focused on a specific type of weird signal DUNE might find. In the language of physics, this is a "Wilson coefficient" (let's call it C-target).

• The Analogy: Imagine DUNE finds a muddy footprint at a crime scene. The size and shape of the print (the C-target) tell us something about the shoe that made it. The researchers asked: "If DUNE finds this specific muddy footprint, what kind of 'shoe' (new physics model) could have made it?"

2. The Suspects: A Massive Lineup

The team created a pipeline (a step-by-step checklist) to test thousands of possible "suspects." These suspects are theoretical models involving new particles (like extra heavy scalars or fermions) that exist at very high energy levels.

• The Analogy: They didn't just look at one suspect; they lined up 338 different suspects (theoretical models) and asked, "Which one of you could have left this specific footprint?"

3. The Interrogation: The "Flavor" Test

Here is where it gets tricky. Just because a suspect could make the footprint doesn't mean they are innocent of other crimes. In physics, if you add a new particle to explain one thing, it often accidentally causes problems elsewhere (like breaking rules about how particles change "flavors," similar to how a suspect might have a history of other crimes).

• The Analogy: The researchers put the suspects through a strict background check. They asked: "If you made this footprint, did you also accidentally break other laws of physics that we already know are true?"
• They used a computer pipeline to simulate this. First, they did a quick scan to see who looked promising. Then, they ran a deep, rigorous "global fit" (a massive statistical test) to see if the suspect could survive the scrutiny of all known data.

4. The Verdict: The Footprint is Too Big

The results were a bit of a letdown for the "exotic" theories, but a very clear answer for the scientists:

• The Finding: Even the best suspect they found (Model 289) could only produce a footprint that was 10 times smaller than the one DUNE is hoping to see.
• The Metaphor: Imagine DUNE is looking for a giant boot print. The researchers tested every possible shoe design they could think of (from simple sneakers to complex boots). The best they could find was a tiny child's shoe. Even if they tweaked the shoe perfectly, it still couldn't make a print as big as the one DUNE is looking for.

5. The Conclusion

The paper concludes that if DUNE does find this specific giant signal, the usual suspects (standard new particles like extra scalars or fermions) cannot be the culprit.

• The Takeaway: If that giant footprint appears, we will need to look for something much more "exotic" and strange than the models currently considered. The "standard" new physics models are too weak to explain such a large signal without breaking other known rules of the universe.

In short: The authors built a machine to test if current theories of new physics could explain a potential future discovery by DUNE. They found that, for the specific signal they tested, current theories fall short. If the signal is real, the answer lies in something far stranger than we currently imagine.

Technical Summary

Technical Summary: Connecting DUNE to UV Models through an EFT Pipeline

Problem Statement
Future neutrino experiments, particularly the Deep Underground Neutrino Experiment (DUNE), are expected to probe signals of new physics (NP) via non-standard interactions (NSI) in neutrino production, propagation, and detection. These effects are conveniently parametrized within the Standard Model Effective Field Theory (SMEFT) framework using Wilson coefficients (WCs). While DUNE is projected to set competitive bounds on the semileptonic coefficient $C^{(1)}_{\ell q, 1311}$, current global fits provide constraints that are either weaker or comparable to DUNE's projected sensitivity.

The central problem addressed is whether a hypothetical anomaly reported by DUNE—specifically a non-vanishing value for $C^{(1)}_{\ell q, 1311}$—can be realized by "standard" Beyond the Standard Model (BSM) UV completions containing weakly coupled states (scalars and/or fermions) with masses above the electroweak scale. The study investigates if such UV models can generate the required coefficient magnitude while simultaneously satisfying existing flavor constraints and perturbativity limits.

Methodology
The authors propose a systematic three-stage pipeline to survey the space of UV models and identify viable candidates:

1. Model Generation and Dictionary Matching:

   • The study utilizes the tool SOLD to generate dictionaries connecting UV models to SMEFT Wilson coefficients at the one-loop level.
   • The initial scan considers 338 possible UV models. This set is restricted to models containing only isosinglets and/or isodoublets (common BSM representations), reducing the pool to 112 models.
   • A simplifying assumption is adopted: BSM states do not couple to the second lepton family ("muonphobic" couplings) to reduce the parameter space, as the target coefficient $C^{(1)}_{\ell q, 1311}$ does not involve the second generation.

2. Stage 1: Coarse Filtering and Seed Identification:

   • A Monte Carlo sampling ($\sim 10^6$ points) is performed on the parameter space of the 112 models.
   • Constraints are applied based on individual SMEFT bounds from smelli (specifically the $U(2)^5$ case at 1 TeV) and perturbativity ($|\theta_i| \leq 1$).
   • Solutions are ranked by the magnitude of the generated target coefficient ($C_{target}$). The top 10% of solutions are clustered, and numerical optimization is performed to find "seed" points that maximize $C_{target}$ while satisfying individual bounds.

3. Stage 2: Global Likelihood Optimization:

   • The 24 most promising models (those with $\Delta\chi^2 < 700$ relative to the SM in the flavio/wilson/smelli frameworks) undergo a rigorous global fit.
   • A constrained optimization is performed to maximize $C_{target}(\theta)$ subject to:
     • $\chi^2(\theta) \leq \chi^2_{SM} + \Delta\chi^2_{max}$ (where $\Delta\chi^2_{max} = 4$, representing a conservative 2$\sigma$ deviation for a one-parameter model).
     • Perturbativity bounds.
   • This stage determines the maximal viable value of the target coefficient for each model while ensuring consistency with the full set of flavor observables.

4. Stage 3: Detailed Scrutiny of the Best Candidate:

   • The best-performing model (Model 289) is analyzed in detail.
   • The authors investigate "minimal" realizations by setting specific couplings to zero to avoid dangerous baryon-violating operators (e.g., proton decay) and to understand the necessity of specific field contents (e.g., vector-like fermions vs. scalars).

Key Results

• Maximal Viable Coefficient: The most promising UV completion (Model 289) generates a maximal value of $C^{(1)}_{\ell q, 1311} \approx 1.32 \times 10^{-2} \, \text{TeV}^{-2}$ when optimizing for flavor constraints.
• Comparison to DUNE Sensitivity: This value is approximately one order of magnitude lower than the DUNE benchmark sensitivity of $9 \times 10^{-2} \, \text{TeV}^{-2}$ (corresponding to $\epsilon_{e\tau} < 0.012$).
• Model Viability: Within the class of UV completions considered (scalars and/or fermions up to isodoublets), no viable candidate was found capable of explaining an anomaly at the DUNE benchmark level.
• Role of Field Content:
  • The best candidate (Model 289) involves a scalar $S$ and vector-like fermions $F_a, F_b$.
  • Tree-level matching contributes $\sim 99\%$ of the target coefficient, suggesting the vector-like fermions play a secondary role in the magnitude but are necessary for the specific operator structure.
  • Minimal realizations with fewer free parameters (e.g., $k=2$ or $k=3$ non-null couplings) yield lower values ($7.66 \times 10^{-3}$ and $9.52 \times 10^{-3} \, \text{TeV}^{-2}$, respectively) compared to the full 13-parameter scan.
  • The inclusion of additional couplings (e.g., $\lambda^{\phi q}_{Fb}$) helps enlarge the allowed parameter space for the primary couplings, slightly increasing the achievable $C_{target}$.
• Constraints: The target coefficient is poorly constrained by current individual bounds, but global fits (specifically referencing [37]) impose a bound of $C^{(1)}_{\ell q, 1311} < 1.4 \times 10^{-2} \, \text{TeV}^{-2}$, which is close to the maximum value achievable by the best UV model found.

Significance and Claims
The paper claims to provide a general, automated pipeline for connecting potential future experimental anomalies (parametrized as SMEFT Wilson coefficients) to their underlying UV completions. The primary conclusion is modest but significant: if DUNE were to observe an anomaly corresponding to the current projected sensitivity for $C^{(1)}_{\ell q, 1311}$, it would not be explainable by standard BSM scenarios involving new scalars or fermions up to isodoublet representations.

The authors state that such a discovery would necessitate invoking more exotic UV completions beyond the scope of the models surveyed. The work serves as a "no-go" result for the specific class of models tested, setting the stage for future investigations into more complex representations if a genuine anomaly is observed. The pipeline itself is presented as a tool applicable to any BSM signal parametrized by SMEFT Wilson coefficients, not limited to DUNE or the specific coefficient analyzed.