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New Physics in $b \to s \tau^+\tau^-$ Processes and Correlations with $R(D^{()})$ and $B\to K^{()}\nu\bar\nu$ : An (SM)EFT Analysis

Motivated by anomalies in $R(D^{(*)})$ and $B\to K^{(*)}\nu\bar\nu$ , this paper presents an SMEFT analysis predicting that New Physics could enhance $b\to s\tau^+\tau^-$ branching ratios by several orders of magnitude, making them accessible to future LHCb, CMS, and Belle II experiments while providing a crucial method to distinguish between different New Physics scenarios.

Original authors: Guillermo Baltà, Andreas Crivellin, Joaquim Matias, Martín Novoa-Brunet

Published 2026-10-01

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CC BY 4.0

Original authors: Guillermo Baltà, Andreas Crivellin, Joaquim Matias, Martín Novoa-Brunet

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the Standard Model, the universe's fundamental building blocks are organized into three families, or generations. The first generation contains the particles that make up ordinary matter, like the electron and the up and down quarks found in protons and neutrons. The second and third generations are heavier, unstable copies of these first-generation particles. While the laws governing how these particles interact with forces are identical for all three generations, their masses are wildly different. This creates a puzzle: why does the third generation, which includes the heavy top quark and the tau lepton, behave so differently from the others? Physicists suspect that this heavy third generation might be a gateway to "New Physics," a set of rules beyond our current understanding that could explain why the universe is built the way it is. To find these clues, scientists look for rare events where a bottom quark transforms into a strange quark while emitting a pair of tau leptons. These events are so rare in our current understanding of physics that even a tiny deviation could signal a hidden force at work.

A team of researchers has now taken a fresh look at these rare transformations, connecting them to other long-standing mysteries in particle physics. For years, experiments have observed that B-mesons, particles containing a bottom quark, decay into tau leptons more often than the Standard Model predicts. This discrepancy, known as the $R(D^{(*)})$ anomaly, suggests that the third generation of particles is indeed special. At the same time, recent measurements of B-mesons decaying into a kaon and invisible neutrinos have also shown rates higher than expected. The researchers in this study asked a simple but profound question: if these anomalies are caused by new physics, what does that imply for the even rarer process where a B-meson decays into a kaon and a pair of tau leptons? They built a detailed theoretical framework to answer this, calculating exactly how much these rare decay rates should increase if the new physics responsible for the other anomalies is real.

The team performed a comprehensive analysis using a mathematical tool called the Standard Model Effective Field Theory, which allows physicists to describe potential new forces without needing to know the exact identity of the new particles. They focused on the specific scenario where new physics interacts with the heavy third generation of particles. Their calculations revealed that if the new physics explains the existing anomalies in tau decays, it would cause the rate of B-mesons decaying into tau pairs to skyrocket. Instead of the tiny, almost invisible rates predicted by the Standard Model, the new physics could boost these rates by several orders of magnitude. This means that a process that is currently too rare to be seen clearly could become bright enough to be detected by current and upcoming experiments. The researchers provided specific predictions for how often these decays should happen across the full range of possible energies, accounting for the complex interactions that occur inside the particles.

Crucially, the study showed that different theoretical scenarios can produce the same result for the neutrino decays, making it difficult to tell them apart based on that data alone. However, the researchers demonstrated that measuring the tau decays would act as a key to unlock this confusion. By comparing the rates of decays into tau pairs against the rates of decays into neutrinos, scientists could distinguish between different types of new physics. For instance, some scenarios involve new forces that interfere constructively with known forces, while others interfere destructively, canceling them out. These two very different physical mechanisms can look identical when observing neutrinos, but they produce distinct, measurable differences when observing tau leptons. This distinction is vital because it allows experimentalists to test specific theories rather than just knowing that "something" is wrong.

The researchers also addressed a practical challenge in observing these events: the presence of a heavy resonance, a short-lived particle called the $\psi(2S)$ , which can mimic the signal scientists are looking for. In previous studies, this resonance made it difficult to get a clear picture of the underlying physics. The team developed a method to include the effects of this resonance accurately across the entire energy range, providing reliable predictions for experiments at facilities like LHCb, CMS, and Belle II. Their work suggests that while current experiments have not yet seen these rare decays, the enhancements predicted by the new physics models are well within the reach of the next generation of data. If the anomalies in tau decays and neutrino decays are indeed signs of new physics, the upcoming data from these experiments should reveal a significant signal in the tau pair channels.

Ultimately, this work serves as a roadmap for the next phase of discovery. It tells experimentalists exactly what to look for and how to interpret the data if they find it. The study confirms that the third generation of particles holds the key to understanding the universe's deeper structure. If the predicted enhancements are observed, it would be a clear indication that the Standard Model is incomplete and that new, heavy particles or forces are influencing the behavior of matter at the most fundamental level. The paper concludes that the time is ripe for these searches, as the theoretical predictions are now precise enough to guide the search for new physics in the tau sector, turning a theoretical possibility into an experimental target.

Technical Summary: New Physics in $b \to s\tau^+\tau^-$ Processes and Correlations with $R(D^{(*)})$ and $B \to K^{(*)}\nu\bar{\nu}$

Problem Statement
The paper addresses the persistent anomalies in $R(D^{(*)})$ (ratios of $B \to D^{(*)}\tau\nu$ to $B \to D^{(*)}\ell\nu$ decays) and recent indications of enhanced $B \to K\nu\bar{\nu}$ rates. These observations suggest New Physics (NP) involving third-generation fermions, potentially violating Lepton Flavour Universality (LFU). While $b \to s\tau^+\tau^-$ transitions are theoretically sensitive probes of such NP, their experimental observation is complicated by long-distance hadronic resonances (specifically the $\psi(2S)$ ) and the difficulty of reconstructing the dilepton invariant mass ( $q^2$ ) in hadronic environments like LHCb and CMS. Furthermore, the relationship between charged-current anomalies ( $R(D^{(*)})$ ) and neutral-current processes ( $b \to s\tau^+\tau^-$ , $b \to s\nu\bar{\nu}$ ) within the Standard Model Effective Field Theory (SMEFT) requires a rigorous re-evaluation, particularly given the new $B \to K\nu\bar{\nu}$ data which suggests possible tree-level contributions to neutrino modes.

Methodology
The authors employ a two-pronged approach combining the Weak Effective Theory (WET) at the $B$ -meson scale and the SMEFT at the TeV scale:

WET Analysis and Hadronic Resonances:
- The authors revisit predictions for $B \to K^{(*)}\tau^+\tau^-$ and $B_s \to \phi\tau^+\tau^-$ over the full kinematically accessible $q^2$ range ( $4m_\tau^2$ to $q^2_{max}$ ).
- They incorporate the dominant $\psi(2S)$ resonance using a data-driven approach (previously established in Ref. [71]) and validate it against the narrow-width approximation.
- Semi-analytic expressions for the branching ratios are derived as functions of the Wilson coefficients $C_9^\tau, C_{10}^\tau$ and their chirally flipped counterparts $C_{9'}^\tau, C_{10'}^\tau$ . These expressions include SM-NP interference and pure NP terms.
SMEFT Analysis and Matching:
- The analysis assumes NP is realized at a scale $\Lambda \sim \text{few TeV}$ , described by dimension-6 operators respecting $SU(2)_L$ gauge invariance.
- The study focuses on four-fermion operators involving left-handed currents ( $O_{\ell q}^{(1)}, O_{\ell q}^{(3)}$ ) and right-handed quark currents ( $O_{\ell d}$ ).
- The authors match SMEFT operators to WET coefficients, explicitly accounting for:
  - Loop effects: The off-shell photon penguin (mixing $O_9^\tau$ into $O_9^U$ for light leptons) and the $W$ -vertex correction (linking $b \to s\tau\tau$ to $b \to s\nu\bar{\nu}$ ).
  - Flavor Structures: Four distinct scenarios are analyzed regarding the hierarchy of Wilson coefficients ( $C_{23}$ vs. $C_{33}$ ) and the presence of right-handed currents.

Key Contributions

Updated Branching Ratio Predictions: The paper provides the first comprehensive predictions for $B_s \to \phi\tau^+\tau^-$ and updated $B \to K^{(*)}\tau^+\tau^-$ branching ratios over the full $q^2$ range, including the $\psi(2S)$ resonance, specifically tailored for experimental conditions at LHCb and CMS where $q^2$ cuts are difficult.
Semi-Analytic Formulas: New semi-analytic formulas (Eq. 2.4) are provided for the branching ratios as a function of Wilson coefficients, facilitating direct comparison with future experimental limits.
Multi-Scenario SMEFT Correlations: The authors systematically explore the correlations between $R(D^{(*)})$ $R (D^{(*)})$ , $B \to K^{(*)}\nu\bar{\nu}$ $B \to K^{(*)} ν \overset{ν}{ˉ}$ , and $b \to s\tau^+\tau^-$ $b \to s τ^{+} τ^{-}$ under four different SMEFT scenarios:
1. $C_{23}^{(1)} = C_{23}^{(3)}$ (no tree-level $b \to s\nu\bar{\nu}$ ).
2. $C_{23}^{(1)} \neq C_{23}^{(3)}$ (tree-level $b \to s\nu\bar{\nu}$ , left-handed currents only).
3. $C_{23}^{(1)} \neq C_{23}^{(3)}$ with $C_{23}^{\ell d} \neq 0$ (including right-handed quark currents).
4. Hierarchical structure where $|C_{33}^{(3)}| \gg |C_{23}^{(3)}|$ .
Disentanglement of Solutions: The analysis reveals that different NP scenarios (constructive vs. destructive interference with the SM in $b \to s\nu\bar{\nu}$ ) can yield identical predictions for $B \to K^{(*)}\nu\bar{\nu}$ branching ratios. The authors demonstrate that measuring $B \to K^{(*)}\tau^+\tau^-$ and $B_s \to \tau^+\tau^-$ is crucial to disentangle these "overcompensation" solutions from standard constructive interference scenarios.

Results

Enhancement Potential: In regions of parameter space preferred by current $R(D^{(*)})$ data, the branching ratios for $b \to s\tau^+\tau^-$ processes can be enhanced by several orders of magnitude (up to $\sim 10^{-5}$ ), significantly exceeding Standard Model predictions ( $\sim 10^{-6}$ to $10^{-7}$ ).
Impact of $B \to K\nu\bar{\nu}$ : The recent observation of an enhanced $B \to K\nu\bar{\nu}$ rate implies that tree-level contributions to neutrino modes may be non-zero. This relaxes the constraint $C_{23}^{(1)} = C_{23}^{(3)}$ , allowing for multiple solutions in the Wilson coefficient space.
Multiple Solutions: In scenarios with $C_{23}^{(1)} \neq C_{23}^{(3)}$ $C_{23}^{(1)} \neq = C_{23}^{(3)}$ , the authors identify up to four distinct solutions for the Wilson coefficients that satisfy current $R(D^{(*)})$ $R (D^{(*)})$ and $B \to K^{(*)}\nu\bar{\nu}$ $B \to K^{(*)} ν \overset{ν}{ˉ}$ constraints. These solutions differ significantly in their predictions for $b \to s\tau^+\tau^-$ $b \to s τ^{+} τ^{-}$ rates.
- Destructive Interference: Solutions where NP destructively interferes with the SM in $B \to K^{(*)}\nu\bar{\nu}$ (overcompensating the SM contribution) lead to the largest enhancements in $b \to s\tau^+\tau^-$ rates.
- Constructive Interference: Solutions with constructive interference yield smaller, though still significant, enhancements.
LHC Constraints: The analysis incorporates constraints from LHC mono-tau searches, which exclude certain regions of the parameter space, particularly those requiring very large couplings.
Hierarchical Scenarios: The scenario where $|C_{33}^{(3)}| \gg |C_{23}^{(3)}|$ is found to be more constrained by LHC data and insufficient to fully explain the central value of $R(D^{(*)})$ without additional contributions.

Significance
The paper claims that $b \to s\tau^+\tau^-$ decays serve as a highly sensitive probe for New Physics connected to the third generation. The authors emphasize that while current experimental limits are still above SM rates, the enhancements suggested by $R(D^{(*)})$ and $B \to K\nu\bar{\nu}$ data imply that forthcoming limits from LHCb, CMS, and Belle II will probe significant regions of the SMEFT parameter space. Crucially, the paper argues that measuring $b \to s\tau^+\tau^-$ is not merely a test of NP existence but a necessary tool to distinguish between different underlying theoretical mechanisms (specifically, different interference patterns in the neutrino sector) that would otherwise appear degenerate in $B \to K^{(*)}\nu\bar{\nu}$ measurements alone. The provided semi-analytic formulas and full $q^2$ predictions are intended to facilitate direct confrontation with experimental data in the high-luminosity era.

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