Searches for $B^0\to K^+\pi^-\tau^+\tau^-$ and $B_s^0\to K^+K^-\tau^+\tau^-$ decays

Using 5.4 fb$^{-1}$ of LHCb collision data, the first searches for $B^0\to K^+\pi^-\tau^+\tau^-$ and $B_s^0\to K^+K^-\tau^+\tau^-$ decays were conducted, resulting in no observed signal and the establishment of new upper limits on their branching fractions, including a tenfold improvement on the previous best limit for $B^0\to K^*(892)^0\tau^+\tau^-$.

The Gist

Imagine the universe as a giant, high-speed racetrack where tiny particles called "B-mesons" zoom around. Usually, these particles decay (break apart) in very predictable ways, following the rulebook of physics known as the Standard Model. However, scientists have noticed that sometimes these particles seem to be breaking the rules, hinting that there might be a "ghost" or a "new player" in the game that we haven't seen yet.

This paper from the LHCb experiment at CERN is like a high-stakes detective story. The detectives are looking for a very specific, rare, and suspicious type of "breakup" involving a particle called a tau lepton (a heavy cousin of the electron).

Here is the breakdown of their investigation in simple terms:

1. The Mystery: Why Look for Tau Leptons?

In the past, scientists noticed that B-mesons sometimes decay into muons (another type of particle) in ways that don't quite match the rulebook. At the same time, other experiments showed that tau leptons behave differently than muons in certain decays. This suggests that "New Physics" (something beyond our current understanding) might be boosting the number of tau leptons produced in these decays.

The scientists wanted to see if they could catch a B-meson decaying into a pair of tau leptons ($\tau^+\tau^-$) along with a pair of other particles (either a kaon and a pion, or two kaons). If they found this happening more often than the Standard Model predicts, it would be a smoking gun for new physics.

2. The Investigation: How They Searched

The LHCb team acted like a massive sieve, sifting through 5.4 billion billion (5.4 fb⁻¹) proton-proton collisions.

• The Challenge: Tau leptons are tricky. They live for a split second and then turn into other things. You can't see them directly. To find them, the scientists looked for a specific "signature": the tau turning into a muon (which is easy to spot) plus some invisible particles (neutrinos) that fly away undetected.
• The Strategy: They looked at two specific "crime scenes":
  1. A B-meson turning into a Kaon, a Pion, and two Taus.
  2. A B-meson turning into two Kaons and two Taus.
• The Filter: Because there is so much "noise" (background events that look similar but aren't the real deal), the team used a super-smart computer algorithm (called a Boosted Decision Tree) to act as a bouncer. This bouncer checks the flight path, the speed, and the shape of the event to decide: "Is this the rare signal we are looking for, or just random noise?"

3. The Results: The "Ghost" Remains Elusive

After sifting through all that data, the detectives found no evidence of the suspicious decays. They didn't see the "ghost" of New Physics hiding in the tau leptons.

• The Verdict: Since they didn't find the signal, they set an "upper limit." Think of this like saying, "If the ghost is there, it's hiding so well that it can't be more than 1 in 10,000 of these events."
• The Improvement: For one specific type of decay (involving a resonance called $K^*$), this new limit is 10 times better (tighter) than the previous best record. It's like upgrading a blurry security camera to a high-definition one; even with the better camera, they still didn't see the intruder, but now they know for sure the intruder isn't lurking in that specific spot.

4. Why This Matters (Even Without Finding Anything)

In science, a "null result" (finding nothing) is still a huge victory.

• Ruling Out Suspects: By proving that these decays don't happen as often as some "New Physics" theories predicted, the scientists are effectively crossing those theories off the suspect list.
• Setting the Bar: They have set a new, stricter standard. Any future theory about how the universe works must now explain why these decays are this rare.

Summary Analogy

Imagine you are looking for a specific, rare type of golden coin in a massive pile of sand. You have a metal detector that is 10 times more sensitive than any previous one. You scan the entire pile. You don't find the golden coin.

Does that mean the coin doesn't exist? Not necessarily. But it does mean:

1. If the coin is there, it is incredibly rare (rarer than we thought).
2. Any story that claimed the coin was common is now proven wrong.
3. You have proven your metal detector works better than anyone else's.

This paper is the report saying, "We used our super-sensitive detector, we didn't find the golden tau-lepton coins, and we have now set a new, stricter limit on how many could possibly be hiding in the sand."

Technical Summary

Technical Summary: Searches for $B^0 \to K^+\pi^-\tau^+\tau^-$ and $B^0_s \to K^+K^-\tau^+\tau^-$ Decays

Problem and Motivation
Over the past decade, analyses of flavor-changing neutral current (FCNC) decays involving the quark-level transition $b \to s\mu^+\mu^-$ have revealed consistent discrepancies with Standard Model (SM) expectations. Concurrently, measurements of branching-fraction ratios in tree-level $b \to c\ell^-\nu_\ell$ decays, specifically $R(D^{(*)})$, have shown deviations from lepton flavor universality. Models of physics beyond the Standard Model (BSM) proposed to explain these anomalies often predict enhancements of several orders of magnitude in the branching fractions of FCNC $b \to s\tau^+\tau^-$ transitions. While SM predictions for decays such as $B^0 \to K^{*0}\tau^+\tau^-$ and $B^0_s \to \phi\tau^+\tau^-$ are of order $10^{-7}$, BSM scenarios consistent with current $R(D^{(*)})$ results could yield branching fractions of order $10^{-5}$. Previous searches for these modes have resulted in upper limits of order $10^{-3}$, leaving a significant gap for experimental exploration. This paper presents the first searches for $B^0 \to K^+\pi^-\tau^+\tau^-$ and $B^0_s \to K^+K^-\tau^+\tau^-$ decays at the LHCb experiment.

Methodology
The analysis utilizes $pp$ collision data corresponding to an integrated luminosity of $5.4 \text{ fb}^{-1}$ collected by the LHCb detector during 2016–2018. The tau leptons are reconstructed via the decay $\tau^+ \to \mu^+\nu_\mu\nu_\tau$. The analysis strategy employs a partial reconstruction technique where the $B^0_{(s)}$ decay vertex is determined from the intersection of the two charged hadron tracks ($K^+\pi^-$ or $K^+K^-$), while the tau decay vertex is inferred from the intersection of the two muon tracks.

Key methodological components include:

• Event Selection: Candidates are required to have a secondary vertex significantly displaced from the primary interaction vertex (PV). The tau flight direction is assumed to align with the $b$-hadron, requiring the muon vertex to be downstream of the hadron vertex.
• Background Suppression: Significant backgrounds from semileptonic cascade decays (e.g., $B^0_{(s)} \to D^-_s(\to h^+_1 h^-_2 \mu^- \nu_\mu)\mu^+ \nu_\mu$) are rejected by requiring the reconstructed $h^+_1 h^-_2 \mu^-$ mass to exceed the known $D^-_s$ mass. Decays involving $D^{(*)}D^{(*)}$ resonances are suppressed using missing-mass squared ($m^2_{\text{miss}}$) and reconstructed $q^2$ variables.
• Multivariate Analysis: A multiclass Boosted Decision Tree (BDT) classifier, implemented using the lightgbm package, discriminates between signal, combinatorial background, and semileptonic cascade background. The BDTs are trained separately for each final state and dihadron mass bin, utilizing features such as the reconstructed tau flight distance and track isolation.
• Signal Extraction: Due to the presence of four unreconstructed neutrinos, no suitable mass variable exists for a direct fit. Instead, signal yields are extracted from unbinned extended maximum-likelihood fits to the BDT classifier output distribution for candidates selected in the signal category. The shapes of fit components are modeled using Gaussian kernel density estimations (KDEs).
• Normalization: Branching fractions are calculated relative to the normalization modes $B^0 \to J/\psi(\to \mu^+\mu^-)K^{*0}(\to K^+\pi^-)$ and $B^0_s \to J/\psi(\to \mu^+\mu^-)\phi(\to K^+K^-)$, which share identical final states and large, well-established branching fractions.

Key Contributions and Results
The analysis is performed in bins of the dihadron invariant mass ($K^+\pi^-$ or $K^+K^-$) to account for resonant and non-resonant contributions. No significant signal is observed in any bin. Consequently, upper limits on the branching fractions are set using the $CL_s$ method.

• $B^0 \to K^+\pi^-\tau^+\tau^-$: The study establishes the first upper limits for this decay outside the $K^*(892)^0$ region. In the bin containing the $K^*(892)^0$ resonance ($792 < m_{K^+\pi^-} < 992 \text{ MeV}/c^2$), the result is recast as a limit on $B^0 \to K^{*0}\tau^+\tau^-$. The 95% confidence level (CL) upper limit is $2.8 \times 10^{-4}$, improving upon the current best limit (from Belle II) by an order of magnitude.
• $B^0_s \to K^+K^-\tau^+\tau^-$: This represents the first search for this decay mode. The 95% CL upper limit in the bin containing the $\phi(1020)$ resonance ($980 < m_{K^+K^-} < 1060 \text{ MeV}/c^2$) is $4.7 \times 10^{-4}$.
• BSM Constraints: Interpreting the results within a weak effective theory framework, limits are set on the shift $\Delta$ in the Wilson coefficients $C_9^{\tau\tau}$ and $C_{10}^{\tau\tau}$. The resulting constraints on $\Delta^2$ are tighter than previous constraints derived from $B^0 \to K^{*0}\mu^+\mu^-$ rescattering effects by more than a factor of three.

Significance
The paper reports the first experimental limits on $B^0 \to K^+\pi^-\tau^+\tau^-$ decays outside the $K^*(892)^0$ mass region and the first limits on $B^0_s \to K^+K^-\tau^+\tau^-$ decays. The improvement on the $B^0 \to K^{*0}\tau^+\tau^-$ limit by an order of magnitude significantly tightens constraints on BSM models that predict large enhancements in $b \to s\tau^+\tau^-$ transitions to explain $R(D^{(*)})$ anomalies. The authors state that these results augur a comprehensive program of $b \to s\tau^+\tau^-$ searches at LHCb, which will further challenge new-physics models with data from ongoing LHC runs.