⚛️ phenomenology

Rare Exclusive Top Decays t , b M and Vector-Meson Helicity

This paper presents a leading-order Standard Model study of rare exclusive top-quark decays into bottom quarks and mesons, deriving compact expressions for branching ratios and helicity amplitudes to establish a baseline for testing anomalous chiral couplings.

Original authors: M. Ahmadi, M. Monemzadeh, N. Tazimi

Published 2026-08-27

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CC0 1.0

Original authors: M. Ahmadi, M. Monemzadeh, N. Tazimi

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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

The universe is built from a small set of fundamental particles, but among them, one stands out for its sheer weight and fleeting existence: the top quark. It is the heaviest known particle, so massive that it behaves differently from all other matter. While other particles often bind together to form stable structures like protons or neutrons, the top quark is so heavy and unstable that it decays almost instantly after it is created. It does not have time to form a bound state; instead, it transforms directly into other particles. In the standard model of physics, which serves as our best map of the subatomic world, the top quark almost always chooses a single path for this transformation, breaking apart into a bottom quark and a W boson. This dominant behavior is so consistent that it acts as a reliable baseline for physicists. However, nature is rarely limited to just one path. Just as a river might have a main channel but also tiny, hidden tributaries, the top quark might occasionally take a much rarer route, decaying into a bottom quark and a different, more complex particle.

A team of researchers at the University of Kashan has taken a close look at these rare, hidden tributaries. They focused on a specific type of decay where the top quark transforms into a bottom quark and a single, short-lived particle called a meson. Mesons are not fundamental particles like the top quark; they are composite objects made of two smaller particles stuck together. The researchers calculated the likelihood of the top quark choosing to create a meson instead of the usual W boson. They examined two main types of mesons: those that spin in a specific way called vector mesons, and those that do not, known as pseudoscalar mesons. By using a mathematical approach that separates the immediate, high-energy event from the slower process of the new particle forming, they derived precise predictions for how often these rare events should happen. Their work provides a clear, updated standard for what we expect to see if the laws of physics are exactly as we currently understand them.

The researchers found that these rare decays are incredibly unlikely, but not impossible. For the most common versions of this process, involving lighter mesons like the pion or the kaon, the chance of it happening is roughly one in ten million to one in a hundred million. When the top quark creates a heavier meson, such as one containing a charm quark, the probability shifts slightly but remains in that same tiny range. The team calculated these numbers by combining known properties of the particles, such as their masses and how strongly they interact with the weak force, with the specific rules governing how the top quark decays. They confirmed that the most frequent rare decays involve the creation of a bottom quark paired with a meson made of an up and an anti-down quark (the pion) or a charm and an anti-strange quark (the Ds meson). These specific combinations are favored by the underlying rules of particle mixing, making them the most likely candidates for future observation.

A key part of their study involved understanding the orientation, or spin, of the mesons created in these decays. When a top quark decays into a vector meson, that meson can spin in different directions relative to its motion. The researchers calculated how often the meson would be found in each of these spinning states. They discovered that in the standard model, the physics strongly favors one specific orientation over the others. In fact, for the heaviest mesons, the rules of the weak force make it almost impossible for the meson to spin in a "right-handed" direction, effectively ruling out that possibility in a perfect scenario. This prediction is crucial because it gives experimentalists a specific signature to look for. If future experiments at high-energy colliders detect these rare decays, they can check the spin of the resulting meson. If the spin matches the team's prediction, it confirms our current understanding of the top quark. If the spin is different, or if the decay happens more often than predicted, it could signal the presence of new, unknown forces or particles interacting with the top quark.

The study also serves as a vital reference point for the next generation of particle physics experiments. As machines like the High-Luminosity Large Hadron Collider come online, they will produce millions of top quarks, offering a chance to spot these incredibly rare events. The researchers' calculations provide a clean, theoretical baseline against which real data can be compared. They have shown that while the standard model predicts these decays to be rare, they are calculable and distinct. By establishing these numbers now, they allow physicists to distinguish between normal background noise and potential signs of new physics. The work does not claim to have discovered these decays, nor does it suggest they have been seen yet. Instead, it offers a precise map of where to look and what to expect, turning a theoretical possibility into a concrete target for future discovery. If these rare events are observed exactly as predicted, it reinforces the standard model; if they deviate, it opens a door to understanding the deeper layers of the universe.

Technical Summary: Rare Exclusive Top Decays $t \to bM$ and Vector-Meson Helicity

Problem Statement
The top quark, as the heaviest particle in the Standard Model (SM), decays before hadronizing, with its dominant mode being the charged-current transition $t \to bW$ . While inclusive observables for this decay are well-studied, rare exclusive hadronic decays of the form $t \to bM$ (where $M$ is a pseudoscalar or vector meson formed via the hadronization of an off-shell $W^*$ boson) offer a complementary, theoretically clean benchmark. These processes are predicted to be highly suppressed in the SM (branching ratios $\sim 10^{-8} - 10^{-7}$ ) but serve as sensitive probes for non-standard charged-current interactions and effective field theory (EFT) interpretations. A precise, updated SM baseline for these exclusive modes, including polarization observables for vector mesons, is required for future high-statistics studies at the High-Luminosity LHC (HL-LHC) and future colliders.

Methodology
The authors perform a leading-order (LO) theoretical study of the exclusive decays $t \to bM$ . The analysis proceeds through the following steps:

Factorization Approximation: Starting from the tree-level transition $t \to bW^* \to b(q\bar{q}')$ , the authors employ a factorization approximation. This separates the short-distance weak interaction (described by quark spinors and the charged-current vertex) from the long-distance QCD dynamics responsible for meson formation. The latter is encoded entirely in the meson decay constants ( $f_M$ ).
Amplitude Derivation:
- The virtual $W$ propagator is expanded in powers of $q^2/m_W^2$ (where $q^2 = m_M^2$ ), retaining only the leading term to derive an effective four-fermion interaction.
- Compact expressions for the decay amplitudes are derived for both pseudoscalar ( $P$ ) and vector ( $V$ ) mesons.
- For vector mesons, the full polarization sum is included to facilitate a helicity decomposition.
Kinematic Treatment: The analysis retains the exact dependence on meson masses through the two-body phase space (Källén function), avoiding approximations that might obscure mass effects for heavier mesons like $D_s$ and $B_c$ .
Numerical Implementation: Using up-to-date input parameters (top and bottom quark masses, CKM matrix elements, and meson decay constants from PDG and lattice/QCD sum rules), the authors calculate partial widths and branching ratios.
Helicity Analysis: For vector final states, the authors derive helicity amplitudes ( $\lambda = 0, \pm$ ) and polarization fractions. They specifically analyze the limit $m_b \to 0$ to demonstrate the suppression of the right-handed transverse amplitude due to the purely left-chiral nature of the SM weak current, and then extend the calculation to finite $m_b$ to quantify helicity-suppressed contributions.

Key Contributions and Results

Updated SM Predictions: The paper provides numerical predictions for branching ratios of representative channels, including $t \to b\pi^+$ $t \to b π^{+}$ , $t \to bK^+$ $t \to b K^{+}$ , $t \to bD_s^{(*)}$ $t \to b D_{s}^{(*)}$ , and $t \to bB_c^{(*)}$ $t \to b B_{c}^{(*)}$ . The predicted branching ratios generally fall in the range of $10^{-8}$ $1 0^{- 8}$ to $10^{-7}$ $1 0^{- 7}$ .
- For $t \to b\pi^+$ , the result is $Br \approx 1.605 \times 10^{-7}$ , which aligns with updated literature (Ref. [12]) and corrects previous discrepancies regarding normalization.
- Results for $t \to bK^+$ , $t \to bD_s$ , and vector modes ( $\rho^+, K^*, D_s^*$ ) show good agreement with recent comprehensive studies, with relative deviations typically under 10%, attributed to differences in input parameters and treatment of heavier meson masses.
Helicity Fractions and Polarization: The study derives explicit formulas for helicity amplitudes. In the limit $m_b \to 0$ , the Standard Model predicts the vanishing of the right-handed transverse helicity amplitude ( $\Gamma_+ = 0$ ) due to angular momentum conservation and the left-chiral structure of the $Wtb$ vertex. The paper quantifies the non-zero contribution of this amplitude when $m_b$ is finite, showing it is suppressed by factors of $m_b^2$ .
Theoretical Uncertainties: The authors explicitly state that non-factorizable QCD effects (soft-gluon interactions) and radiative corrections are not calculated but are treated as theoretical uncertainties. These are expected to be suppressed by $\alpha_s(m_t)$ and power corrections of order $\Lambda_{QCD}/m_t$ .

Significance and Claims
The paper positions its results as an updated, self-contained, and reproducible Standard Model baseline for rare exclusive top-quark decays. The authors claim that their work:

Validates the Factorization Framework: By demonstrating consistency with recent literature (specifically Ref. [12]) and resolving previous normalization discrepancies, the work reinforces the utility of the factorization approximation for top decays, where the large top mass ( $m_t \gg \Lambda_{QCD}$ ) suppresses long-distance gluon exchanges compared to $B$ -meson decays.
Provides a Baseline for New Physics: The derived expressions serve as a starting point for EFT interpretations of non-standard charged-current interactions. The sensitivity of helicity observables to anomalous $tWb$ couplings is highlighted, particularly in the $m_b \to 0$ limit where the SM prediction for right-handed polarization is strictly zero.
Enables Future Experimental Searches: By providing precise branching ratio predictions and polarization fractions, the study offers the necessary theoretical inputs for experimental searches at the HL-LHC and future colliders, where high-statistics samples may eventually allow for the observation of these rare exclusive modes.

The authors remain modest regarding the scope, noting that their results are leading-order predictions within the factorization framework and that a systematic study of non-factorizable corrections would require more advanced effective field theory methods (e.g., SCET).

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