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Predictions for $b$ -baryon lifetimes at NNLO-QCD

This paper presents updated predictions for $b$ -baryon lifetimes and their ratios within the heavy quark expansion framework by incorporating next-to-next-to-leading-order QCD corrections to free $b$ -quark decay and complete next-to-leading-order corrections to dimension-five contributions, resulting in significantly reduced theoretical uncertainties and excellent agreement with experimental data.

Original authors: Alexander Lenz, Maria Laura Piscopo, Aleksey V. Rusov

Published 2026-07-08

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CC BY 4.0

Original authors: Alexander Lenz, Maria Laura Piscopo, Aleksey V. Rusov

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

Imagine the universe as a giant, bustling construction site. In this site, there are massive, heavy trucks (called b-quarks) that are constantly breaking down into smaller, lighter vehicles. Physicists want to know exactly how long these heavy trucks last before they fall apart. This "lifespan" is called a lifetime.

For a long time, scientists have used a set of rules called the Heavy Quark Expansion (HQE) to predict these lifetimes. Think of HQE as a sophisticated blueprint. It says: "To figure out how long the truck lasts, you need to add up a few different factors: the basic engine failure rate, plus some smaller mechanical issues, plus some rare, weird glitches."

In this new paper, the authors (Lenz, Piscopo, and Rusov) have taken that blueprint and given it a major upgrade. Here is what they did, explained simply:

1. The "Engine Tune-Up" (The Big Correction)

Previously, the blueprint calculated the basic engine failure rate (the decay of a free b-quark) with good accuracy, but not perfect accuracy. It was like estimating a car's fuel efficiency based on a rough guess.

In this study, the authors performed a "Next-to-Next-to-Leading Order" (NNLO) calculation.

The Analogy: Imagine you were guessing how fast a car drives by looking at it from a mile away. Then, you zoom in with binoculars (NLO). Now, they have zoomed in with a high-powered microscope (NNLO).
The Result: This microscopic view didn't change the average speed much, but it made the uncertainty (the margin of error) shrink by half. It's like going from saying, "The car lasts between 5 and 10 years," to saying, "The car lasts between 6.7 and 7.0 years." This makes the prediction much sharper.

2. The "Hidden Glitches" (The Small Corrections)

The blueprint also accounts for "glitches" that happen because the truck is heavy. These are called dimension-five contributions (specifically, kinetic and chromomagnetic operators).

The Analogy: Think of these as vibrations in the truck's frame or a slight wobble in the wheels. For a long time, the blueprint only estimated the size of these wobbles roughly.
The New Work: The authors calculated these wobbles with much higher precision (NLO-QCD corrections).
The Result: While these wobbles didn't change the total lifespan of the truck much, they were crucial for comparing different trucks to each other. When you compare two similar trucks, the big engine factors cancel out, and the tiny wobbles become the deciding factor. By calculating these wobbles better, the predictions for how long one truck lasts relative to another finally matched the real-world measurements perfectly.

3. The "Ruler" (Comparing to the Standard)

The scientists didn't just look at the trucks in isolation; they compared them to a standard reference vehicle, the $B^0_d$ meson (a type of B-meson).

They measured the lifetimes of four specific b-baryons (trucks made of three quarks): $\Lambda_b^0$ , $\Xi_b^0$ , $\Xi_b^-$ , and $\Omega_b^-$ .
They compared their new, ultra-precise predictions against the latest data from experimental labs (like LHCb).

The Bottom Line

The paper claims that with these new, sharper calculations:

The predictions are now incredibly accurate. The theoretical "guess" matches the experimental "measurement" almost perfectly.
The uncertainty is much smaller. The "fuzziness" in the theory has been cut in half for total lifetimes.
The ratios are spot on. When comparing the lifetimes of different b-baryons to each other, the new math fixes previous small discrepancies, making the theory and the data agree beautifully.

In short: The authors took an already good map of how heavy particles decay, added a high-definition lens to the most important part of the map, and sharpened the details of the smaller features. The result is a map that aligns perfectly with the territory we actually see in our experiments. They haven't found a new way to build cars or change the laws of physics; they have just proven that our current understanding of how these particles break down is rock-solid and incredibly precise.

Technical Summary: Predictions for b-baryon lifetimes at NNLO-QCD

Problem and Motivation
The lifetimes of hadrons containing a $b$ quark serve as stringent tests of the Heavy Quark Expansion (HQE). Within this framework, decay rates are expressed as a double expansion in inverse powers of the heavy-quark mass ( $1/m_b$ ) and the strong coupling constant ( $\alpha_s$ ). While the HQE has been successfully applied to $B$ -mesons and $b$ -baryons, recent experimental progress has necessitated updated theoretical predictions. Specifically, the Heavy Flavour Averaging Group (HFLAV) has incorporated new, high-precision measurements of the lifetimes of singly $b$ -baryons ( $\Lambda_b^0$ , $\Xi_b^0$ , $\Xi_b^-$ , $\Omega_b^-$ ) and, for the first time, their lifetime ratios relative to the $\Lambda_b^0$ . Previous theoretical analyses, such as Ref. [10], included Next-to-Leading-Order (NLO) QCD corrections for the partonic rate and dimension-six operators but were limited to Leading-Order (LO) accuracy for remaining power-suppressed contributions. This paper addresses the need for a comprehensive analysis that incorporates recent perturbative advancements to match the precision of current experimental data.

Methodology
The authors perform an updated HQE analysis of the total decay widths ( $\Gamma$ ) and lifetime ratios ( $\tau$ ) for singly $b$ -baryons. The decay width is expanded as:
$\Gamma = \Gamma_3 + \frac{\Gamma_5 \langle O_5 \rangle}{m_b^2} + \frac{\Gamma_6 \langle O_6 \rangle}{m_b^3} + \dots$
where $\Gamma_i$ are Wilson coefficients and $\langle O_i \rangle$ are hadronic matrix elements. The analysis implements the following key theoretical updates:

NNLO-QCD Corrections to Free Quark Decay: For the first time in the context of singly $b$ -baryons, Next-to-Next-to-Leading-Order (NNLO) QCD corrections ( $O(\alpha_s^2)$ ) are included for the dimension-three free $b$ -quark decay rate. This includes both semileptonic and non-leptonic contributions. The calculation employs the kinetic scheme for the bottom-quark mass and the $\overline{\text{MS}}$ scheme for the charm-quark mass, utilizing three-loop conversion formulae and RunDec for coupling evolution.
NLO-QCD Corrections to Dimension-Five Operators: The authors include complete NLO QCD corrections ( $O(\alpha_s)$ ) to the dimension-five two-quark operator contributions (kinetic and chromomagnetic operators). While the kinetic operator coefficient is fixed by reparametrization invariance, the chromomagnetic operator coefficients for non-leptonic decays ( $b \to c\bar{u}d$ and $b \to c\bar{c}s$ ) were recently computed and are now incorporated. These corrections lift accidental cancellations present at LO and reduce renormalization-scale dependence.
Updated Non-Perturbative Inputs:
- Dimension-Six Four-Quark Operators: Matrix elements are estimated using the Non-Relativistic Constituent Quark Model (NRCQM), normalized to lattice QCD determinations of the $B$ -meson decay constant. These values are compared with QCD and HQET sum rules, showing consistency within uncertainties.
- Darwin Parameter: The dimension-six two-quark (Darwin) operator matrix element is determined using Equation-of-Motion (EOM) relations linking it to four-quark operators. Crucially, the perturbative contribution to this relation is now included up to three-loop accuracy, resulting in significantly larger values for the Darwin parameter compared to previous studies.
- Kinetic and Chromomagnetic Parameters: Updated values are adopted based on recent determinations for $B$ -mesons and spectroscopy relations.

Key Contributions

First NNLO Inclusion: This work provides the first NNLO-QCD predictions for the total decay rates of singly $b$ -baryons.
First NLO for Dimension-Five: It presents the first inclusion of complete NLO-QCD corrections to the dimension-five contributions for $b$ -baryons.
Consistent Framework: The analysis consistently applies the kinetic mass scheme and updated perturbative inputs, aligning the treatment of $b$ -baryons with recent NNLO analyses of $B$ -meson lifetimes.
Error Budget Analysis: The study quantifies the impact of these corrections on theoretical uncertainties, specifically addressing renormalization scale dependence and hadronic matrix element uncertainties.

Results

Total Decay Rates: The inclusion of NNLO corrections to the free $b$ -quark decay significantly reduces the theoretical uncertainty in total decay rates by approximately a factor of two, primarily by reducing the sensitivity to the renormalization scale. The central values shift only slightly. The resulting predictions for $\Lambda_b^0$ , $\Xi_b^0$ , $\Xi_b^-$ , and $\Omega_b^-$ are in excellent agreement with experimental measurements. For the $\Omega_b^-$ , the theoretical precision now surpasses the current experimental uncertainty.
Lifetime Ratios: The inclusion of NLO corrections to the dimension-five operators induces a sizeable shift in the predicted lifetime ratios, moving them closer to experimental data. This is particularly evident for the chromomagnetic operator contribution. The predictions for ratios such as $\tau(\Xi_b^0)/\tau(\Lambda_b^0)$ and $\tau(\Xi_b^-)/\tau(\Lambda_b^0)$ show excellent agreement with recent LHCb measurements.
Overall Agreement: Within quoted uncertainties, the HQE predictions for both total decay rates and lifetime ratios agree well with current experimental data. The theoretical uncertainties are generally comparable to or smaller than experimental uncertainties, except for the $\Omega_b^-$ lifetime where experimental errors still dominate.

Significance
The paper claims that these results provide a "stringent and consistent test" of the HQE framework in the baryon sector. The excellent agreement between the updated theoretical predictions and experimental data supports the applicability of the HQE to inclusive $b$ -hadron decay widths at the current level of precision. The work demonstrates that the inclusion of higher-order perturbative corrections is essential for reducing theoretical uncertainties and achieving the precision required to constrain potential contributions from physics beyond the Standard Model, particularly through theoretically cleaner observables like lifetime ratios.

Future Outlook
The authors identify specific areas requiring further progress to refine the framework:

Achieving full NLO-QCD accuracy for the Darwin operator coefficient (currently limited by missing non-leptonic corrections).
Extending NNLO-QCD accuracy to dimension-six four-quark operator contributions, which requires resolving operator mixing issues between dimension-six and dimension-three operators.
Improving the determination of two-quark operator matrix elements via fits to semileptonic $b$ -baryon decays.
Performing dedicated first-principles lattice QCD calculations for dimension-six four-quark matrix elements in the baryon sector, which remains less explored than the meson sector.

1. The "Engine Tune-Up" (The Big Correction)

2. The "Hidden Glitches" (The Small Corrections)

3. The "Ruler" (Comparing to the Standard)

The Bottom Line

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