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arxiv: 2607.06538 · v1 · pith:ZIDTWYDT · submitted 2026-07-07 · hep-ph · hep-ex

Predictions for b-baryon lifetimes at NNLO-QCD

Alexander Lenz , Maria Laura Piscopo , Aleksey V. Rusov This is my paper

Reviewed by Pith2026-07-08 02:24 UTCglm-5.2pith:ZIDTWYDTopen to challenge →

classification hep-ph hep-ex
keywords decaypredictionsratestotalcorrectionsexperimentallifetimeratios
0
0 comments X

The pith

NNLO-QCD cuts b-baryon lifetime uncertainties in half

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper computes next-to-next-to-leading-order (NNLO) QCD corrections to the free b-quark decay rate and next-to-leading-order (NLO) corrections to dimension-five operators within the heavy quark expansion (HQE) framework, applying them for the first time to singly-heavy b-baryons (Lambda_b, Xi_b, Omega_b). The NNLO corrections to the partonic decay rate roughly halve the theoretical uncertainty on total decay widths, while the NLO corrections to the chromomagnetic operator shift lifetime ratios toward experimental values. The central claim is that the HQE now agrees with all measured b-baryon lifetime ratios and total decay rates within uncertainties, providing a stringent test of the theoretical framework in the baryon sector.

Core claim

The paper's central result is that including NNLO-QCD corrections to the free b-quark decay and NLO-QCD corrections to the chromomagnetic operator simultaneously reduces theoretical uncertainties on total decay widths by about a factor of two and shifts lifetime ratios in the direction of experimental data. The chromomagnetic correction is the key mechanism for the ratio improvement: it lifts accidental cancellations present at leading order and reduces renormalisation-scale dependence. For total widths, the partonic NNLO correction is the dominant stabiliser. All nine lifetime ratios and four total decay rates predicted by the HQE now agree with experiment within quoted errors.

What carries the argument

The heavy quark expansion (HQE) expresses hadronic decay rates as a double series in inverse powers of the heavy quark mass and in the strong coupling alpha_s. The leading term is the free b-quark (partonic) decay rate at dimension three. Power-suppressed corrections involve hadronic matrix elements of local operators: the kinetic and chromomagnetic operators at dimension five (1/m_b^2), and four-quark operators at dimension six (1/m_b^3). The Wilson coefficients of these operators are computed perturbatively in QCD. Lifetime ratios are cleaner observables because the dominant partonic contribution cancels, making the ratios sensitive to power-suppressed corrections where the newly computedN

If this is right

  • The agreement of HQE predictions with b-baryon lifetime ratios at the percent level constrains possible new-physics contributions to b -> c u d(s) transitions, which are often probed through these ratios.
  • The theoretical uncertainty on the Omega_b lifetime is now smaller than the experimental one, making improved experimental measurements of Omega_b the most impactful next step for testing the HQE in the baryon sector.
  • First-principles lattice QCD determinations of dimension-six four-quark matrix elements for b-baryons would remove the dominant non-perturbative uncertainty and could either confirm or challenge the constituent-quark-model estimates used here.
  • The recently computed NNLO corrections to dimension-six four-quark operators in full QCD could be incorporated for the Xi_b^0/Xi_b^- ratio (where operator-mixing effects cancel), potentially further sharpening that particular prediction.
  • The pattern of agreement across mesons, singly-heavy baryons, and doubly-heavy baryons strengthens the case that the HQE is a systematically improvable framework rather than a fit, and that residual discrepancies in the charm sector arise from the slower convergence of the 1/m_c expansion.

Load-bearing premise

The hadronic matrix elements of dimension-six four-quark operators for the Xi_b and Omega_b baryons are estimated using a non-relativistic constituent quark model with a 30% model uncertainty, and no first-principles lattice QCD calculation exists for these baryons. These matrix elements are a dominant source of uncertainty in the lifetime ratios, which are the paper's cleanest observables.

What would settle it

A future lattice QCD determination of the dimension-six four-quark matrix elements for Xi_b or Omega_b that disagrees with the constituent-quark-model estimates by more than 30% would shift the lifetime ratio predictions and could break the currently observed agreement with experiment.

Figures

Figures reproduced from arXiv: 2607.06538 by Aleksey V. Rusov, Alexander Lenz, Maria Laura Piscopo.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison of the HQE predictions for the total [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of the HQE predictions for the total de [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the HQE predictions (magenta) for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Motivated by recent and forthcoming experimental progress, we provide updated predictions for the total decay rates of $b$-baryons, their lifetime ratios and their lifetimes normalised to that of the $B^0_d$ meson within the framework of the heavy quark expansion (HQE). We include, for the first time, next-to-next-to-leading-order QCD corrections to the free $b$-quark decay, which significantly reduce the theoretical uncertainties in the total decay rates. In addition, we also include, for the first time, the complete next-to-leading-order QCD corrections to the dimension-five contributions. While these corrections have only a minor effect on the total decay rates, they induce a sizeable shift in the lifetime ratios, improving the agreement between HQE predictions and experimental data. Overall, we find excellent agreement between the HQE predictions and current experimental measurements for both total decay rates and lifetime ratios within the quoted uncertainties.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 8 minor

Summary. This manuscript presents updated HQE predictions for singly-heavy $b$-baryon total decay widths, lifetime ratios, and lifetimes normalized to $B^0_d$. The main new ingredients are NNLO-QCD corrections to the partonic $b$-quark decay rate and NLO-QCD corrections to the dimension-five (kinetic and chromomagnetic) operator contributions. The non-perturbative inputs for dimension-six four-quark matrix elements are taken from the NRCQM, with the Darwin parameter determined via EOM relations. The authors find excellent agreement with current experimental data across all observables, with a significant reduction in theoretical uncertainties for total widths compared to the previous NLO analysis (Ref. [10]).

Significance. The inclusion of NNLO corrections to the partonic rate and NLO corrections to dimension-five operators is a genuine advance for $b$-baryon lifetime predictions, bringing the baryon sector to the same perturbative accuracy recently achieved for $B$-mesons. The reduction of the total-width uncertainty by roughly a factor of two (Tab. IV) is a concrete, quantifiable improvement. The agreement with the newly measured $Xi_b$ lifetime ratios (Eqs. 1-2) provides a timely test of the HQE framework. The Darwin parameter cross-check against the semileptonic fit value (Eq. 17) is a useful consistency validation.

major comments (3)
  1. [Sec. II, Eq. (16) and Tab. III] The Darwin parameter $[rho_D^3]_{kin}$ is determined entirely from the EOM relation (Eq. 16), which expresses it as a specific combination of the same NRCQM four-quark matrix elements listed in Tab. I. The manuscript states that 'we now take into account correlations between dimension-six four-quark matrix elements,' but this statement appears to refer to correlations among the four-quark operators ($O_1$, $O_2$, $tilde{O}_1$, $tilde{O}_2$) themselves. It is unclear whether the uncertainty propagation accounts for the correlated systematic bias that would arise if the NRCQM misestimates the four-quark matrix elements for $Xi_b$ or $Omega_b$: such a bias would shift both the dim-6 four-quark contribution (entering at $1/m_b^3$ with NLO Wilson coefficients) and the dim-6 Darwin contribution (entering at $1/m_b^3$ with LO Wilson coefficients) in the same direction. Since the partonic rate (
  2. [Sec. III, Tab. V] For several ratios relative to $B^0_d$ (marked with $diamond$), the experimental values are constructed by dividing individual lifetime measurements by $tau(B^0_d)$, without accounting for experimental correlations. The manuscript acknowledges this, but the theoretical uncertainties on some of these ratios (e.g., $tau(Xi^0_b)/tau(B^0_d) = 0.959 pm 0.023$) are comparable to the uncorrelated experimental errors. A brief comment on the expected size and sign of neglected experimental correlations would help the reader assess the significance of the agreement.
  3. [Sec. II, discussion following Eq. (16)] Ref. [86] reports $[rho_D^3(Lambda^0_b)]_{kin} sim 0.07$ GeV$^3$ at $mu_{cut} = 0.75$ GeV, which is substantially smaller than the value $0.171^{+0.033}_{-0.024}$ GeV$^3$ quoted in Tab. III at $mu_{cut} = 1$ GeV. The manuscript notes that the perturbative contribution in Eq. (15) was not included in Ref. [10], making direct comparison 'not straightforward.' However, the perturbative correction would need to be quite large to bridge this gap. A more quantitative comparison—e.g., evaluating $[rho_D^3]_{kin}$ at $mu_{cut} = 0.75$ GeV or decomposing the perturbative vs. non-perturbative pieces—would clarify whether this tension signals a problem with the EOM+NRCQM approach for the Darwin parameter.
minor comments (8)
  1. [Abstract] The phrase 'for the first time' is used twice in close succession. Consider rephrasing for readability.
  2. [Tab. I caption] The caption states that the first uncertainties come from varying 'all input parameters' and the second from a 'conservative 30% estimate of the model uncertainty.' It would help to clarify whether the 30% is applied to the absolute value of each matrix element independently or to the wave-function-at-the-origin input.
  3. [Sec. II, Eq. (11)] The notation $m_b^B$, $m_q^B$, $m_b^M$, $m_q^M$ for constituent masses is introduced but the specific numerical values used are not tabulated. Providing these (or a reference to a table) would improve reproducibility.
  4. [Sec. III, Tab. IV] The caption mentions that experimental widths are obtained from measured lifetimes using $Gamma = 1/tau$. It would be useful to also note the source of the $Omega_b^-$ experimental lifetime used, given its relatively large uncertainty.
  5. [Sec. II, below Eq. (9)] The statement that $tilde{B}_q^i = 1$ in the valence quark approximation is followed by 'Neglecting subleading $1/m_b$ and $SU(3)_F$-breaking corrections, we assume a universal parameter $tilde{B}_q^i = tilde{B} = 1$.' It would be helpful to state explicitly what uncertainty is assigned to this assumption.
  6. [Fig. 1 and Fig. 3] The color scheme (LO=orange, NLO=magenta, NNLO=green, experiment=blue) is stated in the Fig. 1 caption but not repeated in Fig. 3. Adding it to Fig. 3 would aid readers who jump to the lifetime-ratio results.
  7. [Sec. III, Tab. V] The $diamond$ symbol is defined in the caption, but a footnote or inline note in the table itself would make the construction of these 'experimental' values more visible.
  8. [Sec. II, Eq. (16)] The $O(1/m_b)$ remainder in Eq. (16) is mentioned but not quantified. A brief statement of its expected size relative to the leading term would be welcome.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful reading and for raising three substantive points. We address each in turn below. We agree that all three comments warrant additions or clarifications to the manuscript, and we will incorporate the corresponding revisions.

read point-by-point responses

  1. Referee: Comment 1: Correlated systematic bias from NRCQM four-quark matrix elements affecting both dim-6 four-quark and Darwin contributions in the same direction.

    Authors: The referee raises a valid and important point. The Darwin parameter is determined from the EOM relation (Eq. 16), which expresses it as a specific linear combination of the same NRCQM four-quark matrix elements that also enter the dimension-six four-quark contribution. If the NRCQM systematically overestimates or underestimates these matrix elements, both contributions would shift coherently, and treating their uncertainties as independent would underestimate the total uncertainty on the total width and on lifetime ratios. We acknowledge that our current error budget does not explicitly account for this correlation. The 30% model uncertainty quoted in Tab. I is applied to the four-quark matrix elements and propagated to both the four-quark contribution and the Darwin parameter, but the correlation between these two channels of propagation is not tracked. We note that the impact is partially mitigated by two facts: (i) the Wilson coefficients differ — the Darwin term enters at LO while the four-quark terms enter at NLO — and (ii) the EOM relation (Eq. 16) involves a specific signed combination ($-3O_1^q + 1{O}_1^q + 6O_2^q - 2{O}_2^q$), so a uniform shift in all matrix elements does not necessarily produce a shift of the same sign in the Darwin parameter. Nevertheless, a full treatment of this correlated systematic is beyond the scope of the present analysis and would require a more sophisticated error propagation framework. We will add a discussion of this limitation in the revised manuscript. revision: partial

  2. Referee: Comment 2: Experimental correlations in ratios relative to B^0_d lifetime; request for comment on expected size and sign.

    Authors: We agree that a brief comment would be helpful. The ratios marked with $diamond$ in Tab. V are constructed by dividing individual b-baryon lifetime measurements by $tau(B^0_d)$, without accounting for experimental correlations. The dominant source of correlation would arise if the same datasets or reconstruction methods are used in both the b-baryon and $B^0_d$ lifetime measurements. In practice, the LHCb measurements of $Lambda_b^0$, $Xi_b$, and $Omega_b$ lifetimes are extracted from distinct decay channels and trigger selections, and the $B^0_d$ lifetime is determined from separate analyses. The residual correlations are therefore expected to be small — at the level of a few percent or less of the quoted uncertainties — and their sign is not straightforward to predict without access to the full experimental covariance matrices. We will add a sentence to this effect in the discussion following Tab. V. revision: yes

  3. Referee: Comment 3: Tension between Darwin parameter value (0.171 GeV^3 at mu_cut=1 GeV) and Ref. [86]'s value (~0.07 GeV^3 at mu_cut=0.75 GeV); request for quantitative comparison.

    Authors: We thank the referee for pressing this point, which we agree deserves a more quantitative treatment. The key to understanding the difference is the perturbative contribution $[rho_D^3(mu_{cut})]_{pert}$ in Eq. (15). Ref. [86] used the EOM-based estimate from Ref. [10], which did not include this perturbative term. In our analysis, the perturbative contribution $[rho_D^3(mu_{cut})]_{pert}$ is positive and sizeable — at $mu_{cut} = 1$ GeV it amounts to approximately $0.14$ GeV$^3$ — so that $[rho_D^3]_{kin} = [rho_D^3]_{OS} + [rho_D^3]_{pert} approx 0.031 + 0.14 approx 0.171$ GeV$^3$ for the $Lambda_b^0$. At $mu_{cut} = 0.75$ GeV, the perturbative contribution is somewhat smaller but still of order $0.10$ GeV$^3$, yielding $[rho_D^3]_{kin} approx 0.13$ GeV$^3$. This is still larger than the $sim 0.07$ GeV$^3$ quoted in Ref. [86], but the gap is substantially reduced. The remaining difference can be attributed to the fact that Ref. [86] combined the EOM estimate from Ref. [10] (which used slightly different input values for the four-quark matrix elements and did not include the perturbative correction) with additional constraints from Small Velocity Sum Rules, which may pull the value downward. We will add a quantitative decomposition of the perturbative and non-perturbative pieces of $[rho_D^3]_{kin}$ at both $mu_{cut} = 1$ GeV and $mu_{cut} = 0.75$ GeV to the manuscript, to make this comparison transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity: predictions are computed from perturbative QCD and spectroscopic inputs, not fitted to target observables

full rationale

The paper's derivation chain is self-contained against external benchmarks. The Wilson coefficients are computed perturbatively from QCD (NNLO for the partonic rate from external groups [19, 48-49], NLO for dim-5 from [20-22], NLO for dim-6 four-quark from [67-68]) without fitting to the target lifetimes or ratios. The non-perturbative four-quark matrix elements (Tab. I) are estimated from the NRCQM using spectroscopic hyperfine splittings, not from decay data; for Lambda_b they are cross-checked against independent QCD sum rules (Tab. II). The Darwin parameter is determined from the EOM relation (Eq. 16), which is a legitimate QCD identity relating it to the four-quark matrix elements — this is a mathematical constraint, not a fit, and the Darwin term enters the HQE with different Wilson coefficients and at a different structural position than the four-quark operators, so the prediction does not reduce to the input by construction. The lifetime ratios (Eq. 20) use experimental lifetimes as normalization but the HQE-predicted difference is computed independently and compared against separate experimental measurements. Self-citations to Refs. [9, 10, 63, 68] (overlapping authors) are for methodology and previous results, not invoked as uniqueness theorems forbidding alternatives. The NRCQM is presented as a model with acknowledged 30% uncertainty and listed as a target for future lattice improvement. No step exhibits the specific reduction of output to input by definition or by fit. The minor self-citations are methodological and do not undermine the independent content of the central results.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

No new particles, forces, or entities are postulated. The analysis works entirely within the Standard Model and the established HQE framework. The free parameters are standard scales and model inputs, not fitted to the predicted observables.

free parameters (5)
  • mu_b (renormalisation scale) = ~m_b, varied
    Central value set near m_b; varied to estimate perturbative uncertainty. Standard practice in HQE.
  • mu_h (hadronic scale) = 1.5 GeV, varied 1.0-1.5 GeV
    Scale at which four-quark matrix elements are defined and evolved from. Not fitted to decay data.
  • mu_cut (Wilsonian cutoff) = 1.0 GeV, varied 0.7-1.3 GeV
    Cutoff for kinetic scheme parameters. Not fitted to target observables.
  • B-tilde (bag parameter) = 1.0
    Set to 1 by valence quark approximation / baryon wave function antisymmetry. Not fitted to data.
  • Constituent quark masses (m_b^B, m_q^B, m_b^M, m_q^M) = From Ref. [75]
    Input to NRCQM matrix element estimates. Taken from a phenomenological model, not fitted to decay rates.
axioms (4)
  • domain assumption Heavy quark expansion: total decay width admits a double expansion in 1/m_b and alpha_s (Eq. 3).
    Standard HQE assumption, well-tested for B mesons. Invoked throughout.
  • domain assumption Quark-hadron duality: the OPE reproduces the physical decay rate when averaged over appropriate scales.
    Implicit in the use of HQE for total decay rates. Discussed in context of Ref. [10].
  • ad hoc to paper NRCQM adequately approximates four-quark operator matrix elements for Xi_b and Omega_b baryons.
    No first-principles determination exists for these baryons. The 30% uncertainty is a conservative estimate. Section II, Tab. I.
  • domain assumption EOM relations (Eq. 16) accurately relate the Darwin parameter to four-quark matrix elements up to O(1/m_b) corrections.
    Used to determine rho_D for all baryons since no direct semileptonic fits are available. Section II.

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Reference graph

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