arxiv: 2604.06880 · v1 · submitted 2026-04-08 · ✦ hep-lat

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Untangling the heavy-flavor mess: status of the Fermilab-MILC calculation of the B_{(s)}to D^{(ast)}_{(s)}ellν form factors

Alejandro Vaquero , Carleton DeTar , Aida El-Khadra , Elvira G\'amiz , Steve Gottlieb , William Jay , Hwancheol Jeong , Andreas S. Kronfeld

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Andrew Lytle

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Pith reviewed 2026-05-10 18:14 UTC · model grok-4.3

classification ✦ hep-lat

keywords lattice QCDform factorsB meson decaysheavy flavorHISQ ensemblesFermilab interpretationsemileptonic decays

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The pith

A lattice QCD effort with physical-mass quarks on fine grids computes correlated form factors for B to D decays to address current discrepancies.

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

This paper describes the ongoing calculation of form factors for heavy-to-heavy and heavy-to-light semileptonic decays using lattice QCD. It employs seven N_f=2+1+1 HISQ ensembles with lattice spacings from 0.15 fm to 0.06 fm, more than half at physical pion mass, and heavy quarks at their physical values via the Wilson-clover action with the Fermilab interpretation. Form factors are extracted with full correlations between channels. The work targets the unclear status of B to D* ell nu results and unexplained tensions in heavy-to-light channels, which have not improved despite recent advances in heavy flavor physics. A reader would care because these form factors determine CKM elements like |V_cb| and enter lepton flavor universality tests where tensions remain.

Core claim

We present the status of calculations of the form factors of the most relevant heavy-to-heavy and heavy-to-light decay channels using seven N_f = 2+1+1 HISQ ensembles with lattice spacings ranging from 0.15 fm down to 0.06 fm. More than half of the ensembles have physical pion masses, and heavy quarks are simulated at physical masses with the Wilson-clover action in the Fermilab interpretation. The form factors are computed including correlations among them, as an attempt to resolve the current unclear situation in the B to D* ell nu channel and unexplained tensions in heavy-to-light form factors.

What carries the argument

Seven HISQ gauge ensembles with physical pion masses on most and physical heavy quarks via Wilson-clover action in the Fermilab interpretation, used to extract correlated form factors for B_{(s)} to D^{(*)}_{(s)} ell nu decays.

If this is right

The B to D* ell nu form factors will be determined with improved control over lattice spacing and quark mass effects.
Correlations among multiple decay channels will enable tighter constraints in global fits to data.
Heavy-to-light form factor tensions will be directly confronted with the same controlled setup.
Inputs for |V_cb| extractions from exclusive decays and lepton flavor universality ratios will become more precise.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the results align with one set of prior lattice calculations over another, it would favor that approach for future precision work.
The same ensemble set could be reused for related quantities like decay constants or other semileptonic modes without additional generation cost.
Resolution of the form factor issues would tighten the unitarity triangle constraints from B physics.

Load-bearing premise

The seven HISQ ensembles with physical pion and heavy quark masses will control all systematic errors sufficiently to resolve the current tensions without introducing new uncontrolled effects.

What would settle it

Final numerical values for the B to D* ell nu form factors that fail to reduce the discrepancy with experiment or other lattice results, or that introduce new tensions in heavy-to-light channels, would show the approach has not resolved the issues.

Figures

Figures reproduced from arXiv: 2604.06880 by Aida El-Khadra, Alejandro Vaquero, Andreas S. Kronfeld, Andrew Lytle, Carleton DeTar, Elvira G\'amiz, Hwancheol Jeong, Steve Gottlieb, William Jay.

**Figure 2.** Figure 2: Upper panel: Evolution of the tension between inclusive and exclusive |𝑉𝑢𝑏 | as a function of the year, from the PDG reports. Lower panel: Difference in 𝜎 between the inclusive and the exclusive results. 37.5 40.0 42.5 |Vcb| × 10 3 |Vcb|Incl |Vcb|Excl 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Year 0 2 |Vcb| in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Upper panel: Evolution of the tension between inclusive and exclusive |𝑉𝑐𝑏 | as a function of the year, from the PDG reports. Lower panel: Difference in 𝜎 between the inclusive and the exclusive results. recent FLAG report [1], which agrees very well with previous theoretical expectations. This point has been made possible due to the most recent lattice-QCD calculations of 𝐵 → 𝐷 ∗ ℓ𝜈 [7–9]. The tensions wi… view at source ↗

**Figure 4.** Figure 4: Status of the current lattice-QCD calculations, compared against Belle and BaBar experimental measurements. Left: Decay amplitude extracted from the lattice-QCD form factors and from experiments. The |𝑉𝑐𝑏 | values used to scale the experimental data come from the respective experiments. Right: Individual lattice-QCD results for 𝑅(𝐷) vs 𝑅(𝐷 ∗ ) compared with the HFLAV average. calculations stand by comparin… view at source ↗

**Figure 5.** Figure 5: Tensions in the 𝐵 → 𝜋ℓ𝜈 (left) and the 𝐵𝑠 → 𝐾ℓ𝜈 form factors, according to FLAG 2024. 17 18 19 20 21 22 23 24 q 2 (GeV) 0.5 1.0 1.5 2.0 2.5 3.0 Non-physical f + Non-physical f0 Physical f + Physical f0 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 7.** Figure 7: Ensemble list of the calculation. The size of each circle is proportional to the available statistics. 4. The way forward We have laid out reasons why better calculations are needed in both heavy-to-heavy and heavyto-light sectors. The Fermilab Lattice and MILC collaborations are committed to improving these results, and for this reason we have two different calculations running simultaneously. One of the… view at source ↗

**Figure 8.** Figure 8: Preliminary and blinded results for the ℎ+,− (left, right) form factors for the 𝐵 → 𝐷ℓ𝜈 decay. 1.00 1.05 1.10 1.15 1.20 w 0.7 0.8 0.9 1.0 h s+ Preliminary Blinded 1.00 1.05 1.10 1.15 1.20 w -0.10 -0.05 0.00 0.05 0.10 h s¡ Preliminary Blinded [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 9.** Figure 9: Same as fig. 8, but for the 𝐵𝑠 → 𝐷𝑠ℓ𝜈 channel. 1.00 1.05 1.10 1.15 w 0.7 0.8 0.9 h A1 Preliminary Blinded 1.00 1.05 1.10 1.15 w 0.8 1.0 1.2 1.4 h V Preliminary Blinded [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗

**Figure 10.** Figure 10: Preliminary and blinded results for the ℎ𝐴1,𝑉 (left, right) form factors for the 𝐵 → 𝐷 ∗ ℓ𝜈 decay. 5. Conclusions The current status of the lattice-QCD calculations of the form factors in the heavy-to-heavy and heavy-to-light semileptonic decays is unsatisfactory: On the one hand, even though the heavyto-heavy calculations have greatly improved during the latest years, and show a good agreement, they hav… view at source ↗

**Figure 11.** Figure 11: Same as fig. 10, but for the 𝐵𝑠 → 𝐷 ∗ 𝑠 ℓ𝜈 channel. 18 20 22 24 q 2(GeV2) 1 2 3 4 5 f(q 2) Preliminary Blinded f+ f0 B → π 18 20 22 q 2(GeV2) 0.5 1.0 1.5 2.0 2.5 3.0 f(q 2) Preliminary Blinded Bs → K 16 18 20 22 q 2(GeV2) 0.5 1.0 1.5 2.0 2.5 f(q 2) Preliminary Blinded B → K [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗

**Figure 12.** Figure 12: From left to right, preliminary and blinded results for the chiral continuum limit of the 𝑓+ and 𝑓0 form factors of the 𝐵 → 𝜋ℓ𝜈, 𝐵𝑠 → 𝐾ℓ𝜈 and the 𝐵 → 𝐾ℓℓ decays. discrepancies between lattice-QCD calculations from different collaborations. Our collaboration has a well-defined roadmap to address these issues, with two different calculations that will deliver high-quality results. The calculation presented … view at source ↗

read the original abstract

We present the status of calculations of the form factors of the most relevant heavy-to-heavy and heavy-to-light decay channels. Using seven $N_f = 2+1+1$ HISQ ensembles, with lattice spacings ranging from 0.15 fm down to 0.06 fm, we calculate the form factors of the decays, including correlations among them. More than half of our ensembles feature physical pion masses, and the heavy quarks are simulated at their physical masses using the Wilson-clover action with the Fermilab interpretation. Even though we have recently seen huge qualitative and quantitative leaps in the characterization of heavy-to-heavy decays, these advances have failed to translate into improvements for the inclusive vs exclusive question, or the matter of the Lepton Flavor Universality ratios. In particular, in the $B\to D^{\ast}\ell\nu$ channel, the current situation of the lattice-QCD form factors is far from clear. Further, the latest lattice-QCD results on the heavy-to-light form factors display unexplained tensions that must urgently be resolved. The work presented here is an attempt to address these issues.

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.

Desk Editor's Note private letter to a colleague

This is a status report on Fermilab-MILC's ongoing lattice work for B to D form factors that describes a solid ensemble setup but shows no new numbers or resolutions to the tensions it flags.

read the letter

The core point is that this paper reports the current state of calculations rather than delivering final form factors or a resolution to the inclusive-exclusive or lepton-flavor-universality issues. The group is using seven Nf=2+1+1 HISQ ensembles spanning a=0.15 to 0.06 fm, with physical pion masses on more than half and physical heavy quarks treated via the Fermilab-clover action. They compute the relevant form factors together so that correlations are kept track of. That setup is a reasonable way to control discretization and chiral effects in heavy-to-heavy and heavy-to-light channels. Physical masses on several ensembles reduce the size of extrapolations, which is a practical strength for this kind of work. The description of the ensembles and action choices is clear and standard for the field. The paper does not contain any computed values, error budgets, or preliminary plots. It restates the known tensions in B to D* l nu and the heavy-to-light channels but offers no indication of how far along the current runs are or whether early results already point toward a shift in the discrepancies. Without that, the statement that the work is an attempt to address the issues remains a plan rather than evidence of progress. The citation pattern is typical and does not appear to skip key prior lattice or experimental references. This is mainly of interest to lattice practitioners who follow the Fermilab-MILC heavy-flavor program and want to know the computational strategy they are pursuing. A reader looking for updated numbers to plug into phenomenology or to cite in a review of the B-decay puzzles will not find them here. I would bring it to a reading group focused on lattice QCD or flavor anomalies to discuss the ensemble choices, but I would not cite it in my own work in the next year. It could go to peer review as a conference-style status note if the journal accepts that format, since the methodology is described without internal contradictions, but it is not yet at the stage where a full referee report on results would be useful.

Referee Report

0 major / 3 minor

Summary. The manuscript is a status report on the Fermilab-MILC collaboration's ongoing lattice QCD calculation of form factors for the B_{(s)} → D^{(*)}_{(s)} ℓν decays and related heavy-to-light channels. It employs seven N_f=2+1+1 HISQ ensembles spanning lattice spacings a=0.15–0.06 fm (more than half at physical pion masses) with physical heavy-quark masses simulated via the Fermilab interpretation of the Wilson-clover action, and computes the form factors including correlations among channels. The text reviews persistent tensions between inclusive and exclusive determinations as well as lepton-flavor-universality ratios (especially in B→D*ℓν) and positions the calculation as an effort to clarify the unclear lattice-QCD situation for these quantities.

Significance. If the final results achieve the targeted control over systematics, the work will be significant for heavy-flavor phenomenology. The use of physical light- and heavy-quark masses, a broad range of lattice spacings, and explicit inclusion of correlations among form factors are clear strengths that could help resolve the unexplained tensions in heavy-to-light channels and improve constraints on |V_cb| and new-physics searches in LFU ratios.

minor comments (3)

The abstract states that the calculation includes 'correlations among them' but provides no detail on which channels or form factors are correlated; a brief enumeration in the introduction would improve clarity.
A summary table of the seven ensembles (lattice spacing, pion mass, volume, number of configurations) is missing; its addition would make the setup description more accessible without lengthening the text.
The manuscript refers to 'the latest lattice-QCD results on the heavy-to-light form factors' displaying tensions but does not cite the specific prior works; adding the relevant references would strengthen the motivation section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our status report on the Fermilab-MILC lattice QCD calculations of the B_{(s)} to D^{(*)} form factors. We appreciate the recommendation for minor revision and the recognition of the strengths of our approach, including the use of physical masses, multiple lattice spacings, and correlations among channels. No specific major comments were provided in the report, so we have no points requiring point-by-point rebuttal. We will incorporate any minor editorial suggestions in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity; status report with no derivations or predictions

full rationale

This is a status report describing an ongoing lattice-QCD calculation on seven HISQ ensembles with physical pion and heavy-quark masses. The text contains no equations, no fitted parameters, no quantitative predictions, and no load-bearing derivations that could reduce to inputs by construction. No self-citations, ansatze, or uniqueness theorems are invoked to justify results. The discussion of known tensions in B→D*ℓν and heavy-to-light channels is external to the present work and does not create internal circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no details on specific free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5551 in / 1035 out tokens · 46175 ms · 2026-05-10T18:14:40.052934+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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