Summary of results as of 2023
We provide below an executive summary of the results from our last publication [arXiv:2411.18639]. The complete set of averages from each sub-groups can be found on their respective pages.
b-hadron lifetimes and mixing
Since HFLAV 2022, new results from Belle II, ATLAS, CMS, and LHCb have improved the precision of b-hadron lifetime and mixing averages. Meson and Λb lifetimes are now measured with <10 fs precision, in agreement with Heavy Quark Expansion expectations. Precision for heavier b baryons (Ξb−, Ξb0, Ωb) remains limited by sample size.
The decay width difference for the Bs system is measured with 4% relative precision, matching Standard Model (SM) predictions. For the B0 system, precision is insufficient to confirm the small expected value. CP violation in mixing has not been observed; current results remain consistent with zero.
| b-hadron lifetimes | |
|---|---|
| τ(B0) | 1.517 ± 0.004 ps |
| τ(B+) | 1.638 ± 0.004 ps |
| τ(Bs0) = 1/Γs | 1.516 ± 0.006 ps |
| τ(BsL0) | 1.432 ± 0.006 ps |
| τ(BsH0) | 1.612 ± 0.008 ps |
| τ(Bc+) | 0.510 ± 0.009 ps |
| τ(Λb0) | 1.468 ± 0.009 ps |
| τ(Ξb−) | 1.578 ± 0.021 ps |
| τ(Ξb0) | 1.477 ± 0.032 ps |
| τ(Ωb−) | 1.64 ± 0.16 ps |
| B0 and Bs0 mixing & CP violation | |
|---|---|
| Δmd | 0.5069 ± 0.0019 ps−1 |
| ΔΓd / Γd | 0.001 ± 0.010 |
| |qd / pd| | 1.0010 ± 0.0008 |
| Δms | 17.766 ± 0.006 ps−1 |
| ΔΓs | +0.0781 ± 0.0035 ps−1 |
| |qs / ps| | 1.0003 ± 0.0014 |
| φsc c̄ s | −0.052 ± 0.013 rad |
Semileptonic decays
From the analysis of exclusive semileptonic decays, a global fit gives |Vcb| = (39.77 ± 0.46) × 10−3 and |Vub| = (3.43 ± 0.12) × 10−3. Both differ from inclusive determinations by >3σ. New R(D*) and R(D) measurements keep the combined tension with the SM at 3.14σ.
| Semileptonic b-hadron decay parameters | |
|---|---|
| B(B0 → D*+ℓ−ν̄ℓ) | (4.90 ± 0.12)% |
| B(B− → D*0ℓ−ν̄ℓ) | (5.53 ± 0.22)% |
| B(B0 → D+ℓ−ν̄ℓ) | (2.12 ± 0.06)% |
| B(B− → D0ℓ−ν̄ℓ) | (2.21 ± 0.06)% |
| B(B0 → π+ℓ−ν̄ℓ) | (1.50 ± 0.05) × 10−4 |
| |Vcb| (exclusive B, Bs, Λb) | (39.77 ± 0.46) × 10−3 |
| |Vub| (exclusive B, Bs, Λb) | (3.43 ± 0.12) × 10−3 |
| B(B̄ → Xcℓ−ν̄ℓ) | (10.63 ± 0.15)% |
| B(B̄ → Xℓ−ν̄ℓ) | (10.82 ± 0.15)% |
| |Vcb| (inclusive B) | (41.97 ± 0.48) × 10−3 |
| |Vub| (inclusive B) | (4.06 ± 0.16) × 10−3 |
| R(D) | 0.342 ± 0.026 |
| R(D*) | 0.286 ± 0.012 |
Charmless Decays
Updated LHCb measurements show previous anomalies in RK and RK* have vanished, now agreeing with the SM. However, tensions in angular observables and branching fractions for b → sℓ+ℓ− persist. New limits on lepton-flavor-violating decays, especially involving τ leptons, have been set. In two-body hadronic decays, the “Kπ CP puzzle” remains.
| b-hadron decays to charmless final states | |
|---|---|
| B(B → Xsγ) (Eγ > 1.6 GeV) | (3.49 ± 0.19) × 10−4 |
| RK (1.1 < m²ℓℓ < 6.0 GeV²/c⁴) | 0.947 ± 0.047 |
| RK* (1.1 < m²ℓℓ < 6.0 GeV²/c⁴) | 1.028 ± 0.074 |
| ACP(B0 → K+π−) | −0.0836 ± 0.0032 |
| ACP(B+ → K+π0) | 0.027 ± 0.013 |
| ACP(Bs → K−π+) | 0.224 ± 0.012 |
| B(B0 → μ+τ− + c.c.) | < 12 × 10−6 (90% CL) |
| B(B0 → e+τ− + c.c.) | < 16 × 10−6 (90% CL) |
| B(Bs → φμ+μ−) | 8.38+0.42−0.41 × 10−7 |
Charm Mixing and CP Violation
LHCb has observed dispersive mixing (x ≠ 0) and improved precision on yCP. Global fits exclude the no-mixing hypothesis (>11σ) and show y > 0 (CP-even states have shorter lifetimes). CP violation parameters |q/p| and φ remain compatible with CP symmetry. Direct CP violation in D0 → K+K− / π+π− is confirmed at (−0.159 ± 0.029)%.
| D0 mixing & CP violation | |
|---|---|
| x | (0.41 ± 0.04)% |
| y | (0.65 ± 0.02)% |
| δKπ | (11.4+3.5−3.8)° |
| AD | (−0.77 ± 0.35)% |
| |q/p| | 0.994 ± 0.016 |
| φ | (−2.6 ± 1.2)° |
| x12 (no direct CPV in CF/DCS) | (0.41 ± 0.04)% |
| y12 (no direct CPV in CF/DCS) | (0.64 ± 0.02)% |
| φ12 (no direct CPV in CF/DCS) | (0.65 ± 0.91)° |
| φM2 (no direct CPV in CF/DCS) | (0.48 ± 0.92)° |
| φΓ2 (no direct CPV in CF/DCS) | (2.4 ± 1.5)° |
| aCPind | (−0.010 ± 0.012)% |
| ΔaCPdir | (−0.159 ± 0.029)% |
Other Highlights
We have compiled 717 measurements involving b-hadron decays into states with open or hidden charm from 305 papers by the BABAR, Belle, CDF, D0, LHCb, CMS, and ATLAS collaborations into 503 averages. Examples of precise or new averages follow
| b-hadron decays to charmed hadrons | |
|---|---|
| B(B0 → D−π+) | (2.48 ± 0.12) × 10−3 |
| B(B+ → D̄0π+) | (4.67 ± 0.12) × 10−3 |
| B(Bs → Ds−π+) | (2.83 ± 0.18) × 10−3 |
| B(Λb0 → Λc+π−) | (4.18 ± 0.30) × 10−3 |
| B(B0 → J/ψ K0) | (0.883 ± 0.020) × 10−3 |
| B(B+ → J/ψ K+) | (1.018 ± 0.018) × 10−3 |
| B(Bs → J/ψ φ) | (1.060 ± 0.090) × 10−3 |
| B(Λb0 → J/ψ Λ0) | (0.47 ± 0.29) × 10−3 |
| B(Bc+ → J/ψ Ds+) / B(Bc+ → J/ψ π+) | 3.09 ± 0.55 |
In the charm sector, |Vcd| and |Vcs| are measured precisely from leptonic D decays with lattice QCD uncertainties now <20% of experimental. Branching fraction averages for hadronic two-body D decays account for improved final-state radiation modeling.
| Charm meson (semi-)leptonic decays | |
|---|---|
| fD | (205.1 ± 4.4) MeV |
| fDs | (252.2 ± 2.5) MeV |
| |Vcd| | 0.2208 ± 0.0040 |
| |Vcs| | 0.9701 ± 0.0081 |
| Charm meson hadronic decays | |
| B(D0 → K−π+) | (3.999 ± 0.006 ± 0.031 ± 0.032FSR)% |
| B(D0 → K+π−) / B(D0 → K−π+) | (0.344 ± 0.002)% |
Updated τ mass and branching fraction fits slightly improve lepton universality tests. Upper limits on lepton-flavor-violating τ decays are reported and combined across experiments.
| Tau decays | |
|---|---|
| gτ / gμ | 1.0016 ± 0.0014 |
| gτ / ge | 1.0018 ± 0.0014 |
| gμ / ge | 1.0002 ± 0.0011 |
| Bunie | (17.815 ± 0.023)% |
| Runihad | 3.634 ± 0.008 |
| |Vus|τ-OPE-1 using B(τ− → Xs ντ) and OPE | 0.2184 ± 0.0021 |
| |Vus|τ-latt-incl using B(τ− → Xs ντ) and lattice QCD | 0.2189 ± 0.0019 |
| |Vus| using B(τ− → K−ντ)/B(τ− → π−ντ) | 0.2229 ± 0.0019 |
| |Vus| / |Vud| using B(τ− → K−ντ)/B(τ− → π−ντ) | 0.2289 ± 0.0019 |
| |Vus| using B(τ− → K−ντ) | 0.2224 ± 0.0017 |
| |Vus| τ average | 0.2208 ± 0.0014 |
Note:
We do not scale the error of an average (as is presently done by the Particle Data Group ) in case χ^2/dof > 1, where dof is the number of degrees of freedom in the average calculation. In this case, we examine the systematics of each measurement and try to understand them. Unless we find possible systematic discrepancies between the measurements, we do not make any special treatment for the calculated error. We provide the confidence level of the fit so that one can know the consistency of the measurements included in the average. We attach a warning message in case that some special treatment is done or the approximation used in the average calculation may not be good enough ( eg, Gaussian error is used in averaging though the likelihood indicates non-Gaussian behavior).
All plots and tables created by HFLAV are available under the CC BY 4.0 licence. See licence and citation page for details.