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Averages of b-hadron, c-hadron, and τ-lepton properties as of 2021

Y. Amhis et al. (Heavy Flavor Averaging Group Collaboration)
Phys. Rev. D 107, 052008 – Published 23 March 2023
Physics logo See synopsis: Heavy-Flavor Properties Get an Update
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  • EXECUTIVE SUMMARY
  • INTRODUCTION
  • AVERAGING METHODOLOGY
  • b-HADRON PRODUCTION FRACTIONS
  • LIFETIMES AND MIXING PARAMETERS OF b HAD…
  • MEASUREMENTS RELATED TO UNITARITY…
  • SEMILEPTONIC b HADRON DECAYS
  • DECAYS OF b-HADRONS INTO OPEN OR HIDDEN…
  • b-HADRON DECAYS TO CHARMLESS FINAL…
  • CHARM CP VIOLATION AND OSCILLATIONS
  • CHARM DECAYS
  • TAU LEPTON PROPERTIES
  • ACKNOWLEDGMENTS
    • References

    Abstract

    This paper reports world averages of measurements of b-hadron, c-hadron, and τ-lepton properties obtained by the Heavy Flavor Averaging Group using results available before April 2021. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, CP violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements.

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    • Received 25 June 2022
    • Accepted 20 September 2022

    DOI:https://doi.org/10.1103/PhysRevD.107.052008

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Bound statesCabibbo–Kobayashi–Maskawa matrixChiral perturbation theoryElectroweak interactionFlavor changing neutral currentsForm factorsHadron mixingLattice QCDParticle decaysParticle interactionsParticle mixing & oscillationsQuark mixing
    Particles & Fields

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    Heavy-Flavor Properties Get an Update

    Published 23 March 2023

    The Heavy Flavor Averaging Group has released new world averages for properties of “heavy-flavor” particle decays—an update aimed at improving our understanding of flavor physics.

    See more in Physics

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    Vol. 107, Iss. 5 — 1 March 2023

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    • Figure 1
      Figure 1

      Illustration of the possible dependence of a measured quantity x on a nuisance parameter yi. The plot compares the 68% confidence level contours of a hypothetical measurement’s unconstrained (large ellipse) and constrained (filled ellipse) likelihoods, using the Gaussian constraint on yi represented by the horizontal band. The solid error bars represent the statistical uncertainties σ(x) and σ(yi) of the unconstrained likelihood. The dashed error bar shows the statistical uncertainty on x from a constrained simultaneous fit to x and yi.

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    • Figure 2
      Figure 2

      Illustration of the HFLAV combination procedure for correlated systematic uncertainties. Upper plots (a) and (b) show examples of two individual measurements to be combined. The large (filled) ellipses represent their unconstrained (constrained) iso-likelihood contours, while horizontal bands indicate the different assumptions about the value and uncertainty of yi used by each measurement. The error bars show the results of the method described in the text for obtaining x by performing fits with yi fixed to different values. Lower plots (c) and (d) illustrate the adjustments to accommodate updated and consistent knowledge of yi. Open circles mark the central values of the unadjusted fits to x with y fixed; these determine the dashed line used to obtain the adjusted values.

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    • Figure 3
      Figure 3

      Illustration of the combination of two hypothetical measurements of x using the method described in the text. The ellipses represent the unconstrained likelihoods of each measurement, and the horizontal band represents the latest knowledge about yi that is used to adjust the individual measurements. The filled small ellipse shows the result of the exact method using Lcomb, and the hollow small ellipse and dot show the result of the approximate method using χcomb2.

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    • Figure 4
      Figure 4

      The B0–B¯0 oscillation frequency Δmd as measured by the different experiments. The averages quoted for ALEPH, L3 and OPAL are taken from the original publications, while the ones for DELPHI, CDF, BABAR, Belle and LHCb are computed from the individual results listed in Table 15 without performing any adjustments. The time-integrated measurements of χd from the symmetric B factory experiments ARGUS and CLEO are converted to a Δmd value using τ(B0)=1.519±0.004  ps. The two global averages are obtained after adjustments of all the individual Δmd results of Table 15 (see text).

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    • Figure 5
      Figure 5

      Contours of ΔlnL=0.5 (39% CL for the enclosed 2D regions, 68% CL for the bands) shown in the (Γs,ΔΓs) plane on the left and in the (1/ΓsL,1/ΓsH) plane on the right. The average of all the Bs0→J/ψϕ, Bs0→J/ψK+K− and Bs0→ψ(2S)ϕ results is shown as the red contour, where Γs and ΔΓs are scaled by factors 2.56 and 1.72. The constraints given by the effective lifetime measurements of Bs0 to flavor-specific, pure CP-odd and pure CP-even final states are shown as the blue, green and purple bands, respectively. The average taking all constraints into account is shown as the dark-filled contour. The light-gray bands are theory predictions. The horizontal band is ΔΓs=+0.091±0.013  ps−1 [42, 45, 87, 88] that assumes no new physics in Bs0 mixing. The vertical Γs band is calculated from Ref. [56] assuming the experimental world average for the B0 lifetime, 1.519±0.004  ps.

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    • Figure 6
      Figure 6

      Measurements of Δms, together with their average.

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    • Figure 7
      Figure 7

      Measurements of ASLd and ASLs listed in Table 20 (B-factory average as the gray band, D0 measurements as the green ellipses, LHCb measurements as the blue ellipse) together with their two-dimensional average (red hatched ellipse). The red point close to (0, 0) is the Standard Model prediction of Ref. [87] with error bars multiplied by 10. The prediction and the experimental world average deviate from each other by 0.5σ.

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    • Figure 8
      Figure 8

      68% CL regions shown in the (ϕscc¯s,ΔΓs) plane on the top and in the (Γs,ΔΓs) plane on the bottom, for individual experiments and their combination. The left plots are obtained from all CDF [172], D0 [173], ATLAS [174, 175, 176], CMS [177, 178] and LHCb [93, 179, 180, 181, 182, 183, 227, 229] measurements of Bs0→J/ψϕ, Bs0→J/ψK+K−, Bs0→ψ(2S)ϕ, Bs0→J/ψπ+π− and Bs0→Ds+Ds− decays, while the right plots are obtained from Bs0→J/ψϕ measurements only [172, 173, 174, 175, 176, 177, 178, 179, 182, 183]. The expectation within the Standard Model neglecting penguin contributions [42, 45, 87, 88, 169] is shown as the white rectangle in the top plots. The Γs theory value in the bottom plots is calculated from Ref. [56] assuming the experimental world average for the B0 lifetime, 1.519±0.004  ps.

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    • Figure 9
      Figure 9

      The unitarity triangle.

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    • Figure 10
      Figure 10

      Top: average of measurements of Sb→cc¯s, interpreted as sin(2β), with (bottom left) the same but excluding less precise measurements to allow inspection of the detail. Bottom right: more precise results and the world average for Cb→cc¯s.

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    • Figure 11
      Figure 11

      Constraints on the (ρ¯,η¯) plane, obtained from the average of −ηSb→cc¯s and Eq. (147). Note that the solution with the smaller (larger) value of β has cos(2β)>0 (<0).

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    • Figure 12
      Figure 12

      Averages of (left) sin(2β)≡sin(2ϕ1) and (right) cos(2β)≡cos(2ϕ1) from time-dependent analyses of B0→J/ψK*0 decays.

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    • Figure 13
      Figure 13

      Averages of (left) (Jc/J0), (middle) (2Js1/J0) sin(2β) and (right) (2Js2/J0) cos(2β) from time-dependent analyses of B0→D*+D*−KS0 decays.

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    • Figure 14
      Figure 14

      Averages of sin(2β) measured in color-suppressed b→cu¯d transitions.

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    • Figure 15
      Figure 15

      Averages of (left) Sb→cc¯d and (right) Cb→cc¯d for the mode B0→J/ψπ0.

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    • Figure 16
      Figure 16

      Averages of (left) Sb→cc¯d and (right) Cb→cc¯d for the mode B0→D+D−.

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    • Figure 17
      Figure 17

      Averages of two b→cc¯d dominated channels, for which correlated averages are performed, in the SCP vs. CCP plane. Contours at SCP2+CCP2=1 represent the physical boundary for the parameters. (Left) B0→J/ψπ0 and (right) B0→D+D−.

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    • Figure 18
      Figure 18

      Averages of (left) Sb→cc¯d and (right) Cb→cc¯d for the mode B0→D*+D*−.

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    • Figure 19
      Figure 19

      Averages of (left) −ηSb→cc¯d interpreted as sin(2βeff) and (right) Cb→cc¯d. The −ηSb→cc¯d figure compares the results to the world average for −ηSb→cc¯s (see Sec. 6d1).

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    • Figure 20
      Figure 20

      Compilation of constraints in the −ηSb→cc¯d, interpreted as sin(2βeff), vs Cb→cc¯d plane. The contours at sin(2βeff)2+Cb→cc¯d2=1 represents the physical boundary for the parameters.

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    • Figure 21
      Figure 21

      Top: averages of (left) −ηSb→qq¯s, interpreted as sin(2βeff and (right) Cb→qq¯s. The −ηSb→qq¯s figure compares the results to the world average for −ηSb→cc¯s (see Sec. 6d1). Bottom: same, but only averages for each mode are shown. More figures are available from the HFLAV web pages.

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    • Figure 22
      Figure 22

      Averages of four b→qq¯s dominated channels, for which correlated averages are performed, in the SCP vs. CCP plane, where SCP has been corrected by the CP eigenvalue to give sin(2βeff). Contours at SCP2+CCP2=1 represent the physical boundary for the parameters. Top left: B0→ϕK0, (top right) B0→η′K0, (bottom left) B0→KS0KS0KS0, (bottom right) B0→π0KS0. More figures are available from the HFLAV web pages.

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    • Figure 23
      Figure 23

      Compilation of constraints in the −ηSb→qq¯s, interpreted as sin(2βeff), vs Cb→qq¯s plane. The contours at sin(2βeff)2+Cb→qq¯s2=1 represents the physical boundary for the parameters.

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    • Figure 24
      Figure 24

      Averages of (left) βeff≡ϕ1eff and (right) ACP for the B0→f0KS0 decay including measurements from Dalitz plot analyses of both B0→K+K−KS0 and B0→π+π−KS0.

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    • Figure 25
      Figure 25

      Averages of (left) SCP and (right) CCP for the mode B0→KS0KS0.

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    • Figure 26
      Figure 26

      Averages of (left) Sb→sγ and (right) Cb→sγ. Recall that the data for K*γ is a subset of that for KS0π0γ.

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    • Figure 27
      Figure 27

      Averages of four b→sγ dominated channels in the SCP vs CCP plane. Contours at SCP2+CCP2=1 represent the physical boundary for the parameters. (Top left) B0→K*γ, (top right) B0→KS0π0γ (including K*γ), (bottom left) B0→KS0ηγ, (bottom right) B0→KS0ρ0γ.

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    • Figure 28
      Figure 28

      Averages of (left) SCP and (right) CCP for the mode B0→π+π−.

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    • Figure 29
      Figure 29

      Averages of (left) SCP and (right) CCP for the mode B0→ρ+ρ−.

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    • Figure 30
      Figure 30

      Averages of b→uu¯d dominated channels, for which correlated averages are performed, in the SCP vs CCP plane. Contours at SCP2+CCP2=1 represent the physical boundary for the parameters. Left: B0→π+π− and (right) B0→ρ+ρ−.

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    • Figure 31
      Figure 31

      Averages of CP violation parameters in B0→a1±π∓ in Aa1π−+ vs Aa1π+− space.

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    • Figure 32
      Figure 32

      Summary of the U and I parameters measured in the time-dependent B0→π+π−π0 Dalitz plot analysis.

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    • Figure 33
      Figure 33

      Averages of (left) Sb→uu¯d and (right) Cb→uu¯d for the mode B0→ρ0π0.

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    • Figure 34
      Figure 34

      Averages of b→uu¯d dominated channels, for the mode B0→ρ0π0 in the SCP vs CCP plane. The contour at SCP2+CCP2=1 represents the physical boundary for the parameters.

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    • Figure 35
      Figure 35

      CP violation in B0→ρ±π∓ decays. Left: ACPρπ vs Cρπ space, (right) Aρπ−+ vs. Aρπ+− space.

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    • Figure 36
      Figure 36

      World average of α≡ϕ2, in terms of 1−CL, split by decay mode.

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    • Figure 37
      Figure 37

      Averages for b→cu¯d/uc¯d modes.

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    • Figure 38
      Figure 38

      Averages of ACP and RCP from GLW analyses.

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    • Figure 39
      Figure 39

      Averages of RADS and AADS for B→D(*)K(*) decays.

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    • Figure 40
      Figure 40

      Averages of RADS and AADS for B→D(*)π decays.

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    • Figure 41
      Figure 41

      Contours in the (x±,y±) from model-dependent analysis of B+→D(*)K(*)+, D→KS0h+h− (h=π, K). Left: B+→DK+, (middle) B+→D*K+, (right) B+→DK*+. Note that the uncertainties assigned to the averages given in these plots do not include model uncertainties.

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    • Figure 42
      Figure 42

      Averages of (x±,y±) from model-dependent analyses of B+→D(*)K(*)+ with D→KS0h+h− (h=π, K). Top left: x+, (top right) x−, (bottom left) y+, (bottom right) y−. The top plots include constraints on x± obtained from GLW analyses (see Sec. 6o1). Note that the uncertainties assigned to the averages given in these plots do not include model uncertainties.

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    • Figure 43
      Figure 43

      Contours in the (x±,y±) plane from model-independent analysis of B+→DK+ with D→KS0h+h− (h=π, K).

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    • Figure 44
      Figure 44

      World average of γ≡ϕ3, in terms of 1−CL, split by decay mode.

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    • Figure 45
      Figure 45

      World average of γ≡ϕ3, in terms of 1−CL, split by analysis method.

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    • Figure 46
      Figure 46

      World averages for the hadronic parameters rB in the different decay modes, in terms of 1−CL.

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    • Figure 47
      Figure 47

      Contributions to the combination from different input measurements, shown in the plane of the relevant rB (left) or δB (right) parameter vs. γ≡ϕ3. From top to bottom: B+→DK+, B+→D*K+, B+→DK*+ and B0→DK*0. Contours show the two-dimensional 68% and 95% CL regions.

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    • Figure 48
      Figure 48

      Summary of the constraints on the angles of the unitarity triangle.

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    • Figure 49
      Figure 49

      Branching fractions of exclusive semileptonic B decays: (a) B¯0→D*+ℓ−ν¯ℓ (Table 69) and (b) B−→D*0ℓ−ν¯ℓ (Table 70).

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    • Figure 50
      Figure 50

      Illustration of (a) the average and (b) the dependence of ηEWF(1)|Vcb| on ρ2. The error ellipses correspond to Δχ2=1 (CL=39%). Figure (c) is a zoomed in view of the Belle and BABAR measurements.

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    • Figure 51
      Figure 51

      Branching fractions of exclusive semileptonic B decays: (a) B¯0→D+ℓ−ν¯ℓ (Table 72) and (b) B−→D0ℓ−ν¯ℓ (Table 73).

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    • Figure 52
      Figure 52

      Illustration of (a) the average and (b) dependence of ηEWG(w)|Vcb| on ρ2. The error ellipses correspond to Δχ2=1 (CL=39%). Figure (c) is a zoomed in view of the Belle and BABAR measurements.

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    • Figure 53
      Figure 53

      Average branching fraction of exclusive semileptonic B decays (a) B¯0→D0π+ℓ−ν¯ℓ, (b) B¯0→D*0π+ℓ−ν¯ℓ, (c) B−→D+π−ℓ−ν¯ℓ, and (d) B−→D*+π−ℓ−ν¯ℓ. The corresponding individual results are also shown.

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    • Figure 54
      Figure 54

      Rescaled individual measurements and their averages for (a) B(B−→D10ℓ−ν¯ℓ)×B(D10→D*+π−) and (b) B(B−→D20ℓ−ν¯ℓ)×B(D20→D*+π−).

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    • Figure 55
      Figure 55

      Rescaled individual measurements and their averages for (a) B(B−→D1′0ℓ−ν¯ℓ)×B(D1′0→D*+π−) and (b) B(B−→D0*0ℓ−ν¯ℓ)×B(D0*0→D+π−).

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    • Figure 56
      Figure 56

      Fit to the inclusive partial semileptonic branching fractions and to the lepton energy moments in the kinetic mass scheme. In all plots, the gray band is the theory prediction with total theory error. BABAR data are shown by circles, Belle by squares and other experiments (DELPHI, CDF, CLEO) by triangles. Filled symbols mean that the point was used in the fit. Open symbols are measurements that were not used in the fit.

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    • Figure 57
      Figure 57

      Same as Fig. 56 for the fit to the hadronic mass moments in the kinetic mass scheme.

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    • Figure 58
      Figure 58

      The B→πℓνq2 spectrum measurements and the average spectrum obtained from the likelihood combination (shown in black).

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    • Figure 59
      Figure 59

      Fit of the BCL parametrization to the averaged q2 spectrum from BABAR and Belle and the LQCD and LCSR calculations. The error bands represent the 1σ (dark green) and 2σ (light green) uncertainties of the fitted spectrum.

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    • Figure 60
      Figure 60

      (a) Summary of exclusive determinations of B(B+→ρ0ℓ+ν) and their average. Measurements of B0→ρ−ℓ+ν branching fractions have been scaled by 0.5τB+/τB0 in accordance with isospin symmetry. (b) Summary of exclusive determinations of B+→ωℓ+ν and their average.

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    • Figure 61
      Figure 61

      The averaged q2 spectrum of the measurements listed in the text for the ρ (left) and ω (right) final state on top of the latest Belle and BABAR measurements. The isospin transformation is applied to the B0→ρ−ℓ+ν measurements. In the right figure we also show the model (green band) which was used to split the bins in the averaging procedure.

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    • Figure 62
      Figure 62

      (a) Summary of exclusive determinations of B(B+→ηℓ+ν) and their average. (b) Summary of exclusive determinations of B(B+→η′ℓ+ν) and their average.

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    • Figure 63
      Figure 63

      Measurements of |Vub| from inclusive semileptonic decays and their average based on the BLNP (a) and DGE (b) prescription. The labels indicate the variables and selections used to define the signal regions in the different analyses.

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    • Figure 64
      Figure 64

      Measurements of |Vub| from inclusive semileptonic decays and their average based on the GGOU (a) and ADFR (b) prescription. The labels indicate the variables and selections used to define the signal regions in the different analyses.

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    • Figure 65
      Figure 65

      Measurements of |Vub| from inclusive semileptonic decays and their average in the BLL prescription.

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    • Figure 66
      Figure 66

      Combined average on |Vub| and |Vcb| including the LHCb measurement of |Vub|/|Vcb|, the exclusive |Vub| measurement from B→πℓν, and the |Vcb| average from B→Dℓν, B→D*ℓν and Bs→Ds(*)μν measurements. The dashed ellipse corresponds to a 1σ two-dimensional contour (68% of CL). The point with the error bars corresponds to the inclusive |Vcb| from the kinetic scheme (Sec. 7b2), and the inclusive |Vub| from GGOU calculation (Sec. 7d3).

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    • Figure 67
      Figure 67

      Measurements of R(D) and R(D*) listed in Table 97 and their two-dimensional average. Contours correspond to Δχ2=1, i.e., 68% CL for the bands and 39% CL for the ellipses. The black and blue points with error bars, are two recent SM prediction for R(D*) and R(D). The SM predictions reported are based on results from Refs. [610, 613, 615]. More information is given in the text. An average of these predictions and the experimental average deviate from each other by about 3.3σ. The dashed ellipse correspond to a 3σ contour (99.73% CL).

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    • Figure 68
      Figure 68

      (a) Measurements of R(D) and (b) R(D*). The green bands are the averages obtained from the combined fit. The red bands are the averages of the theoretical predictions obtained as explained in the text.

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    • Figure 69
      Figure 69

      A selection of high-precision charmless mesonic B meson branching fraction measurements.

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    • Figure 70
      Figure 70

      Branching fractions of charmless baryonic B+ and B0 decays into nonstrange baryons.

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    • Figure 71
      Figure 71

      Branching fractions of charmless baryonic B+ and B0 decays into strange baryons.

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    • Figure 72
      Figure 72

      Branching fractions of charmless Λb0 decays.

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    • Figure 73
      Figure 73

      Branching fractions of charmless leptonic Bs0 decays.

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    • Figure 74
      Figure 74

      Branching fractions of charmless nonleptonic Bs0 decays.

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    • Figure 75
      Figure 75

      Branching fractions of B+ and B0 decays of the type b→sℓ+ℓ−.

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    • Figure 76
      Figure 76

      Branching fractions of B+ and B0 decays of the type b→uℓ+ℓ−, purely leptonic and leptonic radiative.

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    • Figure 77
      Figure 77

      Compilation of RK(*) ratios in the low dilepton invariant-mass region. These are ratios between branching fractions of B-meson decays to K(*)μ+μ− and K(*)e+e−, which provide information on lepton universality.

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    • Figure 78
      Figure 78

      Limits on branching fractions of lepton-flavor-violating B+ and B0 decays.

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    • Figure 79
      Figure 79

      Limits on branching fractions of lepton-number-violating B+ and B0 decays.

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    • Figure 80
      Figure 80

      Branching fractions of charmless B decays with neutrinos.

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    • Figure 81
      Figure 81

      A selection among the most precise direct CP asymmetries (ACP) measured in charmless B+ and B0 decay modes.

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    • Figure 82
      Figure 82

      Longitudinal polarization fraction in charmless B decays.

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    • Figure 83
      Figure 83

      Longitudinal polarization fraction in charmless Bs0 decays.

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    • Figure 84
      Figure 84

      World average value of RM=(x2+y2)/2 as calculated from D0→K+ℓ−ν¯ measurements [1202, 1203, 1204, 1205]. The confidence level from the fit is 0.97.

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    • Figure 85
      Figure 85

      World average value of yCP as calculated from D0→K+K−,π+π−,K+K−KS0, and KS0ω measurements [1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230]. The confidence level from the fit is 0.21.

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    • Figure 86
      Figure 86

      World average value of AΓ calculated from D0→K+K−,π+π− measurements [1226, 1228, 1231, 1232]. The confidence level from the fit is 0.73.

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    • Figure 87
      Figure 87

      Two-dimensional contours for theoretical parameters (x12,y12) (top left), (x12,ϕ12) (top right), and (y12,ϕ12) (bottom), under the assumption of no direct CPV in DCS decays (Fit 3).

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    • Figure 88
      Figure 88

      Two-dimensional contours for parameters (x,y) (upper) and (|q/p|−1,ϕ) (lower), allowing for CPV (fit 4).

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    • Figure 89
      Figure 89

      The function Δχ2=χ2−χmin2 for fitted parameters x,y,δ,δKππ,|q/p|, and ϕ. The points where Δχ2=3.84 (denoted by dashed horizontal lines) determine 95% C.L. intervals.

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    • Figure 90
      Figure 90

      Plot of all data and the fit result. Individual measurements are plotted as bands showing their ±1σ range. The no-CPV point (0,0) is shown as a filled circle, and the best fit value is indicated by a cross showing the one-dimensional uncertainties. Two-dimensional 68% C.L., 99.7% C.L., and 99.99997% C.L. regions are plotted as ellipses.

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    • Figure 91
      Figure 91

      Comparison of the results of f+K(0)|Vcs| measured by the Belle [1335], BABAR [1336], CLEO-c [1337], and BESIII [1269, 1334, 1339, 1340] experiments.

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    • Figure 92
      Figure 92

      Decay angles θV, θℓ and χ. Note that the angle χ between the decay planes is defined in the D-meson reference frame, whereas the angles θV and θℓ are defined in the V meson and W reference frames, respectively.

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    • Figure 93
      Figure 93

      WA values for fD|Vcd| (left) and fDs|Vcs| (right). For each point, the first error is statistical and the second error is systematic. BESIII(a) represents results based on 0.48  fb−1 of data recorded at s=4.009  GeV [1412], and BESIII(b) represents results based on 6.32  fb−1 of data recorded at s=4.178–4.226  GeV [1405, 1406, 1407].

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    • Figure 94
      Figure 94

      Comparison of magnitudes of CKM matrix elements |Vcd| (left) and |Vcs| (right), as determined from leptonic and semileptonic D(s) decays. Also listed are results from neutrino scattering, from W decays, and from a global fit of the CKM matrix assuming unitarity [242].

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    • Figure 95
      Figure 95

      The Kπ invariant mass distribution for D0→K−π+(nγ) decays. The three curves correspond to three different configurations of photos for modeling FSR: version 2.02 without interference (blue/gray), version 2.02 with interference (red dashed) and version 2.15 with interference (black). The true invariant mass has been smeared with a typical experimental resolution of 10  MeV/c2. Inset: The corresponding spectrum of total energy radiated per event. The arrow indicates the ∑Eγ value that begins to shift kinematic quantities outside of the range typically accepted in a measurement.

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    • Figure 96
      Figure 96

      FOCUS data (dots), original fits (blue) and toy MC parametrization (red) for D0→K−π+ (left), D0→π+π− (center), and D0→π+π− (right).

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    • Figure 97
      Figure 97

      Comparison of measurements of B(D0→K−π+) (blue) with the average branching fraction obtained here (red, and yellow band). For these measurements only, the partial χ2 is 4.9 in the final fit.

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    • Figure 98
      Figure 98

      The B(D0→K+K−) (left) and B(D0→π+π−) (right) values obtained either from absolute measurements or by scaling the measured branching ratios with the B(D0→K−π+) branching fraction average obtained here. For the measurements (blue points), the error bars correspond to the statistical, systematic and either the Kπ normalization uncertainties or, in case of an absolute measurement, the FSR modeling uncertainty. The average obtained here (red point, yellow band) lists the statistical, systematics excluding FSR, and the FSR systematic. For the measurements related to B(D0→K+K−) [B(D0→π+π−)] only, the partial χ2 is 15.7 [6.0] in the final fit.

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    • Figure 99
      Figure 99

      (a) Average masses for excited Ds mesons; (b) average masses for excited D mesons; (c) average widths for excited Ds mesons; (d) average widths for excited D mesons. The vertical shaded regions distinguish between different spin-parity states.

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    • Figure 100
      Figure 100

      Level diagram for multiplets and transitions for excited charm baryons.

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    • Figure 101
      Figure 101

      Upper limits at 90% C.L. for D0 decays. The top plot shows flavor-changing neutral current and radiative decays, and the bottom plot shows lepton-flavor-changing (LF), lepton-number-changing (L), and both baryon- and lepton-number-changing (BL) decays.

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    • Figure 102
      Figure 102

      Upper limits at 90% C.L. for D+ (top) and Ds+ (bottom) decays. Each plot shows flavor-changing neutral current and rare decays, lepton-flavor-changing decays (LF), and lepton-number-changing (L) decays.

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    • Figure 103
      Figure 103

      Upper limits at 90% C.L. for Λc+ decays. Shown are flavor-changing neutral current decays, lepton-flavor-changing (LF) decays, and lepton-number-changing (L) decays.

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    • Figure 104
      Figure 104

      |Vus| determinations. In the CKM-unitarity evaluation, |Vud| is taken from a 2020 experimental update [1658]. The value |Vus|Kℓ3 from K−→π0μ−ν¯μ decays is taken from a 2021 update [1665]. The value |Vus|Kℓ2 from K−→μ−ν¯μ decays is taken from Ref. [9].

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