Summary of Charm Semileptonic Decay Results

Summarized below are form factor parameters from various experiments on D meson decays
to pseudoscalar and vector mesons. Combined results are also quoted.
Further details can be found in the 2016 HFAG report [HFAG’16].

D meson decays to Pseudoscalar Mesons

Results for the form factor parameters m_pole and α_BK [BK] from various experiments for D → K l ν decays:

D→Klν expt.	Ref.	mpole (GeV/c^2)	αBK
CLEO III (D^0; m, e)	CLEO’05	1.89 ± 0.05 ^+0:04-0.03	0.36 ± 0.10 ^+0:03-0.07
FOCUS (D^0; m)	FOCUS’05	1.93 ± 0.05 ± 0.03	0.28 ± 0.08 ± 0.07
Belle (D^0; m, e)	BELLE’06	1.82 ± 0.04 ± 0.03	0.52 ± 0.08 ± 0.06
BaBar (D^0; e)	BABAR’07	1.889 ± 0.012 ± 0.015	0.366 ± 0.023 ± 0.029
CLEO-c (tagged; D^0, D^+; e)	CLEO’09	1.93 ± 0.02 ± 0.01	0.30 ± 0.03 ± 0.01
CLEO-c (untagged; D^0; e)	CLEO’07	1.97 ± 0.03 ± 0.01	0.21 ± 0.05 ± 0.03
CLEO-c (untagged; D^+; e)	CLEO’07	1.96 ± 0.04 ± 0.02	0.22 ± 0.08 ± 0.03
BES III (D^0; e)	BES’15	1.921 ± 0.010 ± 0.007	0.309 ± 0.020 ± 0.013
BES III (D^+; e)	BES’15p	1.953 ± 0.044 ± 0.036	0.239 ± 0.077 ± 0.065

Results for the form factor parameters m_pole and α_BK [BK] from various experiments for D → π l ν decays:

D→πlν expt.	Ref.	mpole (GeV/c^2)	αBK
CLEO III (D^0; m, e)	CLEO’05	1.86 ^+0:10-0.06 ^+0:07-0.03	0.37 ^+0:20-0.31 ± 0.15
FOCUS (D^0; m)	FOCUS’05	1.91 ^+0:30-0.15 ± 0.07	-
Belle (D^0; m, e)	BELLE’06	1.97 ± 0.08 ± 0.04	0.10 ± 0.21 ± 0.10
CLEO-c (tagged; D^0,D^+; e)	CLEO’09	1.91 ± 0.02 ± 0.01	0.21 ± 0.07 ± 0.02
CLEO-c (untagged; D^0; e)	CLEO’07	1.87 ± 0.03 ± 0.01	0.37 ± 0.08 ± 0.03
CLEO-c (untagged; D^+; e)	CLEO’07	1.97 ± 0.07 ± 0.02	0.14 ± 0.16 ± 0.04
BaBar (D^0; e)	BABAR’15	1.906 ± 0.029 ± 0.023	0.268 ± 0.074 ± 0.059
BES III (D^0; e)	BES’15	1.911 ± 0.012 ± 0.004	0.279 ± 0.035 ± 0.011

Results for the form factor parameters r₁ and r₂ [ZEXP] and the correlation coefficient ρ₁₂ from various experiments for D→ K l ν decays.

FOCUS and Belle results quotes are obtained by refitting from the published data.

The combined result is performed by a fit to all experimental data with updated input values.

D→Klν expt.	Ref.	r1	r2	ρ12
FOCUS (D^0; m)	FOCUS’04	-2.54 ± 0.75	7 ± 13	-0.97
BELLE (D^0; e,m)	BELLE’06	-3.06 ± 0.71	-3.3 ± 17.9	-0.81
BaBar (D^0; e)	BABAR’07	-2.5 ± 0.2 ± 0.2	0.6 ± 6.0 ± 5.0	-0.64
CLEO-c (tagged; D^0; e)	CLEO’09	-2.65 ± 0.34 ± 0.08	13 ± 9 ± 1	-0.82
CLEO-c (tagged; D^+; e)	CLEO’09	-1.66 ± 0.44 ± 0.10	-14 ± 11 ± 1	-0.82
CLEO-c (untagged; D^0; e)	CLEO’07	-2.4 ± 0.4 ± 0.1	21 ± 11 ± 2	-0.81
CLEO-c (untagged; D^+; e)	CLEO’07	-2.8 ± 6 ± 2	32 ± 18 ± 4	-0.84
BES III (D^0; e)	BES’15	-2.334 ± 0.159 ± 0.080	3.42 ± 3.91 ± 2.41
BES III (D^+; e)	BES’15p	-2.23 ± 0.42 ± 0.53	11.3 ± 8.5 ± 8.7
Combined (z-exp, D^0,+)	HFAG’16	-2.38 ± 0.11 ± 0.06	4.7 ± 2.6 ± 1.4	-0.84

Using an effective three-pole model [BLORS] on the previous data, the combined fit gives for the first two residues of the form factor γ₀ and γ₁,

and the effective mass of the third pole m_{D*’’ s eff}:

D→Klν expt.	Ref.	γ0 (GeV^2)	γ1 (GeV^2)	mD*’’s eff (GeV)
Combined (3-poles, D^0,+)	HFAG’16	4.85 ± 0.08	-1.2 ± 0.30	4.46 ± 0.26

Results for the form factor parameters r₁ and r₂ [ZEXP] and the correlation coefficient ρ₁₂ from various experiments for D → π l ν decays.

Belle results quoted in this table are obtained by refitting the published data.

The combined result is performed by a fit to all experimental data with updated input values.

D→πlν expt.	Ref.	r1	r2	ρ12
Belle	BELLE’06	-1.83 ± 1.00	1.5 ± 6.5	-0.91
CLEO-c (tagged, D^0; e)	CLEO’09	-2.80 ± 0.49 ± 0.04	6 ± 3 ± 0	-0.94
CLEO-c (tagged, D^+; e)	CLEO’09	-1.37 ± 0.88 ± 0.24	-4 ± 5 ± 1	-0.96
CLEO-c (untagged, D^0; e)	CLEO’07	-2.1 ± 0.7 ± 0.3	-1.2 ± 4.8 ± 1.7	-0.96
CLEO-c (untagged, D^+; e)	CLEO’07	-0.2 ± 1.5 ± 0.4	-9.8 ± 9.1 ± 2.1	-0.97
BaBar	BABAR’15	-1.31 ± 0.70 ± 0.43	-4.2 ± 4.0 ± 1.9	-0.97
BES III	BES’14	-1.85 ± 0.22 ± 0.07	-1.4 ± 1.5 ± 0.5	-0.93
Combined (z-exp., D^0,+)	HFAG’16	-1.95 ± 0.18 ± 0.01	-0.52 ± 1.17 ± 0.32	-0.94

Using an effective three-pole model [BLORS] on data from the previous experiments,

the combined fit gives for the first two residues of the form factor γ₀ and γ₁,

and the effective mass of the third pole m_D*’’eff:

D→plν expt.	Ref.	γ0 (GeV^2)	γ1 (GeV^2)	mD*’’eff (GeV)
Combined (3-pole, D^0,+)	HFAG’16	3.878 ± 0.090	-1.18 ± 0.30	4.17± 0.41

Figures of the form factors obtained from the combined fit in .pdf format: [FF_K, FF_pi]

Results for the form factor normalization |V_cs|f^K₊(0) and |V_cd|f^π₊(0), using the z-expansion formalism [ZEXP] on published data,

with updated values to PDG. Total decay rates measured by Mark-III, E653, E687, E691, BES II and CLEO II are included in the combination (see [HFAG’16] for details and references).

The result of the D⁺ mode from BES III [BESIIIp15] is included only as a constraint on the normalization.

Experiment	Ref.	|Vcs|f^K+(0)	|Vcd|f^π+(0)
Belle (2006)	BELLE’06	0.700 ± 0.019	0.140 ± 0.004 ± 0.007
BaBar (2007, 2015)	BABAR’07,15	0.7241 ± 0.0064 ± 0.0060	0.137 ± 0.004 ± 0.002
CLEO-c (tagged, D^0,+) (2009)	CLEO’09	0.7189 ± 0.0064 ± 0.0048	0.150 ± 0.004 ± 0.001
CLEO-c (untagged, D^0,+) (2008)	CLEO’07	0.7436 ± 0.0076 ± 0.0079	0.139 ± 0.004 ± 0.003
BES III (2015)	BES’15	0.7195 ± 0.0035 ± 0.0043	0.142 ± 0.002 ± 0.001
Combined (z-exp.,D^0,+)	HFAG’16	0.7226 ± 0.0022 ± 0.0026	0.1426 ± 0.0017± 0.0008

Using V_cs = 0.97343(15) and V_cd = 0.22521(61), results of the form factor are:

f^K₊(0) = 0.7423 ± 0.0035 and f^π₊(0) = 0.6327 ± 0.0086, compatible with Lattice results [FLAG] of f^K₊(0) = 0.747(19) and f^π₊(0)= 0.666(29).

Integrating over the full q2 range, the combined semileptonic branching fractions give:

B(D⁰→K^-l⁺ν) = (3.490 ± 0.011 ± 0.020)%

B(D⁰→ π ^-l⁺ν) = (0.2891 ± 0.0030 ± 0.0022)%

Figures in the .pdf format of the fit projections for D→K l ν decays: [DK_f₊r₁], [DK_f₊r₂], [DK_r₁r₂]

Figures in the .pdf format of the fit projections for D→ π l ν decays: [Dπ_f₊r₁], [Dπ_f₊r₂], [Dπ_r₁r₂]

D_(s) meson decays to Vector Mesons

Results for the form factor parameters r_v and r₂ from various experiments for D → K*lν. Last lines correspond to D_s → ɸlν and D → ρlν decays from BaBar and CLEO-c. BaBar results quoted here use fixed pole masses. Note that in some results the hh s-wave component (h=K or π ) is not isolated in the r_v and r₂ measurements.

Experiment	Ref.	rv	r2
E691 (D^+)	E691’90	2.0 ± 0.6 ± 0.3	0.0 ± 0.5 ± 0.2
E653 (D^+)	E653’92	2.00 ± 0.33 ± 0.16	0.82 ± 0.22 ± 0.11
E687 (D^+)	E687’93	1.74 ± 0.27 ± 0.28	0.78 ± 0.18 ± 0.11
E791 (D^+, e)	E791’98	1.90 ± 0.11 ± 0.09	0.71 ± 0.08 ± 0.09
E791 (D^+,mu)	E791’98	1.84 ± 0.11 ± 0.09	0.75 ± 0.08 ± 0.09
Beatrice (D^+)	Beatrice’99	1.45 ± 0.23 ± 0.07	1.00 ± 0.15 ± 0.03
FOCUS (D^+)	FOCUS’02	1.504 ± 0.057 ± 0.039	0.875 ± 0.049 ± 0.064
BaBar (D^+)	BABAR’11	1.493 ± 0.014 ± 0.021	0.775 ± 0.011 ± 0.011
FOCUS (D^0)	FOCUS’05	1.706 ± 0.677 ± 0.342	0.912 ± 0.370 ± 0.104
BaBar (Ds → ɸ e ν)	BABAR’08	1.849 ± 0.060 ± 0.095	0.763 ± 0.071 ± 0.065
CLEO-c (D → ρ e ν)**	CLEO’06	1.40 ± 0.25 ± 0.03	0.57 ± 0.18 ± 0.06

**Not published.

Figure in .pdf format [DtoV].

Page maintained by A. Oyanguren. Last update: September 2017.