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 (preliminary) are quoted.
Further details can be found in the 2014 HFAG report [HFAG’14] .

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	CLEO’05	1.89 ± 0.05 ^+0:04-0.03	0.36 ± 0.10 ^+0:03-0.07
FOCUS	FOCUS’05	1.93 ± 0.05 ± 0.03	0.28 ± 0.08 ± 0.07
Belle	BELLE’06	1.82 ± 0.04 ± 0.03	0.52 ± 0.08 ± 0.06
BaBar	BABAR’07	1.889 ± 0.012 ± 0.015	0.366 ± 0.023 ± 0.029
CLEO-c (tagged)	CLEO’09	1.93 ± 0.02 ± 0.01	0.30 ± 0.03 ± 0.01
CLEO-c (untagged, D^0)	CLEO’07	1.97 ± 0.03 ± 0.01	0.21 ± 0.05 ± 0.03
CLEO-c (untagged, D^+)	CLEO’07	1.96 ± 0.04 ± 0.02	0.22 ± 0.08 ± 0.03
BES III (preliminary)	BES’14	1.921 ± 0.010 ± 0.007	0.309 ± 0.020 ± 0.013

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	CLEO’05	1.86 ^+0:10-0.06 ^+0:07-0.03	0.37 ^+0:20-0.31 ± 0.15
FOCUS	FOCUS’05	1.91 ^+0:30-0.15 ± 0.07	-
Belle	BELLE’06	1.97 ± 0.08 ± 0.04	0.10 ± 0.21 ± 0.10
CLEO-c (tagged)	CLEO’09	1.91 ± 0.02 ± 0.01	0.21 ± 0.07 ± 0.02
CLEO-c (untagged, D^0)	CLEO’07	1.87 ± 0.03 ± 0.01	0.37 ± 0.08 ± 0.03
CLEO-c (untagged, D^+)	CLEO’07	1.97 ± 0.07 ± 0.02	0.14 ± 0.16 ± 0.04
BaBar (preliminary)	BABAR’14	1.906 ± 0.029 ± 0.023	0.268 ± 0.074 ± 0.059
BES III (preliminary)	BES’14	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. CLEO III and FOCUS results are refitted from the published data.

D→Klν expt.	Ref.	r1	r2	ρ12
CLEO III	CLEO’05	0.2 ^+3.6-3.0	-89 ^+104-120	-0.99
FOCUS	FOCUS’05	-2.54 ± 0.75	7 ± 13	-0.97
BaBar	BABAR’07	-2.5 ± 0.2 ± 0.2	2.5 ± 6.0 ± 5.0	-0.64
CLEO-c (tagged, D^0)	CLEO’09	-2.65 ± 0.34 ± 0.08	13 ± 9 ± 1	-0.82
CLEO-c (tagged, D^+)	CLEO’09	-1.66 ± 0.44 ± 0.10	-14 ± 11 ± 1	-0.82
CLEO-c (untagged, D^0)	CLEO’07	-2.4 ± 0.4 ± 0.1	21 ± 11 ± 2	-0.81
CLEO-c (untagged, D^+)	CLEO’07	-2.8 ± 6 ± 2	32 ± 18 ± 4	-0.84
BES III (preliminary)	BES’14	-2.33 ± 0.16 ± 0.08	3.4 ± 3.9 ± 2.4
Combined (preliminary)*	HFAG’14	-2.39 ± 0.17	6.2 ± 3.8	-0.82

* Uses partial BESIII statistics [BES’12].

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 are refitted using the published data.

D→πlν expt.	Ref.	r1	r2	ρ12
CLEO-c (tagged, D^0)	CLEO’09	-2.80 ± 0.49 ± 0.04	6 ± 3 ± 0	-0.94
CLEO-c (tagged, D^+)	CLEO’09	-1.37 ± 0.88 ± 0.24	-4 ± 5 ± 1	-0.96
CLEO-c (untagged, D^0)	CLEO’07	-2.1 ± 0.7 ± 0.3	-1.2 ± 4.8 ± 1.7	-0.96
CLEO-c (untagged, D^+)	CLEO’07	-0.2 ± 1.5 ± 0.4	-9.8 ± 9.1 ± 2.1	-0.97
Belle	BELLE’06	-1.84 ± 1.02	1.69 ± 6.5	-0.91
BaBar (preliminary)	BABAR’14	-1.31 ± 0.70 ± 0.43	-4.2 ± 4.0 ± 1.9	-0.97
BES III (preliminary)	BES’14	-1.85 ± 0.22 ± 0.07	-1.4 ± 1.5 ± 0.5	-0.93
Combined (preliminary)	HFAG’14	-1.94 ± 0.19	-0.62 ± 0.19	-0.94

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*’’eff:

D→πlν expt.	Ref.	γ0 (GeV^2)	γ1 (GeV^2)	mD*’’eff (GeV)
Combined fit (preliminary)	HFAG’14	3.878 ± 0.090	-1.18 ± 0.30	4.17± 0.41

Figure of the fit projection in .pdf format: [Dpi3pole]

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

Experiment	Ref.	|Vcs|f^K+(0)	|Vcd|f^π+(0)
Belle (2006)	BELLE’06	0.692 ± 0.007 ± 0.022	0.140 ± 0.004 ± 0.007
BaBar (2007, 2014prel.)	BABAR’07,14	0.720 ± 0.007 ± 0.007	0.137 ± 0.004 ± 0.002
CLEO-c (tagged) (2009)	CLEO’09	0.719 ± 0.006 ± 0.005	0.150 ± 0.004 ± 0.001
CLEO-c (untagged, D^0) (2008)	CLEO’07	0.747 ± 0.009 ± 0.009	0.139 ± 0.004 ± 0.003
BES III (2012prel., 2014prel.)	BES’12,BES’14	0.720 ± 0.004 ± 0.004	0.142 ± 0.002 ± 0.001
Combined (preliminary)	HFAG’14	0.728 ± 0.005	0.1425 ± 0.0019

Using V_cs = 0.97340(16) and V_cd = 0.22538(65), results of the form factor are:

f^K₊(0) = 0.7579 ± 0. 0051 and f^π₊(0) = 0.6318 ± 0.0086, compatible with Lattice results [FLAG] of f^K₊(0) = 0.747(19) and f^π₊(0)= 0.666(29).

Figures in .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: October 2014.