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K± I (JP) = 12
(0−)
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K± MASS
VALUE (MeV) DOCUMENT ID TECN CHG COMMENT
493....677±0....016 OUR FIIIIT Error includes scale factor of 2.8.
493....677±0....013 OUR AVERAGE Error includes scale factor of 2.4. See the ideogram
below.
493.696±0.007 1 DENISOV 91 CNTR − Kaonic atoms
493.636±0.011 2 GALL 88 CNTR − Kaonic atoms
493.640±0.054 LUM 81 CNTR − Kaonic atoms
493.670±0.029 BARKOV 79 EMUL ± e+e− → K+K−
493.657±0.020 2 CHENG 75 CNTR − Kaonic atoms
493.691±0.040 BACKENSTO...73 CNTR − Kaonic atoms
• • • We do not use the following data for averages, fits, limits, etc. • • •
493.631±0.007 GALL 88 CNTR − K−Pb (9→ 8)
493.675±0.026 GALL 88 CNTR − K−Pb (11→ 10)
493.709±0.073 GALL 88 CNTR − K−W (9→ 8)
493.806±0.095 GALL 88 CNTR − K−W (11→ 10)
493.640±0.022±0.008 3 CHENG 75 CNTR − K−Pb (9→ 8)
493.658±0.019±0.012 3 CHENG 75 CNTR − K−Pb (10→ 9)
493.638±0.035±0.016 3 CHENG 75 CNTR − K−Pb (11→ 10)
493.753±0.042±0.021 3 CHENG 75 CNTR − K−Pb (12→ 11)
493.742±0.081±0.027 3 CHENG 75 CNTR − K−Pb (13→ 12)
1 Error increased from 0.0059 based on the error analysis in IVANOV 92.
2 This value is the authors’ combination of all of the separate transitions listed for this
paper.
3 The CHENG 75 values for separate transitions were calculated from their Table 7 transition
energies. The first error includes a 20% systematic error in the noncircular contaminant
shift. The second error is due to a ±5 eV uncertainty in the theoretical transition
energies.
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WEIGHTED AVERAGE
493.677±0.013 (Error scaled by 2.4)
Values above of weighted average, error,
and scale factor are based upon the data in
this ideogram only. They are not necessarily
the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.
BACKENSTO... 73 CNTR 0.1
CHENG 75 CNTR 1.0
BARKOV 79 EMUL 0.1
LUM 81 CNTR
GALL 88 CNTR 13.6
DENISOV 91 CNTR 7.7
χ2
22.4
(Confidence Level = 0.000)
493.55 493.6 493.65 493.7 493.75 493.8 493.85
mK± (MeV)
mK+ − mK−
mK+ Test of CPT.
VALUE (MeV) EVTS DOCUMENT ID TECN CHG
−0....032±0....090 1.5M 4 FORD 72 ASPK ±
4 FORD 72 uses m
π+ − m
π− = +28 ± 70 keV.
K± MEAN LIIIIFE
VALUE (10−8 s) EVTS DOCUMENT ID TECN CHG COMMENT
1....2380±0....0021 OUR FIIIIT Error includes scale factor of 1.9.
1....2379±0....0021 OUR AVERAGE Error includes scale factor of 1.9. See the ideogram
below.
1.2347±0.0030 15M 5 AMBROSINO 08 KLOE ± φ → K+K−
1.2451±0.0030 250k KOPTEV 95 CNTR K at rest, U target
1.2368±0.0041 150k KOPTEV 95 CNTR K at rest, Cu target
1.2380±0.0016 3M OTT 71 CNTR + K at rest
1.2272±0.0036 LOBKOWICZ 69 CNTR + K in flight
1.2443±0.0038 FITCH 65B CNTR + K at rest
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.2415±0.0024 400k 6 KOPTEV 95 CNTR K at rest
1.221 ±0.011 FORD 67 CNTR ±
1.231 ±0.011 BOYARSKI 62 CNTR +
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5 Result obtained by averaging the decay length and decay time analyses taking correlations
into account.
6KOPTEV 95 report this weighted average of their U-target and Cu-target results, where
they have weighted by 1/σ rather than 1/σ2.
WEIGHTED AVERAGE
1.2379±0.0021 (Error scaled by 1.9)
Values above of weighted average, error,
and scale factor are based upon the data in
this ideogram only. They are not necessarily
the same as our ‘best’ values,
obtained from a least-squares constrained fit
utilizing measurements of other (related)
quantities as additional information.
FITCH 65B CNTR 2.8
LOBKOWICZ 69 CNTR 8.9
OTT 71 CNTR 0.0
KOPTEV 95 CNTR 0.1
KOPTEV 95 CNTR 5.7
AMBROSINO 08 KLOE 1.2
χ2
18.6
(Confidence Level = 0.002)
1.21 1.22 1.23 1.24 1.25 1.26 1.27
K± mean life (10−8 s)
((τ K+ − τ K−) / τ average
(This quantity is a measure of CPT invariance in weak interactions.
VALUE (%) DOCUMENT ID TECN
0....11 ±0....09 OUR AVERAGE Error includes scale factor of 1.2.
0.090±0.078 LOBKOWICZ 69 CNTR
0.47 ±0.30 FORD 67 CNTR
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K+ DECAY MODES
K− modes are charge conjugates of the modes below.
Scale factor/
Mode Fraction (Γi /Γ) Confidence level
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Lepttttoniiiic and ssssemiiiillllepttttoniiiic modessss
Γ1 K+ → e+νe ( 1.55 ±0.07 ) × 10−5
Γ2 K+ → μ+νμ (63.54 ±0.14 ) % S=1.3
Γ3 K+ → π0 e+νe ( 5.08 ±0.05 ) % S=2.1
Called K+e3.
Γ4 K+ → π0μ+νμ ( 3.35 ±0.04 ) % S=1.9
Called K+μ3.
Γ5 K+ → π0 π0 e+νe ( 2.2 ±0.4 )× 10−5
Γ6 K+ → π+π−e+νe ( 4.09 ±0.10 ) × 10−5
Γ7 K+ → π+π−μ+νμ ( 1.4 ±0.9 )× 10−5
Γ8 K+ → π0 π0 π0 e+νe < 3.5 × 10−6 CL=90%
Hadrrrroniiiic modessss
Γ9 K+ → π+π0 (20.68 ±0.13 ) % S=1.6
Γ10 K+ → π+π0π0 ( 1.761±0.022) % S=1.1
Γ11 K+ → π+π+π− ( 5.59 ±0.04 ) % S=1.5
Lepttttoniiiic and ssssemiiiillllepttttoniiiic modessss wiiiitttth phottttonssss
Γ12 K+ → μ+νμ γ [a,b] ( 6.2 ±0.8 )× 10−3
Γ13 K+ → μ+νμ γ (SD+) [c,d] < 3.0 × 10−5 CL=90%
Γ14 K+ → μ+νμ γ (SD+INT) [c,d] < 2.7 × 10−5 CL=90%
Γ15 K+ → μ+νμ γ (SD− +
SD−INT)
[c,d] < 2.6 × 10−4 CL=90%
Γ16 K+ → e+νe γ (SD+) [c,d] ( 1.52 ±0.23 ) × 10−5
Γ17 K+ → e+νe γ (SD−) [c,d] < 1.6 × 10−4 CL=90%
Γ18 K+ → π0 e+νe γ [a,b] ( 2.56 ±0.16 ) × 10−4
Γ19 K+ → π0 e+νe γ (SD) [c,d] < 5.3 × 10−5 CL=90%
Γ20 K+ → π0μ+νμ γ [a,b] ( 1.5 ±0.4 )× 10−5
Γ21 K+ → π0 π0 e+νe γ < 5 × 10−6 CL=90%
Hadrrrroniiiic modessss wiiiitttth phottttonssss orrrr paiiiirrrrssss
Γ22 K+ → π+π0 γ [a,b] ( 2.75 ±0.15 ) × 10−4
Γ23 K+ → π+π0 γ (DE) [b,e] ( 4.3 ±0.7 )× 10−6
Γ24 K+ → π+π0π0 γ [a,b] ( 7.6 +5.6
−3.0 ) × 10−6
Γ25 K+ → π+π+π−γ [a,b] ( 1.04 ±0.31 ) × 10−4
Γ26 K+ → π+γγ [b] ( 1.10 ±0.32 ) × 10−6
Γ27 K+ → π+3γ [b] < 1.0 × 10−4 CL=90%
Γ28 K± → π+e+e−γ ( 1.19 ±0.13 ) × 10−8
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Lepttttoniiiic modessss wiiiitttth paiiiirrrrssss
Γ29 K+ → e+νe ν ν < 6 × 10−5 CL=90%
Γ30 K+ → μ+νμ ν ν < 6.0 × 10−6 CL=90%
Γ31 K+ → e+νe e+e− ( 2.48 ±0.20 ) × 10−8
Γ32 K+ → μ+νμ e+e− ( 7.06 ±0.31 ) × 10−8
Γ33 K+ → e+νe μ+μ− ( 1.7 ±0.5 )× 10−8
Γ34 K+ → μ+νμ μ+μ− < 4.1 × 10−7 CL=90%
Leptttton Famiiiilllly numberrrr ((((LF)))),,,, Leptttton numberrrr ((((L)))),,,, ΔS = ΔQ ((((SQ))))
viiiiollllattttiiiing modessss,,,, orrrr ΔS = 1 weak neuttttrrrrallll currrrrrrrentttt ((((S1)))) modessss
Γ35 K+ → π+π+e−νe SQ < 1.2 × 10−8 CL=90%
Γ36 K+ → π+π+μ−νμ SQ < 3.0 × 10−6 CL=95%
Γ37 K+ → π+e+e− S1 ( 2.88 ±0.13 ) × 10−7
Γ38 K+ → π+μ+μ− S1 ( 8.1 ±1.4 )× 10−8 S=2.7
Γ39 K+ → π+ν ν S1 ( 1.5 +1.3
−0.9 ) × 10−10
Γ40 K+ → π+π0 ν ν S1 < 4.3 × 10−5 CL=90%
Γ41 K+ → μ−ν e+e+ LF < 2.0 × 10−8 CL=90%
Γ42 K+ → μ+νe LF [f ] < 4 × 10−3 CL=90%
Γ43 K+ → π+μ+e− LF < 1.3 × 10−11 CL=90%
Γ44 K+ → π+μ−e+ LF < 5.2 × 10−10 CL=90%
Γ45 K+ → π−μ+e+ L < 5.0 × 10−10 CL=90%
Γ46 K+ → π−e+e+ L < 6.4 × 10−10 CL=90%
Γ47 K+ → π−μ+μ+ L [f ] < 3.0 × 10−9 CL=90%
Γ48 K+ → μ+νe L [f ] < 3.3 × 10−3 CL=90%
Γ49 K+ → π0 e+νe L < 3 × 10−3 CL=90%
Γ50 K+ → π+γ [g] < 2.3 × 10−9 CL=90%
[a] Most of this radiative mode, the low-momentum γ part, is also included
in the parent mode listed without γ’s.
[b] See the Particle Listings below for the energy limits used in this measurement.
[c] See the “Note on π± → ±νγ and K± → ±νγ Form Factors” in the
π± Particle Listings for definitions and details.
[d] Structure-dependent part.
[e] Direct-emission branching fraction.
[f ] Derived from an analysis of neutrino-oscillation experiments.
[g] Violates angular-momentum conservation.
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CONSTRAIIIINED FIIIIT IIIINFORMATIIIION
An overall fit to the mean life, a decay rate, and 13 branching
ratios uses 31 measurements and one constraint to determine 8
parameters. The overall fit has a χ2 = 51.7 for 24 degrees of
freedom.
The following off-diagonal array elements are the correlation coefficients
δpiδpj/(δpi·δpj ), in percent, from the fit to parameters pi, including the branching
fractions, xi ≡ Γi/Γtotal. The fit constrains the xi whose labels appear in this
array to sum to one.
x3 −42
x4 −40 91
x5 −2 4 4
x9 −77 −13 −15 −1
x10 −4 −5 −5 0 −11
x11 −8 −10 −10 0 −21 5
Γ 2 2 2 0 4 −1 −20
x2 x3 x4 x5 x9 x10 x11
Mode Rate (108 s−1) Scale factor
Γ2 K+ → μ+νμ 0.5132 ±0.0014 1.4
Γ3 K+ → π0 e+νe 0.0410 ±0.0004 2.1
Called K+e3.
Γ4 K+ → π0μ+νμ 0.02709±0.00030 1.9
Called K+μ3.
Γ5 K+ → π0 π0 e+νe (1.77 +0.35
−0.30 ) × 10−5
Γ9 K+ → π+π0 0.1670 ±0.0011 1.6
Γ10 K+ → π+π0π0 0.01423±0.00018 1.1
Γ11 K+ → π+π+π− 0.04518±0.00035 1.5
K± DECAY RATES
Γμ+νμ Γ2
VALUE (106 s−1) DOCUMENT ID TECN CHG
51....32±0....14 OUR FIIIIT Error includes scale factor of 1.4.
• • • We do not use the following data for averages, fits, limits, etc. • • •
51.2 ±0.8 FORD 67 CNTR ±
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Γπ+π+π− Γ11
VALUE (106 s−1) EVTS DOCUMENT ID TECN CHG
4....518±0....035 OUR FIIIIT Error includes scale factor of 1.5.
4....511±0....024 7 FORD 70 ASPK
• • • We do not use the following data for averages, fits, limits, etc. • • •
4.529±0.032 3.2M 7 FORD 70 ASPK
4.496±0.030 7 FORD 67 CNTR ±
7 First FORD 70 value is second FORD 70 combined with FORD 67.
((((Γ((((K+)))) − Γ((((K−)))))))) / Γ((((K))))
K± → μ±νμ RATE DIIIIFFERENCE/AVERAGE
Test of CPT conservation.
VALUE (%) DOCUMENT ID TECN
−0....54±0....41 FORD 67 CNTR
K± → π±π+π− RATE DIIIIFFERENCE/AVERAGE
Test of CP conservation.
VALUE (%) EVTS DOCUMENT ID TECN CHG
0....08±0....12 8 FORD 70 ASPK
• • • We do not use the following data for averages, fits, limits, etc. • • •
−0.02±0.16 9 SMITH 73 ASPK ±
0.10±0.14 3.2M 8 FORD 70 ASPK
−0.50±0.90 FLETCHER 67 OSPK
−0.04±0.21 8 FORD 67 CNTR
8 First FORD 70 value is second FORD 70 combined with FORD 67.
9 SMITH 73 value of K± → π±π+π− rate difference is derived from SMITH 73 value
of K± → π±2π0 rate difference.
K± → π±π0π0 RATE DIIIIFFERENCE/AVERAGE
Test of CP conservation.
VALUE (%) EVTS DOCUMENT ID TECN CHG
0....0 ±0....6 OURAVERAGE
0.08±0.58 SMITH 73 ASPK ±
−1.1 ±1.8 1802 HERZO 69 OSPK
K± → π±π0 RATE DIIIIFFERENCE/AVERAGE
Test of CPT conservation.
VALUE (%) DOCUMENT ID TECN
0....8±1....2 HERZO 69 OSPK
K± → π±π0γ RATE DIIIIFFERENCE/AVERAGE
Test of CP conservation.
VALUE (%) EVTS DOCUMENT ID TECN CHG COMMENT
0....9±3....3 OUR AVERAGE
0.8±5.8 2461 SMITH 76 WIRE ± Eπ 55–90 MeV
1.0±4.0 4000 ABRAMS 73B ASPK ± Eπ 51–100 MeV
K+ BRANCHIIIING RATIIIIOS
Lepttttoniiiic and ssssemiiiillllepttttoniiiic modessss
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Γe+νeeee/Γμ+νμ Γ1/Γ2
See the note on “Decay Constants of Charged Pseudoscalar Mesons” in the D+s
Listings.
VALUE (units 10−5) EVTS DOCUMENT ID TECN CHG
2....45±0....11 OUR AVERAGE
2.51±0.15 404 HEINTZE 76 SPEC +
2.37±0.17 534 HEARD 75B SPEC +
2.42±0.42 112 CLARK 72 OSPK +
Γμ+νμ/Γttttottttallll Γ2/Γ
See the note on “Decay Constants of Charged Pseudoscalar Mesons” in the D+s
Listings.
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
63....54±0....14 OUR FIIIIT Error includes scale factor of 1.3.
63....60±0....16 OUR AVERAGE
63.66±0.09±0.15 865k 10 AMBROSINO 06A KLOE +
63.24±0.44 62k CHIANG 72 OSPK + 1.84 GeV/c K+
10 Fully inclusive. Used tagged kaons from φ decays.
Γπ0e+νeeee/Γttttottttallll Γ3/Γ
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
5....08 ±0....05 OUR FIIIIT Error includes scale factor of 2.1.
4....94 ±0....05 OUR AVERAGE
4.965±0.038±0.037 11 AMBROSINO 08A KLOE ±
4.86 ±0.10 3516 CHIANG 72 OSPK + 1.84 GeV/c K+
• • • We do not use the following data for averages, fits, limits, etc. • • •
4.7 ±0.3 429 SHAKLEE 64 HLBC +
5.0 ±0.5 ROE 61 HLBC +
11Depends on K+ lifetime τ. AMBROSINO 08A uses PDG 06 value of τ = (1.2385 ±
0.0024) × 10−8 sec. The correlation between K+e3
and K+μ3
branching fraction measurements
is 62.7%.
Γπ0e+νeeee/Γμ+νμ Γ3/Γ2
VALUE EVTS DOCUMENT ID TECN CHG
0....0799±0....0008 OUR FIIIIT Error includes scale factor of 1.8.
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.069 ±0.006 350 ZELLER 69 ASPK +
0.0775±0.0033 960 BOTTERILL 68C ASPK +
0.069 ±0.006 561 GARLAND 68 OSPK +
0.0791±0.0054 295 12 AUERBACH 67 OSPK +
12AUERBACH 67 changed from 0.0797 ± 0.0054. See comment with ratio Γπ0μ+νμ/
Γμ+νμ. The value 0.0785 ± 0.0025 given in AUERBACH 67 is an average of
AUERBACH 67 Γπ0 e+νe/Γμ+νμ and CESTER 66 Γπ0 e+νe /Γμ+νμ +
Γπ+π0.
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Γπ0 e+νe/Γμ+νμ+Γπ+π0 Γ3/(Γ2+Γ9)
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG
6....03±0....06 OUR FIIIIT Error includes scale factor of 2.1.
6....02±0....15 OUR AVERAGE
6.16±0.22 5110 ESCHSTRUTH 68 OSPK +
5.89±0.21 1679 CESTER 66 OSPK +
• • • We do not use the following data for averages, fits, limits, etc. • • •
5.92±0.65 13 WEISSENBE... 76 SPEC +
13Value calculated from WEISSENBERG 76 (π0 e ν), (μν), and (ππ0) values to eliminate
dependence on our 1974 (π2π0) and (ππ+π−) fractions.
Γπ0 e+νe/Γπ0μ+νμ+Γπ+π0 +Γπ+π0 π0 Γ3/(Γ4+Γ9+Γ10)
π0π0VALUE EVTS DOCUMENT ID TECN CHG
0....1968±0....0020 OUR FIIIIT Error includes scale factor of 3.0.
0....1962±0....0008±0....0035 71k SHER 03 B865 +
Γπ0 e+νe/Γπ+π0 Γ3/Γ9
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....2455±0....0029 OUR FIIIIT Error includes scale factor of 3.2.
0....2470±0....0009±0....0004 87k BATLEY 07A NA48 ±
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.221 ±0.012 786 14 LUCAS 73B HBC − Dalitz pairs only
14 LUCAS 73B gives N(Ke3) = 786 ± 3.1%, N(2π) = 3564 ± 3.1%. We use these values
to obtain quoted result.
Γπ0e+νeeee/Γπ+π+π− Γ3/Γ11
VALUE EVTS DOCUMENT ID TECN CHG
0....907±0....012 OUR FIIIIT Error includes scale factor of 1.8.
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.867±0.027 2768 BARMIN 87 XEBC +
0.856±0.040 2827 BRAUN 75 HLBC +
0.850±0.019 4385 15 HAIDT 71 HLBC +
0.846±0.021 4385 15 EICHTEN 68 HLBC +
0.94 ±0.09 854 BELLOTTI 67B HLBC
0.90 ±0.06 230 BORREANI 64 HBC +
15HAIDT 71 is a reanalysis of EICHTEN 68. Not included in average because of large
discrepancy in Γ(π0 μ+ν)/Γ(π0 e+ν) with more precise results.
Γπ0μ+νμ/Γttttottttallll Γ4/Γ
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
3....35 ±0....04 OUR FIIIIT Error includes scale factor of 1.9.
3....24 ±0....04 OUR AVERAGE
3.233±0.029±0.026 16 AMBROSINO 08A KLOE ±
3.33 ±0.16 2345 CHIANG 72 OSPK + 1.84 GeV/c K+
• • • We do not use the following data for averages, fits, limits, etc. • • •
2.8 ±0.4 17 TAYLOR 59 EMUL +
16Depends on K+ lifetime τ. AMBROSINO 08A uses PDG 06 value of τ = (1.2385 ±
0.0024) × 10−8 sec. The correlation between K+e3 and K+μ3 branching fraction measurements
is 62.7%.
17 Earlier experiments not averaged.
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Γπ0μ+νμ/Γμ+νμ Γ4/Γ2
VALUE EVTS DOCUMENT ID TECN CHG
0....0528±0....0006 OUR FIIIIT Error includes scale factor of 1.7.
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.054 ±0.009 240 ZELLER 69 ASPK +
0.0480±0.0037 424 18 GARLAND 68 OSPK +
0.0486±0.0040 307 19 AUERBACH 67 OSPK +
18GARLAND 68 changed from 0.055 ± 0.004 in agreement with μ-spectrum calculation
of GAILLARD 70 appendix B. L.G.Pondrom, (private communication 73).
19AUERBACH 67 changed from 0.0602 ± 0.0046 by erratum which brings the μ-spectrum
calculation into agreement with GAILLARD 70 appendix B.
Γπ0μ+νμ/Γπ0e+νeeee Γ4/Γ3
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....6608±0....0030 OUR FIIIIT Error includes scale factor of 1.1.
0....6618±0....0027 OUR AVERAGE
0.6511±0.0064 20 AMBROSINO 08A KLOE ±
0.663 ±0.003 ±0.001 77k BATLEY 07A NA48 ±
0.671 ±0.007 ±0.008 24k HORIE 01 SPEC
0.670 ±0.014 21 HEINTZE 77 SPEC +
0.667 ±0.017 5601 BOTTERILL 68B ASPK +
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.608 ±0.014 1585 22 BRAUN 75 HLBC +
0.705 ±0.063 554 23 LUCAS 73B HBC − Dalitz pairs only
0.698 ±0.025 3480 24 CHIANG 72 OSPK + 1.84 GeV/c K+
0.596 ±0.025 25 HAIDT 71 HLBC +
0.604 ±0.022 1398 25 EICHTEN 68 HLBC
0.703 ±0.056 1509 CALLAHAN 66B HLBC
20 Not used in the fit. This result enters the fit via correlation of K+e 3
and K+μ3
branching
fraction measurements of AMBROSINO 08A.
21 HEINTZE 77 value from fit to λ0. Assumes μ-e universality.
22BRAUN 75 value is from form factor fit. Assumes μ-e universality.
23 LUCAS 73B gives N(Kμ3) = 554 ± 7.6%, N(Ke3) = 786 ± 3.1%. We divide.
24 CHIANG 72 Γπ0μ+νμ/Γπ0 e+νe is statistically independent of CHIANG 72
Γπ0 μ+νμ/Γtotal and Γπ0 e+νe /Γtotal.
25HAIDT 71 is a reanalysis of EICHTEN 68. Not included in average because of large
discrepancy with more precise results.
Γπ0μ+νμ+Γπ+π0/Γtotal (Γ4+Γ9)/Γ
We combine these two modes for experiments measuring them in xenon bubble chamber
because of difficulties of separating them there.
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG
24....03±0....13 OUR FIIIIT Error includes scale factor of 1.4.
• • • We do not use the following data for averages, fits, limits, etc. • • •
25.4 ±0.9 886 SHAKLEE 64 HLBC +
23.4 ±1.1 ROE 61 HLBC +
Γπ0μ+νμ/Γπ+π0 Γ4/Γ9
VALUE EVTS DOCUMENT ID TECN CHG
0....1637±0....0006±0....0003 77k BATLEY 07A NA48 ±
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Γπ0μ+νμ/Γπ+π+π− Γ4/Γ11
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....600±0....008 OUR FIIIIT Error includes scale factor of 1.7.
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.503±0.019 1505 26 HAIDT 71 HLBC +
0.510±0.017 1505 26 EICHTEN 68 HLBC +
0.63 ±0.07 2845 27 BISI 65B BC + HBC+HLBC
26HAIDT 71 is a reanalysis of EICHTEN 68. Not included in average because of large
discrepancy in Γ(π0 μ+ν)/Γ(π0 e+ν) with more precise results.
27 Error enlarged for background problems. See GAILLARD 70.
Γπ0π0e+νee/Γttttottttallll Γ5/Γ
VALUE (units 10−5) EVTS DOCUMENT ID TECN CHG
2....2 ±0....4 OURFIIIIT
2....54±0....89 10 BARMIN 88B HLBC +
Γπ0π0e+νeeee/Γπ0e+νeeee Γ5/Γ3
VALUE (units 10−4) EVTS DOCUMENT ID TECN CHG
4.3+0.9
4.3−0.7 OUR FIT
+−4.1+1.0
4.1−0.7 OUR AVERAGE
+−4.2+1.0
−0.9 25 BOLOTOV 86B CALO −
3.8+5.0
−1.2 2 LJUNG 73 HLBC +
Γπ+π−e+νeeee/Γπ+π+π− Γ6/Γ11
VALUE (units 10−4) EVTS DOCUMENT ID TECN CHG
7....31±0....16 OUR AVERAGE
7.35±0.01±0.19 388k 28 PISLAK 01 B865
7.21±0.32 30k ROSSELET 77 SPEC +
• • • We do not use the following data for averages, fits, limits, etc. • • •
7.36±0.68 500 BOURQUIN 71 ASPK
7.0 ±0.9 106 SCHWEINB... 71 HLBC +
5.83±0.63 269 ELY 69 HLBC +
28 PISLAK 01 reports Γ(π+π−e+νe )/Γtotal= (4.109 ± 0.008 ± 0.110) × 10−5 using
the PDG 00 value Γ(π+π+π−)/Γtotal= (5.59 ± 0.05) × 10−2. We divide by the
PDG value and unfold its error from the systematic error. PISLAK 03 gives additional
details on the branching ratio measurement and gives improved errors on the S-wave π-π
scattering length: a00
= 0.216 ± 0.013(stat.) ±0.002(syst.) ±0.002(theor.).
Γπ+π−μ+νμ/Γttttottttallll Γ7/Γ
VALUE (units 10−5) EVTS DOCUMENT ID TECN CHG
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.77+0.54
−0.50 1 CLINE 65 FBC +
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Γπ+π−μ+νμ/Γπ+π+π− Γ7/Γ11
VALUE (units 10−4) EVTS DOCUMENT ID TECN CHG
2....57±1....55 7 BISI 67 DBC +
• • • We do not use the following data for averages, fits, limits, etc. • • •
∼ 2.5 1 GREINER 64 EMUL +
Γπ0π0π0e+νeeee/Γttttottttallll Γ8/Γ
VALUE (units 10−6) CL% EVTS DOCUMENT ID TECN CHG
<3....5 90 0 BOLOTOV 88 SPEC −
• • • We do not use the following data for averages, fits, limits, etc. • • •
<9 90 0 BARMIN 92 XEBC +
Hadrrrroniiiic modessss
Γπ+π0/Γtotal Γ9/Γ
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
20....68±0....13 OUR FIIIIT Error includes scale factor of 1.6.
21....18±0....28 16k CHIANG 72 OSPK + 1.84 GeV/c K+
• • • We do not use the following data for averages, fits, limits, etc. • • •
21.0 ±0.6 CALLAHAN 65 HLBC See Γπ+π0/
Γπ+π+π−
Γπ+π0/Γπ+π+π− Γ9/Γ11
VALUE EVTS DOCUMENT ID TECN CHG
3....70±0....04 OUR FIIIIT Error includes scale factor of 1.6.
• • • We do not use the following data for averages, fits, limits, etc. • • •
3.96±0.15 1045 CALLAHAN 66 FBC +
Γπ+π0/Γμ+νμ Γ9/Γ2
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....3254±0....0026 OUR FIIIIT Error includes scale factor of 1.4.
0....3325±0....0032 OUR AVERAGE
0.3329±0.0047±0.0010 45k USHER 92 SPEC + p p at rest
0.3355±0.0057 29 WEISSENBE... 76 SPEC +
0.3277±0.0065 4517 30 AUERBACH 67 OSPK +
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.328 ±0.005 25k 29 WEISSENBE... 74 STRC +
0.305 ±0.018 1600 ZELLER 69 ASPK +
29 WEISSENBERG 76 revises WEISSENBERG 74.
30AUERBACH 67 changed from 0.3253 ± 0.0065. See comment with ratio Γπ0μ+νμ/
Γμ+νμ.
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π+π0π0/Γtotal Γ10/Γ
ΓVALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
1....761±0....022 OUR FIIIIT Error includes scale factor of 1.1.
1....775±0....028 OUR AVERAGE Error includes scale factor of 1.2.
1.763±0.013±0.022 ALOISIO 04A KLOE ±
1.84 ±0.06 1307 CHIANG 72 OSPK + 1.84 GeV/c K+
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.53 ±0.11 198 31 PANDOULAS 70 EMUL +
1.8 ±0.2 108 SHAKLEE 64 HLBC +
1.7 ±0.2 ROE 61 HLBC +
1.5 ±0.2 32 TAYLOR 59 EMUL +
31 Includes events of TAYLOR 59.
32 Earlier experiments not averaged.
Γπ+π0π0 /Γπ+π0 Γ10/Γ9
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....0852±0....0013 OUR FIIIIT Error includes scale factor of 1.1.
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.081 ±0.005 574 33 LUCAS 73B HBC − Dalitz pairs only
33 LUCAS 73B gives N(π2π0) = 574 ± 5.9%, N(2π) = 3564 ± 3.1%. We quote
0.5N(π2π0) N(2π) where 0.5 is because only Dalitz pair π0’s were used.
Γπ+π0π0/Γπ+π+π− Γ10/Γ11
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....315±0....005 OUR FIIIIT Error includes scale factor of 1.1.
0....303±0....009 2027 BISI 65 BC + HBC+HLBC
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.393±0.099 17 YOUNG 65 EMUL +
Γπ+π+π−/Γttttottttallll Γ11/Γ
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
5....59±0....04 OUR FIIIIT Error includes scale factor of 1.5.
• • • We do not use the following data for averages, fits, limits, etc. • • •
5.56±0.20 2330 34 CHIANG 72 OSPK + 1.84 GeV/c K+
5.34±0.21 693 35 PANDOULAS 70 EMUL +
5.71±0.15 DEMARCO 65 HBC
6.0 ±0.4 44 YOUNG 65 EMUL +
5.54±0.12 2332 CALLAHAN 64 HLBC +
5.1 ±0.2 540 SHAKLEE 64 HLBC +
5.7 ±0.3 ROE 61 HLBC +
34Value is not independent of CHIANG 72 Γμ+νμ/Γtotal, Γπ+π0/Γtotal,
Γπ+π0 π0/Γtotal, Γπ0μ+νμ/Γtotal, and Γπ0 e+νe /Γtotal.
35 Includes events of TAYLOR 59.
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Leptonic Leptttoniiic and ssssemiiiillllepttttoniiiic modessss wiiiitttth phottttonssss
Γμ+νμγ/Γttttottttallll Γ12/Γ
VALUE (units 10−3) EVTS DOCUMENT ID TECN CHG COMMENT
6....2±0....8 OUR AVERAGE
6.6±1.5 36,37 DEMIDOV 90 XEBC P(μ) <231.5 MeV/c
6.0±0.9 BARMIN 88 HLBC + P(μ) <231.5 MeV/c
• • • We do not use the following data for averages, fits, limits, etc. • • •
3.5±0.8 37,38 DEMIDOV 90 XEBC E(γ) > 20 MeV
3.2±0.5 57 39 BARMIN 88 HLBC + E(γ) >20 MeV
5.4±0.3 40 AKIBA 85 SPEC P(μ) <231.5 MeV/c
36 P(μ) cut given in DEMIDOV 90 paper, 235.1MeV/c, is a misprint according to authors
(private communication).
37DEMIDOV 90 quotes only inner bremsstrahlung (IB) part.
38 Not independent of above DEMIDOV 90 value. Cuts differ.
39 Not independent of above BARMIN 88 value. Cuts differ.
40 Assumes μ-e universality and uses constraints from K → e νγ.
Γμ+νμγ((((SD+))))/Γttttottttallll Γ13/Γ
Structure-dependent part with +γ helicity (SD+ term). See the “Note on π± →
±νγ and K± → ±ν γ Form Factors” in the π± section of the Particle Data
Listings above.
VALUE (units 10−5) CL% DOCUMENT ID TECN
<3....0 90 AKIBA 85 SPEC
Γμ+νμγ((((SD+IIIINT))))/Γttttottttallll Γ14/Γ
Interference term between internal Bremsstrahlung and SD+ term. See the “Note on
π± → ±νγ and K± → ±νγ Form Factors” in the π± section of the Particle
Data Listings above.
VALUE (units 10−5) CL% DOCUMENT ID TECN
<2....7 90 AKIBA 85 SPEC
Γμ+νμγ((((SD−+SD−IIIINT))))/Γttttottttallll Γ15/Γ
Sum of structure-dependent part with −γ helicity (SD− term) and interference term
between internal Bremsstrahlung and SD− term. See the “Note on π± → ±ν γ and
K± → ±νγ Form Factors” in the π± section of the Particle Data Listings above.
VALUE (units 10−4) CL% DOCUMENT ID TECN
<2....6 90 41 AKIBA 85 SPEC
41 Assumes μ-e universality and uses constraints from K → e νγ.
Γe+νee γ((((SD+))))/Γttttottttallll Γ16/Γ
Structure-dependent part with +γ helicity (SD+ term). See the “Note on π± →
±νγ and K± → ±ν γ Form Factors” in the π± section of the Particle Data
Listings above.
VALUE (units 10−5) CL% DOCUMENT ID TECN CHG COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
<7.1 90 MACEK 70 OSPK + P(e) 234–247
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Γe+νeeee γ((((SD+))))/Γe+νeeee Γ16/Γ1
Structure-dependent part with +γ helicity (SD+ term). See the “Note on π± →
±νγ and K± → ±ν γ Form Factors” in the π± section of the Particle Data
Listings above.
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.05+0.25
−0.30 56 42 HEARD 75 SPEC + P(e) 236–247
42 This value is included in the first HEINTZE 79 value in the section on Γe+νe γ (SD+)/
Γμ+νμ above.
Γe+νeeee γ((((SD+))))/Γμ+νμ Γ16/Γ2
Structure-dependent part with +γ helicity (SD+ term). See the “Note on π± →
±νγ and K± → ±ν γ Form Factors” in the π± section of the Particle Data
Listings above.
VALUE (units 10−5) EVTS DOCUMENT ID TECN CHG
2....40±0....36 107 43 HEINTZE 79 SPEC +
• • • We do not use the following data for averages, fits, limits, etc. • • •
2.33±0.42 51 43 HEINTZE 79 SPEC +
43 First HEINTZE 79 result is second combined with HEARD 75 result from section
Γe+νe γ (SD+)/Γe+νe below.
Γe+νeeee γ((((SD−))))/Γttttottttallll Γ17/Γ
Structure-dependent part with −γ helicity (SD− term). See the “Note on π± →
±νγ and K± → ±ν γ Form Factors” in the π± section of the Particle Data
Listings above.
VALUE (units 10−4) CL% DOCUMENT ID TECN CHG
<1....6 90 44 HEINTZE 79 SPEC +
44 Implies (axial vector/vector) amplitude ratio outside range from −1.8 to −0.54.
Γπ0e+νeeee γ/Γπ0e+νeeee Γ18/Γ3
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG COMMENT
0....505±0....032 OUR AVERAGE Error includes scale factor of 1.3. See the ideogram below.
0.47 ±0.02 ±0.03 4476 45 AKIMENKO 07 ISTR − Eγ > 10 MeV, 0.6 <
cos(θeγ) < 0.9
0.46 ±0.08 82 46 BARMIN 91 XEBC Eγ > 10 MeV, 0.6 <
cos(θeγ) < 0.9
0.56 ±0.04 192 47 BOLOTOV 86B CALO − Eγ > 10 MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.81 ±0.03 ±0.07 4476 45 AKIMENKO 07 ISTR − Eγ>10 MeV, θeγ >10◦
0.63 ±0.02 ±0.03 4476 45 AKIMENKO 07 ISTR − Eγ>30 MeV, θeγ >20◦
1.51 ±0.25 82 46 BARMIN 91 XEBC Eγ > 10 MeV, cos(θeγ)
< 0.98
0.48 ±0.20 16 48 LJUNG 73 HLBC + Eγ > 30 MeV
0.22 +0.15
−0.10
48 LJUNG 73 HLBC + Eγ > 30 MeV
0.76 ±0.28 13 49 ROMANO 71 HLBC Eγ > 10 MeV
0.53 ±0.22 49 ROMANO 71 HLBC + Eγ > 30 MeV
1.2 ±0.8 BELLOTTI 67 HLBC Eγ > 30 MeV
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45AKIMENKO 07 provides values for three kinematic regions. For averaging, we use value
with Eγ > 10 MeV and 0.6 < cos(θeγ) < 0.9.
46BARMIN 91 quotes branching ratio Γ(K → e π0νγ)/Γall. The measured normalization
is [Γ(K → e π0 ν) + Γ(K → π+π+π−)]. For comparison with other experiments we
used Γ(K → e π0 ν)/Γall = 0.0482 to calculate the values quoted here.
47 cos(θeγ) between 0.6 and 0.9.
48 First LJUNG 73 value is for cos(θeγ) <0.9, second value is for cos(θeγ) between 0.6
and 0.9 for comparison with ROMANO 71.
49Both ROMANO 71 values are for cos(θeγ) between 0.6 and 0.9. Second value is for
comparison with second LJUNG 73 value. We use lowest Eγ cut for Summary Table
value. See ROMANO 71 for Eγ dependence.
WEIGHTED AVERAGE
0.505±0.032 (Error scaled by 1.3)
BOLOTOV 86B CALO 1.9
BARMIN 91 XEBC 0.3
AKIMENKO 07 ISTR 1.0
χ2
3.1
(Confidence Level = 0.207)
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Γ
π0 e+νe γ /Γ
π0 e+νe (units 10−2)
Γπ0e+νeeee γ((((SD))))/Γttttottttallll Γ19/Γ
Structure-dependent part.
VALUE (units 10−5) CL% DOCUMENT ID TECN CHG
<5....3 90 BOLOTOV 86B CALO −
Γπ0μ+νμγ/Γttttottttallll Γ20/Γ
VALUE (units 10−5) CL% EVTS DOCUMENT ID TECN CHG COMMENT
1....46±0....22±0....32 153 50 TCHIKILEV 07 ISTR − 30 < Eγ < 60 MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
2.4 ±0.5 ±0.6 125 SHIMIZU 06 K470 + Eγ > 30 MeV;
Θμγ >20◦
<6.1 90 0 LJUNG 73 HLBC + E(γ) >30 MeV
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50Obtained from measuring B(Kμ3γ) / B(Kμ3) and using PDG 02 value B(Kμ3) = 3.27%.
B(Kμ3γ) = (8.82 ± 0.94 ± 0.86) × 10−5 is obtained for 5 MeV < Eγ < 30 MeV.
Γπ0π0e+νeeee γ/Γttttottttallll Γ21/Γ
VALUE (units 10−6) CL% EVTS DOCUMENT ID TECN CHG COMMENT
<5 90 0 BARMIN 92 XEBC + Eγ > 10 MeV
Hadrrrroniiiic modessss wiiiitttth phottttonssss
Γπ+π0γ/Γttttottttallll Γ22/Γ
VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN CHG COMMENT
2....75±0....15 OUR AVERAGE
2.71±0.45 140 BOLOTOV 87 WIRE − Tπ− 55–90 MeV
2.87±0.32 2461 SMITH 76 WIRE ± Tπ± 55–90 MeV
2.71±0.19 2100 ABRAMS 72 ASPK ± Tπ+ 55–90 MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.5 +1.1
−0.6
51 LJUNG 73 HLBC + Tπ+ 55–80 MeV
2.6 +1.5
−1.1
51 LJUNG 73 HLBC + Tπ+ 55–90 MeV
6.8 +3.7
−2.1 17 51 LJUNG 73 HLBC + Tπ+ 55–102 MeV
2.4 ±0.8 24 EDWARDS 72 OSPK Tπ+ 58–90 MeV
<1.0 0 52 MALTSEV 70 HLBC + Tπ+ <55 MeV
<1.9 90 0 EMMERSON 69 OSPK Tπ+ 55–80 MeV
2.2 ±0.7 18 CLINE 64 FBC + Tπ+ 55–80 MeV
51 The LJUNG 73 values are not independent.
52MALTSEV 70 selects low π+ energy to enhance direct emission contribution.
Γπ+π0γ((((DE))))/Γttttottttallll Γ23/Γ
Direct emission (DE) part of Γπ+π0 γ/Γtotal, assuming that interference (INT)
component is zero.
VALUE (units 10−6) EVTS DOCUMENT ID TECN CHG COMMENT
4....3±0....7 OUR AVERAGE
3.8±0.8±0.7 10k ALIEV 06 K470 + Tπ+ 55–90 MeV
3.7±3.9±1.0 930 UVAROV 06 ISTR − Tπ− 55–90 MeV
4.7±0.8±0.3 20k 53 ADLER 00C B787 + Tπ+ 55–90 MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
3.2±1.3±1.0 4k ALIEV 03 K470 + Tπ+ 55–90 MeV
6.1±2.5±1.9 4k ALIEV 03 K470 + Tπ+ full range
20.5±4.6+3.9
−2.3 BOLOTOV 87 WIRE − Tπ− 55–90 MeV
15.6±3.5±5.0 ABRAMS 72 ASPK ± Tπ± 55–90 MeV
53 ADLER 00C measures the INT component to be (−0.4 ± 1.6)% of the inner
bremsstrahlung (IB) component.
Γπ+π0π0 γ/Γπ+π0 π0 Γ24/Γ10
VALUE (units 10−4) DOCUMENT ID TECN CHG COMMENT
4.3+3.2
4.3−1.7
+−BOLOTOV 85 SPEC − E(γ) > 10 MeV
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Γπ+π+π−γ/Γttttottttallll Γ25/Γ
VALUE (units 10−4) EVTS DOCUMENT ID TECN CHG COMMENT
1....04±0....31 OUR AVERAGE
1.10±0.48 7 BARMIN 89 XEBC E(γ) > 5 MeV
1.0 ±0.4 STAMER 65 EMUL + E(γ) >11 MeV
Γπ+γγ/Γttttottttallll Γ26/Γ
VALUE (units 10−7) CL% EVTS DOCUMENT ID TECN CHG COMMENT
11±3 ±1 31 54 KITCHING 97 B787
• • • We do not use the following data for averages, fits, limits, etc. • • •
< 0.083 90 55 ARTAMONOV 05 B949 + Pπ > 213MeV/c
< 10 90 0 ATIYA 90B B787 Tπ 117–127 MeV
< 84 90 0 ASANO 82 CNTR + Tπ 117–127 MeV
−420 ± 520 0 ABRAMS 77 SPEC + Tπ < 92 MeV
< 350 90 0 LJUNG 73 HLBC + 6–102, 114–127 MeV
< 500 90 0 KLEMS 71 OSPK + Tπ < 117 MeV
−100 ± 600 CHEN 68 OSPK + Tπ 60–90 MeV
54 KITCHING 97 is extrapolated from their model-independent branching fraction (6.0 ±
1.5± 0.7)×10−7 for 100 MeV/c<P
π+ < 180 MeV/c using Chiral Perturbation Theory.
55ARTAMONOV 05 limit assumes ChPT with ˆc= 1.8 with unitarity corrections. With ˆc=
1.6 and no unitarity corrections they obtain < 2.3 × 10−8 at 90% CL. This partial
branching ratio is predicted to be 6.10 × 10−9 and 0.49 × 10−9 for the cases with and
without unitarity correction.
Γπ+3γ/Γttttottttallll Γ27/Γ
Values given here assume a phase space pion energy spectrum.
VALUE (units 10−4) CL% DOCUMENT ID TECN CHG COMMENT
<1....0 90 ASANO 82 CNTR + T(π) 117–127
MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
<3.0 90 KLEMS 71 OSPK + T(π) >117 MeV
Γπ+e+e−γ/Γttttottttallll Γ28/Γ
VALUE (units 10−8) EVTS DOCUMENT ID TECN COMMENT
1....19±0....12±0....04 113 56 BATLEY 08 NA48 me e γ > 260 MeV
56BATLEY 08 also reports the Chiral Perturbation Theory parameter ˆc = 0.9 ± 0.45
obtained using the shape of the e+e−γ invariant mass spectrum. By extrapolating
the theoretical amplitude to me e γ < 260 MeV, it obtains the inclusive B(K+ →
π+e+e−γ) = (1.29 ± 0.13 ± 0.03) × 10−8, where the first error is the combined
statistical and systematic errors and the second error is from the uncertainty in ˆc.
Lepttttoniiiic modessss wiiiitttth paiiiirrrrssss
Γe+νeeee νν/Γe+νeeee Γ29/Γ1
VALUE CL% EVTS DOCUMENT ID TECN CHG
<3....8 90 0 HEINTZE 79 SPEC +
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Γμ+νμνν/Γttttottttallll Γ30/Γ
VALUE (units 10−6) CL% EVTS DOCUMENT ID TECN CHG
<6....0 90 0 57 PANG 73 CNTR +
57 PANG 73 assumes μ spectrum from ν-ν interaction of BARDIN 70.
Γe+νeeee e+e−/Γttttottttallll Γ31/Γ
VALUE (units 10−8) EVTS DOCUMENT ID TECN CHG COMMENT
2....48± 0....14±0....14 410 POBLAGUEV 02 B865 + me e >150 MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
20 ±20 4 DIAMANT-... 76 SPEC + m
e+ e− >140 MeV
Γμ+νμe+e−/Γttttottttallll Γ32/Γ
VALUE (units 10−8) EVTS DOCUMENT ID TECN CHG COMMENT
7....06± 0....16±0....26 2.7k POBLAGUEV 02 B865 + me e >145 MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
100 ±30 14 DIAMANT-... 76 SPEC + m
e+ e− >140 MeV
Γe+νeeee μ+μ−/Γttttottttallll Γ33/Γ
VALUE (units 10−8) CL% DOCUMENT ID TECN
1....72±0....45 MA 06 B865
• • • We do not use the following data for averages, fits, limits, etc. • • •
<50 90 ADLER 98 B787
Γμ+νμμ+μ−/Γttttottttallll Γ34/Γ
VALUE (units 10−7) CL% DOCUMENT ID TECN CHG
<4....1 90 ATIYA 89 B787 +
Leptttton Famiiiilllly numberrrr ((((LF)))),,,, Leptttton numberrrr ((((L)))),,,, ΔS = ΔQ ((((SQ))))
viiiiollllattttiiiing modessss,,,, orrrr ΔS = 1 weak neuttttrrrrallll currrrrrrrentttt ((((S1)))) modessss
Γπ+π+e−νeeee/Γttttottttallll Γ35/Γ
Test of ΔS = ΔQ rule.
VALUE (units 10−7) CL% EVTS DOCUMENT ID TECN CHG
• • • We do not use the following data for averages, fits, limits, etc. • • •
< 9.0 95 0 SCHWEINB... 71 HLBC +
< 6.9 95 0 ELY 69 HLBC +
<20. 95 BIRGE 65 FBC +
Γπ+π+e−νeeee/Γπ+π−e+νeeee Γ35/Γ6
Test of ΔS = ΔQ rule.
VALUE (units 10−4) CL% EVTS DOCUMENT ID TECN
< 3 90 3 58 BLOCH 76 SPEC
• • • We do not use the following data for averages, fits, limits, etc. • • •
<130. 95 0 BOURQUIN 71 ASPK
58BLOCH 76 quotes 3.6 × 10−4 at CL = 95%, we convert.
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Γπ+π+μ−νμ/Γttttottttallll Γ36/Γ
Test of ΔS = ΔQ rule.
VALUE (units 10−6) CL% EVTS DOCUMENT ID TECN CHG
<3....0 95 0 BIRGE 65 FBC +
Γπ+e+e−/Γttttottttallll Γ37/Γ
Test for ΔS = 1 weak neutral current. Allowed by combined first-order weak and
electromagnetic interactions.
VALUE (units 10−7) EVTS DOCUMENT ID TECN CHG
2....88±0....13 OUR AVERAGE
2.94±0.05±0.14 10300 59 APPEL 99 SPEC +
2.75±0.23±0.13 500 60 ALLIEGRO 92 SPEC +
2.7 ±0.5 41 61 BLOCH 75 SPEC +
59APPEL 99 establishes vector nature of this decay and determines form factor f(Z)=
f0(1+δZ), Z=M2
e e/m2
K , δ=2.14 ± 0.13 ± 0.15.
60ALLIEGRO 92 assumes a vector interaction with a form factor given by λ = 0.105 ± 0.035 ± 0.015 and a correlation coefficient of −0.82.
61BLOCH 75 assumes a vector interaction.
Γπ+μ+μ−/Γttttottttallll Γ38/Γ
Test for ΔS = 1 weak neutral current. Allowed by higher-order electroweak interactions.
VALUE (units 10−8) CL% EVTS DOCUMENT ID TECN CHG
8....1 ±1....4 OURAVERAGE Error includes scale factor of 2.7. See the ideogram
below.
9.8 ±1.0 ±0.5 110 62 PARK 02 HYCP ±
9.22±0.60±0.49 402 63 MA 00 B865 +
5.0 ±0.4 ±0.9 207 64 ADLER 97C B787 +
• • • We do not use the following data for averages, fits, limits, etc. • • •
9.7 ±1.2 ±0.4 65 PARK 02 HYCP +
10.0 ±1.9 ±0.7 35 PARK 02 HYCP −
<23 90 ATIYA 89 B787 +
62 PARK 02 “±” result comes from combining K+ → π+μ+μ− and K− → π−μ+μ−,
assuming CP is conserved.
63MA 00 establishes vector nature of this decay and determines form factor f(Z)=
f0(1+δZ), Z=M2
μμ
/m2
K , δ=2.45+1.30
−0.95. .
64 ADLER 97C gives systematic error 0.7 × 10−8 and theoretical uncertainty 0.6 × 10−8,
which we combine in quadrature to obtain our second error.
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WEIGHTED AVERAGE
8.1±1.4 (Error scaled by 2.7)
ADLER 97C B787 10.0
MA 00 B865 2.1
PARK 02 HYCP 2.3
χ2
14.3
(Confidence Level = 0.001)
0 5 10 15 20
Γ
π+μ+μ− /Γtotal Γ38/Γ
Γπ+νν/Γttttottttallll Γ39/Γ
Test for ΔS = 1 weak neutral current. Allowed by higher-order electroweak interactions.
Branching ratio values are extrapolated from the momentum or energy regions
shown in the comments assuming Standard Model phase space except for those labeled
“Scalar” or “Tensor” to indicate the assumed non-Standard-Model interaction.
VALUE (units 10−9) CL% EVTS DOCUMENT ID TECN CHG COMMENT
0.147+0.130
0.147−0.089
+−3 65 ANISIMOVSK...04 B949 + 211<Pπ <229MeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
< 2.2 90 66 ADLER 04 B787 + 140<Pπ <195 MeV
0.157+0.175
−0.082 2 ADLER 02 B787 Pπ >211 MeV/c
< 4.2 90 1 ADLER 02C B787 140<Pπ <195 MeV
< 4.7 90 ADLER 02C B787 Scalar
< 2.5 90 ADLER 02C B787 Tensor
0.15 +0.34
−0.12 1 ADLER 00 B787 In ADLER 02
0.42 +0.97
−0.35 1 ADLER 97 B787
< 2.4 90 ADLER 96 B787
< 7.5 90 ATIYA 93 B787 + T(π) 115–127 MeV
< 5.2 90 67 ATIYA 93 B787 +
< 17 90 0 ATIYA 93B B787 + T(π) 60–100 MeV
< 34 90 ATIYA 90 B787 +
<140 90 ASANO 81B CNTR + T(π) 116–127 MeV
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65Value obtained combining the previous E787 result ADLER 02 with 2 evts and the present
E949 with 1 evt. The additional event has a signal-to-background ratio 0.9.
66Value obtained combining the previous result ADLER 02C with 1 event and the present
result with 0 events to obtain an expected background 1.22 ± 0.24 evts and 1 evt
observed.
67 Combining ATIYA 93 and ATIYA 93B results. Superseded by ADLER 96.
Γπ+π0νν/Γttttottttallll Γ40/Γ
Test for ΔS = 1 weak neutral current. Allowed by higher-order electroweak interactions.
VALUE (units 10−5) CL% DOCUMENT ID TECN
<4....3 90 68 ADLER 01 SPEC
68 Search region defined by 90 MeV/c<P
π+ <188 MeV/c and 135 MeV<E
π0 <180 MeV.
Γμ−ν e+e+/Γπ+π−e+νe Γ41/Γ6
Test of lepton family number conservation.
VALUE (units 10−3) CL% EVTS DOCUMENT ID TECN CHG
<0....5 90 0 69 DIAMANT-... 76 SPEC +
69 DIAMANT-BERGER 76 quotes this result times our 1975 π+π−e ν BR ratio.
Γμ+νeeee/Γttttottttallll Γ42/Γ
Forbidden by lepton family number conservation.
VALUE CL% EVTS DOCUMENT ID TECN COMMENT
<0....004 90 0 70 LYONS 81 HLBC 200 GeV K+ narrow
band ν beam
• • • We do not use the following data for averages, fits, limits, etc. • • •
<0.012 90 70 COOPER 82 HLBC Wideband ν beam
70COOPER 82 and LYONS 81 limits on νe observation are here interpreted as limits on
lepton family number violation in the absence of mixing.
Γπ+μ+e−/Γttttottttallll Γ43/Γ
Test of lepton family number conservation.
VALUE (units 10−10) CL% DOCUMENT ID TECN CHG
<0....13 90 71 SHER 05 RVUE +
• • • We do not use the following data for averages, fits, limits, etc. • • •
<0.21 90 SHER 05 B865 +
<0.39 90 APPEL 00 B865 +
<2.1 90 LEE 90 SPEC +
71This result combines SHER 05 1998 data, APPEL 00 1996 data, and data from
BERGMAN 97 and PISLAK 97 theses, all from BNL-E865, with LEE 90 BNL-E777
data.
Γπ+μ−e+/Γtotal Γ44/Γ
Test of lepton family number conservation.
VALUE (units 10−10) CL% EVTS DOCUMENT ID TECN CHG
< 5....2 90 0 APPEL 00B B865 +
• • • We do not use the following data for averages, fits, limits, etc. • • •
<70 90 0 72 DIAMANT-... 76 SPEC +
72 Measurement actually applies to the sum of the π+μ−e+ and π−μ+e+ modes.
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π−μ+e+/Γtotal Γ45/Γ
ΓTest of total lepton number conservation.
VALUE (units 10−10) CL% EVTS DOCUMENT ID TECN CHG
< 5....0 90 0 APPEL 00B B865 +
• • • We do not use the following data for averages, fits, limits, etc. • • •
<70 90 0 73 DIAMANT-... 76 SPEC +
73 Measurement actually applies to the sum of the π+μ−e+ and π−μ+e+ modes.
Γπ−e+e+/Γtotal Γ46/Γ
Test of total lepton number conservation.
VALUE CL% EVTS DOCUMENT ID TECN CHG
<6....4×10−10 90 0 APPEL 00B B865 +
• • • We do not use the following data for averages, fits, limits, etc. • • •
<9.2 × 10−9 90 0 DIAMANT-... 76 SPEC +
<1.5 × 10−5 CHANG 68 HBC −
Γπ−μ+μ+/Γtotal Γ47/Γ
Forbidden by total lepton number conservation.
VALUE CL% EVTS DOCUMENT ID TECN CHG
<3....0×10−9 90 0 APPEL 00B B865 +
• • • We do not use the following data for averages, fits, limits, etc. • • •
<1.5 × 10−4 90 74 LITTENBERG 92 HBC
74 LITTENBERG 92 is from retroactive data analysis of CHANG 68 bubble chamber data.
Γμ+νee/Γttttottttallll Γ48/Γ
Forbidden by total lepton number conservation.
VALUE (units 10−3) CL% DOCUMENT ID TECN COMMENT
<3....3 90 75 COOPER 82 HLBC Wideband ν beam
75COOPER 82 limit on νe observation is here interpreted as a limit on lepton number
violation in the absence of mixing.
Γπ0e+νeeee/Γttttottttallll Γ49/Γ
Forbidden by total lepton number conservation.
VALUE CL% DOCUMENT ID TECN COMMENT
<0....003 90 76 COOPER 82 HLBC Wideband ν beam
76COOPER 82 limit on νe observation is here interpreted as a limit on lepton number
violation in the absence of mixing.
Γπ+γ/Γttttottttallll Γ50/Γ
Violates angular momentum conservation and gauge invariance. Current interest in
this decay is as a search for non-commutative space-time effects as discussed in ARTAMONOV
05 and for exotic physics such as a vacuum expectation value of a new
vector field, non-local Superstring effects, or departures from Lorentz invariance, as
discussed in ADLER 02B.
VALUE (units 10−9) CL% DOCUMENT ID TECN CHG
< 2....3 90 ARTAMONOV 05 B949 +
• • • We do not use the following data for averages, fits, limits, etc. • • •
< 360 90 ADLER 02B B787 +
<1400 90 ASANO 82 CNTR +
<4000 90 77 KLEMS 71 OSPK +
77Test of model of Selleri, Nuovo Cimento 60A 291 (1969).
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LONGITUDINAL K+ LONGIIITUDIIINAL POLARIIIIZATIIIION OF EMIIIITTED μ+
VALUE CL% DOCUMENT ID TECN CHG COMMENT
<−0....990 90 78 AOKI 94 SPEC +
• • • We do not use the following data for averages, fits, limits, etc. • • •
<−0.990 90 IMAZATO 92 SPEC + Repl. by
AOKI 94
−0.970±0.047 79 YAMANAKA 86 SPEC +
−1.0 ±0.1 79 CUTTS 69 SPRK +
−0.96 ±0.12 79 COOMBES 57 CNTR +
78AOKI 94 measures ξPμ =−0.9996 ± 0.0030 ± 0.0048. The above limit is obtained by
summing the statistical and systematic errors in quadrature, normalizing to the physically
significant region ( ξPμ < 1) and assuming that ξ=1, its maximum value.
79 Assumes ξ=1.
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ENERGY DEPENDENCE OF K± DALIIIITZ PLOT
matrix element
2 = 1 + gu + hu2 + kv2
where u = (s3 − s0) / m2
π
and v = (s2 − s1) / m2
π
LIIIINEAR COEFFIIIICIIIIENT g FOR K± → π±π+π−
Some experiments use Dalitz variables x and y. In the comments we give ay =
coefficient of y term. See note above on “Dalitz Plot Parameters for K → 3π
Decays.” For discussion of the conversion of ay to g, see the earlier version of the
same note in the Review published in Physics Letters 111B 70 (1982).
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
−0....21134±0....00017 471M 80 BATLEY 07B NA48 ±
• • • We do not use the following data for averages, fits, limits, etc. • • •
−0.2221 ±0.0065 225k DEVAUX 77 SPEC + ay=.2814±.0082
−0.199 ±0.008 81k 81 LUCAS 73 HBC − ay =0.252±0.011
−0.2157 ±0.0028 750k FORD 72 ASPK + ay=.2734±.0035
−0.2186 ±0.0028 750k FORD 72 ASPK − ay=.2770±.0035
−0.200 ±0.009 39819 82 HOFFMASTER72 HLBC +
−0.196 ±0.012 17898 83 GRAUMAN 70 HLBC + ay =0.228±0.030
−0.193 ±0.010 50919 MAST 69 HBC − ay =0.244±0.013
−0.218 ±0.016 9994 84 BUTLER 68 HBC + ay =0.277±0.020
−0.190 ±0.023 5778 84,85 MOSCOSO 68 HBC − ay =0.242±0.029
−0.22 ±0.024 5428 84,85 ZINCHENKO 67 HBC + ay =0.28 ± 0.03
−0.220 ±0.035 1347 86 FERRO-LUZZI 61 HBC − ay =0.28 ± 0.045
80 Final state strong interaction and radiative corrections not included in the fit.
81 Quadratic dependence is required by K0
L experiments.
82HOFFMASTER 72 includes GRAUMAN 70 data.
83Emulsion data added — all events included by HOFFMASTER 72.
84 Experiments with large errors not included in average.
85Also includes DBC events.
86 No radiative corrections included.
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QUADRATIC QUADRATIIIC COEFFIIIICIIIIENT h FOR K± → π±π+π−
VALUE (units 10−2) EVTS DOCUMENT ID TECN CHG
1....848±0....040 471M 87 BATLEY 07B NA48 ±
• • • We do not use the following data for averages, fits, limits, etc. • • •
−0.06 ±1.43 225k DEVAUX 77 SPEC +
1.87 ±0.62 750k FORD 72 ASPK +
1.25 ±0.62 750k FORD 72 ASPK −
−0.9 ±1.4 39819 HOFFMASTER72 HLBC +
−0.1 ±1.2 50919 MAST 69 HBC −
87 Final state strong interaction and radiative corrections not included in the fit.
QUADRATIIIIC COEFFIIIICIIIIENT k FOR K± → π±π+π−
VALUE (units 10−3) EVTS DOCUMENT ID TECN CHG
− 4....63± 0....14 471M 88 BATLEY 07B NA48 ±
• • • We do not use the following data for averages, fits, limits, etc. • • •
−20.5 ± 3.9 225k DEVAUX 77 SPEC +
− 7.5 ± 1.9 750k FORD 72 ASPK +
− 8.3 ± 1.9 750k FORD 72 ASPK −
−10.5 ± 4.5 39819 HOFFMASTER72 HLBC +
−14 ±12 50919 MAST 69 HBC −
88 Final state strong interaction and radiative corrections not included in the fit.
(−(g+ − g −) / (g+ + g) FOR K± → π±π+π−
−) This is a CP violating asymmetry between linear coefficients g+ for K+ → π+π+π−
decay and g− for K− → π−π+π− decay.
VALUE (units 10−4) EVTS DOCUMENT ID TECN
− 1....5± 1....5±1....6 3.1G 89 BATLEY 07E NA48
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.7± 2.1±2.0 1.7G 90 BATLEY 06 NA48
−70.0±53 3.2M FORD 70 ASPK
89BATLEY 07E includes data from BATLEY 06. Uses quadratic parametrization and value
g++ g− = 2g from BATLEY 07B. This measurement neglects any possible charge
asymmetries in higher order slope parameters h or k.
90 This measurement neglects any possible charge asymmetries in higher order slope parameters
h or k.
LIIIINEAR COEFFIIIICIIIIENT g FOR K± → π±π0π0
Unless otherwise stated, all experiments include terms quadratic
in (s3 − s0) / m2
π+. See note above on “Dalitz Plot Parameters for K → 3π Decays.”
See BATUSOV 98 for a discussion of the discrepancy between their result and others,
especially BOLOTOV 86. At this time we have no way to resolve the discrepancy so
we depend on the large scale factor as a warning.
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....626 ±0....007 OUR AVERAGE
0.6259±0.0043±0.0093 493k AKOPDZHAN...05B TNF ±
0.627 ±0.004 ±0.010 252k 91,92 AJINENKO 03B ISTR −
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• • • We do not use the following data for averages, fits, limits, etc. • • •
0.736 ±0.014 ±0.012 33k BATUSOV 98 SPEC +
0.582 ±0.021 43k BOLOTOV 86 CALO −
0.670 ±0.054 3263 BRAUN 76B HLBC +
0.630 ±0.038 5635 SHEAFF 75 HLBC +
0.510 ±0.060 27k SMITH 75 WIRE +
0.67 ±0.06 1365 AUBERT 72 HLBC +
0.544 ±0.048 4048 DAVISON 69 HLBC + Also emulsion
91 Measured using in-flight decays of the 25 GeV negative secondary beam.
92 They form new world averages g− = (0.617 ± 0.018) and g+ = (0.684 ± 0.033) which
give Δgτ = 0.051 ± 0.028.
QUADRATIC QUADRATIIIC COEFFIIIICIIIIENT h FOR K± → π±π0π0
VALUE EVTS DOCUMENT ID TECN CHG COMMENT
0....052 ±0....008 OUR AVERAGE
0.0551±0.0044±0.0086 493k AKOPDZHAN...05B TNF ±
0.046 ±0.004 ±0.012 252k 93 AJINENKO 03B ISTR −
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.128 ±0.015 ±0.024 33k BATUSOV 98 SPEC +
0.037 ±0.024 43k BOLOTOV 86 CALO −
0.152 ±0.082 3263 BRAUN 76B HLBC +
0.041 ±0.030 5635 SHEAFF 75 HLBC +
0.009 ±0.040 27k SMITH 75 WIRE +
−0.01 ±0.08 1365 AUBERT 72 HLBC +
0.026 ±0.050 4048 DAVISON 69 HLBC + Also emulsion
93 Measured using in-flight decays of the 25 GeV negative secondary beam.
QUADRATIIIIC COEFFIIIICIIIIENT k FOR K± → π±π0π0
VALUE EVTS DOCUMENT ID TECN CHG
0....0054±0....0035 OUR AVERAGE Error includes scale factor of 2.5.
0.0082±0.0011±0.0014 493k AKOPDZHAN...05B TNF ±
0.001 ±0.001 ±0.002 252k 94 AJINENKO 03B ISTR −
• • • We do not use the following data for averages, fits, limits, etc. • • •
0.0197±0.0045±0.0029 33k BATUSOV 98 SPEC +
94 Measured using in-flight decays of the 25 GeV negative secondary beam.
(−(g+ − g −) / (g+ + g) FOR K± → π±π0 π0
−) A nonzero value for this quantity indicates CP violation.
VALUE (units 10−4) EVTS DOCUMENT ID TECN
1....8± 1....8 OUR AVERAGE
1.8± 1.7±0.6 91.3M 95 BATLEY 07E NA48
2 ±18 ±5 619k 96 AKOPDZHAN...05 TNF
• • • We do not use the following data for averages, fits, limits, etc. • • •
1.8± 2.2±1.3 47M 97 BATLEY 06A NA48
95BATLEY 07E includes data from BATLEY 06A. Uses quadratic parametrization and
PDG 06 value g = 0.626 ± 0.007 to obtain g+−g− = (2.2 ± 2.1 ± 0.7) × 10−4.
Neglects any possible charge asymmetries in higher order slope parameters h or k.
96Asymmetry obtained assuming that g++g− = 2×0.652 (PDG 02) and that asymmetries
in h and k are zero.
97 Linear and quadratic slopes from PDG 04 are used. Any possible charge asymmetries in
higher order slope parameters h or k are neglected.
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ALTERNATIVE PARAMETERIZATION ALTERNATIIIVE PARAMETERIIIZATIIION OF K± → π±π0π0 DALIIIITZ PLOT
The following functional form for the matrix element suggested by ππ
rescattering in K+ → π+“π+π−”→ π+π0 π0 is used for this fit
(CABIBBO 04A, CABIBBO 05): Matrix element = M0 + M1 where M0
= 1 + (1/2)g0 u + (1/2) h u2 with u = (s3 − s0)/(m
π+)2 and where
M1 takes into account the non-analytic piece due to pi pi rescattering
amplitudes a0 and a2; The parameters g0 and h are related to the parameters
g and h of the matrix element squared given in the previous
section by the approximations g0 ∼ gPDG and h ∼ hPDG − (g/2)2.
LIIIINEAR COEFFIIIICIIIIENT g0 FOR K± → π±π0π0
VALUE EVTS DOCUMENT ID TECN CHG
0....645±0....004±0....009 23M 98 BATLEY 06B NA48 ±
98 This fit is obtained with the CABIBBO 05 matrix element in the 2π0 invariant
mass squared range 0.074 GeV2 < m2
2π0 < 0.097 GeV2, assuming k = 0 (no
term proportional to (s2 − s1)2) and excluding the kinematic region around the cusp
(m2
2π0 = (2m
π+)2 ± 0.000525 GeV2). Also π-π phase shifts a0 and a2 are measured:
(a0 − a2)m
π+ = 0.268 ± 0.010 ± 0.004 ± 0.013(external) and a2 m
π+ =
−0.041 ± 0.022 ± 0.014.
QUADRATIIIIC COEFFIIIICIIIIENT h FOR K± → π±π0π0
VALUE EVTS DOCUMENT ID TECN CHG
−0....047±0....012±0....011 23M 99 BATLEY 06B NA48 ±
99 This fit is obtained with the CABIBBO 05 matrix element in the 2π0 invariant
mass squared range 0.074 GeV2 < m2
2π0 < 0.097 GeV2, assuming k = 0 (no
term proportional to (s2 − s1)2) and excluding the kinematic region around the cusp
(m2
2π0 = (2m
π+)2 ± 0.000525 GeV2). Also π-π phase shifts a0 and a2 are measured:
(a0 − a2)m
π+ = 0.268 ± 0.010 ± 0.004 ± 0.013(external) and a2 m
π+ =
−0.041 ± 0.022 ± 0.014.
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K±3 FORM FACTORS
In the form factor comments, the following symbols are used.
f+ and f− are form factors for the vector matrix element.
fS and fT refer to the scalar and tensor term.
f0 = f+ + f− t/(m2
K+ − m2
π0 ).
t = momentum transfer to the π.
λ+ and λ0 are the linear expansion coefficients of f+ and f0:
f+(t) = f+(0) (1 + λ+t /m2
π+)
For quadratic expansion
f+(t) = f+(0) (1 + λ+t /m2
π+ +
λ+
2 t2/m4
π+ )
as used by KTeV. If there is a non-vanishing quadratic term, then λ+
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represents an average slope, which is then different from λ+.
NA48 and ISTRA quadratic expansion coefficients are converted with
λ+
PDG =