---

Table 8: By-reference measurements list.

Reference / Branching Fraction	Value
BARATE 98 (ALEPH) [70]
B85 =  B(τ− → K− π+ π− ντ (ex.K0))	0.002140 ± 0.000370 ± 0.000290
B88 =  B(τ− → K− π− π+ π0 ντ (ex.K0))	(0.61 ± 0.39 ± 0.18)· 10−3
B93 =  B(τ− → π− K− K+ ντ)	0.001630 ± 0.000210 ± 0.000170
B94 =  B(τ− → π− K− K+ π0 ντ)	(750 ± 290 ± 150)· 10−6
BARATE 98E (ALEPH) [47]
B33 =  B(τ− → KS0 (particles)− ντ)	0.00970 ± 0.00058 ± 0.00062
B37 =  B(τ− → K− K0 ντ)	0.001580 ± 0.000420 ± 0.000170
B40 =  B(τ− → π− K0 π0 ντ)	0.002940 ± 0.000730 ± 0.000370
B42 =  B(τ− → K− K0 π0 ντ)	0.001520 ± 0.000760 ± 0.000210
B47 =  B(τ− → π− KS0 KS0 ντ)	(260.0 ± 100.0 ± 50.0)· 10−6
B48 =  B(τ− → π− KS0 KL0 ντ)	0.00101 ± 0.00023 ± 0.00013
B51 =  B(τ− → π− KS0 KL0 π0 ντ)	(0.31 ± 0.11 ± 0.05)· 10−3
B53 =  B(τ− → K0 h− h− h+ ντ)	(0.23 ± 0.19 ± 0.07)· 10−3
BARATE 99K (ALEPH) [38]
B10 =  B(τ− → K− ντ)	0.00696 ± 0.00025 ± 0.00014
B16 =  B(τ− → K− π0 ντ)	0.004440 ± 0.000260 ± 0.000240
B23 =  B(τ− → K− 2π0 ντ (ex.K0))	0.00056 ± 0.00020 ± 0.00015
B28 =  B(τ− → K− 3π0 ντ (ex.K0,η))	(0.37 ± 0.21 ± 0.11)· 10−3
B35 =  B(τ− → π− K0 ντ)	0.009280 ± 0.000450 ± 0.000340
B37 =  B(τ− → K− K0 ντ)	0.001620 ± 0.000210 ± 0.000110
B40 =  B(τ− → π− K0 π0 ντ)	0.003470 ± 0.000530 ± 0.000370
B42 =  B(τ− → K− K0 π0 ντ)	0.001430 ± 0.000250 ± 0.000150
BARATE 99R (ALEPH) [54]
B44 =  B(τ− → π− K0 2π0 ντ (ex.K0))	(0.26 ± 0.24 ± 0.00)· 10−3
BUSKULIC 96 (ALEPH) [84]
B150 / 66 =   B(τ− → h− ω ντ)  B(τ− → h− h− h+ π0 ντ (ex.K0))	0.431 ± 0.033 ± 0.000
BUSKULIC 97C (ALEPH) [77]
B126 =  B(τ− → π− π0 η ντ)	0.001800 ± 0.000400 ± 0.000200
B128 =  B(τ− → K− η ντ)	(290 −120+130 ± 70)· 10−6
B150 =  B(τ− → h− ω ντ)	0.0191 ± 0.0007 ± 0.0006
B152 =  B(τ− → h− π0 ω ντ)	0.0043 ± 0.0006 ± 0.0005
SCHAEL 05C (ALEPH) [25]
B3 =  B(τ− → µ− νµντ)	0.17319 ± 0.00070 ± 0.00032
B5 =  B(τ− → e− νe ντ)	0.1784 ± 0.0007 ± 0.0004
B9 =  B(τ− → π− ντ)	0.1083 ± 0.0007 ± 0.0008
B14 =  B(τ− → π− π0 ντ)	0.2547 ± 0.0010 ± 0.0008
B20 =  B(τ− → π− 2π0 ντ (ex.K0))	0.0924 ± 0.0009 ± 0.0009
B27 =  B(τ− → π− 3π0 ντ (ex.K0))	0.0098 ± 0.0007 ± 0.0006
B30 =  B(τ− → h− 4π0 ντ (ex.K0,η))	0.00112 ± 0.00037 ± 0.00035
B62 =  B(τ− → π− π+ π− ντ (ex.K0,ω))	0.0904 ± 0.0006 ± 0.0008
B69 =  B(τ− → π− π+ π− π0 ντ (ex.K0))	0.0460 ± 0.0006 ± 0.0006
B76 =  B(τ− → h− h− h+ 2π0 ντ (ex.K0))	0.00435 ± 0.00030 ± 0.00035
B103 =  B(τ− → 3h− 2h+ ντ (ex.K0))	(720 ± 90 ± 120)· 10−6
B104 =  B(τ− → 3h− 2h+ π0 ντ (ex.K0))	(210 ± 70 ± 90)· 10−6
B980 =  B(a1− → π− γ)	0.0021 ± 0.0008 ± 0.0000
ALBRECHT 88B (ARGUS) [75]
B103 =  B(τ− → 3h− 2h+ ντ (ex.K0))	(640 ± 230 ± 100)· 10−6
ALBRECHT 92D (ARGUS) [30]
B3 / 5 =   B(τ− → µ− νµντ)  B(τ− → e− νe ντ)	0.9970 ± 0.0350 ± 0.0400
AUBERT 07AP (BaBar) [44]
B16 =  B(τ− → K− π0 ντ)	0.004160 ± 0.000030 ± 0.000180
AUBERT 08 (BaBar) [62]
B60 =  B(τ− → π− π+ π− ντ (ex.K0))	0.08830 ± 0.00010 ± 0.00130
B85 =  B(τ− → K− π+ π− ντ (ex.K0))	0.002730 ± 0.000020 ± 0.000090
B93 =  B(τ− → π− K− K+ ντ)	0.001346 ± 0.000010 ± 0.000036
B96 =  B(τ− → K− K− K+ ντ)	(15.8 ± 1.3 ± 1.2)· 10−6
AUBERT 10F (BaBar) [31]
B3 / 5 =   B(τ− → µ− νµντ)  B(τ− → e− νe ντ)	0.9796 ± 0.0016 ± 0.0036
B9 / 5 =   B(τ− → π− ντ)  B(τ− → e− νe ντ)	0.5945 ± 0.0014 ± 0.0061
B10 / 5 =   B(τ− → K− ντ)  B(τ− → e− νe ντ)	0.03882 ± 0.00032 ± 0.00057
DEL-AMO-SANCHEZ 11E (BaBar) [80]
B128 =  B(τ− → K− η ντ)	(142 ± 11 ± 7)· 10−6
LEES 12X (BaBar) [85]
B811 =  B(τ− → π− 2π0 ω ντ)	(73 ± 12 ± 12)· 10−6
B812 =  B(τ− → 2π− π+ 3π0 ντ (ex.K0,η,ω,f1))	(10 ± 8 ± 30)· 10−6
B821 =  B(τ− → 3π− 2π+ ντ (ex.K0,ω,f1))	(768 ± 4 ± 40)· 10−6
B822 =  B(τ− → K− 2π− 2π+ ντ (ex.K0))	(0.6 ± 0.5 ± 1.1)· 10−6
B831 =  B(τ− → 2π− π+ ω ντ (ex.K0))	(84 ± 4 ± 6)· 10−6
B832 =  B(τ− → 3π− 2π+ π0 ντ (ex.K0,η,ω,f1))	(36.0 ± 3.0 ± 9.0)· 10−6
B833 =  B(τ− → K− 2π− 2π+ π0 ντ (ex.K0))	(1.1 ± 0.4 ± 0.4)· 10−6
B910 =  B(τ− → 2π− π+ η(3π0) ντ (ex.K0))	(83 ± 9 ± 8)· 10−6
B911 =  B(τ− → π− 2π0 η(π+ π− π0) ντ (ex.K0))	(46 ± 8 ± 5)· 10−6
B920 =  B(τ− → π− f1(2π− 2π+) ντ)	(52.0 ± 3.1 ± 3.7)· 10−6
B930 =  B(τ− → 2π− π+ η(π+ π− π0) ντ (ex.K0))	(53.9 ± 2.7 ± 4.1)· 10−6
B944 =  B(τ− → 2π− π+ η(γ γ) ντ (ex.K0))	(82.6 ± 3.5 ± 5.1)· 10−6
LEES 12Y (BaBar) [55]
B47 =  B(τ− → π− KS0 KS0 ντ)	(231.0 ± 4.0 ± 8.0)· 10−6
B50 =  B(τ− → π− KS0 KS0 π0 ντ)	(16.0 ± 2.0 ± 2.2)· 10−6
LEES 18B (BaBar) [53]
B37 =  B(τ− → K− K0 ντ)	0.001478 ± 0.000022 ± 0.000040
FUJIKAWA 08 (Belle) [42]
B13 =  B(τ− → h− π0 ντ)	0.25670 ± 0.00010 ± 0.00390
INAMI 09 (Belle) [78]
B126 =  B(τ− → π− π0 η ντ)	0.001350 ± 0.000030 ± 0.000070
B128 =  B(τ− → K− η ντ)	(158 ± 5 ± 9)· 10−6
B130 =  B(τ− → K− π0 η ντ)	(46 ± 11 ± 4)· 10−6
B132 =  B(τ− → π− K0 η ντ)	(88 ± 14 ± 6)· 10−6
LEE 10 (Belle) [63]
B60 =  B(τ− → π− π+ π− ντ (ex.K0))	0.08420 ± 0.00000 −0.00250+0.00260
B85 =  B(τ− → K− π+ π− ντ (ex.K0))	0.003300 ± 0.000010 −0.000170+0.000160
B93 =  B(τ− → π− K− K+ ντ)	0.001550 ± 0.000010 −0.000050+0.000060
B96 =  B(τ− → K− K− K+ ντ)	(32.9 ± 1.7 −2.0+1.9)· 10−6
RYU 14vpc (Belle) [50]
B35 =  B(τ− → π− K0 ντ)	0.008320 ± 0.000025 ± 0.000150
B37 =  B(τ− → K− K0 ντ)	0.001480 ± 0.000013 ± 0.000055
B40 =  B(τ− → π− K0 π0 ντ)	0.003860 ± 0.000031 ± 0.000135
B42 =  B(τ− → K− K0 π0 ντ)	0.001496 ± 0.000019 ± 0.000073
B47 =  B(τ− → π− KS0 KS0 ντ)	(233.0 ± 3.3 ± 9.3)· 10−6
B50 =  B(τ− → π− KS0 KS0 π0 ντ)	(20.0 ± 2.2 ± 2.0)· 10−6
Belle II ADACHI 2024 [2]
B3 / 5 =   B(τ− → µ− νµντ)  B(τ− → e− νe ντ)	0.9675 ± 0.0007 ± 0.0036
BEHREND 89B (CELLO) [56]
B54 =  B(τ− → h− h− h+ ≥ 0  neutrals ≥ 0   KL0  ντ)	0.1500 ± 0.0040 ± 0.0030
ANASTASSOV 01 (CLEO) [67]
B78 =  B(τ− → h− h− h+ 3π0 ντ)	(220 ± 30 ± 40)· 10−6
B104 =  B(τ− → 3h− 2h+ π0 ντ (ex.K0))	(170 ± 20 ± 20)· 10−6
ANASTASSOV 97 (CLEO) [15]
B3 / 5 =   B(τ− → µ− νµντ)  B(τ− → e− νe ντ)	0.9777 ± 0.0063 ± 0.0087
B5 =  B(τ− → e− νe ντ)	0.1776 ± 0.0006 ± 0.0017
B8 =  B(τ− → h− ντ)	0.1152 ± 0.0005 ± 0.0012
ARTUSO 92 (CLEO) [79]
B126 =  B(τ− → π− π0 η ντ)	0.001700 ± 0.000200 ± 0.000200
ARTUSO 94 (CLEO) [43]
B13 =  B(τ− → h− π0 ντ)	0.25870 ± 0.00120 ± 0.00420
BALEST 95C (CLEO) [61]
B57 =  B(τ− → h− h− h+ ντ (ex.K0))	0.0951 ± 0.0007 ± 0.0020
B66 =  B(τ− → h− h− h+ π0 ντ (ex.K0))	0.0423 ± 0.0006 ± 0.0022
B150 / 66 =   B(τ− → h− ω ντ)  B(τ− → h− h− h+ π0 ντ (ex.K0))	0.464 ± 0.016 ± 0.017
BARINGER 87 (CLEO) [83]
B150 =  B(τ− → h− ω ντ)	0.0160 ± 0.0027 ± 0.0041
BARTELT 96 (CLEO) [81]
B128 =  B(τ− → K− η ντ)	(260 ± 50 ± 50)· 10−6
BATTLE 94 (CLEO) [39]
B10 =  B(τ− → K− ντ)	0.00660 ± 0.00070 ± 0.00090
B16 =  B(τ− → K− π0 ντ)	0.005100 ± 0.001000 ± 0.000700
B23 =  B(τ− → K− 2π0 ντ (ex.K0))	0.00090 ± 0.00100 ± 0.00030
B31 =  B(τ− → K− ≥ 0  π0 ≥ 0  K0 ≥ 0  γ ντ)	0.01700 ± 0.00120 ± 0.00190
BISHAI 99 (CLEO) [82]
B130 =  B(τ− → K− π0 η ντ)	(177 ± 56 ± 71)· 10−6
B132 =  B(τ− → π− K0 η ντ)	(220 ± 70 ± 22)· 10−6
BORTOLETTO 93 (CLEO) [66]
B76 / 54 =   B(τ− → h− h− h+ 2π0 ντ (ex.K0))  B(τ− → h− h− h+ ≥ 0  neutrals ≥ 0   KL0  ντ)	0.0340 ± 0.0020 ± 0.0030
B152 / 76 =   B(τ− → h− ω π0 ντ)  B(τ− → h− h− h+ 2π0 ντ (ex.K0))	0.81 ± 0.06 ± 0.06
COAN 96 (CLEO) [49]
B34 =  B(τ− → h− K0 ντ)	0.00855 ± 0.00036 ± 0.00073
B37 =  B(τ− → K− K0 ντ)	0.001510 ± 0.000210 ± 0.000220
B39 =  B(τ− → h− K0 π0 ντ)	0.00562 ± 0.00050 ± 0.00048
B42 =  B(τ− → K− K0 π0 ντ)	0.001450 ± 0.000360 ± 0.000200
B47 =  B(τ− → π− KS0 KS0 ντ)	(230.0 ± 50.0 ± 30.0)· 10−6
EDWARDS 00A (CLEO) [65]
B69 =  B(τ− → π− π+ π− π0 ντ (ex.K0))	0.0419 ± 0.0010 ± 0.0021
GIBAUT 94B (CLEO) [73]
B102 =  B(τ− → 3h− 2h+ ≥ 0   neutrals  ντ (ex.K0))	0.00097 ± 0.00005 ± 0.00011
B103 =  B(τ− → 3h− 2h+ ντ (ex.K0))	(770 ± 50 ± 90)· 10−6
PROCARIO 93 (CLEO) [46]
B19 / 13 =   B(τ− → h− 2π0 ντ (ex.K0))  B(τ− → h− π0 ντ)	0.342 ± 0.006 ± 0.016
B26 / 13 =   B(τ− → h− 3π0 ντ)  B(τ− → h− π0 ντ)	0.0440 ± 0.0030 ± 0.0050
B29 =  B(τ− → h− 4π0 ντ (ex.K0))	0.0016 ± 0.0005 ± 0.0005
RICHICHI 99 (CLEO) [68]
B80 / 60 =   B(τ− → K− π− h+ ντ (ex.K0))  B(τ− → π− π+ π− ντ (ex.K0))	0.0544 ± 0.0021 ± 0.0053
B81 / 69 =   B(τ− → K− π− h+ π0 ντ (ex.K0))  B(τ− → π− π+ π− π0 ντ (ex.K0))	0.0261 ± 0.0045 ± 0.0042
B93 / 60 =   B(τ− → π− K− K+ ντ)  B(τ− → π− π+ π− ντ (ex.K0))	0.01600 ± 0.00150 ± 0.00300
B94 / 69 =   B(τ− → π− K− K+ π0 ντ)  B(τ− → π− π+ π− π0 ντ (ex.K0))	0.0079 ± 0.0044 ± 0.0016
ARMS 05 (CLEO3) [71]
B88 =  B(τ− → K− π− π+ π0 ντ (ex.K0))	(0.74 ± 0.08 ± 0.11)· 10−3
B94 =  B(τ− → π− K− K+ π0 ντ)	(55 ± 14 ± 12)· 10−6
B151 =  B(τ− → K− ω ντ)	(0.41 ± 0.06 ± 0.07)· 10−3
BRIERE 03 (CLEO3) [64]
B60 =  B(τ− → π− π+ π− ντ (ex.K0))	0.09130 ± 0.00050 ± 0.00460
B85 =  B(τ− → K− π+ π− ντ (ex.K0))	0.003840 ± 0.000140 ± 0.000380
B93 =  B(τ− → π− K− K+ ντ)	0.001550 ± 0.000060 ± 0.000090
ABDALLAH 06A (DELPHI) [36]
B8 =  B(τ− → h− ντ)	0.1157 ± 0.0012 ± 0.0011
B13 =  B(τ− → h− π0 ντ)	0.25740 ± 0.00201 ± 0.00138
B19 =  B(τ− → h− 2π0 ντ (ex.K0))	0.0950 ± 0.0032 ± 0.0027
B25 =  B(τ− → h− ≥ 3  π0  ντ (ex.K0))	0.0140 ± 0.0021 ± 0.0022
B57 =  B(τ− → h− h− h+ ντ (ex.K0))	0.0932 ± 0.0009 ± 0.0008
B66 =  B(τ− → h− h− h+ π0 ντ (ex.K0))	0.0454 ± 0.0011 ± 0.0010
B74 =  B(τ− → h− h− h+ ≥ 2  π0  ντ (ex.K0))	0.00561 ± 0.00068 ± 0.00095
B103 =  B(τ− → 3h− 2h+ ντ (ex.K0))	(970 ± 150 ± 50)· 10−6
B104 =  B(τ− → 3h− 2h+ π0 ντ (ex.K0))	(160 ± 120 ± 60)· 10−6
ABREU 92N (DELPHI) [33]
B7 =  B(τ− → h− ≥ 0   KL0  ντ)	0.1240 ± 0.0070 ± 0.0070
ABREU 94K (DELPHI) [40]
B10 =  B(τ− → K− ντ)	0.00850 ± 0.00180 ± 0.00000
B31 =  B(τ− → K− ≥ 0  π0 ≥ 0  K0 ≥ 0  γ ντ)	0.01540 ± 0.00240 ± 0.00000
ABREU 99X (DELPHI) [27]
B3 =  B(τ− → µ− νµντ)	0.17325 ± 0.00095 ± 0.00077
B5 =  B(τ− → e− νe ντ)	0.1788 ± 0.0011 ± 0.0011
BYLSMA 87 (HRS) [74]
B102 =  B(τ− → 3h− 2h+ ≥ 0   neutrals  ντ (ex.K0))	0.00102 ± 0.00029 ± 0.00000
B103 =  B(τ− → 3h− 2h+ ντ (ex.K0))	(510 ± 200 ± 0)· 10−6
ACCIARRI 01F (L3) [28]
B3 =  B(τ− → µ− νµντ)	0.17342 ± 0.00110 ± 0.00067
B5 =  B(τ− → e− νe ντ)	0.1781 ± 0.0010 ± 0.0008
ACCIARRI 95 (L3) [34]
B7 =  B(τ− → h− ≥ 0   KL0  ντ)	0.1247 ± 0.0026 ± 0.0043
B13 =  B(τ− → h− π0 ντ)	0.25050 ± 0.00350 ± 0.00500
B19 =  B(τ− → h− 2π0 ντ (ex.K0))	0.0888 ± 0.0037 ± 0.0042
B26 =  B(τ− → h− 3π0 ντ)	0.0170 ± 0.0024 ± 0.0038
ACCIARRI 95F (L3) [51]
B35 =  B(τ− → π− K0 ντ)	0.009500 ± 0.001500 ± 0.000600
B40 =  B(τ− → π− K0 π0 ντ)	0.004100 ± 0.001200 ± 0.000300
ACHARD 01D (L3) [59]
B55 =  B(τ− → h− h− h+ ≥ 0   neutrals  ντ (ex.K0))	0.1456 ± 0.0010 ± 0.0008
B102 =  B(τ− → 3h− 2h+ ≥ 0   neutrals  ντ (ex.K0))	0.00170 ± 0.00022 ± 0.00026
ADEVA 91F (L3) [57]
B54 =  B(τ− → h− h− h+ ≥ 0  neutrals ≥ 0   KL0  ντ)	0.1440 ± 0.0060 ± 0.0030
ABBIENDI 00C (OPAL) [52]
B35 =  B(τ− → π− K0 ντ)	0.009330 ± 0.000680 ± 0.000490
B38 =  B(τ− → K− K0 ≥ 0   π0  ντ)	0.00330 ± 0.00055 ± 0.00039
B43 =  B(τ− → π− K0 ≥ 1   π0  ντ)	0.00324 ± 0.00074 ± 0.00066
ABBIENDI 00D (OPAL) [72]
B92 =  B(τ− → π− K− K+ ≥ 0   neutrals  ντ)	0.001590 ± 0.000530 ± 0.000200
ABBIENDI 01J (OPAL) [41]
B10 =  B(τ− → K− ντ)	0.00658 ± 0.00027 ± 0.00029
B31 =  B(τ− → K− ≥ 0  π0 ≥ 0  K0 ≥ 0  γ ντ)	0.01528 ± 0.00039 ± 0.00040
ABBIENDI 03 (OPAL) [29]
B3 =  B(τ− → µ− νµντ)	0.17340 ± 0.00090 ± 0.00060
ABBIENDI 04J (OPAL) [45]
B16 =  B(τ− → K− π0 ντ)	0.004710 ± 0.000590 ± 0.000230
B85 =  B(τ− → K− π+ π− ντ (ex.K0))	0.004150 ± 0.000530 ± 0.000400
ABBIENDI 99H (OPAL) [32]
B5 =  B(τ− → e− νe ντ)	0.1781 ± 0.0009 ± 0.0006
ACKERSTAFF 98M (OPAL) [37]
B8 =  B(τ− → h− ντ)	0.1198 ± 0.0013 ± 0.0016
B13 =  B(τ− → h− π0 ντ)	0.25890 ± 0.00170 ± 0.00290
B17 =  B(τ− → h− ≥ 2   π0  ντ)	0.0991 ± 0.0031 ± 0.0027
ACKERSTAFF 99E (OPAL) [76]
B103 =  B(τ− → 3h− 2h+ ντ (ex.K0))	(910 ± 140 ± 60)· 10−6
B104 =  B(τ− → 3h− 2h+ π0 ντ (ex.K0))	(270 ± 180 ± 90)· 10−6
AKERS 94G (OPAL) [48]
B33 =  B(τ− → KS0 (particles)− ντ)	0.00970 ± 0.00090 ± 0.00060
AKERS 95Y (OPAL) [60]
B55 =  B(τ− → h− h− h+ ≥ 0   neutrals  ντ (ex.K0))	0.1496 ± 0.0009 ± 0.0022
B57 / 55 =   B(τ− → h− h− h+ ντ (ex.K0))  B(τ− → h− h− h+ ≥ 0   neutrals  ντ (ex.K0))	0.6600 ± 0.0040 ± 0.0140
ALEXANDER 91D (OPAL) [35]
B7 =  B(τ− → h− ≥ 0   KL0  ντ)	0.1210 ± 0.0070 ± 0.0050
AIHARA 87B (TPC) [58]
B54 =  B(τ− → h− h− h+ ≥ 0  neutrals ≥ 0   KL0  ντ)	0.1510 ± 0.0080 ± 0.0060
BAUER 94 (TPC) [69]
B82 =  B(τ− → K− π− π+ ≥ 0   neutrals  ντ)	0.00580 −0.00130+0.00150 ± 0.00120
B92 =  B(τ− → π− K− K+ ≥ 0   neutrals  ντ)	0.001500 −0.000700+0.000900 ± 0.000300

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