Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

I (J P ) = 21 (0− )K0

K 0 MASSVALUE (MeV)EVTS

DOCUMENT ID

TECNCOMMENT

497.611± 0.013 OUR FIT Error includes scale factor of 1.2.
497.611± 0.013 OUR AVERAGE Error includes scale factor of 1.2.
1 TOMARADZE 14
497.607± 0.007 ± 0.015 261k
ψ(2S) → K 0 X
S0497.583± 0.005 ± 0.020 35k
AMBROSINO 07B KLOE e + e − → K 0L KS
497.625± 0.001 ± 0.031 655k
LAI02 NA48 K 0 beam
L497.661± 0.033
3713
BARKOV
87B CMD e + e − → K 0 K 0
L S
497.742± 0.085
780
BARKOV
85B CMD e + e − → K 0 K 0L S
• • • We do not use the following data for averages, fits, limits, etc. • • •497.44 ± 0.50
FITCH
67 OSPK
498.9 ± 0.54500
BALTAY66 HBCK 0 from p p
497.44 ± 0.33
2223
KIM
65B HBCK 0 from p p
498.1 ± 0.4
CHRISTENS... 64 OSPK
1 Obtained by analyzing CLEO-c data but not authored by the CLEO Collaboration.

mK 0 − mK ±VALUE (MeV)EVTS

DOCUMENT ID

TECN

CHG

COMMENT

3.934± 0.020 OUR FIT Error includes scale factor of 1.6.
• • • We do not use the following data for averages, fits, limits, etc. • • •3.95 ± 0.21
417
HILL
68B DBC+K+ d → K0 p p
3.90 ± 0.25
9
BURNSTEIN 65 HBC−3.71 ± 0.35
7KIM
65B HBC−K− p → nK05.4
3.9± 1.1± 0.6

CRAWFORDROSENFELD

5959

HBC
HBC+−K 0 MEAN SQUARE CHARGE RADIUS
VALUE (fm2 )EVTS

DOCUMENT IDTECN− 0.077± 0.010 OUR AVERAGE− 0.077± 0.007 ± 0.011 5037

ABOUZAID

06− 0.087± 0.046

BLATNIK79− 0.050± 0.130

FOETH

69B

https://pdg.lbl.gov

Page 1COMMENTKTEV K 0 → π + π − e + e −L− 0.090± 0.021
LAI03C NA48 K 0 → π + π − e + e −L− 0.054± 0.026
MOLZON78
KS regen. by electrons• • • We do not use the following data for averages, fits, limits, etc. • • •VMD + dispersion relations
KS regen. by electrons

Created: 7/25/2024 17:21

Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

T-VIOLATION PARAMETER IN K 0 -K 0 MIXING
Γ(K 0 →K 0 )−Γ(K 0 →K 0 )must vanish if
The asymmetry AT =
Γ(K 0 →K 0 )+Γ(K 0 →K 0 )T invariance holds.

ASYMMETRY AT IN K 0 -K 0 MIXINGVALUE (units 10−3 )EVTS

DOCUMENT ID

TECN

1 ANGELOPO... 98E CPLR

6.6± 1.3± 1.0
640k
1 ANGELOPOULOS 98E measures the asymmetry A = [Γ(K 0→e + π − ν t=τ ) −Tt=0
Γ(K 0→e − π + ν t=τ )]/[Γ(K 0→e + π − ν t=τ ) + Γ(K 0→e − π + ν t=τ )]t=0t=0t=0
as a function of the neutral-kaon eigentime τ . The initial strangeness of the neutralkaon is tagged by the charge of the accompanying charged kaon in the reactions p p →K − π + K 0 and p p → K + π − K 0 . The strangeness at the time of the decay is tagged by
the lepton charge. The reported result is the average value of AT over the interval 1τs <τ < 20τs . From this value of AT ANGELOPOULOS 01B, assuming CPT invariance inthe e π ν decay amplitude, determine the T-violating as ∆S=∆S conserving parameter(for its definition, see Review below) 4Re(ǫ) = (6.2 ± 1.4 ± 1.0) × 10−3 .

See the related review(s):CPT Invariance Tests in Neutral Kaon Decay
CP-VIOLATION PARAMETERS
Re(ǫ)
VALUE (units 10−3 )DOCUMENT ID

TECN

1 AMBROSINO 06H KLOE
1.596± 0.013• • • We do not use the following data for averages, fits, limits, etc. • • •2 LAI
1.664± 0.010
05A NA48
1 AMBROSINO 06H uses Bell-Steinberger relations with the following measurements:
B(K 0 → π + π − ) in AMBROSINO 06F, B(K 0 → π 0 π 0 π 0 ) in AMBROSINO 05B, theLS
K 0 -semileptonic charge asymmetry in AMBROSINO 06E, and K 0 -semileptonic results
Sin ANGELOPOULOS 98F.
2 LAI 05A values are obtained through unitarity (Bell-Steinberger relations), improving
determination of η 000 and combining other data from PDG 04 and APOSTOLAKIS 99B.

CPT-VIOLATION PARAMETERS
In K 0 -K 0 mixing, if CP-violating interactions include a T conserving partthenq
KS = [ K1 +(ǫ + δ) K2 ]/ 1+ ǫ+δ 2q
KL = [ K2 +(ǫ − δ) K1 ]/ 1+ ǫ−δ 2whereand√
K1 = [ K 0 + K 0 ]/ 2√
K2 = [ K 0 − K 0 ]/ 2
K 0 = CP K 0 .

https://pdg.lbl.gov

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

The parameter δ specifies the CPT-violating part.
Estimates of δ are given below assuming the validity of the ∆S=∆Q rule.
See also THOMSON 95 for a test of CPT-symmetry conservation in K 0decays using the Bell-Steinberger relation.

REAL PART OF δA nonzero value violates CPT invariance.
VALUE (units 10−4 )EVTS

DOCUMENT ID

TECNCOMMENT

1 ABOUZAID

2.51± 2.25
11 KTEV• • • We do not use the following data for averages, fits, limits, etc. • • •2 AMBROSINO 06H KLOE
2.3 ± 2.73
2.4 ± 2.8
APOSTOLA... 99B RVUE
4 ANGELOPO... 98F CPLR
2.9 ± 2.6 ± 0.6
1.3M
5 DEMIDOV
180 ± 2006481
95Kℓ3 reanalysis
1 ABOUZAID 11 uses Bell-Steinberger relations.
2 AMBROSINO 06H uses Bell-Steinberger relations with the following measurements:
B(K 0 → π + π − ) in AMBROSINO 06F, B(K 0 → π 0 π 0 π 0 ) in AMBROSINO 05B, theLS
K 0 -semileptonic charge asymmetry in AMBROSINO 06E, and K 0 -semileptonic results
Sin ANGELOPOULOS 98F.
3 APOSTOLAKIS 99B assumes only unitarity and combines CPLEAR and other results.
4 ANGELOPOULOS 98F use ∆S=∆Q. If ∆S=∆Q is not assumed, they find Reδ=(3.0 ±3.3 ± 0.6) × 10−4 .
5 DEMIDOV 95 reanalyzes data from HART 73 and NIEBERGALL 74.

IMAGINARY PART OF δ
A nonzero value violates CPT invariance.
VALUE (units 10−5 )EVTS

DOCUMENT ID

TECNCOMMENT

1 ABOUZAID−
1.5±1.6
11 KTEV• • • We do not use the following data for averages, fits, limits, etc. • • •2 AMBROSINO 06H KLOE
0.4±2.1
3 LAI−0.2±2.005A NA48
4 APOSTOLA... 99B RVUE
2.4±5.0
5 ANGELOPO... 98F CPLR
− 90 ± 290 ± 100
1.3M
6 DEMIDOV
2100 ± 37006481
95
Kℓ3 reanalysis
1 ABOUZAID 11 uses Bell-Steinberger relations.
2 AMBROSINO 06H uses Bell-Steinberger relations with the following measurements:
B(K 0 → π + π − ) in AMBROSINO 06F, B(K 0 → π 0 π 0 π 0 ) in AMBROSINO 05B, theLS
K 0 -semileptonic charge asymmetry in AMBROSINO 06E, and K 0 -semileptonic results
Sin ANGELOPOULOS 98F.
3 LAI 05A values are obtained through unitarity (Bell-Steinberger relations), improving
determination of η 000 and combining other data from PDG 04 and APOSTOLAKIS 99B.
4 APOSTOLAKIS 99B assumes only unitarity and combines CPLEAR and other results.
5 If ∆S=∆Q is not assumed, ANGELOPOULOS 98F finds Imδ=(− 15 ± 23 ± 3) × 10−3 .
6 DEMIDOV 95 reanalyzes data from HART 73 and NIEBERGALL 74.

https://pdg.lbl.gov

Page 3Created: 7/25/2024 17:21

Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)Re(y)A non-zero value would violate CPT invariance in ∆S = ∆Q amplitude. Re(y) is thefollowing combination of Ke3 decay amplitudes:
A(K 0 →e − π + ν e )∗ −A(K 0 →e + π − νe )Re(y) = Re
A(K 0 →e − π + ν e )∗ +A(K 0 →e + π − νe )VALUE (units 10−3 )EVTS

DOCUMENT ID

TECN

1 AMBROSINO 06E KLOE
0.4± 2.513k• • • We do not use the following data for averages, fits, limits, etc. • • •2 APOSTOLA... 99B CPLR
0.3± 3.1
1 They use the PDG 04 for the K 0 semileptonic charge asymmetry and PDG 04 (CPLreview, CPT NOT ASSUMED) for Re(ǫ).
2 Constrained by Bell-Steinberger (or unitarity) relation.

Re(x− )

A non-zero value would violate CPT invariance in decay amplitudes with ∆S 6= ∆Q.
x− , used here to define Re(x− ), and x+ , used below in the ∆S = ∆Q section are
the following combinations of Ke3 decay amplitudes:
0+ −0− +∗ 1 A(K →π e νe ) ± A(K →π e ν e )x± = 2.
A(K 0 →π − e + νe )A(K 0 →π + e − ν e )∗VALUE (units 10−3 )EVTS

DOCUMENT ID

TECNCOMMENT

1 AMBROSINO 06H KLOE− 2.9± 2.0• • • We do not use the following data for averages, fits, limits, etc. • • •2 AMBROSINO 06E KLOE− 0.8± 2.513k
3− 0.5± 3.0
APOSTOLA... 99B CPLR Strangeness tagged

2 ± 13 ± 3650k
ANGELOPO... 98F CPLR Strangeness tagged
1 AMBROSINO 06H uses Bell-Steinberger relations with the following measurements:
B(K 0 → π + π − ) in AMBROSINO 06F, B(K 0 → π 0 π 0 π 0 ) in AMBROSINO 05B, theLSK 0 -semileptonic charge asymmetry in AMBROSINO 06E, and K 0 -semileptonic results
Sin ANGELOPOULOS 98F.
2 Uses PDG 04 for the K 0 semileptonic charge asymmetry and Re(δ) from CPLEAR,LANGELOPOULOS 98F.
3 Constrained by Bell-Steinberger (or unitarity) relation.

m K 0 − m K 0 / m average
A test of CPT invariance. “Our Evaluation” is described in the “Tests ofConservation Laws” section. It assumes CPT invariance in the decay andneglects some contributions from decay channels other than π π.
VALUE

CL%

DOCUMENT ID

TECN<6 × 10−1990
PDG12• • • We do not use the following data for averages, fits, limits, etc. • • •1 ANGELOPO... 99B RVUE(− 3 ± 4) × 10−18

1 ANGELOPOULOS 99B assumes only unitarity and combines CPLEAR and other results.

https://pdg.lbl.gov

Page 4Created: 7/25/2024 17:21

Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)(Γ K 0 − Γ K 0 )/m average
A test of CPT invariance.
VALUE

DOCUMENT ID

TECN

1 ANGELOPO... 99B RVUE
(7.8± 8.4) × 10−18
1 ANGELOPOULOS 99B assumes only unitarity and combines CPLEAR with other results.
Correlated with (m 0 − m 0 ) / m average with a correlation coefficient of − 0.95.
KK

TESTS OF ∆S = ∆Q RULERe(x+ )A non-zero value would violate the ∆S = ∆Q rule in CPT conserving transitions. x+
is defined above in the Re(x− ) section.

VALUE (units 10−3 )EVTS

DOCUMENT ID

TECN− 0.9± 3.0 OUR AVERAGE
1 BATLEY− 2 ± 1007D NA48
2− 0.5± 3.613k
AMBROSINO 06E KLOE
3 ANGELOPO... 98D CPLR
− 1.8± 6.1
1 Result obtained from the measurement Γ(K 0 → π e ν) / Γ(K 0 → π e ν) = 0.993 ± 0.34,SLneglecting possible CPT non-invariance and using PDG 06 values of B(K 0 → π e ν) =L0.4053 ± 0.0015, τ L = (5.114 ± 0.021)×10−8 s and τ S = (0.8958 ± 0.0005)×10−10 s.
2 Re(x ) can be shown to be equal to the following combination of rates:+001 Γ(K S →π e ν)−Γ(K L →π e ν)Re(x+ ) = 2
Γ(K 0S →π e ν)+Γ(K 0L →π e ν)which is valid up to first order in terms violating CPT and/or the ∆S = ∆Q rule.
3 Obtained neglecting CPT violating amplitudes.

K 0 REFERENCESTOMARADZE 14
PR D89 031501
PDG
12
PR D86 010001
ABOUZAID11
PR D83 092001
AMBROSINO 07B JHEP 0712 073
BATLEY07D PL B653 145
ABOUZAID06
PRL 96 101801
AMBROSINO 06E PL B636 173
AMBROSINO 06F PL B638 140
AMBROSINO 06H JHEP 0612 011
PDG
06
JP G33 1
AMBROSINO 05B PL B619 61
LAI
05A PL B610 165
PDG04
PL B592 1LAI
03C EPJ C30 33
LAI02
PL B533 196
ANGELOPO... 01B EPJ C22 55ANGELOPO... 99B PL B471 332
APOSTOLA... 99B PL B456 297
ANGELOPO... 98D PL B444 38Also
EPJ C22 55
ANGELOPO... 98E PL B444 43
ANGELOPO... 98F PL B444 52
Also
EPJ C22 55
DEMIDOV95
PAN 58 968
From YAF 58 1041.
THOMSON95
PR D51 1412

https://pdg.lbl.gov

A. Tomaradze et al.
(NWES, WAYN)
J. Beringer et al.
(PDG Collab.)
E. Abouzaid et al.
(FNAL KTeV Collab.)
F. Ambrosino et al.
(KLOE Collab.)
J.R. Batley et al.
(CERN NA48 Collab.)
E. Abouzaid et al.
(KTeV Collab.)
F. Ambrosino et al.
(KLOE Collab.)
F. Ambrosino et al.
(KLOE Collab.)
F. Ambrosino et al.
(KLOE Collab.)
W.-M. Yao et al.
(PDG Collab.)
F. Ambrosino et al.
(KLOE Collab.)
A. Lai et al.
(CERN NA48 Collab.)
S. Eidelman et al.
(PDG Collab.)
A. Lai et al.
(CERN NA48 Collab.)
A. Lai et al.
(CERN NA48 Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
A. Apostolakis et al.
(CPLEAR Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
A. Angelopoulos et al.
(CPLEAR Collab.)
V. Demidov, K. Gusev, E. Shabalin(ITEP)
G.B. Thomson, Y. Zou

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

BARKOV

87B

BARKOV

85B

BLATNIKMOLZONNIEBERGALL
HART
FOETH
HILL
FITCH
BALTAYBURNSTEINKIMCHRISTENS...
CRAWFORDROSENFELD

7978
7473
69B
68B
6766
65
65B
645959SJNP 46 630
L.M. Barkov et al.
(NOVO)
Translated from YAF 46 1088.
JETPL 42 138
L.M. Barkov et al.
(NOVO)
Translated from ZETFP 42 113.
LNC 24 39
S. Blatnik, J. Stahov, C.B. Lang(TUZL, GRAZ)
PRL 41 1213
W.R. Molzon et al.
(EFI+)PL 49B 103
F. Niebergall et al.
(CERN, ORSAY, VIEN)
NP B66 317
J.C. Hart et al.
(CAVE, RHEL)
PL 30B 276
H. Foeth et al.
(AACH, CERN, TORI)
PR 168 1534
D.G. Hill et al.
(BNL, CMU)
PR 164 1711
V.L. Fitch et al.
(PRIN)PR 142 932
C. Baltay et al.
(YALE, BNL)PR 138 B895
R.A. Burnstein, H.A. Rubin(UMD)
PR 140 B1334
J.K. Kim, L. Kirsch, D. Miller(COLU)
PRL 13 138
J.H. Christenson et al.
(PRIN)
PRL 2 112
F.S. Crawford et al.
(LRL)
PRL 2 110
A.H. Rosenfeld, F.T. Solmitz, R.D. Tripp(LRL)

https://pdg.lbl.gov

Page 6Created: 7/25/2024 17:21