Charged kaon mass 1

Charged Kaon Mass
Revised 1994 by T.G. Trippe (LBNL).
The average of the six charged kaon mass measurements which we use in the Particle
Listings is(1)mK ± = 493.677 ± 0.013 MeV (S = 2.4) ,where the error has been increased by the scale factor S. The large scale factor indicates aserious disagreement between different input data. The average before scaling the error ismK ± = 493.677 ± 0.005 MeV ,χ2 = 22.9 for 5 D.F., Prob. = 0.04% ,(2)22where the high χ and correspondingly low χ probability further quantify thedisagreement.
The main disagreement is between the two most recent and precise results,DENISOV 91
mK ± =493.696 ± 0.007 MeV
mK ± =493.636 ± 0.011 MeV (S = 1.5) GALL 88
Average =493.679 ± 0.006 MeV
χ2 = 21.2 for 1 D.F., Prob. = 0.0004% ,(3)
both of which are measurements of x-ray energies from kaonic atoms. Comparing theaverage in Eq. (3) with the overall average in Eq. (2), it is clear that DENISOV 91 [1]and GALL 88 [2] dominate the overall average, and that their disagreement is responsible
for most of the high χ2 .
The GALL 88 measurement was made using four different kaonic atom transitions,K − Pb (9 → 8), K − Pb (11 → 10), K − W (9 → 8), and K − W (11 → 10). The mK ±values they obtain from each of these transitions is shown in the Particle Listings and inFig. 1. Their K − Pb (9 → 8) mK ± is below and somewhat inconsistent with their otherthree transitions. The average of their four measurements ismK ± = 493.636 ± 0.007 ,χ2 = 7.0 for 3 D.F., Prob. = 7.2% .
(4)This is a low but acceptable χ2 probability so, to be conservative, GALL 88 scaled up theerror on their average by S=1.5 to obtain their published error ±0.011 shown in Eq. (3)above and used in the Particle Listings average.
The ideogram in Fig. 1 shows that the DENISOV 91 measurement and the GALL 88−K Pb (9 → 8) measurement yield two well-separated peaks. One might suspect theGALL 88 K − Pb (9 → 8) measurement since it is responsible both for the internal
inconsistency in the GALL 88 measurements and the disagreement with DENISOV 91.
To see if the disagreement could result from a systematic problem with the−K Pb (9 → 8) transition, we have separated the CHENG 75 [3] data, which also used
K − Pb, into its separate transitions. Figure 1 shows that the CHENG 75 and GALL 88
K − Pb (9 → 8) values are consistent, suggesting the possibility of a common effect such
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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2Charged kaon mass

WEIGHTED AVERAGE493.664±0.011 (Error scaled by 2.5)
Values above of weighted average, error,and scale factor are based upon the data inthis 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.

2χDENISOV 91
GALL 88
K Pb 9-8
GALL 88
K Pb 11-10
GALL 88
K W 9-8
GALL 88
K W 11-10
LUM 81BARKOV 79
CHENG 75 K Pb 9-8
CHENG 75 K Pb 10-9
CHENG 75 K Pb 11-10
CHENG 75 K Pb 12-11
CHENG 75 K Pb 13-12
BACKENSTO... 73

20.5
22.6
0.2
0.4
2.2
0.2
0.0
1.1
0.1
0.5
3.6
0.8
0.4
52.6
(Confidence Level 0.001)

493.5

493.6

493.7

493.8

493.9

494mK ± (MeV)
Figure 1: Ideogram of mK ± mass measurements. GALL 88 and CHENG 75
measurements are shown separately for each transition they measured.
as contaminant nuclear γ rays near the K − Pb (9 → 8) transition energy, although theCHENG 75 errors are too large to make a strong conclusion. The average of all 13
measurements has a χ2 of 52.6 as shown in Fig. 1 and the first line of Table 1, yielding
an unacceptable χ2 probability of 0.00005%. The second line of Table 1 excludes boththe GALL 88 and CHENG 75 measurements of the K − Pb (9 → 8) transition andyields a χ2 probability of 43%. The third [fourth] line of Table 1 excludes only theGALL 88 K − Pb (9 → 8) [DENISOV 91] measurement and yields a χ2 probability of20% [8.6%]. Table 1 shows that removing both measurements of the K − Pb (9 → 8)transition produces the most consistent set of data, but that excluding only the GALL 88
K − Pb (9 → 8) transition or DENISOV 91 also produces acceptable probabilities.
Yu.M. Ivanov, representing DENISOV 91, has estimated corrections needed for theolder experiments because of improved 192 Ir and 198 Au calibration γ-ray energies. Heestimates that CHENG 75 and BACKENSTOSS 73 [4] mK ± values could be raised
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Charged kaon mass 3
Table 1:mK ± averages for some combinations of Fig. 1 data.

mK ± (MeV)χ2D.F.

Prob. (%)

493.664 ± 0.004
493.690 ± 0.006
493.687 ± 0.006
493.642 ± 0.006

52.6
10.1
14.6
17.8

121011110.00005
4320
8.6

Measurements usedall 13 measurements
no K − Pb(9→8)
no GALL 88 K − Pb(9→8)
no DENISOV 91

by about 15 keV and 22 keV, respectively. With these estimated corrections, Table 1
becomes Table 2. The last line of Table 2 shows that if such corrections are assumed, then
GALL 88 K − Pb (9 → 8) is inconsistent with the rest of the data even when DENISOV 91
is excluded. Yu.M. Ivanov warns that these are rough estimates. Accordingly, we do not
use Table 2 to reject the GALL 88 K − Pb (9 → 8) transition, but we note that a futurereanalysis of the CHENG 75 data could be useful because it might provide supporting
evidence for such a rejection.
Table 2: mK ± averages for some combinations of Fig. 1 data after raising CHENG
75 and BACKENSTOSS 73 values by 0.015 and 0.022 MeV respectively.
mK ± (MeV)χ2D.F.

Prob. (%)

493.666 ± 0.004
493.693 ± 0.006493.690 ± 0.006
493.645 ± 0.006

53.9
9.0
11.5
23.0

121011110.00003
53
40
1.8

Measurements usedall 13 measurements
no K − Pb(9→8)
no GALL 88 K − Pb(9→8)
no DENISOV 91

The GALL 88 measurement uses a Ge semiconductor spectrometer which has aresolution of about 1 keV, so they run the risk of some contaminant nuclear γ rays.
Studies of γ rays following stopped π − and Σ− absorption in nuclei (unpublished) do notshow any evidence for contaminants according to GALL 88 spokesperson, B.L. Roberts.
The DENISOV 91 measurement uses a crystal diffraction spectrometer with a resolutionof 6.3 eV for radiation at 22.1 keV to measure the 4f-3d transition in K − 12 C. The
high resolution and the light nucleus reduce the probability for overlap by contaminant
γ rays, compared with the measurement of GALL 88. The DENISOV 91 measurement issupported by their high-precision measurement of the 4d-2p transition energy in π − 12 C,
which is good agreement with the calculated energy.
While we suspect that the GALL 88 K − Pb (9 → 8) measurements could be theproblem, we are unable to find clear grounds for rejecting it. Therefore, we retain theirmeasurement in the average and accept the large scale factor until further information canbe obtained from new measurements and/or from reanalysis of GALL 88 and CHENG 75
data.
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4

Charged kaon mass

We thank B.L. Roberts (Boston Univ.) and Yu.M. Ivanov (Petersburg Nuclear Physics
Inst.) for their extensive help in understanding this problem.
References:
1.
2.
3.
4.

A.S. Denisov, et al. [DENISOV 91], Sov. Phys. JETP Lett. 54, 558 (1991).
K.P. Gall, et al. [GALL 88], Phys. Rev. Lett. 60, 186 (1988).
S.C. Cheng, et al. [CHENG 75], Nucl. Phys. A254, 381 (1975).
G. Backenstoss, et al. [BACKENSTOSS 73], Phys. Lett. 43B, 431 (1973).

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