Determination of the ppπ0coupling constant and breaking of charge independence

Pion-nucleon coupling constant

“…In view of the above findings, it may be better to fix the coupling constant in the 1 S 0 channel at a value of 0.075 and determine f 2 ppπ 0 from the remaining partial waves. We then find for 1612 degrees of freedom χ 2 min = 1787 and the coupling constant becomes f 2 ppπ 0 = 0.0746 (6). This is within one standard deviation from the value quoted above f 2 ppπ 0 = 0.0750(5) determined from all partial waves including the 1 S 0 .…”

“…[18], the same statement can be found in a different form, where it is said that the 3 P phase shifts around 10 MeV are very important in the determination. However, these arguments only reflect our statements based on a preliminary pp analysis by our group [6]. Apparently, these critics have overlooked our amendment to these statements as discussed in our paper on the completed 0-350 MeV pp analysis [1], where we incorporated many theoretical improvements and included much more experimental data.…”

“…Since the values f 2 NN π ≃ 0.075 found by us (see also Refs. [5,6,7,8,9]) are consistently lower than the value f 2 NN π = 0.079 found in the Karlsruhe-Helsinki analyses of π ± p scattering data [10,11,12], a number of papers [13,14,15,16,17,18,19] have been published commenting on our results. In several of these papers one attempts to find an explanation for the difference by trying to point out alleged shortcomings and so-called systematic errors pertaining to our method of analysis.…”

“…As expected, we find a somewhat smaller coupling constant f 2 ppπ 0 = 0.0743(6) instead of 0.0750(5). If we fix the coupling constant in the 1 S 0 channel at 0.075, we find in the 3-350 MeV analysis f 2 ppπ 0 = 0.0744 (6). So there are strong indications that the value for the neutral-pion coupling constant as determined in the pp partial-wave analysis is somewhat smaller than 0.075.…”

“…So there are strong indications that the value for the neutral-pion coupling constant as determined in the pp partial-wave analysis is somewhat smaller than 0.075. In the last line of Table I we quote f 2 ppπ 0 = 0.0745 (6). In order to demonstrate that it is not only the data at low energies that pin down the coupling constant, Table VII also contains the results for the ppπ 0 coupling constant obtained from a number of analyses in different energy ranges.…”