Branching ratios of ψ(2S), χc0,1,2 and ηc (1S) 1

Branching Ratios of ψ(2S), χc0,1,2 and ηc (1S)
Updated March 2024 by J.J. Hernández-Rey (IFIC, Valencia), R. Mitchell (Indiana U.),S. Navas (U. of Granada), and C. Patrignani (Bologna Univ., INFN)
Since 2002, the treatment of the branching ratios of the ψ(2S) and χc0,1,2 hasundergone an important restructuring. Since the 2023 online edition, the ηc (1S) is now
treated in a similar way (see the end of this note).
When measuring a branching ratio experimentally, it is not always possible tonormalize the number of events observed in the corresponding decay mode to the total
number of particles produced. Therefore, the experimenters sometimes report the numberof observed decays with respect to another decay mode of the same or another particle
in the relevant decay chain. This is actually equivalent to measuring combinations ofbranching fractions of several decay modes.
To extract the branching ratio of a given decay mode, the collaborations use somepreviously reported measurements of the required branching ratios. However, the values
are frequently taken from the Review of Particle Physics (RPP), which in turn uses thebranching ratio reported by the experiment in the following edition, giving rise either tocorrelations or to plain vicious circles, as discussed in more detail in earlier editions of
this review [1,2].
The way to avoid these dependencies and correlations is to extract the branchingratios through a fit that uses the truly measured combinations of branching fractions andpartial widths. This fit, in fact, should involve decays from the four concerned particles,
ψ(2S), χc0 , χc1 , and χc2 , and occasionally some combinations of branching ratios of morethan one of them. This is what is done since the 2002 edition [3].
The PDG policy is to quote the results of the collaborations in a manner as
close as possible to what appears in their original publications. However, in order toavoid the problems mentioned above, we had in some cases to work out the values
originally measured, using the number of events and detection efficiencies given by thecollaborations, or rescaling back the published results. The information was sometimes
spread over several articles, and some articles referred to papers still unpublished, which
in turn contained the relevant numbers in footnotes.
Even though the experimental collaborations are entitled to extract whateverbranching ratios they consider appropriate by using other published results, we would
like to encourage them to also quote explicitly in their articles the actual quantities
measured, so that they can be used directly in averages and fits of different experimental
determinations.
To inform the reader how we computed some of the values used in this edition of RPP,
we use footnotes to indicate the branching ratios actually given by the experiments andthe quantities they use to derive them from the true combination of branching ratios
actually measured.
None of the branching ratios of the χc0,1,2 are measured independently of the ψ(2S)
radiative decays. We tried to identify those branching ratios which can be correlated ina non-trivial way, and although we cannot preclude the existence of other cases, we areconfident that the most relevant correlations have already been removed. Nevertheless,S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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2Branching ratios of ψ(2S), χc0,1,2 and ηc (1S)

correlations in the errors of different quantities measured by the same experiment havenot been taken into account.
The ηc (1S) can be produced in γγ collisions, in the radiative decays of vector andaxial-vector charmonia (J/ψ, ψ(2S) and hc (1P)) or in B meson decays. As for theψ(2S) and χc0,1,2 , correlations can be introduced if the derived branching ratios are
not properly extracted. We now obtain the corresponding branching ratios using theproducts of branching ratios originally measured by the experiments, sometimes among
different particles (cross-particle branching ratios) and performing an overall fit. In
some cases, we were obliged to infer the original product from the information given by
the collaborations. However, for recent experiments our policy is not to use anymore
extracted branching ratios, so that if the original measured quantity is missing in therelevant publication, the value will not be used in our averages and fits.

1. Fit Information for the ψ(2S) and χc0,1,2This is an overall fit to 4 total widths, 1 partial width, 25 combinations of partialwidths, 10 branching fractions, and 76 branching ratios or combinations thereof. Of thelatter, 58 involve decays of more than one particle.
The overall fit uses 253 measurements to determine 49 parameters and gives a χ2 of389.6 for 204 degrees of freedom. We have applied scaling factors in the final errors of thefitted values following the procedure described in section 5.2.3 of our Introduction. After
rescaling, the total χ2 is 149.6.
In the listing we provide the inter-particle correlation coefficients < δxi δxj >/ (δxi · δxj ), in percent, from the fit to the corresponding parameter xi .

2. Fit Information for the ηc (1S)This is an overall fit to 1 total width, 10 combinations of partial widths, 6 branching
fractions and 32 branching ratios or combinations thereof. Of the latter, 31 involve decaysof more than one particle.
The overall fit uses 113 measurements to determine 19 parameters and has a χ2 of
184.6 for 94 degrees of freedom. We have applied scaling factors in the final errors of thefitted values following the procedure described in section 5.2.3 of our Introduction. After
rescaling, the total χ2 is 74.1.
In the listing we provide the inter-particle correlation coefficients < δxi δxj >/ (δxi · δxj ), in percent, from the fit to the corresponding parameter xi .
References:
1. Y.F. Gu and X.H. Li, Phys. Lett. B449, 361 (1999).
2. C. Patrignani, Phys. Rev. D64, 034017 (2001).
3. K. Hagiwara et al. (Particle Data Group), Phys. Rev. D68, 010001 (2002).

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