Addendum to"Overview of $\Lambda_c$ decays''

An earlier analysis of observed and anticipated $\Lambda_c$ decays [M. Gronau and J. L. Rosner, Phys.\ Rev.\ D {\bf 97}, 116015 (2018)] is provided with a table of inputs and a figure denoting branching fractions. This addendum is based on the 2018 Particle Data Group compilation and employs a statistical isospin model to estimate branching fractions for as-yet-unseen decay modes.

The decays of the charmed baryon Λ c [2] appear to be within about 10% of fully mapped out [1] when a statistical isospin model [3,4] is used to estimate branching fractions for asyet-unseen decay modes. In this addendum to Ref. [1] we display graphically the modes which have been seen and those anticipated. Part of the ∼ 10% shortfall may be composed of decay modes such as Λ c → Λ * ℓ + ν ℓ , where Λ * is an excited resonance, or may be due to a shortcoming in the statistical isospin model. Cabibbo-suppressed modes appear to be less well-represented by known or anticipated decays, and are worthy of more experimental study. In order for this analysis to serve as a model-independent counterpart to a Particle Data Group analysis of D s decays [5], measurements of inclusive branching fractions of Λ c decays need to be undertaken.
[An example is the result from BESIII [6], B(Λ c → Λ + X) = (38.2 +2.8 −2.2 ± 0.8)%.] Λ c branching fractions and their sources are listed in Tables I and II. These serve as inputs to Fig. 1, in which the branching fractions are indicated by the areas of the boxes. Shaded areas correspond to processes not represented by observed decays, but whose rates are anticipated using a statistical isospin model [1]. The figures show only central values; errors are quoted in the tables.
Some qualifying remarks are in order. The pK − π + decay mode, frequently used to normalize others, is not firmly pinned down yet, with an S-value of 1.4 [2]. The statistical isospin model is poorly obeyed for the NKπ and Σ3π modes but well obeyed for the Σ2π modes [1], possibly indicating the need to take account of resonant substructure. Nevertheless, one can draw some general conclusions.
(1) We see a shortfall of about 10% in accounting for all Λ c decays. This could be filled in part by semileptonic decays to excited final states, but a measurement B(Λ c → Λe + ν e + X) = (3.95 ± 0.34 ± 0.09)% by the BESIII Collaboration [12] limits this possibility.
(2) The Cabibbo-suppressed (CS) modes are not as well represented as the Cabibbo-favored (CF) ones, though the anticipated totals are not far from the expected ratio |V cd /V cs | 2 , where V ij are elements of the Cabibbo-Kobayashi-Maskawa matrix.
(4) There is sufficient phase space to accommodate higher-multiplicity modes, such as Σ4π and N5π, but no evidence for them has been presented so far.
(5) The statistical isospin model itself may be at fault. Inclusive branching fractions in Λ c decays would be very helpful in anticipating as-yet-unseen modes without the help of models, as has been done for D s decays [5].
We urge more studies of Λ c decay modes containing neutrons, η, and η ′ ; greater investigation of the singly-Cabibbo-suppressed and higher-multiplicity modes; and inclusive studies. Determination of resonant substructure is a crucial ingredient in filling gaps only partially addressed by an imperfect statistical isospin model.