First-hand information for everyone
Scientists used the BESIII detector to make the first detailed energy-scan measurement of how often electron–positron collisions produce a pair of charged kaons (K+K−) near the ψ(2S) particle. By sweeping the collision energy across the ψ(2S) resonance and measuring the production rate, they extracted a fundamental quantity called the relative phase between the strong force and the electromagnetic force contributions to the ψ(2S) decay. The study is based on 495 pb−1 of data collected at the BEPCII collider.
In an energy scan experiment, physicists change the collision energy in small steps and record how the production rate (cross section) of a given final state varies. The team analyzed the shape of the cross section as a function of energy around the ψ(2S). That shape contains information about how the ψ(2S) resonance and the non-resonant background add together. From this shape they determined the relative phase between the strong and electromagnetic amplitudes that produce K+K−.
An amplitude is a contribution to the probability for a process. The phase between amplitudes is like a timing difference. When two amplitudes combine, they can interfere. Constructive interference makes the observed rate larger. Destructive interference makes it smaller. Measuring the phase therefore matters because interference changes the apparent branching fraction, which is the probability that ψ(2S) decays into K+K−.
The analysis produced two mathematically allowed solutions. In one (constructive interference) the branching fraction B(ψ(2S)→K+K−) is (7.49 ± 0.41) × 10−5 with a phase Φ = (110.1 ± 6.7)°. In the other (destructive interference) B = (10.94 ± 0.48) × 10−5 with Φ = (−106.8 ± 5.7)°. The authors report a clear correlation between the phase and the branching fraction and emphasize that interference must be taken into account when measuring ψ(2S) branching fractions.
The paper also gives the first results in this energy region for the ψ(2S) strong form factor and for the energy-dependent electromagnetic form factor of the charged kaon. Form factors are functions that summarize how the internal structure and the interaction strength change with energy. Reporting these form factors helps other researchers compare models of how ψ(2S) couples to kaons and how kaons respond to electromagnetic probes.
There are important caveats. The extraction of the phase assumes that the electromagnetic amplitude of the ψ(2S) resonance has the same phase as the smooth electromagnetic continuum; that is a model assumption and not directly measured. The two numerical solutions show a remaining ambiguity tied to interference and to that assumption. These are the first measurements of their kind in this channel and region, and resolving the ambiguity will likely need more data or complementary analyses under different assumptions.