Phase Shift in ψ(2S) Decay to Proton–Antiproton express
When a ψ(2S) particle decays into a proton and an antiproton, two different mechanisms act simultaneously: the strong interaction, like glue holding quarks together, and the electromagnetic one, like light pushing charges apart. Their contributions add up with a certain phase shift. This shift is like the meeting of two waves from stones thrown into a pond: if the crest of one coincides with the trough of the other, they cancel out, but if crest meets crest, they reinforce. The phase shift determines how strongly these two processes interfere.
In the BESIII experiment at the electron–positron collider in Beijing, data were collected at collision energies from 3.58 to 3.71 GeV — right around the mass of the ψ(2S). They measured how often proton–antiproton pairs are produced, and from the shape of this energy dependence, the resonance curve, they extracted the relative phase: 105.9° or −105.3°. The two possibilities arise from a symmetry, as if a clock face could be turned by the same angle in either direction and yield the same picture.
Previously, no such data existed in this energy region, and now the gap has been filled for the first time. The obtained phase values agree with measurements in other ψ(2S) decay channels and with BaBar results, supporting the hypothesis of phase universality: that is, the same shift applies to different final states. This is important for understanding how the strong interaction transitions into the electromagnetic one at hadronic scales.
Two estimates of the branching fraction of ψ(2S) → proton–antiproton were also obtained: (3.21±0.13)×10⁻⁴ and (3.47±0.19)×10⁻⁴. This means that out of about ten thousand ψ(2S) mesons, only three or four will decay into a proton–antiproton pair. Such rarity makes the measurement especially valuable: it requires high statistics and precise background control.
This result is another step toward understanding how quarks and gluons organize into hadrons and how different fundamental interactions coexist in a single process. The phase shift between the strong and electromagnetic contributions is not just a number but a window into the dynamics of the strong interaction at distances on the order of the proton size.
Original abstract
as written by the authors arXiv:2608.15074v1
This paper uses the data corresponding to an integrated luminosity of $$495$$~pb$$^{-1}$$ in the center-of-mass energy region from 3.58~GeV to 3.71~GeV to study the relative phase between strong and electromagnetic amplitudes in the $$\psi(2S)\to p\bar{p}$$ decay. The cross sections and the effective form factors around $$\psi(2S)$$ of proton-antiproton pairs are presented thereby filling the gap in the experimental results around the $$\psi(2S)$$ resonance for the first time, and the results are consistent with the previous BESIII and BaBar results. The relative phase is extracted from the cross-section line shape as $$\Phi_{g,\gamma}=(105.9\pm9.4)^\circ$$ or $$\Phi_{g,\gamma}=(-105.3\pm9.1)^\circ$$. Correspondingly, two solutions for the $$\psi(2S)\to p\bar{p}$$ branching fractions are obtained as $$\mathcal{B}=(3.21\pm0.13)\times10^{-4}$$ and $$\mathcal{B}=(3.47\pm0.19)\times10^{-4}$$. These results support the universality of the phase and provide new insights into its underlying mechanism.
The phase shift between the strong and electromagnetic amplitudes in ψ(2S) decays turned out to be close to 106°, nearly matching the value previously measured for J/ψ — the lighter 'brother' of ψ(2S). This points to a common mechanism independent of the resonance mass.