Uncertainty relations in curved spaces

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde

Observation of D → a₀(980)π in the decays D⁰ → π⁺π^(−)η and D⁺ → π⁺π⁰η

We report the first amplitude analysis of the decays D0→π+π−η and D+→π+π0η using a data sample taken with the BESIII detector at the center-of-mass energy of 3.773 GeV, corresponding to an integrated luminosity of 7.9 fb−1. The contribution from the process D0(+)→a0(980)+π−(0) is significantly larger than the D0(+)→a0(980)−(0)π+ contribution. The ratios B(D0→a0(980)+π−)/B(D0→a0(980)−π+) and B(D+→a0(980)+π0)/B(D+→a0(980)0π+) are measured to be 7.5+2.5−0.8stat.±1.7syst. and 2.6±0.6stat.±0.3syst., respectively. The measured D0 ratio disagrees with the theoretical predictions by orders of magnitudes, thus implying a substantial contribution from final-state interactions

Observation of η_(c)(1S, 2S) and χ_(cJ) decays to 2(π⁺π^(−))η via ψ(3686) radiative transitions

Based on 2.7×109 ψ(3686) decays collected with the BESIII detector, the radiative decay ψ(3686)→γ2(π+π−)η is investigated to measure properties of S- and P-wave charmonium states. The branching fraction of the decay ηc(1S)→2(π+π−)η, which is found to have a strong dependence on the interference pattern between ηc(1S) and non-ηc(1S) processes, is measured in both destructive and constructive interference scenarios for the first time. The mass and width of the ηc(1S) are measured to be M=(2984.14±0.13±0.38) MeV/c2 and Γ=(28.82±0.11±0.82) MeV, respectively. Clear signals for the decays of the χcJ(J=0,1,2) and the ηc(2S) to 2(π+π−)η are also observed for the first time, and the corresponding branching fractions are measured. The ratio of the branching fractions between the ηc(2S) and ηc(1S) decays is significantly lower than the theoretical prediction, which might suggest different dynamics in their decays

Search for e⁺e^(−) → η′ψ(2S) at center-of-mass energies from 4.66 to 4.95 GeV

Using data samples with an integrated luminosity of 4.67 fb−1 collected by the BESIII detector operating at the BEPCII collider, we search for the process e+e−→η′ψ(2S) at center-of-mass energies from 4.66 to 4.95 GeV. No significant signal is observed, and upper limits for the Born cross sections σB(e+e−→η′ψ(2S)) at the 90\% confidence level are determined