CERN Accelerating science

Probability $P_\mathrm{br}^{\mathrm{tot}}(\mathrm{Pt})$ calculated as a function of $\alpha$ (see text). The horizontal lines correspond to the measured value $P_\mathrm{br}^{\mathrm{tot}}(\mathrm{Pt}) = \left. 0.0257^{+0.0097}_{-0.0036}\right|_\mathrm{tot}$ (\ref{eq:pBr}) together with the total errors. The value $\alpha=1$, which corresponds to pure QED calculations, is within the error band of the measurement.

Method to investigate long-lived $A_{2\pi}^L$ by means of a breakup foil (side view). $N_A$ is the number of the totally produced $A_{2\pi}$ and $N_A^L$ the number of excited $A_{2\pi}^L$ with $l>0$.

Lab momentum spectrum of $A_{2\pi}$ produced in Be, as used in the simulation.

Top view of the DIRAC setup: 1 -- target station with insertion, showing the Be target, magnetic field and Pt breakup foil; 2 -- first shielding; 3 -- microdrift chambers (MDC); 4 -- scintillating fiber detector (SFD); 5 -- ionisation hodoscope (IH); 6 -- second shielding; 7 -- vacuum tube; 8 -- spectrometer magnet; 9 -- vacuum chamber; 10 -- drift chambers (DC); 11 -- vertical hodoscope (VH); 12 -- horizontal hodoscope (HH); 13 -- aerogel Cherenkov; 14 -- heavy gas Cherenkov; 15 -- nitrogen Cherenkov; 16 -- preshower (PSh); 17 -- muon detector. (The plotted symmetric and asymmetric events are a $\pi \pi$ and $\pi K$ pair, respectively.)

Summed populations $\sum P_n^L$ of all long-lived atomic states at the exit of the Be target as a function of $n$ used for ``tail'' estimation. For each $n$, the two upper curves show the sum of state populations for the given $n$ plus different ``tail'' estimations calculated from populations for $n$ and $n-1$ (exponential ``tail'' -- $\bullet$, hyperbolic ``tail'' -- $\blacktriangle$). The lower curve ($\blacksquare$) presents the sum of the population for the given $n$ plus the population for $n+1$ instead of the ``tail''.

Populations $P_n^L$ of long-lived states $A_{2\pi}^L$ versus $n$, summed over $l$ and $m$, at the exit of the Be target ($\bullet$) and at the Pt foil entry ($\blacksquare$).

$|Q_L|$ distribution of $\pi^+\pi^-$ pairs for $Q_T<2.0$~MeV/$c$. Plot a) presents the experimental distribution (+ with statistical error bar) and the simulated background (solid line). Plot b) shows the experimental distribution after background subtraction (+ with statistical error bar) and the simulated distribution of atomic pairs from $A_{2\pi}^L$ broken up in Pt (dotted-dashed line). The fit procedure has been applied to the 2-dimensional ($|Q_L|,Q_T$) distribution.

Experimental $Q_L$ distribution of $\pi^+\pi^-$ pairs (+ with error bar) for the beryllium (Be) target fitted by the sum of simulated distributions of ``atomic'', ``Coulomb'' and ``non-Coulomb'' pairs. The summed distribution of free (``Coulomb'' and ``non-Coulomb'') pairs is shown as black line.