In ultra-peripheral heavy ion collisions, a photon from the electromagnetic field of one nucleus can fluctuate to a quark-antiquark pair and scatter from the other nucleus, emerging as a $\rho^0$. The $\rho$ production is well localized at the two nuclei, forming a 2-source interferometer. The two sources interfere, and $\rho^0$ production at low transverse momentum is suppressed. We measure this interference in 200 GeV per nucleon Au-Au collisions, and observe interference at $93\pm 6\pm x\%$ of the expected level, and find a maximum decoherence, due to wave function collapse or other factors, of x\% at the 90\% confidence level.

This interference occurs even though the $\rho^0$ decay before their pre-decay wave functions can overlap. In one interpretation, the interference requires that the post-decay wave functions retain amplitudes for all possible decay modes, long after the decay occurs.

Figure 1

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Fig. 1. A schematic diagram of the two possibilities: a photon from nucleus 1 scattering from nucleus 2, or vice versa.

Figure 2

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Fig. 2. The rapidity distribution for exclusive rho^0 (right) and the Coulomb breakup sample (left). The data is in red, while the blue histogram are the result of a simulation based on the soft Pomeron model, after detector acceptance.

Figure 3

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Fig. 3. The uncorrected t distribution for rho^0 production with 0.1 < |y| <0.5. The data is red, while the blue and green histogram are simulations with and without interference respectively. The black histogram is the like sign background.

Figure 4

Figure 4a: XnXn 0.1 < |y|<0.5

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Figure 4b: XnXn 0.5 < |y| < 1.0

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Figure 4c: topology 0.1 < |y| < 0.5

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Figure 4d: topology 0.5 < |y| < 1.0

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Figure 4. Efficiency Corrected dN/dt, compared with a fit to the form dN/dt = a exp(-bt)[1+ c(R(t)-1)], where R(t) =Int(t)/Noint(t); Int(t) and Noint(t) are the calculated t-spectra with and without interference respectively. Note: this fit and the justification will be extensively discussed in the paper (and is already described in the supporting documentation).

Conclusions

The conclusion of the paper is that we see the interference at the expected level. This shows that the post-rho-decay wave function must retain amplitudes for all possible decays, long after the decay occurs. Since the pi^=pi^- wave function is spread out in space, this requires a non-local wave function.