1. QM Interference in τ ± →π ± π + π - π 0 ν τ decays at BaBar Tim West The University of Manchester

2. Talk Outline Summary of τ ± →π ± π + π - π 0 ν τ analysis so far The cuts used to obtain data used here Description of the interference that I have been looking at Explaination of the model used for the interference Method Model predictions Results Future work

3. τ ± →π ± π + π - π 0 ν τ Analysis originally started by Roger Barlow. One task is looking for second class currents in τ decays, in particular the decays: –τ ± →a 0 ν τ →ηπ ± ν τ → π ± π + π - π 0 ν τ –τ ± →b 1 ν τ →ωπ ± ν τ → π ± π + π - π 0 ν τ The work presented here is based on the data produced by Roger’s cuts (details given in B.A.D. 327.

4. Cuts

5. I have been looking at the ω resonance ω can be involved in the decay for both first and second class currents: –First class currents produce the ωπ in a p-wave state. –Second class currents produce them in either s- or d-wave. Can take two possible three π mass combinations for the ω and plot them against each other.

6. Obtain resonance bands in both x and y direction. We are interested in what happens at the intersection of these bands. Model full and no intereference and compare to observations. Slight asymmetries as pions ordering is taken from pion lists.

7. Case I: No QM interference Events involving ω have a definite set of three pions coming from the ω. Assume that ‘incorrect’ 3π mass spectrum is linear in the resonance region. The number of events in the intersection is the sum of three terms: –n ω 1 – the events where ω 1 is the correct combination, –n ω 2 – the events where ω 2 is the correct combination, –n o – events that do not involve an ω. Use linear interpolation around the peak to calculate the number of events expected in the case of no quantum mechanical interference.

8. Method Count events in resonances off-intersection (red) and away from resonances (green) Count events at intersection (black). Use interpolation and scaling to predict the number of events in the case of no interference. Compare to the actual number. Need a model for full interference...

9. Case II: full interference Fit mass spectrum with a Breit-Wigner convolved with the sum of two gaussians. For the case of no interference we are effectively adding the Breit-Wigner intensities. For full interference, add the Breit-Wigner amplitudes (one in x, one in y) and take the modulus squared...

10. Case II (continued...) Find that the difference between full interference and no interference (under this model) is given by: Use r to measure the interference, where Can see that -1<r<1. Expect r to vary with box size.

11. Results

12. Further Work Look for a better model of the interference. Are the assumptions about the background fair? See if the same approach can be applied to the eta resonance. Can it help with second class currents? Is the ω  +  -  0 branching fraction altered by the presence of the other charged pion?