Calculation

We start from a spatial Gaussian in the LCMS frame (where there is one transverse and one longitudinal size): exp(-(r_x²+r_y²)/2R_T²-r_z²/2R_L²), and a Dirac delta in coordinate proper time: delta(τ-τ₀). Then we perform a Fourier transformation (by doing a second order expansion in the exponent, needed because of the t→τ transition. The absolute square of this (imaginary) quantity is the correlation function minus unity, so we add one, and obtain the result for the Bose-Einstein correlation function. Since I don't know as of now how to include complicated formulas to this webpage, I refrain from doing so.

Results

Our correlation function result is given as a function of q_T,q_L,q₀, so we first introduce pair pseudorapidity η, and then we can express our results as a function of |q|² and q₀². Let us show results for τ₀=R_L>R_T:

One can immediately see that at midrapidity, dependence is (almost) only on |q|, not on q₀, hence also not on q_inv²=|q|²-q₀², constant values of which are parallel to the diagonal of this plot, and q_inv=0 is represented by the diagonal.
For other source parameters (note that R_L only matters if |η|>0; and η only matters if R_L≠R_T) the plot changes slightly, but not dramatically:

I.e. the peak is less tilted towards the diagonal if emission time is larger than the spatial dimensions.

Data

The data show striking similarity with the above toy model:

Appendix

For those interested, here is the analytically expressable result for the Gaussian case, to be used e.g. in ROOT, assuming q2 and q02 are the above variables, eta the pair pseudorapidity, while RT2, RL2 and tau0 are the source parameters (squared, and in c²/GeV² units, i.e. divided by hbarc²).

  double qT2 = q2/cosh(eta)/cosh(eta);
  double qL2 = q2*tanh(eta)*tanh(eta);
  double AT = (RT2+tau02)*RT2*tau02/((RT2+tau02)*(RT2+tau02)+tau02*RT2*RT2*q02);
  double AL = (RL2+tau02)*RL2*tau02/((RL2+tau02)*(RL2+tau02)+tau02*RL2*RL2*q02);
  double C2 = 1 + exp(-qT2*AT-qL2*AL);
  if(q02>q2) C2 = 0;

Sidenote

Let us, contrary to the above, take a source wich may be characterized by a maximal emission point proportional to momentum and proper-time, i.e. xbar = a*τ*p, and an emission distribution in proper time H(τ) being a one-sided Lévy distribution. This now not the spatial emission probability density, but the one in proper time. This source results in a correlation function where q_inv appears as the only momentum-difference carrying term. Hence, the correlation function will look like:

Such a source is expected in e⁺e^- collisions where multiple jets were created - but our case seems to be very different from this.