Today's Progress 25. Oct. 2006

Definition of &pi-momentum

Methods

Since momentum selection is only available for &pi penetrates the C layer as it is, momentum selection with A VS B+C is available only for the &pi with over 140 MeV/c, very unfortunately. Hence, momentm separation for lower momentum range up to 140 MeV/c, should be done with A VS B. Therefore, we prepare 2 kinds of selections. Since momentum selection is only available for &pi penetrates the C layer as it is, momentum selection with A VS B+C is available only for the &pi with over 140 MeV/c, very unfortunately. Hence, momentm separation for lower momentum range from ~100 MeV/c up to 140 MeV/c, should be done with A VS B. Therefore, we do need to prepare 2 kinds of selections. Pion selection is now defined as

"pi" = a .OR. b .OR. (c.AND.(&beta .OR. &delta)) .OR. f .OR. g .

Note that (a) and (f) correspond to very slow pion with < 55 MeV/c, while no momentum analysis is available for (b) and (g).

First, we define the "passing-through-pion-polygon" on the dE/dx-dE/dx correlation, as shown below.

Case 1 - usage of A vs B if cutting momentum is 100MeV/c~140 MeV/c

Here we first apply dE/dx(A)-dE/dx(B) momentum definition for the subset c.AND.(&beta .OR. &delta). The definition is carried out as follows:

(1) Define the "passing-through-pions", for which the momentum value can be numerically given.

(2) Find the "averaged correlation" between dE/dx (A) and dE/dx (B) for "passing-through-pions". The momentum value is defined as the function of dE/dx (B) on the curve.

(3) For each dE/dx(B) value on the averaged correlation, pion momentum is given by the calculated(simulated) value. We assume that all the pions on a normal to the "averaged correlation" have equal momeunta, then the momentum values are well-defined for all the events inside the "passing-through-pions". Therefore, cutting-off-line is defined as the normal.

(note1) Stop pions are defined to have lower momentum values than the slowest ones among the "passing-through-pions". Therefore, upper limit of their momenta could be known.

(note2) If a pion is neither the "passing-through-pions" nor the stoping, they are eliminated from both the pion-momentum-selectable events.

A correlation between dE/dx(A)-dE/dx(B) for the "passing-through-pion" events. The averaged correlation is also overlayed by red color. In order to make the polygon clearer, C hit is imposed. Note that simulated correlation for &pi^- is shown by green color.
A simulated correlation between dE/dx(B) and &pi^- momentum for the "passing-through-pion" events. The averaged correlation is also overlayed by red color. The application region would be 3~ 5 MeVee/cm.

Case 2 - usage of A vs B+C if cutting momentum is > 140 MeV/c

Here we apply dE/dx(A)-dE/dx(B+C) momentum definition for the subset c.AND.(&beta .OR. &delta). The procedure is identical to that for the case1, replacing (B) by (B+C) .
A correlation between dE/dx(A)-dE/dx(B+C) for the "passing-through-pion" events. The averaged correlation is also overlayed by red color. In order to make the polygon clearer, D hit is imposed. Note that simulated correlation for &pi^- is shown by green color.
A simulated correlation between dE/dx(B+C) and &pi^- momentum for the "passing-through-pion" events. The averaged correlation is also overlayed by red color.

Expected resolution by Monte-Carlo simulation

In order to estimate the expected resolution, the same analysis procedure is applied to the Monte-Carlo data, and the momentum-dependent resolution is evaluated. Below, expected momentum resolution is plotted, together with the simulated values with TOF method assuming 100/200 psec resolution.

Since the realistic TOF resolution is ~200 psec even with C-layer, dE/dx method is superior for all the momentum region. For the detail of the simulated energy, refer this document.