-- PeterKammel - 15 Feb 2007
* SET ALLOWTOPICCHANGE=Main.MuCapGroup ## TIIE distortions caused by wrong electron effect

## TIIE distortions caused by wall stop effect

## TDIE distortions caused by wall stop effect

## Dangerous wall stop fraction

## Snipped from Tom's Dec 2006 study

## Overall Summary

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* SET ALLOWTOPICCHANGE=Main.MuCapGroup

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TIIE is determined from the muon drift distribution.

TIIE (muSC+muPCX+muPCY) | |

Tom analysis rep | obsolete |

Tom corrected | 8. |

Steve new analysis rep | 3.2 |

Tom's fast MC indicates a significant start time dependence of
the fitted lifetime, which is not observed in the data? Tom pointed out that we don't have enough statistics to see this.

The correction due to this effect scales with TIIE, in the same manner as the BB. Thus there relative importance is independent from TIIE.

Let us pessimistically assume TIIE= 8 ppm. The probability that a mu' fakes a good TPC stop after mu is TIIE * 0.63 * 21 kHz 0.024 ms = 2.5 ppm

Thus a contribution P(te-tmuSC)* 2.5 ppm is added to the undisturbed time distribution. According Tom's report, the most dangerous components are P(te-mu)= ... + 0.03 exp(-t/854ns) + 0.08 exp (-t/151ns). The total distorting amplitudes thus are 0.08 ppm for Al and 0.2 ppm for Fe, which should be ok.

According to Tom's estimate TDIE=126 ppm. I.e. the wall stop effect is 15x larger than for the TIIE case. Such a contribution would lead to 10 Hz start time sensitivity of the fitted lifetime.

Tom's later studied indicate show that this effect scales with the deadtime for deadtime <200 ns.

But Steve does not see the expected 100 Hz effect in the start time fits with 150 ns artificial deadtime nor does he find a change of the fitted lifetime of more than 3 Hz. Thus the TDIE seems to be at least an order of magnititude smaller than estimated by Tom.

Tom's evidence of deadtime in the drift plots comes from Figures 11 and 12 of his 5/9/06 report. I don't quite understand these figures, but it seems to me that a 8 ns deadtime cannot generate a long step in the spectra. Moreover, it is hard to trust such an analysis anyway, because we don't understand the tail at the end of the drift distribution.

Locally we discussed 3 potential sources for such a tail:

- TDIE due to mPC in the us range
- Long drift times for poor field drift paths in the TPC
- Physically later events (capture ...) misidentified as mu stop.

I did a quick study to determine the dangerous wall stop fraction. Assume that, for whatever reason, a fraction f_sup of incident muons gets accepted, irrespective of whether they have a good stop track in the TPC or not. What is their effect on the lifetime?

For the study I used Tom's parametrization of the muSC/muPC1 - eSC 25 us PP time spectrum from his muon detector inefficiency study. Define

// electrons after entrance counter (no good TPC mu stop) TF1 *e_ngood= new TF1("e_ngood","[0]*exp(-[0]*x)*([1]+[2]*exp(-[3]*x)+[4]*exp(-[5]*x)+[6]*exp(-[7]*x))", tlow, tup); e_ngood->SetParameters(decay,0.19,0.07,0.0079,0.03,0.716,0.08,6.127); // electrons after entrance counter (good TPC mu stop) TF1 *e_good= new TF1("e_good","0.64*[0]*exp(-[0]*x)", tlow, tup); e_good->SetParameter(0,decay);The total electron distribution is then generated as e(t)= e_ngood + acc + f_sup * ( e_ngood + e_good)

The detailed procedure is given in the ROOT script mudet.cpp, function create_n.
The spectrum is scaled and randomized and the fitted with a 3 par fit.

The input parameters were:
repeat=100
Stat=1.0e+11
fit stop=24.00
acc=1.0e-03

f_sup | del_lambda (Hz) | del_lambda (Hz) |
---|---|---|

(ppm) | start=0.1 us | start= 0.2 us |

10000 | 79 | 67 |

5000 | 40 | 34 |

1000 | 7.7 +- 0.2 | 6.3 +- 0.2 |

500 | 4.2 +- 0.2 | 3.3 +- 0.2 |

100 | 0.8 +- 0.2 | 0.5 +- 0.2 |

The fit residuals for f_sup=5E-3 are shown below.

For a TDIE effect one has to account for this component (mu-e) and the smeared out one (mu-e'). The latter one is not accounted for in this study. Let us estimate the f_sup, for the case of TIIE and TDIEs.

overall TIIE | R (kHz) | drift (ms) | +MWPC | f_sup (ppm) |

1.00E-02 | 21 | 0.024 | 5040.0 | |

1.00E-03 | 21 | 0.024 | 504.0 | |

1.00E-04 | 21 | 0.024 | 50.4 | |

muSC TDIE | R (kHz) | deadtime(ms) | f_sup (ppm) | |

2.10E+01 | 21 | 1.00E-05 | 0.1 | 21.0 |

In the estimate we have ignored that only 64% of the unseen muons can generate a good stop track in the TPC. In the TDIE estimate we have ignored the mu'-e' contribution (i.e. the unseen muon stops in the wall), which might double the effect. Both effects should be reduced by the impact parameter cut.

The muon entrance detector inefficiencies produce three distorting effects:

- Wallstops in the decay signal: Comparing the "pure" and "w/wallstops" decay signals, it appears that wallstops increase the fitted rate by ~ + 4-5 Hz.
- Time-independent ABG: The Banks bump is pretty small (illustration), and pulls down the rates, by - 1-2 Hz
- Time-dependent ABG (deadtime): Appears to increase the fitted rate by + 2-3 Hz, due to wallstop contributions just like the ones in the decay signal (Illustration).

The combined effect is to increase the fitted rate by ~ + 6 Hz from the input "reality." (This result seems consistent with the results presented in my report, when one considers the variations in the inefficiency settings.) Of course, I should point out that my MC software makes certain assumptions about the muon stopping fractions and detector materials, so there is some implicit model dependence. In fact, as my report explains, I made somewhat conservative assumptions about the stopping fractions and rates, so this might be a larger effect than is actually occurring in the Run8 data. Nevertheless, I think it sets the scale for the effects. The remaining question is then how to best incorporate this information into our final result.

I should also mention that the results above are corroborated by an existing file, so I don't think the indicated scale of effects is anomolous. I will perform additional simulations, but I anticipate that they will confirm the initial estimates above.

- TDIE

**wall stops**: correction=0, Steve sees only < 3Hz when enhancing this effect by 10-15x. Compatible with <0.2 additional protection from muPC OR.

**wrong electron**: correction=0, uncontroversial

- TIIE

**wall stops**: correction=0, My estimate above based on 3 par fit. In agreement with Tom?

**wrong electron**: Tom's simulation correction=0, Steve's extrapolation correction=?, not final yet.

Topic revision: r5 - 2007-02-17 - PeterKammel

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