New estimators for the straw T0 and time resolution

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1 New estimators for the straw T0 and time resolution
Straw WG New estimators for the straw T0 and time resolution D. Madigozhin JINR Dubna

2 Outline: 1) The front time as a t0 esimator and a new fit function
2) Results for t0 3) Results for resolution 4) The fit in the almost full region 5) Conclusions Data : runs 4740 (kaons), 4871(kaons). “First-hit” leading time distributions are considered. All numberings start from 0 (C-like) RO channel = (chamber*8+srb)*256 + cover*16 + (straw channel) Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

3 Old fit with the asymmetric Gaussian works well only for the visible T0 estimation:
F5(t) = A + B exp( -(t -Tmax)2/(2 s(t)2 ) ), where s(t) = s0 + k(t-Tmax) When one think mainly about the peak position and width, usually people try to make some asymmetric Gaussian width. For example, one can add a separate front resolution sf . F8(t) = A + B f(t)/[1+exp(n(t-Tend))] If (t > Tmax ) f(t) = exp[ -(t -Tmax)2/(2 (s0 + k(t-Tmax))2 ) ] else f(t) = exp[ -(t -Tmax)2/(2 sf2 ) ] But all these sigma and Tmax were found to be sensitive to the background and reference time smearing via the correlations between parameters, especially for small statistics.

4 Which parameter of the leading time distribution is the best for T0 estimation?
If one knows the distribution shape, it doesn't matter: one can just use the peak position, or the “visible T0“, or somethig else, and then introduce a corresponding constant “magic Dt” in order to match the MC model (and RT dependence) with its definite threshold/signal assumed. But in the case if there is an additional channel-dependent time smearing outside of the straw physics, we are not sure that we know the true distribution of leading time. At least two sources of the external smearing are known: Smearing due to the signal proparation along the straw Smearing due to the reference time jitter (say, reference CHOD time subtracted from STRAW time) Extra constant offsets are not a problem at all. In first approximation there is an additional symmetric smearing with an unknown width. It is simulated in the present example as a Gaussian random smearing applied to initial distribution. Both the peak position and the “visible T0” are shifted by the smearing. But the point of maximum slope – “front” – is almost stable. So front is the best T0 estimator with a minimum sensitivity to external time smearing. Peak position Smeared with a 10 ns width Gaussian front Visible T0

5 We propose to define the new measureable t0 as the point of maximum slope.
So one can try to fit a peak of derivative histogram (differences between the neighboring bins) with a Gaussian. It corresponds to the definition of measureable t0 as a front position, and it is a simple, background-independent procedure. It works, but unfortunately it requires an essentially larger statistics than it is needed for the successful fit of primary histogram. So we use this differential procedure for cross-checks mainly. t0 Gaussian fit of the peak Derivative histogram

6 fpeak(t) = A + B exp[ -t/L ] / [1+exp((F-t)/S)]
New parameterization of the peak has a “natural” front parameter F (first approximation front). A steepness parameter S represent about a half of time resolution. A Length parameter L represents the exponential slope at the beginning of distribution. fpeak(t) = A + B exp[ -t/L ] / [1+exp((F-t)/S)] In general case it is better to avoid the region of “early” background, where a big overlay effects happen with the reference (CHOD) time at high intensities (leading to the “dip” in front of the “front”). But it means that one need to estimate background separately and fix it for the fit. So a few-stages fit procedure is used for stable results. For t0 and resolution one should fit only the peak region in order to avoid the parameters correlations with another regions. First time we have a reasonable c2 at least for the peak region.

7 f'(t) = 0 for the peak position, that is not used
The peak and the front positions are found from the fit parameters solving analytically the following equations for derivatives: f'(t) = 0 for the peak position, that is not used f''(t) = 0 for the front (lowest of two solutions). Solution is: t0 = F + 2S log( (sqrt(q2+4(q-1))-q)/2 ), where q = L/S (makes a small correction to F parameter). Another way is a Gaussian fit of the derivative time distribution that has a good peak at the front. The both techniques have been tested and were found to be compatible within 1 ns. Now the precision and stability is good enough for the detailed look on the t0 pattern. Front from the Gaussian fit of derivative Second solution Front from the new fit parameters Peak from the fit parameters

8 For the special processing of the 2016 year data the only “t0 correction” applied is the shift for the chambers 0 and 1 by 200 ns and for the chambers 2 and 3 – by 400 ns (just in order to keep all the registerd hits inside the histogram windows). So we can see now the “almost hardware” t0 positions for each of the channels for the run 4740: U V X Y U V X Y U V X Y U V X Y t0(ns) Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

9 Are these t0 stable? Try to overlay the similar run 4871 results (red). No, the patterns are rather different! t0(ns) Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

10 8 ns t0(ns) 4871 gap Second Y layer, Chamber 0 4740
On the detailed view one can see, that many covers (half-covers in one layer) change their t0 between the runs by 25 ns or 50 ns. It explains the general pattern: For each layer we have a ~ constant slope (formed by the cover-related ~ flat steps), that seems to be caused by the increasing of cable length, plus there are a jumps by 25 ns, that are not stable between the runs. Individual t0 patterns are repeated reasonably well (they are not just a statistical fluctuations), so exact t0 corrections will improve the final resolution. After the run-by-run “quantum” corrections for cover jumps the exact cover and straw t0 can be made for the big joint statictics. 8 ns 7 ns are expected for the light speed at 2.1 m t0(ns) Nothing special happens near the gap, front is stable. 4871 gap Second Y layer, Chamber 0 4740 Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

11 For all the RO channels the found t0 jump between the two different runs have only 5 approximate values: ~ 0, +/- 25 ns, +/- 50 ns (that means 4 coarse time slots) . May be firmware will solve this feature? Otherwise we should develop a special technique for t0 treatment based on the fast finding of the choosen 25 ns timeslots and implementing a big “quantum” cover-related correction at the beginning of every run or even for smaller periods (rarely the jump happens during the run). With such a correction the rest of t0 tuning (individual straws) may be done on the basis of much larger statistics. t04871 – t04740 (ns)

12 Resolution estimation
A front-width resolution estimator S is more stable vs geometry position and statistics than any peak-width related estimators. It has usually about two times lower value than the smallest sigma estimators. But it has its own physical meaning – it is a front (half-)size rather than a peak width. The resolution estimator S is increasing slightly with the distance from the beam gap. It may happen due to the shape of the beam that may be not a quite multiplicative function of X,Y. In such a case the wider hits distribution along the straw will lead to the larger extra time resolution due to the larger smearing of the signal propagation time (along the straw). S(ns) Run 4740 Run 4871 Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

13 Problematic single channels
Stable from the last year Self-recovered between the runs Large wire shift, the picture is stable from 2015 Old problemstic channels A new single-straw troubles

14 There are two covers (one cell) with the increased resolution, here is the example on one layer.
S(ns) Run 4740 Run 4871 Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

15 Picture from the Interactive Straw Map (application is now available for everybody).
Run 4871 Increased resolution zone is a complete cell, but not a complete HV channel. Gas? Thresholds? Looks like a threshold/gain effect rather than a drif time scale or general smearing (tail is also well shifted) Chamber 3 (0-3)

16 Apart from that, on some X projections there are a cases of sharp S increase in the visinity of the beam gap. It is a purely position dependent effect. It may be a result of the worsened reference time (CHOD in the present case) near the gap, when the tracks are (partially) lost for the hodoscope. On Y,U,V projections the effect is weaker and looks more symmetric. Run 4740 Run 4871 t0(ns) S(ns) Straw position index = (16*chamber + 4*view + 2*half + layer)*122 + (straw number)

17 The gap effect on the individual straws
Geom closer to the beam gap Same cover Geom 7270 normalized CHOD time become smeared near the CHOD gap? Reference time looks smeared Less visible on the tails as expected for general smearing

18 A more general fit for the full region is also possible
Ffull(t) = A + B f(t) /( [1+exp((F-t)/S)] [1+exp((t-Ft)/St)] ) f( t < F ) = exp[ -t/L ] f( t > F ) = exp[ -t/(L + P (t-F)D )]

19 The full region fit works even when the (wire-tube) shift is considerable.
Ffull(t) = A + B (f(t) /( [1+exp((F-t)/S)]) x ( frac/[1+exp((t-Ft1)/St1)] + (1-frac)/[1+exp((t-Ft2)/St2)] ) f( t < F ) = exp[ -t/L ] f( t > F ) = exp[ -t/(L + P (t-F)D )] Preliminary simplified (another formula) fits of the two tagged distributions with a known sides of the tails. It defines the tail ends Ft1,Ft2,St1,St2, that are then fixed for the next step. Stage 1 The most general fit of the full distribution. A fraction of the shorter component is a free fit parameter. Stage 2

20 Conclusions A new approach to the t0 estimation based on the front time is proposed, as well as the time resolution estimation based on the front width instead of the usual peak position and any kinds of “asymmetric peak witdth”. A new kind of parameterization for the peak region, that is natural for this “front” approach is tested. The “hardware” dependence of t0 vs geometrical straw position is checked, the expected cable-length dependent shift is observed. A random 25-ns cover-related jumps between the runs are found. It will help to improve the t0 setting strategy, that may become a technique, that is very specific for straw detector. A front width resolution estimator is investigated vs straw position, the expected slow dependence on the distance to beam is observed. Apart from the few single problematic straws, a complete cell with an increased time resolurion is found. The reason up to now is not clear. Also there are narrow regions near the gaps with the increased t resolution. CHOD reference time is the suspect. The full region fit procedure with a wire shift is developed in order to compare individual straws Data/MC in the future.


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