CENTRAL VALUES FOR STD MODEL + OBSERVED VARIATIONS -------------------------------------------------- Location of this file: /afs/cern.ch/delphi/tasks/scan95/summary/variation.txt 8/5/97 - initial proposal GW 15/5/97 - modified proposal: add QFQD, BOM and '94 GW 2/6/97 - add some numbers + section on IP dependent corrections GW 3/6/97 - after TC/PR/MK/GW discussion, more entries added GW 11/6/97 - update central values; many '93 variations added GW/PR 13/6/97 - new 95 central values GW 16/6/97 - minor mods to MK NMR48 temperature shifts + new shifts + new central values GW 17/6/97 - more shifts added... GW 18/6/97 - more shifts added... tiny changes to 95 central values GW 19/6/97 - 93 ring temp discrepancy understood... GW 20/6/97 - add new MK corrector numbers, CT48 94 numbers, rise numbers, bmod GW 1/7/97 - update with 'final' central values; add shifts w.r.t. Warsaw GW 3/7/97 - add some new shifts from PR GW 4/7/97 - new shifts + L3 & DELPHI central values GW 7/7/97 - additional GW shifts added - revised MK corrector numbers (now we agree!) GW 9/7/97 - new MK shifts + BOF/EOF section GW 11/7/97 - add new MK BOM numbers GW 22/7/97 - add new rise numbers + MK temperature numbers GW 23/7/97 - add new variations + new information on BOF/EOF fills GW 24/7/97 - correct some BOF/EOF fill info... add new 6 fill subset info GW 25/7/97 - more info on rises GW 28/7/97 - and more on CT48 GW 29/7/97 - and more... GW 30/7/97 - new rise numbers from Mike GW 5/8/97 - new info on BOF/EOF fills GW 2/10/97 - postscript on 'initial temperature coefficient' GW MEAN BEAM ENERGY ---------------- Note: * All values given in Eb * All shifts signed in sense 'alternative-default' Central values for 'standard model' (ALEPH lumi weighting) =========================================================== 2 sets of numbers are given: the current best values, and values where it was certain that both analyses were using identical strategies (it is this section which should be studied to assess technical agreement). Current best values (last updated: 1/7/97) ------------------- (MK and GW/PR strategies may differ) M K G W / P R M K G W / P R 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 value 44718.94 45639.99 46483.36 44718.89 45639.96 46483.34 44715.00 45593.03 46507.26 44715.45 46507.56 scatter 3.37 / 1.59 3.25 1.52 3.88 / 1.92 3.9 2.0 M K 94P value 45600.66 scatter 2.43 (NB difference in 95 rms' between GW and MK understood to be in definition of rms. MK uses 1/sqrt(N-1) whereas GW uses 1/sqrt(N). With the same definition the numbers become identical.) Change w.r.t. Warsaw (last updated: 1/7/97) -------------------- Warsaw-S97 1995 P-2 -.08 1995 P -1.47 1995 P+2 .42 1993 P-2 -.64 1993 P -1.46 1993 P+2 -1.15 1994 P -1.43 Numbers evaluated by MK, 25/6/97 Shifts almost fully accounted for by new temperature model + correctors. Last available values when MK and GW/PR strategies thought to be same (last updated: 1/7/97) --------------------------------------------------------------------- M K G W / P R M K G W / P R 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 value 44718.94 45639.99 46483.36 44718.89 45639.96 46483.34 44715.43 45593.09 46507.34 44715.45 46507.56 scatter 3.37 / 1.59 3.25 1.52 4.06 / 1.82 3.9 2.0 M K 94P value 45600.66 scatter 2.43 Comments -------- * Pete on his '93 numbers: 1) I use the median corrector strategy 2) In general I have no lumi weighting inside a fill; but the mean energies are lumi weighted with the fill lumi 3) For my 'best' mean value I make a correction of 0.2 MeV (beam) to correct for the lumi weighting of the rise. This comes from a toy model where I assume a linear variation with time. I would add an error of dE(beam) = +- 0.2 MeV to my numbers for this. NB the lumi weighting will also effect the horiz. corrector correction, I have not made an estimate of this but the total effect here is smaller. 4) QFQD. This I cannot do fully. I use epol values from Joerg which are already corrected for this. My numbers refer to the difference in applying the correction in the model or not. 5) BOM I use always the one value per fill strategy. SInce I dont compute the energies every 15 mins the interpolation method is not very meaningful for me. 6) I make a correction of 0.3 MeV for E(e+) (as does Mike) * GW on Pete's '93 numbers: Pete in fact is using an earlier (in principle) more correct definition of T0 than Mike. Then to be consistent he should use a rise routine with the same definition of T0. I will give him this routine and he will see if this changes anything... 11/6/97 Indeed when Pete uses new rise routine with same definition of T0 he gets the numbers now above - the agreement with Mike (who uses alternative definition, but in consistent manner) is improved. * For 'current best' new calibration file is used. Pete has not used this for his '93 numbers, hence 'same strategy' retains old file values for '93. Central values as evaluated by experiments ========================================== (These include IP dependent effects, ie. RF and dispersion) OPAL ---- Summer 97 Warsaw-S97 RMS spread 1995 P-2 44720.8143 - 0.1941 4.1808 1995 P 45641.6159 - 1.5965 5.9432 1995 P+2 46485.8654 0.5398 5.1120 1993 P-2 44725.3747 - 0.5519 6.2777 1993 P 45603.3873 - 1.3577 5.8135 1993 P+2 46517.6319 - 0.9147 5.6513 1994 P 45609.9483 - 1.0645 6.1376 All numbers are lumi-weighted beam energy averages in MeV. RMS spread refers to distribution of beam energy variation over the year (scan only in 93 & 95). Multiply by 2 to get c.m. energy means and spreads, i.e. assume e- and e+ beam energy variations 100% correlated. This c.m. energy spread must be added in quadrature with the instantaneous c.m. energy spread due to the intrinsic beam energy spread. CMH 26/6/97 ALEPH ----- Summer 97 Warsaw-S97 RMS spread 1995 P-2 44719.76 -0.13 3.41 1995 P 45640.95 -1.51 4.23 1995 P+2 46484.04 0.47 3.73 1993 P-2 44716.02 -0.51 6.38 1993 P 45593.59 -1.47 5.93 1993 P+2 46507.64 -1.09 5.93 1994 P 45598.39 -1.27 5.99 Numbers from PBT 26/6/97 Divided by 2 by GRW (hopefully without error!) L3 -- Summer 97 Warsaw-S97 RMS spread 1995 P-2 44725.930 -0.124 3.23 1995 P 45647.848 -1.253 3.50 1995 P+2 46491.322 0.425 3.32 1993 P-2 44724.876 -0.551 6.66 1993 P 45602.538 -1.422 6.40 1993 P+2 46517.606 -1.095 5.82 1994 P 45610.094 -0.971 6.03 Numbers from JM 3/7/97 DELPHI ----- Summer 97 Warsaw-S97 RMS spread 1995 P-2 44718.81 0.01 3.90 1995 P 45639.20 -1.41 4.08 1995 P+2 46482.65 0.56 3.80 1993 P-2 44715.41 -0.59 6.71 1993 P 45593.51 -1.48 5.64 1993 P+2 46507.37 -1.09 5.71 1994 P 45600.17 -1.29 5.90 Numbers from AD 4/7/97 Divided by 0.002 by GRW (hopefully without error!) Variations w.r.t. 'standard model' ================================== Issues considered: * NMR48 temp coeff * Ring temp coeff * Category of rise routine used * Tide coefficients * Corrector strategy * Jump size for bending mod * QFQD * BOM's QUANTITY: NMR48 temp coeff ======== ================ Central Value: CTMAX=15, CT=-5 ------------- --------------- Variations w.r.t. above ----------------------- Assume CTMAX+CT known to +-60% CT known to +-50% Correlations to be assessed: propose that we estimate the variations for a range of settings and then proceed from there. GW to produce rise routines for these settings and give to MK and PR. M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P CTMAX CT 10.0 -5.0 -0.37 -0.48 -0.38 -0.38 -0.48 -0.41 -0.23 0.05 -0.21 -0.19 -0.18 -0.17 9.0 -5.0 -0.23 -0.23 20.0 -5.0 0.39 0.51 0.43 0.39 0.52 0.39 0.21 -0.05 0.22 0.18 0.19 0.17 21.0 -5.0 0.22 0.24 15.0 -2.5 -0.05 0.09 -0.04 -0.06 -0.13 15.0 -7.5 0.05 -0.09 0.02 0.04 0.14 12.5 -2.5 -0.25 -0.15 -0.24 -0.14 -0.25 17.5 -7.5 0.24 0.15 0.23 0.15 0.05 QUANTITY: Ring temp coeff ======== =============== Central Value: CTMAX=15, CT=-5 ------------- --------------- Variations w.r.t. above ----------------------- Assume CTMAX+CT known to +-30% CT known to +-50% Correlations to be assessed: propose that we estimate the variations for a range of settings and then proceed from there. M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P CTMAX CT 20.0 -5.0 -0.24 0.47 -0.22 -0.13 -0.32 -0.34 -0.02 -0.22 -0.19 18.0 -5.0 -0.14 0.03 -0.17 -0.02 -0.12 17.5 -5.0 -0.02 -0.10 12.5 -5.0 0.01 0.11 12.0 -5.0 0.14 -0.02 0.16 0.01 0.13 10.0 -5.0 0.25 -0.47 0.22 0.12 0.32 0.35 0.19 15.0 -2.5 0.02 0.03 0.02 - - 15.0 -7.5 -0.02 -0.02 -0.03 - - 12.5 -2.5 0.13 -0.01 0.15 0.01 0.00 0.01 0.01 17.5 -7.5 -0.14 -0.01 -0.16 -0.01 0.00 -0.01 -0.01 (NB MK/PR discrepancy for '93 is 'understood'. When MK repeats PR's run selection, flat lumi weighting, and single temperature coefficient he obtains similar numbers. What then does this mean?? ) NB all above makes implicit assumption that the 'initial temperature' coefficient is identical to CTMAX+CT (ie. = 10) Test this on '95 by running with a value of CINI set to 5. Observe shifts of 0.01 and -0.03 MeV at P-2 and P+2 respectively. Also observe a marginal degradation in the RMS. GW 2/10/97 QUANTITY: Rise ======== ==== Central Value: GW 2D model (smoothed DB, fine binning) ------------- --------------------------------------- Variations w.r.t. above ----------------------- The estimation of the rise error is non trivial. We need to look at the BOF/EOF fills, consider the correlation with the temperature etc. Certainly we will want to know the effect of different rise routines. Which routines should we consider? The below are suggestions... M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P No rise routine 1.08 1.17 1.01 1.10 1.18 1.09 1.36 1.43 1.27 1.20 1.02 1.63 Raw NMR48 data 0.05 0.48 0.36 n/a n/a MK `Tuesdays' -0.17 -0.27 -0.05 -0.03 -1.82 -0.69 - - -0.55 MK `new Tuesdays' -0.19 -0.03 -0.11 0.00 -2.27 -0.88 -0.39 MK histo projection 0.01 0.31 0.12 0.39 1.70 0.00 - - -0.08 GW 2D smt DB,coarse -0.08 -0.29 0.00 -0.08 -0.73 0.01 0.33 0.15 GW 2D standard DB 0.13 -0.17 0.12 0.45 0.54 Default P-2 0.11 -0.25 -0.16 0.70 -0.13 Default P+2 -0.25 2.04 -0.41 -0.13 0.28 PR DELTAE4 func -0.81 -0.81 -0.17 -0.71 PR DELTAE5 func -0.50 -0.04 -0.08 -0.61 PR DELTAEPOL func -0.97 -0.83 -0.53 -1.39 (NB 'Default P-2/P+2' refers to default function, but evaluated from P-2/P+2 data alone.) (NB DELTAE4 - fit to NMR assuming tday and tphy independent; DELTAE5 assumes not independent; DELTAEPOL - fit to polarisation data in '93 and '95. Large difference observed by GW when using these routines in 95 is partly explained by the fact that they were derived using end of ramp as T0, but are here applied with start of physics as T0. For DELTA4/5 it has been verified by Monte Carlo that this inconsistency is responsible for most of shift, as aswell as offset there is a double counting of bending modulations. ) Related info ------------ Using 'default P-2' and 'default P+2' routines in many Monte Carlo scans, the following mean rises are observed (in E beam): Default P-2 1.69 MeV (rms = 0.18 MeV) Default P+2 2.32 MeV (rms = 0.15 MeV) QUANTITY: Tide ======== ==== Central Value: -0.82E-6 (New, from Joerg) ------------- -------- Variations w.r.t. above ----------------------- Assign 10% variation in amplitude (is this now conservative? - yes JW now recommends 5%) Assign 15 minute variation in phase (let us argue about whether this is needed later!) M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P -0.74E-6 0.05 0.04 0.02 -0.02 -0.18 -0.90E-6 -0.05 -0.03 -0.03 -0.05 -0.02 -0.03 0.01 -0.34 0.20 0.02 0.19 -0.11 +15 mins -0.16 -0.04 0.04 -0.15 -0.02 0.05 0.02 0.04 -0.08 0.02 -0.05 0.13 -15 mins 0.17 0.03 -0.04 -0.04 0.04 QUANTITY: Correctors ======== ========== Central Value: `best model', correction relative w.r.t. SOF ------------- -------------------------------------------- Variations w.r.t. above ----------------------- To be discussed. It is interesting to know the effect of using the `naive model' even if we dont choose to take the difference between the two as the systematic. Also interesting is the size of shift when an absolute correction is applied, or no correction at all. Naive (arc+strght)=col 1, Naive (arc)=col 2, central value=col 3 in Tiziano's file. M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P No correctors 0.48 0.23 1.07 0.48 0.21 1.05 -0.02 -1.22 -0.21 0.05 -0.19 -0.13 Naive (arc+strght) -0.12 -0.27 -0.09 -0.12 -0.27 -0.09 0.02 0.18 -0.20 0.06 -0.11 0.11 Naive (arc) 0.19 0.23 0.33 0.19 0.23 0.33 0.00 -0.28 -0.02 0.10 0.06 -0.07 Absolute corr ) -0.05 -1.99 -0.38 -0.73 -5.52 -0.71 - -0.71 + rms vals ) 3.29 2.27 5.35 4.46 2.14 QUANTITY: Bending mod ======== =========== Central Value: 2.5 MeV jump ------------- ------------ Variations w.r.t. above ----------------------- What jump to assign for bending mod? Assume variation of +-1 MeV M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P 1.5 MeV 0.02 0.68 0.15 0.02 0.69 0.14 / / / / / / / 3.5 MeV -0.01 -0.68 -0.14 / / / / / / / QUANTITY: QFQD ======== ==== Central Value: Apply if necessary! ------------- ------------------- Variations w.r.t. above ----------------------- 93 error was taken as being 50% of the correction. Recheck shift if not applied. No error in '94 and '95? M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P Not applied / / / / / / 0.40 0.33 0.34 0.68 0.41 -0.07 QUANTITY: BOM ======== === Central Value: One measured value per fill, interpolate between fills ------------- ------------------------------------------------------ Variations w.r.t. above ----------------------- Mike's standard model allows the xarc value to vary between fills as he applies an interpolation. As this is how the files are being produced, this is by definition the standard model. Of interest is to see the difference if one takes a single value per fill, with no interpolation (PR/GW approach). Another thing to know is how the scatter decreases when the BOM is applied. For this correction, record epol-model RMS scatters as well as shifts. M K G W / P R M K G W / P R M K 95P-2 95P 95P+2 95P-2 95P 95P+2 93P-2 93P 93P+2 93P-2 93P 93P+2 94P no BOM shift scatter single shift 0.15 -0.01 -0.17 -0.66 -0.13 -0.21 0.21 value scatter 3.73 2.25 3.41 1.49 4.07 2.13 alter- shift -0.02 -0.20 -0.03 0.15 0.02 -0.07 native scatter 3.48 1.64 3.87 1.95 files NB MK single value numbers old. GW numbers use single value per fill - but closest lying value in time, rather than necessarily value assigned for that fill (for convenience). IP DEPENDENT CORRECTIONS ------------------------ Info given on differences in Vernier + RF strategy - these are stability checks to complement the full error analyses. * Numbers given in ECM (sic) * All shifts signed in sense 'alternative-default' QUANTITY: Vernier ======== ======= Central Value: Use Yamartino file -------------- ------------------ Variations w.r.t. above ----------------------- Use MK file, evaluated by MK. M K 95P-2 95P 95P+2 IP2 0.02 0.50 0.16 IP4 -0.06 -0.24 0.16 IP6 0.10 -0.20 0.34 IP8 -0.14 -0.02 0.12 BOF-EOF FILLS ------------- 6 experiments in 1995, 6 in 1993, 4 in 1994. For each experiment a 'first' epol reading is derived, by averaging readings within 30 mins of first sub-calib, and a 'last' epol, by averaging readings within 30 mins of last sub-calib. All values in MeV/beam. Meanings of columns: fill - fill number Tbeg - time between start of fill and first Epol (hr) Tdur - time between last and first Epol (hr) Epol - rise seen in raw epol tide - tide correction bom - bom correction magte- ring temperature correction refte- ?? Emodd- dipole rise predicted by rise routine (ie. train contrib) + corrector effect qfqd - qfqd correction offs - model-epol, where model=tide+bom+magte+Emodd+qfqd Cor - corrector contribution (included in Emodd) At present all numbers from MK 8/7/97, 22/7/97 1995 ==== fill Tbeg Tdur Epol tide bom magte refte Emodd qfqd offs Cor ---- ---- ---- ----- ----- ----- ----- ----- ----- ----- ---- --- 2929.0 4.36 6.01 -1.29 -2.81 .01 .32 .00 .84 .00 -.35 .00 3022.0 1.52 15.57 .62 -2.66 -.21 .60 .00 2.61 .00 -.27 .27 3029.0 1.96 15.48 5.68 -1.06 .46 2.24 .00 4.09 .00 .05 3.16 3030.0 1.16 20.69 5.27 .17 .70 .70 .00 3.43 .00 -.26 2.53 3036.0 1.62 15.18 3.15 1.57 -.42 1.40 .00 1.13 .00 .54 -.43 3064.0 1.04 6.52 3.09 2.07 -.02 .91 .00 .68 .00 .55 -.52 Here Emodd (& therefore offs) from routine used for central values. With this: *** mean offset is 0.4192341492E-01 *** rms of offset is 0.4127774239 alternative models: Tues NMR48 New Tues Default, but with Default, but with ctmax=20,ct=-5 ctmax=10,ct=-5 offs offs offs 2929 -0.69 0.54 -0.77 3022 -1.72 -1.34 -1.59 3029 -0.02 0.26 0.42 3030 1.16 -1.55 1.23 3036 3.02 0.19 2.47 3064 -1.26 0.75 -1.14 0.08 -0.19 0.10 -0.75 0.84 rms 1.76 0.99 1.56 0.46 0.43 (numbers for different temp coeffs confirmed by PR) additional info: * If MK uses 'Tuesdays model', but in fact varies the day by increments of one, he obtains 7 different 'offs' The rms's of these 'offs' are: rms 2929 0.46 3022 0.38 3029 0.67 3030 0.65 3036 0.88 3064 0.34 Using a different day of the week to start the '95 scan (giving 7 separate values) results in the following rms's: rms P-2 0.14 P 0.66 P+2 0.16 * GW has selected many subsets of 6 fills from the scan (see minutes of meeting 21/3/97 + subsequent mails). All fills of duration > 4 hrs. Comparing the model and the NMR rise for each fill enables a mean offset to be determined from each subset, together with an rms. Histogramming this mean offset + RMS for many subsets give distributions whose RMS gives an idea of the statistical and systematic scatter expected from our 6 bof/eof fills. This procedure was performed for fills without bending modulation, fills with bending modulation and fills with no distinction. RMS of mean rms mean rms bend mod -0.17 0.36 0.88 0.36 no bend mod 0.72 0.54 1.40 0.41 no distinction 0.26 0.52 1.21 0.41 1993 ==== fill Tbeg Tdur Epol tide bom magte refte Emodd qfqd offs Cor ---- ---- ---- ----- ----- ----- ----- ----- ----- ----- ---- --- 1636.0 2.02 3.48 6.14 4.73 .07 1.13 .00 .75 .00 .55 .00 1734.0 2.15 3.86 .57 -1.08 -.02 1.18 .00 .01 .00 -.47 -.03 1772.0 1.87 21.12 6.09 -1.65 .27 2.81 .00 2.29 .00 -2.36 -.03 1811.0 20.54 5.18 2.59 3.45 .43 .02 .00 .87 .00 2.19 .00 1849.0 13.32 10.52 4.03 .59 .34 .04 .00 -.18 .00 -3.25 -.02 1892.0 11.68 2.12 -.02 -.25 -.11 .04 .00 .34 .00 .03 .00 Here Emodd (& therefore offs) from routine used for central values. With this: *** mean offset is -0.5544112921 *** rms of offset is 1.979576945 alternative models: Tues New Tues Default, but with Default, but with ctmax=20,ct=-5 ctmax=10,ct=-5 offs offs 1636 0.26 0.02 1734 -1.53 -1.25 1772 0.37 0.33 1811 1.63 1.60 1849 -3.03 -2.91 1892 -0.33 -0.33 -0.44 -0.42 -0.80 -0.31 rms 1.63 1.53 1.99 1.99 1994 ==== fill Tbeg Tdur Epol tide bom magte refte Emodd qfqd offs Cor ---- ---- ---- ----- ----- ----- ----- ----- ----- ----- ---- --- 2234.0 11.92 7.44 -.97 -1.56 -.03 .08 .00 .70 .00 .15 .00 2255.0 13.07 5.79 .80 .31 .13 .24 .00 -.29 .00 -.41 -.02 2395.0 21.49 3.46 -3.25 -2.49 -.12 -.09 .00 .00 .00 .56 .00 2569.0 7.12 8.43 2.71 2.07 -.15 .61 .00 .11 .00 -.07 .00 Here Emodd (& therefore offs) from routine used for central values. With this: *** mean offset is 0.5533423275E-01 *** rms of offset is 0.4067951441 alternative models: Tues New Tues offs offs 2234 -0.24 -0.29 2255 -0.34 -0.26 2395 0.64 0.64 2569 -0.60 -0.16 -0.13 -0.02 rms 0.54 0.44