INPUTS AND ASSUMPTIONS IN LEP ERROR MATRIX ------------------------------------------ Location of this file: /afs/cern.ch/delphi/tasks/scan95/summary/error.txt 11/7/97 - initial version of error matrix + file: VERY preliminary GW 26/7/97 - first attempt at final version PR still missing i) NMR48 CT error ii) rigorous EOF scatter error for 94 iii) cross-checks 29/7/97 - second attempt at final version PR still missing i) Joerg to confirm 1993/4 dispersion error ii) cross-checks ! 6/8/97 - minor mod to dispersion error: points i) & ii) above now OK GW 15/8/97 - clarify some correlations (ie. add more explanation - matrix itself unchanged) GW General comments _______________ 1)For some error components the correlation between energy points would be 100% if we took the model used to evaluate the systematic error at face value. For the case of equal errors (ie dE_p-2 = dE_p+2 rho = 1 gives no error on GZ. But the specific model we use to calculate the systematic error may hide some further ignorance. There is thus some uncertainty as to whether the energy points are really 100% correlated. We therefore generally take in these cases rho = 75%. This gives dMZ = 0.94*dE and dGZ = 0.50*dE 2) There is some degree of double counting in that some of the variations in the model components give rise to the rms EOF scatter error which we take into account. We ignore this potential double counting, so are being conservative in our estimates from this respect. ERROR MATRIX ============ At present a 7x7 error matrix is provided for the 'common LEP experiment'. This is the one to be used for combining the 5 and 9 parameter fits of the 4 collaborations, ie. IP dependent correlations and anti-correlations have (in principle) been accounted for. In time, separate matrices will be provided for each IP. The matrix is in units of MeV**2 for ECM. The indices are (93P-2 93P 93P+2 94P 95P-2 95P 95P+2). 93 and 95 refers to scan only - prescan is NOT included here. Bunch train running is NOT included for 94. Date of this version of matrix: 6/8/97 (given to EWWG, but formally still preliminary) 11.95 7.81 6.94 5.26 1.69 1.44 1.48 7.81 45.05 7.17 5.87 1.33 1.46 1.36 6.94 7.17 8.93 4.87 1.54 1.60 1.79 5.26 5.87 4.87 13.64 1.54 1.71 1.56 1.69 1.33 1.54 1.54 3.30 1.62 1.58 1.44 1.46 1.60 1.71 1.62 29.21 1.88 1.48 1.36 1.79 1.56 1.58 1.88 2.96 COMPONENTS IN ERROR MATRIX ========================== All values given in MeV for ECM. Signs sometimes included to indicate sense of correlations. 1 Ring temperature ------------------ Assume CT' = CTMAX+CT known to +-30% CT known to +-50% For 93 & 94 variation with CT is small. The errors are found by varying the two parameters by their quoted errors and computing the shifts on the luminosity weighted mean energies. These parameters (CT' and CT) are taken to be independent and we add the effects of variations from CT' and CT in quadrature. The shifts in the energies are essentially symmetric. 93P-2 0.14 93P 0.38 93P+2 0.40 94P 0.22 95P-2 0.38 95P 0.30 95P+2 0.42 Take 75% correlation between years and between energy points. (All positive correlations for off-peak points for each coeff.) 2 RF ---- Changed since Warsaw (when OPAL neglected!). Use 7*7 LEP error matrix of Mike Hildreth. Note this involves a revision of the 1993 numbers which are now treated consistently with other years. From the matrix the energy errors are 93P-2 0.53 93P 0.53 93P+2 0.53 94P 0.57 95P-2 0.69 95P 0.69 95P+2 0.69 Correlation coeffs are built into matrix implicitly. They are for 1993 0.96, for 1995 0.63. Inter-year correlations : 93/94 0.70, 93/95 0.22, 94/95 0.18. 3 Polarisation systematic ------------------------- * For Warsaw: * * 93 numbers and correlation from 1993 paper (IP average) * 95 numbers are from discussion at 21/6/96 meeting * full correlation between 1993 and 1995 * (from discussion at 21/6/96 meeting) * ( I believe Joerg would take years to be uncorrelated) * all values 0.5 MeV (94 is a guess) * FINAL : from TC. Keep as 0.5 MeV. * Correlation is 0.04, from electron mass error ! * QUESTION: is this really the only correlation ?? 93P-2 0.5 93P 0.5 93P+2 0.5 94P 0.5 95P-2 0.5 95P 0.5 95P+2 0.5 Correlation of 0.04 assigned between points. 4 e+ vs e- ---------- * Warsaw: 94 value set to same as 93, * * 93 numbers and correlation from 1993 paper * 95 number from Angelika (energy meeting 21/6/96) * no correlation between years (energy meeting 21/6/96) * 93P-2 0.3 93P 0.3 93P+2 0.3 94P 0.3 95P-2 0.25 95P 0.25 95P+2 0.25 Point to point correlation set at 0.50 for 93/4 and 95 sets 5 Tide - amplitude ------------------ Warsaw assume: a +-10% uncertainty, but take new shifts. Now use 82 +- 4 ie 5% error (JW) 93P-2 0.02 93P -0.34 93P+2 0.20 94P -0.12 95P-2 -0.05 95P -0.03 95P+2 -0.03 Sign of correlations from patterns of shifts for increase in tide amplitude etc 6 Tide - phase -------------- Vary phase by +-7.5 mins. (cf +- 15 for Warsaw) 93P-2 0.02 93P 0.04 93P+2 -0.08 94P 0.13 95P-2 -0.16 95P -0.03 95P+2 0.05 Take full correlations/anticorrelations as sign of shift when advance phase within a year. Between years take 50%. 7 Rise term - scatter & model dependence ---------------------------------------- ****************************************************************************** * Warsaw: (for comparison) * * 1995: 1 MeV ) these determined from independent sets of epol * 1993: 2 MeV ) experiments so should give essentially uncorrelated * ) errors on MZ between years * * In addition, we have estimate from NMR data on P-2/P+2 rises which * leads to 0.6 MeV error on GZ (90th ECAL meeting: AB, 17/5/96). * This analysis only possible with '95 data so for '93 assume same * error on GZ, fully correlated with '95. * * Correlation coefficients frigged up by hand to give these results. * ****************************************************************************** * PR 29/7 * FINAL values: * this term also includes model dependence * which was separate term for Warsaw * * 1993 : take 100% of rise as error. This gives dMZ = 2.6 MeV. * This is average of p-2 and p+2 shifts. * This covers all variations with different models of rise * so do not add extra model dependence for mass error. * For dGZ there are several considerations * i) Epol values at p+2 are (on average) later in fill than for p-2 * ii) fills at p+2 are longer (on average) than for p-2 * iii) models show significant shifts in GZ eg * a) "Tuesday" model gives 0.9 MeV * b) "new Tuesday" model gives 1.2 MeV * note models a) and b) do not assume * factorisation of rise and temp. effects. * c) use NMR p-2 coeffs on p+2 and p+2 coeffs on p-2, * gives dGZ = 0.9 MeV. * So compute energies and correlation to give dMZ = 2.6, dGZ = 1.0 * This gives rho = 0.86, with energy errors essentially unchanged * (increase of 3%, which is taken into account). * * 1994 : take +- 100% error; full rise = 3.3 MeV. * * 1995 : Here we have more data (Epols and NMRs) and are better * constrained. * Use 6 bof/eof epol fills as main tool. This is a direct test of * the model. Expected rms (from GW) is 1.2 MeV. * This translates to dMZ = 0.55 MeV. * For GZ look at * i) variations with different models * ii) using NMR48 data directly. * iii) difference between using default p-2 and p+2 * in Monte Carlo scan analysis (GW: see variation.txt) * These all give dGZ = 0.4 MeV. * Again convert dMZ and dGZ to dE (= 0.62) and rho (= 0.47) * * inter-year correlations: take all to be 50% * * 93 p-2 2.7*1.03 * 93 p 2.9*1.03 * 93 p+2 2.5*1.03 * 94 p 3.3 * 95 p-2 0.62 * 95 p 0.62 * 95 p+2 0.62 8 Rise term - model dependence ------------------------------ Now include this term in rise term above. 9 E.O.F. normalisation scatter ------------------------------ Values as determined by PR taking account of luminosity weighting, for all years. 93 and 95 peaks are average rms of p-2/p+2. Use RMS's as evaluated by MK. Small difference with GW now understood ( definition of rms!). 93P-2 1.73 93 P 5.90 of P-2/P+2 93P+2 0.87 94 P 1.10 95P-2 0.83 95 P 4.96 of P-2/P+2 95P+2 0.45 No correlation. 10 Dispersion error ------------------- * For Warsaw (only 3 experiments were considered!): * From John Yamartino for 1995. * 1993 from JW (CERN-SL-95-64) * Uncorrelated part averaged over 3 expts (rather than 4) * FINAL for 1995 from Mike Hildreth 28/7/97 in form of error matrix * 1993/4 as Warsaw (needs to be verified by Joerg) 93P-2 0.40 93P 0.40 93P+2 0.40 94P 0.70 95P-2 0.35 95P 0.35 95P+2 0.35 0.75 correlation assigned between 93 points. 0.50 correlation assigned between 93 and 94 Matrix for 95 corresponds to 50% correlation between 95 points. No correlation between years. 11 QFQD ------- Take 30% of effect (was 50% for Warsaw)). 93P-2 0.24 93P 0.20 93P+2 0.20 94P 0.04 95P-2 0.00 95P 0.00 95P+2 0.00 Take 75% correlation between points and years. 12 NMR48 temperature coefficient -------------------------------- Assume CTMAX+CT known to +-60% CT known to +-50% add these in quadrature 93P-2 0.60 93P 0.32 93P+2 0.60 94P 0.51 95P-2 1.04 95P 1.04 95P+2 1.08 Take 75% correlation between energy points and years. 13 Correctors ------------- Take 100% of difference between 'best' and 'naive (arc+straight)' models. 93P-2 0.04 93P 0.36 93P+2 -0.40 94P 0.22 95P-2 -0.24 95P -0.54 95P+2 -0.18 Take 75% of correlations/anti-correlations, keeping the the significance of the signs of the shifts above. This for energy points AND between years. 14 Bending modulation jump -------------------------- Take 2.5+-1.0 MeV 93P-2 0.00 93P 0.00 93P+2 0.00 94P 0.00 95P-2 0.04 95P 1.36 95P+2 0.28 Take 75% correlation between points.