Top Mass Systematic Uncertainties

(1/2) Jet Energy Scale / Residual JES

Use tag jetCorr12, which is valid for all runII data up to p13, or newer, as per the recommendations of the jet corrections group
Evaluate the separate uncertainties for ALL levels of the JES systematic (including higher levels in case you only correct up to L5). Add those pieces in quadrature to get the systematic on the top mass.
The "total JES systematic" (all levels at once) can be used as a cross-check; this cross-check is in fact recommended for analyses without in situ calibration.
If your background is evaluated from MC, apply the same +- one sigma JES variations to your dominant background sources simultaneously with the signal variations
You should rerun event selection to pick up events moving in and out of your sample with the shifted jet energies. So you will have a different number of events in e.g. the L5+ sample to use as pseudodata than you do in the nominal sample. However, you do not need to change the number of events of each type you draw for a given pseudoexperiment.

(3) PDF

Some information about PDFs: CTEQ6, hep-ph/0201195, hep-ph/0303013.
For gen6 analyses, please follow: Joint Physics Instructions
Some initial information, go to: Joint Physics from April 2, 2004
Add in quadrature the difference between CTEQ6M 20 pairs of eigenvectors
Add in quadrature the difference between MRST with two different values of Λ_QCD (e.g. MRST72 Λ_QCD=228MeV vs. MRST75 Λ_QCD=300MeV)
Check CTEQ5L and MRST central values are consistent
Add in quadrature the effect of reweighting gg contribution from 5% (LO) to 20% (=15+5) (NLO)

Note: Updated recipe for PDF uncertainties (April 30, 2008)

for "a" &equiv quadrature sum of CTEQ eigenvectors and "b" &equiv difference between MRST72 and CTEQ5L

Old recipe: If b > a, add b and a in quadrature otherwise just take a.
Modified recipe: simply taking the larger of a or b

In all cases you still need to additionally add in quadrature the differences due to other effects: changes in alpha_s by comparing MRST72 and MRST75, effect of reweighting gg contribution.

(4) ISR/FSR

~~Use ISR/FSR less/more ttbar samples.~~ Use the new IFSR less/more ttbar samples: otop03 and otop04. (See CDF 6804 for some documentation on the general idea behind these samples.) In the new samples, ISR and FSR are varied simultaneously.
Find the largest difference between the nominal sample and otop03 or otop04. Calculate the uncertainty on that difference due to sample statistics (only the part due to signal stats, since you're using the same background events in both sets of PEs!). Use the larger of the largest difference or its uncertainty as your systematic.
For more info see this page.

(5) MC Generator

(Use updated prescription)
Difference between Herwig (~~htop75~~ otop1s) and Pythia (ttop75)
- The old htop75 sample had incorrect JIMMY settings
- The sample otop01 is same as otop1s, but otop01 has 0.5M events, while otop1s has 4M.
Cross-check your result with MC@NLO(mtop75, ctop75) samples and ALPGEN (atop0p+atop1p)
- MC@NLO samples have ~10% of events with negative weight!
  - The weight is not directly stored in TopNtuple. Instead, as a workaround, it is encoded in the hepg energy of the proton vs anti-proton.
  - In practice: hepg.E[0]=980 for W=+1 and hepg.E[0]=980.09997 for W=-1.
- mtop75 and ctop75 differ in the PDFs used. See the top group MC page for details.
- Finally, there are random number issues with these MC@NLO samples. Events are duplicated many times within the sample at the hard-scatter level (though the showering/hadronization is then not identical). So the statistical uncertainties on quantities derived from these samples are not understood!
- The ALPGEN samples should be combined according to the cross-sections listed on the MC web page.
- There also exists another sample which is ALPGEN tt+0p (inclusive): otop1q. Comparing atop0p+atop1p vs otop1q probes the importance of the higher-order ME.

(6) Background fraction and shape

This will depend on your channel and analysis. Please take into account how your top mass measurement is affected by the background fraction and the modeling of the shape
We suggest to compare the different background shapes for different Q² values using ALPGEN MC samples (4M_W², M_W²/4). These are currently available at least for W(e,mu)+bb+np: btop[e-p]w.

(7) b-tagging efficiency

This systematic has been removed because it is typically vanishingly small. However, analyses that might be particularly sensitive to an Et-dependent mismodeling of the b-tagging efficiency (e.g. those using L2D as an observable!) should still evaluate a related systematic.

(8) b-jet energy scale

(Use updated prescription)
Take into account the b-jet energy scale uncertainty. For a template l+jets analysis it is found to be 0.6 GeV. See CDF 7252. This is the procedure recommended for other analyses:
- run S+B pseudo-experiments where the B-jets have their input energies shifted by +/-1%
- the B-jets are identified using hepg information; other groups only identified signal B-jets (ie. ignored real Bjets in Bgd)
- the energies are shifted so that their inputs to the kinematic fit (or whatever the equivalent is for a given analysis method) are +/-1% higher/lower than when using the default jet energy corrections
- in these studies we've _ignored_ changed in the acceptance on account of these shifts and _ignored_ changes in the ratio of single-to-double tag events (Btag efficiency doesn't have that steep of a dependence on Bjet energy that 1% shifts should dramatically change any of this relative to dflt)
- compare the mean fitted M_top for these two shifted samples with the mean fitted M_top using default jet energy corrections; from this you can estimate that a 1% shift in Bjet energy corresponds to a X.X GeV shift in top mass
- your final systematic needs to be scaled to 0.6%, which is our best estimate of how 1-sigma changes to B-fragmentation, B-semi-leptonic-BranchingRatios, and B-color-flow affect the B-jet energy scale. thus your final "B-Jet Energy Scale systematic" will be 0.6*X.X = Y.Y GeV

(9) Lepton P_T

A 1% uncertainty on the lepton energy scale needs to translated into M_top and added in quadrature to the other uncertatinties. The scale should be shifted separately for electrons and muons, i.e. those are uncorrelated systematic effects.