Improving b-jet energy resolution b-resolution mtg Sept. 26, 2007 P. Grannis Improving b-jet energy resolution and raising the di-b jet tag efficiency could substantially improve the Higgs search sensitivity. I comment here on old work † that might be of use in improving the energy resolution and b-jet selection efficiency. † Notes 1 (estimating B hadron momentum) 2 (distinguishing quark and gluon jets) 9 (merging b jet FSR)

1994 OPAL study: how to make the best estimate of momentum of a semileptonic B meson for oscillation measurements? OPAL had a complicated lookup function based on several kinematic quantities. My method used a property of the H matrix that allows an unmeasured quantity x N (in OPAL, case B momentum) to be predicted from a set of observed quantitites {x i }, i = 1 … N  1. Let {  i } be the mean value of the {x i } over a training sample. From MC training sample (or special data) generate M ij = (1/N evt ) ∑ evts (x i  i )(x j  j ). Form H = M -1 ; For each event in real sample,  = ∑ ij (  x i H ij  x j ) (  x j = x j  j ) (With no unknown variable x N,  would be the H matrix  2 as used for e-ID) Can decompose  =  1 +  2, with  1 = ∑  x i H ij  x j (i,j summed from 1 to N  1) and  2 =2  x N H iN  x i +  x N H NN  x N (sum on i) Then minimizing  with respect to x N yields best shift from  N to true x N for this event: x N =  N – (∑ H iN  x i )/ H NN Estimating unknown kinematic quantities (e.g. b-jet energy)

For OPAL study (paper 1 above), took observed variables (E vis, E frag, lepton momentum, decay length, DL error, jet mass, multiplicity, etc) to predict the B hadron momentum. Estimated momentum for MC B’s improved older method by ~6%. Non-gaussian tail was also present in the older method, but could be reduced by breaking the sample into different decay length bands. Can this method be used to estimate the b-parton energies for each jet in DØ Higgs studies? (Is there a corresponding method for predicting the unmeasured using NN’s?) Requiring DL > 2mm reduced spread by another 10%.

What variables might be used to predict E b ? A separate OPAL study (paper 2 above) sought to distinguish quark and gluon jets using energy (and multiplicity) in a set of 10 annular cones around the jet axis. The H matrix chisquares,  g and  q, for conforming to gluon or quark hypotheses were formed and the difference,  (Fisher discriminant), obtained.  quark like gluon like quarks gluons Keeping only subsample of events to left of red line or right of blue line could give ~65% quark/gluon purity with ~60% efficiency. Not great, but enhanced samples. But the variables used do seem to have some discrimination power. b-jets are perhaps more different from light quarks than gluons! A potential set of variables for b-jet energy estimate might be:  Visible jet energy  Energy profile (energy into annular subcones)  Jet mass  Nearby lepton energy, p T rel  Info on nearest jet  R and Ejet (to account for FSR gluon radiation) (I tried once to improve Higgs di-b resolution by merging jets near a b-jet if low invariant mass … no success!) (paper 9 above) Ideas, study and optimization clearly needed.

Comment on b-jet tagging Any gain in b-tag efficiency is worth having. Current analyses (e.g. Z( ll )H use fixed cuts on NN probability for both b-jets. Doing 2-dimensional cuts on b-ID may offer significant efficiency improvement for fixed background. Study in Y. Mutaf thesis (Zb cross section): a) Selecting di-lepton with cut on product of isolation probabilities raises efficiency for fixed background significantly. This method is now incorporated in the p17 analyses. b) The same technique can be used in selecting the di-b jets (currently not used for the double tag p17 analyses). The optimization of a 2-d cut depends on the channel and background/signal ratios. For the p14 analysis, Mutaf found that a single jet fake rate of 3.6% optimized S/√(S+B), higher than that used then. p17 analysis now uses 6% fake rate for DT NN analysis. Further, he found that using a cut on the product P 1 *P 2 (P i = prob. jet i is light quark) gave 50% improvement in signal efficiency for the optimum fake background. This is not being done in the current p17 analyses, and should be pursued. product cut independent cuts optimum mistag rate product cut independent cuts   !