CDF/ANAL/TOP/CDFR/3189

June 23, 1995 V2.0

B-Jet Energy Correction for Top Mass Determination (II)

- as a Function of Top Mass - S. Aota, T. Kikuchi, S. Kim and K. Kondo University of Tsukuba

We derived energy correction for b-jets in tt̄events using HERWIG+QFL tt̄production simulation data for top masses of 140, 160, 170, 180, 200, 220 and 240 GeV/c^{2} to determine top quark mass with top candidates events accurately.

The b-jet energy correction was obtained for dilepton +≥2 jet events. We call this correction DLJSCO.

The magnitude of the correction depends on top quark mass. We parametrized the correction coefficients as a quadratic function of top quark mass. Using this parametrization, we obtained the topmass-dependent b-jet energy correction function.

1 Reconstruction of simulated jets

In order to obtain the deviation of b-jet P_{T} from b-quark P_{T}, the following procedure was performed:

1. Find b/b̄ quarks originating from t/t̄ quark decay.

2. We use only b/b̄ quark with P_{T} > 5 GeV/c.

3. Find a b-jet from JETS banks with a jet cone size of 0.4 in η − ϕ plane as follows: pick up all jets within a cone radius of 0.4 around a b/b̄ quark. Apply the jet energy correction of QDJSCO^{1} to the jets. Compare the ratio of bquark P_{T} to jet P_{T} between the above jets. We identify a jet with the ratio closest to 1 as a b-jet.

4. Find soft lepton( e or μ ) with P_{T} > 2 GeV/c within a cone radius of 0.4 around a b/b̄ quark. If the b-jet has at least one soft lepton, the b-jet is tagged with soft lepton.

1In this note, QDJSCO means JTC90S and is always applied for a cone size of 0.4, with underlying event energy correction and with out-of-cone correction.

5. In the case of soft muon tagging, after we apply QDJSCO to the jet, we deal with the jet in two ways:

(a) we do not apply any muon momentum correction.

(b) we subtract muon energy deposit from the jet energy, and add muon momentum to the jet energy, where muon energy deposit is 2.2 GeV which is the average energy deposit in calorimeter by a minimum ionizing particle.

2 Jet energy correction factors

After the procedure of jet reconstruction described above, we obtained the ratio of b-quark P_{T} to b-jet P_{T} which we call R hereafter: R = P_{T}^{H}/P_{T}^{Q}, whereP_{T}^{H} is b-quark P_{T} and P_{T}^{Q} is the jet P_{T} corrected by QDJSCO. We made the distributions of R for 4 GeV/c bins of P_{T}^{Q} with P_{T}^{Q} ≥ 12 GeV/c. The average value of R and its error are plotted as a function of the b-jet P_{T} for b jets

1. without lepton tagging ( generic b jets ),

2. with soft electron tagging,

3. with soft muon tagging and jet P_{T} not including muon momentum,

4. with soft muon tagging and jet P_{T} including muon momentum .

For each plot, we fitted it with a function Y = exp(p1 + p2·P_{T}^{Q}) + p3 in the same way as AAJSCO was obtained [2].

3 DLJSCO

This Monte Carlo data was generated with HER-WIG, and simulated with QFL. We made 50,000 tt̄ → dilepton + ≥ 2 jets events for each of top masses of 140, 160, 170, 180, 200, 220 and 240 GeV/c^{2}. Then we applied the following selection cuts of the top candidates:

• Number of leptons ≥ 2 with E_{T}^{e} > 20 GeV and P_{T}^{μ} > 20 GeV/c,

• / E_{T} > 25 GeV,

The distribution of b-quark P_{T} is shown for these simulation data in Fig. 1. We plotted the average value of R and its error as a function of the bjet P_{T} and fitted it with a function Y = exp(p1 + p2·P_{T}^{Q}) + p3 as shown in Figs. 2 and 3. The absolute magnitude of the correction is 35% at b-jet P_{T} of 20 GeV/c and less than 5% at b-jet P_{T} above 40 GeV/c for b-jet without lepton tagging for a top mass of 170 GeV/c^{2}. We can obtain an overall correction by making the R distribution accumulated over all b-jet P_{T} as shown in Fig 4. The mean and RMS of R are 1.020±0.002 and 0.262, respectively, for generic b jets.

We compared DLJSCO for a top mass of 170 GeV/c^{2} with DLJSCO for top masses of 140, 160, 180, 200, 220 and 240 GeV/c^{2} in order to check the dependence of correction on top mass. as shown in Fig. 5. The difference in DLJSCO errors are also shown in Fig. 6. We parametrized the correction coefficients p1, p2 and p3 as a quadratic function of top mass, A + B·M_{top} + C·M_{top}^{2}, to get the topmass-dependent correction. The correction and its error thus obtained are consistent with the original DLJSCO for top masses of 140, 160, 180, 200, 220 and 240 GeV/c^{2} within an error of 2% as shown in Figs. 7 and 8.

4 Conclusions

Energy correction DLJSCO for b-jets in tt̄ → dilepton events was derived using HERWIG+QFL tt̄ production simulation data. The absolute magnitude of the energy correction is 35% at b-jet P_{T} of 20 GeV/c and less than 5% at b-jet P_{T} above 40 GeV/c for b-jet without lepton tagging for a top mass of 170 GeV/c^{2}.

As we have a large dependence of DLJSCO on a top mass between 140 GeV/c^{2} and 240 GeV/c^{2}, we made the DLJSCO correction as a quadratic function of top mass. The correction and its error thus obtained were found to be consistent with the original DLJSCO for top masses of 140, 160, 170, 180, 200, 220 and 240 GeV/c^{2} within an error of 2%.

References

[1] J. Tonnison CDF/ANAL/JET/CDFR/2189 J. Tonnison CDF/ANAL/JET/CDFR/2053 L. Keeble and B. Flaugher CDF/ANAL/JET/CDFR/1513 ’Inclusive Jet Cross Section Measurement’ F.Abe et al., Phys. Rev. Lett. 68, 1104 (1992) T. Hessing, Ph.D. Thesis, DOE-ER40039-47, December 1990

[2] A. Caner et al. CDF/ANAL/TOP/CDFR/2469

[3] S. Kim CDF/ANAL/TOP/CDFR/2254 S. Kim, S. Aota, K. Kondo and T. Uchida CDF/ANAL/TOP/CDFR/2662

Figure 1: B-quark P_{T} for top quark masses of (a) 140 GeV/c^{2}, (b) 160 GeV/c^{2}, (c) 170 GeV/c^{2}, (d) 180 GeV/c^{2}, (e) 200 GeV/c^{2}, (f) 220 GeV/c^{2}and (g) 240 GeV/c^{2}.

Figure 2: average of R vs. b-jet P_{T} for b-jets without soft lepton tagging ( solid line ), with soft electron tagging ( dashed line ), with soft muon tagging and jet P_{T} not including muon momentum ( dotted line ), and with soft muon tagging and jet P_{T} including muon momentum (dot-dashed line ) in HERWIG+QFL tt̄ → dilepton + ≥ 2 jets events at top masses of (a) 140 GeV/c^{2}, (b) 160 GeV/c^{2}, (c) 170 GeV/c^{2}, (d) 180 GeV/c^{2}, (e) 200 GeV/c^{2}, (f) 220 GeV/c^{2} and (f) 240 GeV/c^{2} ( DLJSCO ).

Figure 3: RMS of R vs. b-jet P_{T} for b-jets without soft lepton tagging ( solid line ), with soft electron tagging ( dashed line ), with soft muon tagging and jet P_{T} not including muon momentum ( dotted line ), and with soft muon tagging and jet P_{T} including muon momentum (dot-dashed line ) in HERWIG+QFL tt̄ → dilepton + ≥ 2 jets events at top masses of (a) 140 GeV/c^{2}, (b) 160 GeV/c^{2}, (c) 170 GeV/c^{2}, (d) 180 GeV/c^{2}, (e) 200 GeV/c^{2}, (f) 220 GeV/c^{2} and (f) 240 GeV/c^{2} ( DLJSCO ).

Figure 4: the R distribution accumulated over all b-jet P_{T} for b-jets (a) without soft lepton tagging, (b) with soft electron tagging, (c) with soft muon tagging and jet P_{T} not including muon momentum, and (d) with soft muon tagging and jet P_{T} including muon momentum in HERWIG+QFL tt̄ → dilepton + ≥ 2 jets events for a top quark mass of 170 GeV/c^{2} ( DLJSCO ).

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