# Page History

## Key

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Physics Motivation: measure Higgs Yukawa coupling to muons, which provides a useful test for ratio of Yukawa coupling between 2nd/3rd generation leptons (with

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body H\tau \tau
); between 2nd generation lepton/quark (with
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body Hcc
).

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Two different works are ongoing or finish in soon.

1. Work using DBD-world samples: explored at
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body \sqrt{s}
of 250/500 GeV, left-/right-handed beam polarization, two processes of
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body e^+e^- \to q\overline{q}H
and
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body e^+ e^- \to \nu \overline{\nu} H

2. Work using IDR-world samples: written in above

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Two muons are selected using IsolatedLeptonTagging (without

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body E_{\mathrm{yoke}}
and impact parameters) as the
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body H \to \mu ^+ \mu ^-
candidate. Various pre-cuts are applied to select signal and reject background. Further background rejection is done using TMVA(BDTG). Estimating the precision on
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body \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-)
is done using the toy MC technique. In the signal process, two processes are mixed up:
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body e^+ e^- \to ZH \to \nu \overline{\nu} \mu ^+ \mu ^-
and
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body e^+ e^- \to \nu \overline{\nu}H \to \nu \overline{\nu} \mu ^+ \mu ^-
via
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body WW
-fusion. These two should be separated in the end, but such separation is not considered in the analysis; it is beyond the scope of this analysis.

## Candidate Plots for IDR.

Some comparison comparisons between IDR-L and IDR-S in reconstructed particle level has done. More details can be found in my talk on 2019Apr03. All plots are left-handed beam polarization. All histograms are normalized to 1.

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Similar plot for "barrel category"; require requires both muons are in barrel region

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body |\cos \theta _{\mu ^{\pm}}| < 0.7
.
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body M_{\mu ^+ \mu ^-}
is significantly better in IDR-L,
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body \sigma (M_{\mu ^+ \mu ^-})
as well.

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Only ~5% events are the case with both muons flying in endcap/forward region. We will not discuss it here.

## Remaining Events After All Cuts.

A toy MC technique is applied by using overall

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body M_{\mu ^+ \mu ^-}
distribution after BDTG score cut to estimate the precision on
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body \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-)
. Two detector models and two beam polarization cases are considered. Next The next table shows the total remaining events in the full range (120 - 130 GeV) after BDTG score cut for each detector model and each beam polarization.

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• In the right-handed case,
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body N_{\mathrm{sig}}
is pretty small, hard to perform the precise measurement. We only have ~8 signal events with 1600 fb-1 statistics from the beginning. We will not consider the right-handed case for further discussion.
• We see some differences in in
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body N_{\mathrm{bkg}}
between IDR-L and IDR-S, but this is due to statistical fluctuation caused by the lack of MC statistics for SM background.

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From the table above,

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body N_{\mathrm{sig}}
and
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body N_{\mathrm{bkg}}
in the full range are pretty much the same between IDR-L and IDR-S. The level of total background fluctuates due to the limited number of MC statistics, thus, we can conclude that the background distribution and the total number of backgrounds in full range are the same. For further analysis, we treat the background condition is common in IDR-L and IDR-S. We take the average number of
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body N_{\mathrm{bkg}}
and average slope in background modeling of IDR-L and IDR-S, for generating pesudopseudo-background data. We perform toy MC using common parametrization for background , and evaluate the precision. Next The next table shows the final result of the precision on
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body \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-)
after 50000 times pseudo-experiments. The theoretical number is provided in addition which assumes 100% signal efficiency, no backgrounds, and no detector effects.

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• My real analysis is about a factor of 3 worse than the theoretical number. There are several reasons mixed up: imperfection of cuts, existence of irreducible backgrounds mainly come from
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body e^+ e^- \to W^+ W^- \to 2\mu 2\nu
, detector effect, and so on.
• IDR-L gives relatively 2.8% better precision than IDR-S.
• Because overall
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body M_{\mu ^+ \mu ^-}
distribution is better in IDR-L. In detail, IDR-L gives significantly better performance in "barrel category", and similar performance in "mixed category". Almost all events are categorized in these two groups, resulting in better result results with IDR-L.
• The number of signal events in
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body M_{\mu ^+ \mu ^-}
peak region is basically the same between IDR-L and IDR-S, but ~10% more backgrounds lyng lying in the peak region with IDR-S due to ~10% wider width caused by worse momentum resolution. This ~10% more backgrounds background can translate into ~3~2.3% 6% difference in the statistical significance. This 2.8% difference is consistent to with the estimation from statistics.

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• IDR-L gives better result than IDR-S, because of better momentum resolution in barrel region.
• Worse momentum resolution makes wider width of
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body M_{\mu ^+ \mu ^-}
distribution of signal, resulting in more backgrounds lying in peak region, and resulting in worse precision on
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body \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-)
.Specifically for this analysis,

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## IDR note.

You can see my private overleaf project from here. The contents are only IDR-world.

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