Evaluation of measurement accuracy of h\to\tau^{+}\tau^{-} branching ratio at the ILC with \sqrt{s}=250 GeV and 500 GeV

Evaluation of measurement accuracy of branching ratio
at the ILC with GeV and 500 GeV

Shin-ichi Kawada, Keisuke Fujii, Taikan Suehara,
Tohru Takahashi, Tomohiko Tanabe
July 14, 2019
Abstract
111This write-up is intended to supplement a white paper on the Higgs physics at the ILC. A white paper on the Higgs physics at the ILC to be submitted to the Snowmass process 2013.

We evaluate the measurement accuracy of the branching ratio of at GeV and 500 GeV at the ILC with the ILD detector simulation. For the GeV, we assume the Higgs mass of GeV, branching ratio of , beam polarization of , and integrated luminosity of . The Higgs-strahlung process with , , mode are analyzed. The measurement accuracy is calculated to be . The scaled result to GeV is estimated to be . For the GeV, we assume the Higgs mass of GeV, branching ratio of , beam polarization of , and integrated luminosity of . The Higgs-strahlung process with mode and -fusion process are analyzed. The measurement accuracy is calculated to be for Higgs-strahlung with and for -fusion.

1: Advanced Sciences of Matter (AdSM), Hiroshima University, 1-3-1, Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8530, Japan
2: High Energy Accelerator Research Organization (KEK), 1-1, Oho, Tsukuba, Ibaraki, 305-0801, Japan
3: Department of Physics, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai, Miyagi, 980-8578, Japan
4: International Center for Elementary Particle Physics (ICEPP), The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

: s-kawada@huhep.org

1 Introduction

Since the discovery of Higgs boson by the ATLAS and the CMS experiments [1, 2], one of the next important themes for particle physics is the investigation of Higgs boson, especially the mass generation mechanism. One of the important properties of Higgs boson is its branching ratio. In the Standard Model (SM) of particle physics, the Yukawa coupling constant of matter fermions with the Higgs boson is proportional to the fermion mass. However, if there are new physics, the coupling constant will deviate from the SM prediction. Besides, the deviation from the SM can be the few-percent level if no additional new particles are to be found at the LHC [3]. Therefore, measuring the branching ratio precisely is a crucial problem from the viewpoint of new physics.

In this document, we focus on the branching ratio of . We estimate the measurement accuracy of the branching ratio at GeV and 500 GeV at the ILC with the ILD full detector simulation.

2 Signal and Background

2.1 Signals

There are several Higgs production process as summarized in Figure 1.

Figure 1: The diagrams of Higgs production processes. (left): Higgs-strahlung process, (middle): -fusion process, (right): -fusion process.

The Higgs-strahlung process is the dominant process at GeV. There are three types of signal depending on the decay of boson, as shown in Figure 2. The most sensitive channel at GeV is mode because of the high statistics. In this document, we concentrate on mode and mode, because mode contributes negligibly than mode. Besides, we only consider mode and mode as the signal process of the analysis of mode. The cross section of mode is 19.8 fb, mode is 1.9 fb, respectively.

Figure 2: The diagrams of Higgs-strahlung process with boson decay. (left): mode, (middle): mode, (right): mode.

At the GeV, the -fusion process and mode of Higgs-strahlung process contributes significantly. We concentrate on these two modes of the analyses of GeV, and we ignore other processes from the analyses. The cross section of -fusion and Higgs-strahlung at GeV is 149.5 fb and 100.4 fb.

2.2 Backgrounds

For the mode, the possible backgrounds are the processes which including four leptons in the final state. The left diagram of Figure 3 shows the example of process via . Other possible processes are reactions with the Higgs boson does not decay to tau pairs ().

For the mode, the , , and which comes from and processes should be the main background. The middle diagram of Figure 3 shows the background of process.

On the other hand, the possible backgrounds for -fusion process are and with . The diagram of latter process is shown in the right of Figure 3.

Figure 3: The example diagrams of backgrounds. (left): background for mode, (middle): background for mode, (right): background for -fusion process.

3 Simulation Conditions

We perform the detector simulation with Mokka [4], a Geant4-based [5] full simulation, with the ILD detector model. TAUOLA [6] is used for the tau decay simulation. The ILD detector model is consists of a vertex detector, a time projection chamber (TPC), an electromagnetic calorimeter (ECAL), a hadronic calorimeter (HCAL), a return yoke, muon systems, and forward components.

For the analysis of GeV, we use the signal and background samples which were generated in the context of the Letter of Intent [7], and use ILD_00 detector model. The effects of beamstrahlung and initial state radiation are included. We assume a Higgs mass of GeV, a branching ratio of as assumed by PYTHIA [9], an integrated luminosity of , and a beam polarization of . We also rescale the final result to the case of GeV and the branching ratio which includes the NNLO corrections [10].

For the analysis of GeV, we use the signal and background samples which were generated in the context of ILC Technical Design Report [11, 12, 13, 14], and use ILD_o1_v05 model. In these samples, the effects of hadron(s) overlay process are also included. We use the processes of , , , 2f, 4f, 5f, 6f, and 4f (f fermions). We assume a Higgs mass of GeV, a branching ratio of  [10], an integrated luminosity of , and a beam polarization of .

4 Event Reconstruction and Event Selection

4.1 mode at GeV

In this mode, we take the strategy of reconstructing the boson first, followed by the reconstruction of the tau pairs from the Higgs decay.

We apply lepton identification at first for dividing events and events by using the information of energy deposit in the calorimeter ( and , where is the energy deposit in ECAL(HCAL)) and track momentum (). Figures 57 are the plots of and .

Figure 4: The plot of for the in samples.
Figure 5: The plot of for the in samples.
Figure 6: The plot of for the in samples.
Figure 7: The plot of for the in samples.

From these plots, we define the criteria for lepton identification. The criteria for electron identification (-ID) and muon identification (-ID) are summarized in Table 1.

-ID -ID
Table 1: The criteria for lepton identification for mode at GeV.

After the lepton identification, we apply selections to remove secondary leptons from tau decays. The strategy of this selection is to remove tracks which do not come from the interaction point (IP) by using the track energy and impact parameter in the transverse direction and longitudinal direction with respect to the beam axis. Figures 913 show the , , and plots which through the lepton identification.

Figure 8: The plot of of of process. Blue, red, and black histograms show the from , the from , and the hadrons from decay, respectively.
Figure 9: The plot of of of process. Blue, red, and black histograms show the from , the from , and the hadrons from decay, respectively.
Figure 10: The plot of of of process. Blue, red, and black histograms show the from , the from , and the hadrons from decay, respectively.
Figure 11: The plot of of of process. Blue, red, and black histograms show the from , the from , and the hadrons from decay, respectively.
Figure 12: The plot of of of process. Blue, red, and black histograms show the from , the from , and the hadrons from decay, respectively.
Figure 13: The plot of of of process. Blue, red, and black histograms show the from , the from , and the hadrons from decay, respectively.

We define the tau rejection cut for the objects through the -ID and the -ID respectively as shown in Table 2.

-ID -ID
GeV GeV
Table 2: The criteria for lepton identification for mode at GeV.

We apply the energy recovery procedure to correct the effect of bremsstrahlung and final state radiation. In order to reconstruct the original boson, we have to use both the charged particles and the radiated photons. To achieve this, we define the cone as shown in Figure 14. The four-momenta of the neutral particles in the cone are combined with that of the lepton candidate. We define the half-opening angle of the cone with and apply the recovery procedure to the lepton candidates. The results are shown in Figures 16 and 16.

Figure 14: The definition of the cone. Black arrow shows the lepton candidate. is the angle of the cone.
Figure 15: The results of recovery for mode. The horizontal axis shows the . Black and red histograms show the results of without recovery and with recovery (), respectively.
Figure 16: The results of recovery for mode. The horizontal axis shows the . Black and red histograms show the results of without recovery and with recovery (), respectively.

After that, we apply the tau finder to the remaining objects to reconstruct tau leptons. First of all, the objects which already used at boson reconstruction are rejected from tau reconstruction analysis. Then the finder searches the highest energy track from the remaining objects, and combine the neighboring particles (which satisfies the angle with respect to the highest energy track less than 1.0 radian) with the combined mass less than 2 GeV. We regard the combined object as a tau candidate. Then repeat these processes until there are no charged particles.

After finishing the event reconstruction, we apply the cuts for selecting signal, rejecting background. Before optimizing the cuts, we apply the preselection as follows for mode: number of and , number of and , and for mode: number of and , number of and .

We apply the following cuts sequentially for mode: number of tracks , 115 GeV GeV, , 81 GeV GeV, , , GeV, , , , and 116 GeV GeV, where is the visible energy, is the missing momentum angle with respect to beam axis, is the angle with respect to beam axis, is the energy, is the angle between and , is the angle with respect to beam axis, and is the recoil mass, respectively. Figure 17 shows the recoil mass distribution. Table 3 shows the cut statistics of this mode. After the cuts, the signal events of 108.9 and background events of 76.0 remained. The statistical significance is calculated to be .

Figure 17: The distribution of recoil mass in the unit of GeV.
with other other signi.
4 leptons SM bkg.
No cut 228.3 211.1 214.6 7325 0.0019
preselection 171.3 0.155 1.532 47.05 0.053
# of tracks 169.4 0.155 1.532 41.56 0.053
162.3 0.155 0.912 38.36 0.074
160.6 0.155 0.912 38.03 8719 1906 0.22
148.0 0 0.017 29.09 2408 501.2 1.2
133.9 0 0.009 25.40 1067 101.5 729.7 3.0
133.0 0 0.009 24.93 690.3 78.70 629.7 3.4
130.8 0 0 3.536 254.9 30.70 155.4 5.5
123.4 0 0 3.074 212.1 9.161 3.817 6.6
108.9 0 0 2.474 72.35 1.134 0.034 8.0
Table 3: The cut statistics of mode at GeV.

We apply the following cuts sequentially for mode: number of tracks , 115 GeV GeV, , 72 GeV GeV, GeV, , and 118 GeV GeV. Figure 18 shows the recoil mass distribution. Table 4 shows the cut statistics of this mode. For the mode case, 131.2 signal events and 91.2 background events are remained. The significance is .

Figure 18: The distribution of recoil mass in the unit of GeV.
with other other signi.
4 leptons SM bkg.
No cut 211.1 228.3 214.6 7325 3513 0.0017
preselection 168.5 0 0.155 43.01 1698 7546 7732 1.3
# of tracks 167.4 0 0.155 39.65 1684 7537 7400 1.3
162.9 0 0.155 37.40 1586 2285 3713 1.9
158.6 0 0.155 36.51 1386 227.5 55.48 3.7
153.2 0 0 32.84 1038 55.28 42.54 4.2
153.2 0 0 32.70 738.6 42.41 36.72 4.8
146.3 0 0 3.638 259.4 20.19 0.756 7.1
131.2 0 0 2.875 82.36 5.311 0.301 8.8
Table 4: The cut statistics of mode at GeV.

4.2 mode at GeV

In this mode, the tau pairs are reconstructed first, followed by the dijet reconstruction of the decay.

At first we apply the tau finder to all objects to reconstruct taus. This tau finder searches the highest energy track and combine the neighboring particles, which satisfy , with the combined mass less than 2 GeV. We regard the combined object as a tau candidate. Then we apply the selection cuts as following: GeV, with , and rejecting 3-prong with neutral particles events. These selection cuts are tuned for minimizing misidentification of part of quark jets as tau jets. A survived tau candidate is regarded as a tau jet. After the selection cuts, we apply the charge recovery to obtain better efficiency. The charged particles in tau jet which have the energy less than 2 GeV are detached one by one from smallest energy from the tau jet until satisfying the conditions as following: the charge of tau jet is , and the number of track(s) in tau jet is 1 or 3. The tau jet after detaching is rejected if it does not satisfy the above conditions. After the selection cuts and detaching, we repeat the above processes until there are no charged particles which have the energy greater than 2 GeV.

After the tau reconstruction, we apply the collinear approximation [15] to reconstruct tau pair. In this approximation, we assume that the visible decay products of tau and the neutrino(s) from tau is collinear, and the contribution of missing transverse momentum is only comes from the neutrino(s) of tau decay. The invariant mass of the tau pair with the collinear approximation shown in Figure 19.

Figure 19: The plot of in the unit of GeV, the invariant mass of tau pair with collinear approximation. Blue histogram shows the signal process .

After that, we apply the Durham jet clustering method [16] with two jets for the remaining objects to reconstruct boson.

After the all reconstruction, we apply the cuts to select signal process. Before optimizing cuts, we apply the preselection as follows: number of quark jets , number of and , number of tracks in a tau , and the events which have tracks in both taus are rejected (double 3-prong cut). We apply the following cuts sequentially to reject the background: number of tracks , 110 GeV GeV, , 77 GeV GeV, 80 GeV GeV, , , , GeV, GeV, 100 GeV GeV, 100 GeV GeV, and 112 GeV GeV, where and is the invariant mass and energy of tau pair without using collinear approximation, and is the invariant mass and energy of tau pair with collinear approximation, respectively. Figure 20 shows the distribution of recoil mass. Table 5 shows the cut statistics of this mode. After the cuts, the signal events and background events are remained 1026 and 554.4. The statistical significance of mode is calculated to be .

Figure 20: The distribution of recoil mass in the unit of GeV.
with other signi.
SM bkg
No cut 4233 5377 2596 0.035
preselection 1647 578.8 2761 765.4 0.32
# of tracks 1644 549.8 2680 765.4 1.9
1607 492.3 1015 744.2 4443 2.4
1572 474.7 860.5 725.1 2127 8315 5939 3.6
1440 376.1 791.3 682.8 778.6 4987 8674 8189 3288 997.3 8.3
1429 352.0 782.7 528.7 505.0 4797 7857 7703 3061 609.9 8.6
1386 46.28 442.2 255.6 191.4 1468 2001 2831 1154 475.6 13.7
1338 30.29 235.1 244.3 131.4 854.9 1928 1786 1044 248.1 15.1
1287 19.54 105.0 234.7 81.77 408.2 1845 909.9 883.4 244.6 16.6
1286 19.39 103.2 234.7 72.05 349.1 1837 883.5 883.4 243.9 16.7
1282 19.39 103.0 234.7 72.05 324.7 1836 873.2 883.4 243.9 16.7
1065 3.074 18.76 47.94 10.28 72.83 616.9 150.8 137.0 0.746 23.1
1062 2.454 18.01 46.72 10.28 71.27 612.1 93.05 93.52 0.454 23.7
1026 2.144 14.54 21.24 9.938 57.07 366.3 39.64 43.31 0.161 25.8
Table 5: The cut statistics of mode at GeV.

4.3 mode at GeV

We take the same analysis strategy which described in Section 4.2. We apply the same tau finder to all objects to reconstruct taus from Higgs boson, followed by collinear approximation [15], then apply Durham algorithm [16] to remaining objects to reconstruct boson. Figure 21 shows the distribution of tau pair mass with collinear approximation for the signal process.

Figure 21: The plot of of the signal process in the unit of GeV, the invariant mass of tau pair with collinear approximation.

After the reconstruction we apply the cuts to select signal process. Before optimizing, we apply the preselection cut as; number of quark jet = 2, number of , number of tracks in a tau . Then we apply following cuts: number of tracks , thrust , , 70 GeV GeV, GeV, 20 GeV GeV, GeV, , 115 GeV GeV, 205 GeV GeV, , and . Figure 22 shows the distribution of . Table 6 shows the cut statistics of this mode. The statistical significance of this mode is calculated to be . This result corresponds to the precision of

Figure 22: The distribution of .
with 2f 4f 5f 6f 4f , signi.
No cut 2158 0.39
preselection 1019 604.9 9713 7694 0.67
# of tracks 994.5 600.8 6960 5187 5403 1.3
thrust 964.1 574.5 6663 4822 5821 1.7
898.3 486.4 4195 2379 3955 2.1
855.3 321.2 7682 3467 1741 3441 2.5
849.7 318.5 5164 2884 1243 3147 2.7
806.1 259.4 1530 1483 665.4 1974 3.1
800.3 258.0 1154 1436 645.7 1112 3.4
795.9 137.5 744.6 1093 490.4 472.8 3.7
557.8 6.435 52.91 770.4 38.19 579.6 17.78 36.81 12.3
511.3 5.265 38.91 351.5 20.44 90.13 7.943 31.67 15.7
468.6 2.047 20.44 179.9 5.623 28.35 1.995 24.30 17.3
453.7 1.462 20.44 148.4 0 24.57 1.995 22.58 17.5
Table 6: The cut statistics of mode at GeV.

4.4 -fusion process at GeV

At first in this mode, we apply the algorithm [17, 18] to remove objects from hadron(s) overlaid process. We use FastJet package [19] as the clustering package. We choose the value of generalized radius of clustering of 1.0 currently (more optimization needed).

We apply the same tau finder which described in Section 4.1 to all survived objects through the clustering, the only difference is the maximum associated angle has been changed from 1.0 radian to 0.76 radian. The most energetic candidate and candidate are combined as it comes from Higgs boson.

After the reconstruction, we apply the preselection as the number of , because the hadron(s) processes produce additional charged particles, and the tau finder which used for this process repeat finding process until there are no charged particles.

Then we apply following cuts: number of tracks , 5 GeV GeV, GeV, GeV, , GeV, , , , , where is visible energy, is acoplanarity, is smaller impact parameter value between and , respectively. Figure 23 shows the distribution of . Table 7 shows the cut statistics of this mode. The statistical significance of this mode is calculated to be .

Figure 23: The distribution of .
with 2f 4f 4f 5f 6f 4f , signi.
others
No cut 5401 0.98
preselection 4676 6062 2650 1.6
# of tracks 4274 2461 7035 1126 1.9
4258 2394 7220 2773 262.9 3.0
4251 2386 6886 2736 205.9 3.4
3992 2166 5229 2683 9244 205.9 4.0
3294 1876 2702 1978 4368 148.7 5.9
3245 1865 2485 1696 4157 141.7 6.2
2837 923.6 1757 1224 2866 64.59 7.4
2742 909.3 7384 1722 1201 2792 63.65 7.5
1733 77.50 745.2 8293 8051 159.9 134.0 261.7 11.71 12.4
1469 40.49 542.5 6989 2744 84.90 76.22 126.4 7.755 13.4
Table 7: The cut statistics of -fusion process at GeV.

In events, there are two contributions from -fusion and Higgs-strahlung. The number of remained events can be written as:

where and are the selection efficiency for Higgs-strahlung process and -fusion process, respectively. The signal significance is for the .

5 Summary and Prospects

We evaluate the measurement accuracy of the branching ratio of the mode at GeV and 500 GeV at the ILC with ILD detector full simulation. For the analysis of GeV, we assume GeV, , , and beam polarization . The analysis results and scaled results to GeV are summarized in Table LABEL:250GeV_summary.

Combined
Results of GeV
Scaled results to GeV
Table 8: The analysis results of GeV with assuming GeV and scaled results to GeV.

For the GeV, the analyses are still ongoing, but we obtain the statistical significance and measurement accuracy as summarized in Table LABEL:500GeV_summary, with assuming GeV, , , and beam polarization . The result of -fusion is better than the expected accuracy in the Technical Design Report [12]. We expect improvement by better treatment of hadron(s) background and more optimizing tau reconstruction.

-fusion
significance
Table 9: The analysis results of GeV with assuming GeV.

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