Studies of measuring Higgs selfcoupling with at the future hadron colliders
Abstract
We present a feasibility study of observing at the future hadron colliders with 14, 33, and 100 TeV. The measured cross section then can be used to constrain the Higgs selfcoupling directly in the standard model. Any deviation could be a sign of new physics. The signal and background events are estimated using Delphes 3.0.10 fast Monte Carlo simulation based on the ATLAS detector capabilities. With 3 ab data, it would be possible to measure the Higgs selfcoupling with a 50%, 20%, and 8% statistical accuracy by observing at 14, 33, and 100 TeV colliders, respectively.
I Introduction
The ATLAS and CMS have recently discovered a new boson with a mass near 125 GeV/c discovery (), which is a giant leap for science. The updated results are consistent with the expectation of a Higgs boson higgs (), the missing cornerstone of particle physics. In order to directly test whether the Higgs mechanism is responsible for the electroweak symmetry breaking, we need to determine the Higgs selfcoupling constants directly from data by observing the double Higgs production process . In the standard model (SM), the Higgs selfcoupling is equal to where GeV and is the measured Higgs boson mass. An accurate test of this relation may reveal the extended nature of the Higgs sector, which can be achieved by observing a significant deviation from the SM prediction above ilc (); baur04 (); zurita (); baglio (). Recent studies indicate that observing is challenging at the high luminosity run of LHC (HLLHC) with an integrated luminosity of 3000 fb atlashh (), due to destructive interference between and processes that are shown in Fig. 1 (left).
In this study we study how feasible it is to measure Higgs selfcoupling at the LHC and the future higher energy colliders(VLHC). We will focus on as the baseline. The advantage of measuring the Higgs selfcoupling at the higher energy colliders is their large production cross section rate as shown in Fig. 1 (right), which increases from 34 fb to 1418 fb when increasing the center mass of energy from 14 to 100 TeV baglio (). Recent studies indicate that the resummation effects will further increase the NLO cross section by 20%30% and reduce the scale uncertainties NNLO (), which would improve the chance of measuring the Higgs selfcoupling at HLLHC.
Ii Simulation setup
Following the community summer studies 2013 (CSS 2013) guidelines, we use Delphes delphes () V3.0.10 to simulate the ATLAS detector responses. More specifically, the photon energy is smeared according to the electromagnetic calorimeter (Ecal) responses of . The jet is clustered using the anti algorithm with a radius of 0.5. The tagging operation point is chosen to have 75% of efficiency and 1% of mistags. In Fig. 2, we show the identification efficiencies for photons and jets as a function of as well as the invariant mass distributions for and , respectively. The photon identification efficiency is about 80% for photon with GeV and .
The signal is generated using HPAIR + PYTHIA6.2 package hpair (). All treelevel background processes up to 1 or 2 partons are generated using Madgraph 5 madgraph () + PYTHIA8.0 pythia8.0 () with MLM matching mlm () to avoid double counting in certain regions of phase space. The production cross section of signal and background is evaluated using the CTEQ6L parton distribution functions cteq6l () with the corresponding value of at the investigated order in perturbative QCD. The signal and background processes for their cross section times branching ratio and the number of generated events are summarized in Table 1 for the colliders with 14, 33, and 100 TeV.
Samples  Gen. cuts  HLLHC  TeV33  TeV100  

(fb)  Eevent  (fb)  Events  (fb)  Events  
0.0892  80000  0.545  80000  3.73  80000  
294  1033875  1085  952811  5037  763962  
0.109  97168  0.278  82088  0.876  68585  
2.23  120617  9.843  110663  50.49  99611  
0.68  83491  4.76  71790  37.26  63904  
Iii Event kinematics and selections
The characteristic distributions of the gluon fusion process are compared for several observables at the hadron colliders with 14, 33, and 100 TeV. In Fig. 3, we show for the Higgs pairs the normalized distributions of the transverse momentum , the pseudorapidity , the invariant mass ,and the rapidity . They seem quite similar between the colliders so we use the common set of event selections to separate the signal from the backgrounds. The photons (npho) are required to be isolated and have GeV and . The jets (njet) are required to have GeV and . The jet candidate is a jet that has a tag. We select two jets and two photons in the final states to be consistent with the signature of where each of the jets and photons is required to GeV. The invariant mass of two photons is then required to be consistent within 5 GeV/c of GeV/c while the invariant mass of two jets is required to be between 85 and 135 GeV/c. In order to reject events, we also identify the number of isolated electrons and muons (nleps) with and . If there is missing GeV, we count nmet=1, otherwise nmet=0.
For , we compare the kinematic distributions between the signal and backgrounds for the subleading , the separation, the , and the invariant mass of as shown in Fig. 4. For , the photon kinematic distributions are shown in Fig. 5 for the subleading , the separation, the , and the invariant mass of . We also compare the kinematic distributions of the pair of Higgs between the signal and backgrounds for the invariant mass of , , the minimum between the photons and the jets, and the , as shown in Fig. 6.
Based on these distributions, we further apply the following cuts to optimize the sensitivity:

and

and

and GeV

GeV/c

, the Higgs decay angle in the rest frame of HH.

Iv Preliminary Results
After applying the event selection described above, the remaining number of signal and background events are summarized in Table 2 for an integrated luminosity of 3000 fb. The background seems dominated by the QCD production of , which can be further reduced using a multivariant analysis technique once a realistic simulation is available.
Samples  HLLHC (3 ab)  TeV33 (3 ab)  TeV100 (3 ab)  

Acc.  Expect  Acc.  Expect  Acc.  Expect  
(fb)  (%)  Evnts  (fb)  (%)  Evnts  (fb)  (%)  Evnts  
HH()  0.089  6.2  16.6  0.545  5.04  82.4  3.73  3.61  403.9 
294  0.0045  40.1  1085  0.0039  126.4  5037  0.00275  415.4  
0.109  1.48  4.86  0.278  1.41  11.8  0.875  1.57  41.2  
2.23  0.072  4.82  9.84  0.084  24.8  50.5  0.099  150.5  
0.676  0.178  3.62  4.76  0.12  16.5  37.3  0.11  124.2  
Total B      53.4      179.5      731.3 
S/      2.3      6.2      15.0 
For the high luminosity running of LHC at 14 TeV, it’s possible to observe a statistical significance of 2.3 signal with 3000 fb data, which is consistent with the previous studies atlashh (). For the higher energy colliders with =33, and 100 TeV, we would expect to observe a signal with a statistic significance of 6.2 and 15.0 with 3000 fb data, respectively. In Fig. 7  9, we show the projections of the final invariant mass of two photons or two jets after selecting or for 14, 33, and 100 TeV colliders, respectively. After the signal is established, we would measure its production cross section and derive the Higgs selfcoupling constants from the dependence of the production cross section as a function of the Higgs selfcoupling constants. Based on the estimation of from Fig. 13 in ref. baglio () and the significance of signal, the Higgs selfcoupling can be measured to be a statistical accuracy of 50%, 20%, and 8% with 3 ab data at the future colliders with =14, 33, and 100 TeV, respectively. However, it is worth to note that the event acceptance needs a correction for the dependence of Higgs selfcoupling due to tight cuts used. In the future, we may have to loose some of selections while exploring kinematc distributions (shapes) that are most sensitive to the Higgs selfcoupling to improve the measurement beyond simple event counting.
V Conclusion
We present a feasibility study of observing at the future hadron colliders with 14, 33, and 100 TeV. The measured cross section then can be used to constrain the Higgs selfcoupling directly in the standard model. Any deviation could be a sign of new physics. The signal and background events are estimated using Delphes 3.0.10 fast Monte Carlo simulation based on the ATLAS detector capabilities. With 3 ab data, it would be possible to measure the Higgs selfcoupling with a 50%, 20%, and 8% statistical accuracy by observing at 14, 33, and 100 TeV colliders, respectively.
Vi Acknowledgement
We would like to thank C. Barrera, A. Nisati and N. Styles for their useful cross checks and valuable discussions.
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