WIMP Searches at the International Linear Collider
Moritz Habermehl, Keisuke Fujii, Jenny List, Shigeki Matsumoto, Tomohiko Tanabe
WWIMP searches at the International Linear Collider
Keisuke Fujii
High Energy Accelerator Research Organization, JapanE-mail: [email protected]
Moritz Habermehl ∗ Deutsches Elektron-Synchrotron, GermanyE-mail: [email protected]
Jenny List
Deutsches Elektronen-Synchrotron, GermanyE-mail: [email protected]
Shigeki Matsumoto
Kavli Institute for the Physics and Mathematics of the Universe, JapanE-mail: [email protected]
Tomohiko Tanabe
International Center for Elementary Particle Physics, University of Tokyo, JapanE-mail: [email protected]
Weakly Interacting Massive Particles (WIMPs, χ ) are candidates for Dark Matter. WIMPsearches at lepton colliders are complementary to searches at hadron colliders and direct de-tection, since they directly probe the coupling to electrons which a priori is independent of thecoupling to hadrons. Like at hadron colliders, WIMP pair production can be observed via anadditional visible particle, in particular a photon from initial state radiation ( e + e − → χ χγ ). Withthis technique WIMP masses to nearly half the centre-of-mass energy can be probed. Polarisedbeams are essential to reduce Standard Model backgrounds and to characterise the properties ofthe new particles in case a signal is discovered. Prospects for a mono-photon WIMP study atthe International Linear Collider will be discussed in the context of EFT. In addition, detectorrequirements critical to this analysis are discussed. ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ h e p - e x ] F e b IMPs at the ILC
Moritz Habermehl
1. Introduction
The International Linear Collider (ILC) is a future electron-positron collider with a maturetechnology [1]. Currently, a political decision in Japan is awaited. The centre-of-mass energy canbe tuned between 250 GeV and 500 GeV and is upgradable to 1 TeV. The instantaneous luminosityfor √ s = 500 GeV is 1.8 × cm − s − which can be doubled to 3.6 × cm − s − after a lumi-nosity upgrade. Both the electron and position beams are foreseen to be polarised to at least ± ± e + e − → χ χγ whose signature is a singlephoton in an otherwise "empty" detector. This approach is quasi model-independent. Due to theknown initial state, the missing four-momentum can be calculated using two observables, namelythe photon energy E γ and the photon polar angle θ γ . Figure 1:
Pseudo-Feynman diagram for the signal process and example Feynman diagrams for the two mainbackground processes: radiative neutrino pair production and Bhabha scattering.
The two main background processes are neutrino pair production and Bhabha scattering, bothwith an associated photon from initial state radiation, or in the latter case also from final stateradiation (see fig.1). The neutrino background is irreducible, but can be enhanced or suppressed bychanging the polarisation combination. Bhabha scattering has a huge cross section and mimics thesignal if both leptons escape undetected. For the suppression of this background process the bestpossible hermeticity in the forward region of the detector is required.
2. Motivation for an ILC Simulation Study
The theoretical framework used in this analysis are effective operators, where the underlyingidea is to classify the WIMP based on its quantum numbers (spin and weak isospin) and the medi-ator by its spin and construct the minimal effective Lagrangian. The only parameter that remains, Λ , can be called the energy scale of new physics and is a function of the mediator mass and thecoupling to the fermions g f and the coupling to the WIMPs g χ : Λ = M mediator / √ g f g χ .In such a framework, considering the full Lagrangian, a likelihood analysis of data of exist-ing experiments, together with extrapolations of expected exclusion limits at the time the ILC isrunning is being performed. Figure 2 shows the surviving region assuming that no WIMP signalis detected, for the example of a singlet-like fermion WIMP [3]. Data from the following exper-iments are considered: from the Planck satellite, from the direct detection experiments PICO-2L,1 IMPs at the ILC
Moritz Habermehl
LUX and XENON100, from collider searches at LEP and LHC and from future experiments likeLZ and PICO250. Here, the couplings are tested in the range [-1,1]. Above the grey area this sim-plified model reproduces the results of effective operators. The yellow region shows the parameterspace which will not be explored by other experiments before the ILC starts.
Figure 2:
The parameter space which will not be covered bydark matter experiments by the time the ILC will be running isshown in yellow (68% confidence level) and blue (95% C.L.).The computations are based on extrapolations of current and fu-ture experiments assuming that no WIMP signal is detected. Thegrey area reflects the parameter space in which the approach ofeffective operators is not valid: Λ has to be larger than three timesthe WIMP mass and above 300 GeV. [3]
3. Modelling of Signal and Background
The signal definition in this analysis comprises three requirements on the photon: a minimumenergy of 10 GeV, a maximum energy of 220 GeV and | cos θ γ | < γ = 242 GeV for √ s = 500 GeV. The angle is restricted to the parts ofthe detector in which the tracking performance guarantees that photons can be distinguished fromelectrons and positrons.The events are generated using WHIZARD version 2.2.8 [4], with the matrix element gener-ator O’Mega [5]. Polarised beams are included as well as the beam energy spectrum. The gener-ated background processes are neutrino pairs plus several photons and for the Bhabha scatteringelectron-positron pairs plus several photons. The signal events χ χγ are obtained by reweightingthe ν ¯ νγ events using the differential cross section formulas expressed in terms of the WIMP massand spin.For modelling the photons, WHIZARD offers an ISR parametrisation that comprises all or-ders of soft-collinear photons and the first three orders of hard-collinear photons. With this thecross sections of the considered processes are calculated with high accuracy. However, a realisticdistribution of the photon polar angle is obtained by including the photons in the matrix element.By doing so, double counting of photons is avoided. Both approaches are combined by generatingthe events with the photons in the matrix element and reweighting the cross section to the one withthe ISR parametrisation.The events are simulated in a Geant4 based simulation of the full ILD detector model presentedin the Technical Design Report [2]. 2 IMPs at the ILC
Moritz Habermehl e + e − γ [6] new analysis p T E vis Table 1:
Fractions of signal-like Bhabha scatteringevents surviving the three conditions for an "empty"detector. The central column shows the latest fullanalysis [6] and the right one our update.
4. Results
Signal-like events with only very little detector activity besides the photon are selected byrequiring the following three criteria. There must be no tracks with a transverse momentum ex-ceeding 3 GeV. The visible energy, excluding that of the photon, has to be smaller than 20 GeV.Finally, there must be no electrons and positrons detected in the forward region, or more techni-cally speaking: no clusters may be reconstruced in the forward detector BeamCal.Table 1 shows the percentage of Bhabha scattering events surviving the three conditions, forthe full analysis done in 2013 [6] (central column) together with our update of the analysis. Inthe new analysis the Bhabha background is suppressed to a sub-permille level with respect to thesignal definition, which is approximatly fifteen times more effective compared to the last analysis.The requirement of a low visible energy leads to an eight times higher rejection, which is due toimprovements in particle flow and photon reconstruction. With an optimised BeamCal reconstruc-tion algorithm [7], an additional factor of two is achieved. This shows that both detector resolutionand detailed reconstruction are crucial for a reliable performance estimate.Figure 3 shows a comparison between the previous sensitivity [8] which is based on the back-ground rejection efficiency of [6] (red dashed line) and our update (blue solid line). For right-handed electrons and left-handed positrons the level of the exclusion limit can be improved by upto 300 GeV in Λ , for a centre-of-mass energy of 500 GeV and an integrated luminosity of 500 fb − . Figure 3:
The area below the curves shows the excluded Λ valuesas a function of the WIMP mass for a vector-like fermion WIMPand a vector-like operator, √ s = 500 GeV, 500 fb − , right-handedelectrons and left-handed positrons. The red dashed curve is forthe Bhabha scattering background suppression shown in the cen-tral column of the table and the blue solid line is for the improvedbackground rejection as shown in the right column of the table. High numbers of electron-positron pairs created from beamstrahlung hit the inner part ofBeamCal. As a consequence, the reconstruction efficiency of particles coming from the hard inter-action decreases dramatically at very low polar angles θ . The identification of Bhabha scatteringevents hence strongly depends on the design of the forward region.3 IMPs at the ILC
Moritz Habermehl
Because the ILC detectors share the same interaction region, both are required to have thesame focal distance of the final quadrupole magnet (L*). In order to equalise that length for bothdetectors, the forward region of the ILD detector is currently being redesigned [9]. BeamCalhas to be moved closer to the interaction point by 40 cm. While the detailed redesign and theimplementation in the ILD simulation is ongoing, we estimate the impact in the following way:Firstly, we assume that area in BCal polluted by the pairs is the same for all considered distances.Secondly, the lepton reconstruction efficiency is approximated to be 100% for polar angles above aneffective angle θ e f f and 0% below. The number of events with both leptons not being reconstructedusing the full detector simulation corresponds to an effective angle of approximately 15.5 mrad.With these assumptions, the hermeticity in the forward region depends purely geometrically onthe distance of BeamCal to the interaction point. This means that the effective polar angle growslinearly with the distance by which BeamCal is moved in towards the interaction point.Figure 4 shows how the number of Bhabha scattering events with both leptons not being recon-structed changes as a function of the effective polar angle. With the new position of the subdetector,the Bhabha backgrond would be three to four times higher. With this higher background level theimprovement presented in section 4.1 would be partially lost. Figure 4:
The number of Bhabha scattering events with both lep-tons lying within an effective polar angle, normalised to the numberof events with both leptons not being reconstructed using the full de-tector simulation, which corresponds to θ e f f ≈ Based on the results of the previous study [6] performed at √ s = 500 GeV and 500 fb − wedeveloped a scheme to extrapolate the results to other energies and integrated luminosities. Thisextrapolation is restricted to WIMP masses below 100 GeV, where the sensitivity does not dependon the WIMP mass. This study allows to give estimates of the sensitivity for different time scalesand different running scenarios, i.e. how much integrated luminosity is collected at which centre-of-mass energy, in which order this occurs and how the integrated luminosity is distributed betweenthe different polarisation combinations (fig. 5).The running scenario H-20 [10] starts with √ s = 500 GeV at which initially 500 fb − arecollected (fig.6). After the first four years an exclusion limit of Λ ≈ √ s = 500 GeV after aluminosity upgrade. After the full ILC programme the runs at √ s = 500 GeV will have contributedto an exclusion limit of Λ ≈ √ s = 1 TeV the reachable Λ is approximately4.5 TeV. 4 IMPs at the ILC
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Figure 5:
Extrapolation of the exclusion limits from the full simu-lation to the full range of ILC centre-of-mass energies and differentintegrated luminosities, for fractions of 22.5% (left) and 40% of thedata collected with right-handed electrons and left-handed positrons.
Figure 6:
The H-20 run-ning scenario which is oneof the possible 20 years pro-grammes for the ILC[10].
The sensitivity strongly depends on the fraction of the integrated luminosity collected withright-handed electrons and left-handed positrons for which the neutrino background is stronglysuppressed. The rather large fraction in H20 (40%) is clearly favoured over 22.5% (compare fig.5).A full update of the whole analysis to the new detector performance for all types of WIMPs isunderway.
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D94 no.~6,(2016) 065034, arXiv:1604.02230 [hep-ph] .[4] W. Kilian, T. Ohl, and J. Reuter, “WHIZARD: Simulating Multi-Particle Processes at LHC and ILC,”
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C71 (2011) 1742, arXiv:0708.4233 [hep-ph] .[5] M. Moretti, T. Ohl, and J. Reuter, “O’Mega: An Optimizing matrix element generator,” arXiv:hep-ph/0102195 [hep-ph] .[6] C. Bartels, M. Berggren, and J. List, “Characterising WIMPs at a future e + e − Linear Collider,”
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