Displaced vertices as probes of sterile neutrino mixing at the LHC

# Displaced vertices as probes of sterile neutrino mixing at the LHC

## Abstract

We investigate the reach at the LHC to probe light sterile neutrinos with displaced vertices. We focus on sterile neutrinos with masses (5-30) GeV, that are produced in rare decays of the Standard Model gauge bosons and decay inside the inner trackers of the LHC detectors. With a strategy that triggers on the prompt lepton accompanying the displaced vertex and considers charged tracks associated to it, we show that the 13 TeV LHC with /fb is able to probe active-sterile neutrino mixings down to , with , which is an improvement of up to four orders of magnitude when comparing with current experimental limits from trileptons and proposed lepton-jets searches. In the case when mixing is present, mixing angles as low as can be accessed.

1

## I Introduction

Searches for new physics responsible for the lightness of neutrino masses Olive et al. (2014) has been in the program of the LHC experiments for decades Deppisch et al. (2015). This new physics beyond the Standard Model (SM) may be explained by the so-called see-saw mechanism Minkowski (1977) that introduces the existence of heavy right-handed (sterile) neutrinos that mix with the neutrinos in the Standard Model Mohapatra and Senjanovic (1980); Schechter and Valle (1980). For low enough mixing angles and sterile neutrino masses below the electroweak scale, the sterile neutrino can be long-lived, and may decay with a characteristic displaced vertex (DV) signature inside particle detectors.

Experimental efforts to search for these states at hadron colliders normally focus on promptly decaying sterile neutrinos with masses GeV. Earlier searches by ATLAS Aad et al. (2015a) and CMS Khachatryan et al. (2015, 2014) have focus on the Majorana signature of same-sign dileptons and jets Keung and Senjanovic (1983). Only recently the CMS experiment has provided limits for masses below GeV in the search for three prompt charged leptons Sirunyan et al. (2018). Attention to displaced vertex signatures, which can probe masses in the GeV range, is vastly growing. Recent phenomenological studies assessing the LHC sensitivity with displaced vertices to light sterile neutrinos in various models are studied in Deppisch et al. (2018); Helo et al. (2018); Nemevšek et al. (2018); Lara et al. (2018); Dev et al. (2017). Despite the technical challenges in the reconstruction and modeling of the detector response to displaced vertices, this is an important signal of new physics as it is scarce in the Standard Model, and has to be explored further in order to ensure the successful exploration of new physics at the LHC, and across all mass ranges.

In this work we use a strategy motivated by the ATLAS multitrack displaced vertex search Aaboud et al. (2018); Aad et al. (2015b), recently validated in our previous work Cottin et al. (2018) in the context of a left-right symmetric model. Here we focus on a simplified model in which the Standard Model field content is extended by one heavy sterile neutrino, briefly described in Section II. We consider three cases for active-sterile neutrino mixing , for each of the active flavours . The displaced vertex strategy implemented in each case is described in Section III. Discovery prospects and reach at the LHC are discussed in IV. We close the paper and summarize in Section V.

## Ii Sterile neutrino simplified model

We consider a simplified see-saw model of neutrinos based on the Standard Model gauge group, in which only one massive sterile neutrino is present in the kinematic range of our interest. In this generic framework, couples to the SM leptons via a small mixing in the electroweak currents. The charged and neutral current interactions of this model are described in Helo et al. (2014).

We consider one neutrino flavour at a time, or , produced in boson decays in association with the respective lepton flavour: . The decays proceed via , and . The proper lifetime is given by Helo et al. (2014)

 cτN∼3.7(1GeVmN)5(0.1|VlN|2)[mm]. (1)

The relevant parameters are the sterile neutrino mass and active-sterile neutrino mixing , which we treat as independent. In general, small neutrino masses and mixing lead to macroscopic lifetimes. In principle one can have a large lifetime by making the mixing very small (instead of the sterile neutrino mass). However, for smaller values of the mixing, the production rate of also becomes smaller. We are interested in masses in the GeV range to access lifetimes of the order of picoseconds while scanning over mixings as low as .

In Figure 1 we show different values of the proper lifetime in the - plane. We highlight the approximated region where vertices can efficiently be reconstructed inside the tracker region of ATLAS, for proper decay distances between 4 and 300 mm. We are interested in sterile neutrino mass between GeV GeV, which can be probed with a multitrack displaced vertex search at ATLAS or CMS.

## Iii Simulations and selection of displaced events

We generate a UFO Degrande et al. (2012) model with SARAH Staub (2014) and use SPheno Porod and Staub (2012); Porod (2003) for the spectrum calculation of the sterile neutrino simplified model. We simulate events at TeV for the process . Generation is performed with MadGraph5_aMC@NLOv2.4.3 Alwall et al. (2014) at leading order. We normalize the corresponding value to match experimental cross section in Ref Aad et al. (2016). The generated events are then interfaced to Pythia8 v2.3 Sjöstrand et al. (2015) for showering, hadronization and computation of the decays. Plots are generated with matplotlib Hunter (2007).

The promising decay channels for the sterile neutrino are semileptonically and leptonically . Decays via a neutral current such that are also possible Helo et al. (2014). All these modes will lead to displaced vertices with charged tracks associated to them. For the case when only mixing is present, both semileptonic and leptonic decays lead to the presence of a lepton coming from the displaced vertex.

We propose a search inspired by the ATLAS multitrack displaced vertex analysis Aaboud et al. (2018); Aad et al. (2015b), which is sensitive to lifetimes of the order of picoseconds to about a nanosecond, so particle decays can be reconstructed with a displaced vertex signature inside the inner tracker. This strategy was developed in our recent work in Ref. Cottin et al. (2018), where we trigger on the prompt lepton coming from the boson decay, impose cuts on the neutrino displaced vertex and its decay products, and apply vertex-level efficiencies (made public by ATLAS in Aaboud et al. (2018)) to DVs that pass the required particle-level acceptance cuts. Since the parametrized selection efficiencies provided by ATLAS assumes all decay products are prompt from the DV, they are not directly applicable to the case when there is a lepton coming from the displaced vertex 2, so we consider decays to only when mixing is present.

Prompt leptons are reconstructed considering the following:

For electrons: We require an isolated electron within . We smear their momenta with a resolution of at 10 GeV, falling linearly to at 100 GeV, and then flat.

For muons: We require an isolated muon within . We smear their momenta with a resolution between of and , linearly falling from to .

For taus: We implement a basic reconstruction following Ref. Aad et al. (2015c). We start by reconstructing jets with FastJet 3.1.3 Cacciari et al. (2012) using the anti algorithm with distance parameter . Only jets with GeV and are taken as seeds for reconstruction. Charged constituents inside the jet must have GeV. If a truth candidate falls within a cone centered on the jet axis, it is selected.

The following selections are then imposed:

1. One prompt lepton (as reconstructed above) with GeV.

2. Decay position of the DV contained within transverse distance mm, and mm. The distance between the interaction point and the decay position must be bigger than mm.

3. Decay products must be charged (i.e tracks) with GeV and transverse impact parameter mm. is defined as , with being the azimuthal angle between the decay product and the trajectory of the long-lived .

4. The number of selected tracks must be at least 3. The invariant mass of the DV must be GeV, and assumes all tracks have the mass of the pion.

5. Parametrized selection efficiencies are applied depending on the displaced vertex distance (within 4 and 300 mm, between the pixel and the SCT), number of tracks and mass.

As pointed out in Cottin et al. (2018), with these selections we are still in a zero background region, where background comes mostly from instrumental sources.

## Iv Sensitivity reach

We analyze the region where a displaced search with the above selections can have sensitivity. The relevant parameters in the sterile neutrino model are the neutrino mass and active-sterile neutrino mixing .

As already noted in the context of a left-right symmetric model in Cottin et al. (2018), for sterile neutrinos with masses below the electroweak scale this search strategy looses sensitivity, as lower masses will lead to softer decay products with limited amount of tracks available to make up a vertex. However, given the low background nature of this signature, the discovery of a displaced vertex signal in the sterile neutrino model is possible at the high-luminosity LHC.

Figures 23 and 4 show the estimated reach in the case of electron, muon and tau mixing, respectively. In Figure 2 we see that mixings as low as for fb and 13 TeV can be probed for GeV. Current neutrinoless double beta decay () experiments and searches for trileptons at the LHC are also sensitive to GeV sterile neutrino masses. We show an update of the limits calculated in Helo et al. (2014) using the latest limit on from the GERDA experiment Agostini et al. (2018). LHC limits for sterile neutrino masses below GeV are presented for the first time in the CMS 13 TeV search for three prompt charged leptons in the final state Sirunyan et al. (2018). Other significant constrain in our mass region of interest comes from LEP data, where the DELPHI collaboration provides limits on sterile states produced in decays of the boson Abreu et al. (1997).

In Figure 3, mixings as low as for fb and 13 TeV can be probed for GeV. We also show limits from proposals with lepton-jets searches, which is a complementary strategy. The curve labeled “lepton-jets-1” shows the exclusion form Ref. Izaguirre and Shuve (2015) at 13 TeV and fb, where zero background is assumed. The curve labeled “lepton-jets-2” shows the 13 TeV limit in Dube et al. (2017) and fb, and considers additional background sources to the ones in Izaguirre and Shuve (2015). An improvement of roughly two orders of magnitude in sensitivity is achieved with our strategy with fb for masses GeV. The CL exclusion of the CMS 13 TeV prompt trileptons search Sirunyan et al. (2018) is also shown, proving to be competitive with DELPHI Abreu et al. (1997).

Finally, we show in Figure 4 the reach when there is mixing. Experimental limits for mixing have not been addressed yet at the LHC. We show the DELPHI limit Abreu et al. (1997) from decays for comparison. For taus, a large luminosity sample will be needed for obtaining meaningful constraints. As the figure shows there is only a very narrow region testable with /fb. Mixings as low as for GeV at /fb can be probed with this strategy.

## V Summary and Conclusions

We study the potential of the LHC to probe light sterile neutrinos, and active-sterile neutrino mixing angles, with a displaced vertex strategy motivated by current multitrack DV searches at the 13 TeV LHC. We focus on a simplified model where the Standard Model is extended with one sterile neutrino . Mixing with the three flavours and , are treated separately. In all cases, to our knowledge, we see that this strategy probes to be the most sensitive to date in the mass region of interest ( GeV GeV).

For mixing, we show that this DV search is more sensitive than current neutrinoless double beta decay experiments. In the case of mixing, parts of the parameter space not accessible with other LHC searches (such as lepton-jets or trileptons) is possible. In both cases, with /fb, an improvement of up to four orders of magnitude ( for sterile neutrino masses between and GeV) in sensitivity is gained when comparing with the current experimental limits from trileptons searches at CMS Sirunyan et al. (2018).

Accessing mixing is less straightforward due to to the difficulty in reconstructing leptons, and also since the presence of a subsequently displaced coming from the displaced vertex affects the vertex reconstruction efficiency in a way that is not trivial to quantify. We access mixing by considering sterile neutrino decays via a neutral current only, which still leads to a displaced vertex formed from hadronized tracks, to which publicly available DV efficiencies can be applied, thus avoiding the problematic in the DV. This may be an advantage of a multitrack based strategy, as opposed to tagging leptons coming from the DV, in constraining mixing.

We briefly comment on prospects for testing sterile neutrinos at LHCb. The authors in Antusch et al. (2017) discuss limits for a different model than the one presented in this work. They show that sterile neutrino masses around GeV and mixings down to can be constrained in semileptonic sterile neutrino decays () at the CL with current LHCb data Aaij et al. (2017). Mixings up to (for masses between GeV) can be further probed at higher luminosity, suggesting limits for mixing from LHCb could be competitive in this mass region to the ones we derived here in the context of ATLAS.

Finally, the sensitivity of this displaced strategy at the LHC is complementary to that of future fixed-target experiments, such as SHiP, or the MATHUSLA surface detector, which can probe sterile neutrino masses below 5 GeV. This makes a tracker based DV search for light sterile neutrinos unique, as it has no competition from other experiments within GeV GeV.

###### Acknowledgements.
G.C. acknowledges support by the Ministry of Science and Technology of Taiwan under grant No. MOST-106-2811-M-002-035. J.C.H. is supported by Chile grants Fondecyt No. 1161463, Conicyt PIA/ACT 1406 and Basal FB0821. M. H. was funded by Spanish MICINN grant FPA2017-85216-P and SEV-2014-0398 (from the Ministerio de Economía, Industria y Competitividad), as well as PROMETEOII/2014/084 (from the Generalitat Valenciana).

### Footnotes

1. preprint: IFIC/18-25
2. The further displacement of ’s inside the vertex will affect the vertex reconstruction efficiency from the subsequent displacement of taus (and from any heavy flavour quark in general). This was addressed for example in Ref. Allanach et al. (2016), when there are two s coming from the displaced vertex. By allowing a bigger merging distance of mm (instead of mm) when forming a vertex, some efficiency is recovered. Since we do not implement a vertex reconstruction algorithm in this work, the loss in efficiency can not be estimated.

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