Probing new physics with displaced vertices: muon tracker at CMS

TL;DR

This paper explores the potential of CMS muon trackers to detect long-lived particles through displaced vertices, using heavy neutral leptons and Chern-Simons portal as case studies.

Contribution

It demonstrates how CMS muon trackers can be utilized to search for and analyze long-lived particles via displaced vertices, highlighting their importance in new physics detection.

Findings

CMS muon tracker can effectively identify displaced vertices.

Heavy neutral leptons can be studied through this method.

Chern-Simons portal provides a viable scenario for long-lived particle detection.

Abstract

Long-lived particles can manifest themselves at the LHC via "displaced vertices" - several charged tracks originating from a position separated from the proton interaction point by a macroscopic distance. Here we demonstrate a potential of the muon trackers at the CMS experiment for displaced vertex searches. We use heavy neutral leptons and Chern-Simons portal as two examples of long-lived particles for which the CMS muon tracker can provide essential information about their properties.

Tables

Table 1. Table 1: The values of the selection efficiencies for HNLs of different flavors e , μ , τ 𝑒 𝜇 𝜏 e,\mu,\tau in the case of realistic and optimistic selection criteria

${ϵ}_{\text{sel}}$	$e$	$\mu$	$\tau$
Realistic	0.16	0.17	$7\cdot {10}^{-3}$
Optimistic	0.26	0.31	$3.2\cdot {10}^{-2}$

Equations

$$N_{\mathrm{events}}=N_{\text{parent}}\cdot {\mathrm{Br}}_{\text{prod}}\cdot P_{\mathrm{dec}}\cdot ϵ,$$

$$\begin{gathered} P_{\mathrm{dec}}=\int d{\theta }_{X}d{p}_{X}f(p_X,{\theta }_X)\times \\ \times \left(e^{-l_{\min }/c{\tau }_X{\gamma }_X}-e^{-l_{\max }/c{\tau }_X{\gamma }_X}\right), \end{gathered}$$

$$ϵ={ϵ}_{\text{sel}}\cdot {ϵ}_{\text{rec}}\cdot {\text{Br}}_{X\to \mu \mu },$$

$$l_{\mathrm{dec}}\equiv c{\tau }_X{\gamma }_X\gg l_{\text{max}}$$

$$N_{\text{prod}}\cdot {\text{Br}}_{X\to \mu \mu }>3,$$

$$\begin{gathered} {\mathcal{L}}_{CS}=c_W{ϵ}^{\mu \nu \lambda \rho }{X}_{\mu }{W}_{\nu }{\partial }_{\lambda }{W}_{\rho }+ \\ {c}_{\gamma }\cos {\theta }_W{ϵ}^{\mu \nu \lambda \rho }{X}_{\mu }{Z}_{\nu }{\partial }_{\lambda }{\gamma }_{\rho }+c_Z\sin {\theta }_W{ϵ}^{\mu \nu \lambda \rho }{X}_{\mu }{Z}_{\nu }{\partial }_{\lambda }{Z}_{\rho } \end{gathered}$$

$${\mathcal{L}}_{X\mu \mu }=c_W{g}_{Xll}{X}^{\nu }\sum _{l=e,\mu ,\tau }\bar{l}{\gamma }_5{\gamma }_{\nu }l,$$

$$W\to X+l+{\bar{\nu }}_l,X\to {\mu }^{+}+{\mu }^{-}$$

$$\begin{gathered} {\mathcal{M}}_{W\to X+f+f^{\prime }}=\frac{g{c}_W}{2\sqrt{2}}{\epsilon }^{\mu \nu \alpha \beta }{ϵ}_{\mu }(p)(2p+k_X{)}_{\nu }{ϵ}_{\alpha }^{\ast }(k_X)\times \\ \times D_{\beta \gamma }(k_f+k_{f^{\prime }})\bar{u}(k_f){\gamma }^{\gamma }(1-{\gamma }_5)v(k_{f^{\prime }}), \end{gathered}$$

$${\Gamma }_{W\to X+f+f^{\prime }}\approx c_W^2\frac{{\alpha }_W{m}_W^3}{432{\pi }^2{m}_X^2}$$

$${\text{Br}}_{W\to X+l+{\nu }_l}\approx 2.9(1\text{ GeV}/m_X{)}^2{c}_W^2$$

$${\Gamma }_{X\to f{f}^{\prime }{f}^{\prime \prime }{f}^{\prime \prime \prime }}\sim c_W^2\frac{{\alpha }_W^2}{(2\pi {)}^3}\frac{m_X^9}{m_W^8}$$

$$\frac{{\Gamma }_{X\to f{f}^{\prime }{f}^{\prime \prime }{f}^{\prime \prime \prime }}}{{\Gamma }_{X\to \mu \mu }}\simeq {\left(\frac{{\alpha }_W}{2\pi g_{X\mu \mu }}\right)}^2{\left(\frac{m_X}{m_W}\right)}^8\simeq \frac{10^{-7}}{g_{X\mu \mu }^2}{\left(\frac{m_X}{40\text{ GeV}}\right)}^8,$$

Full text

I Introduction

The Standard model (SM) of particle physics is very successful in describing known elementary particles and their interactions. However it does not incorporate a number of observations in particle physics and cosmology: neutrino oscillations, generation of baryon asymmetry of the Universe, the nature of dark matter. These phenomena imply that new particles beyond the Standard Model exist. Many extensions of the SM introduce new particles with macroscopic decay lengths ($c\tau>1$ cm) Giudice:1998bp ; Barbier:2004ez ; Asaka:2005an ; Asaka:2005pn ; Chacko:2005pe ; Strassler:2006im ; Strassler:2006ri ; Burdman:2006tz ; Cai:2008au ; Baumgart:2009tn ; Kaplan:2009ag ; Chan:2011aa ; Fan:2011yu ; Arvanitaki:2012ps ; Fan:2012jf ; ArkaniHamed:2012gw ; Dienes:2012yz ; Csaki:2013jza ; Chacko:2015fbc ; Batell:2016zod ; Fradette:2017sdd ; Dienes:2011ja . Such particles are often called long-lived particles (LLPs).

LLPs can be copiously produced at colliders. Their decays present a distinct experimental signature – the position of an LLP decay vertex is highly displaced from its production vertex (PV), see Fig. 1. Therefore, in order to probe the parameter space of the LLP, experiments must have large length of the decay volume.

Searches for the displaced vertex (DV) events have been performed at the LHC in the past, including searches for displaced hadronic jets Aaboud:2018aqj ; Aaboud:2017iio ; Sirunyan:2018pwn ; Sirunyan:2017jdo ; Sirunyan:2018vlw , dimuon vertices Aaboud:2018jbr ; CMS:2015pca and decays into specific final states (for example, the process $B^{\pm}\to\mu^{\pm}\mu^{\pm}\pi^{\mp}$ with one prompt and one displaced muon at LHCb Aaij:2014aba ).

In this paper, we propose a scheme of DV searches exploiting the muon trackers of the CMS experiment. Its advantage is large length of the decay volume, which is essential to probe the parameter space of the LLPs with the decay lengths about $1\text{ meter}$ or larger.

The use of the muon chambers to reconstruct di-muon DV signatures has been explored in the past in Bobrovskyi:2011vx ; Bobrovskyi:2012dc ; Izaguirre:2015pga and recently in Boiarska:2019jcw . Ref. Drewes:2019fou that appeared when this work was at its final stage employed the event selection criteria that may be too optimistic with regard to the background estimates. Ref. CMS:2015pca explored a potential of the CMS muon chambers alone to reconstruct dimuon DV. This search however, was constructed to be much more general, and hence could not profit from the presence of a prompt lepton in the event. This necessarily implied much more stringent cuts on $p_{T}$ of either of the two muons in the muon tracker since these muons were used to record an event by a trigger, and therefore lower sensitivity.

This paper is organized as follows. In Sec. II we discuss the “long DV search scheme”, selection criteria and conditions for an LLP model under which the scheme is the most efficient. In Sec. III we discuss the potential of the scheme for specific models — the neutrino portal and the Chern-Simons vector portal. We conclude in Sec. IV and provide additional material in Appendices.

II Displaced vertices with the muon tracker

Description of the scheme. CMS (compact muon solenoid) is a beam line azimuthally symmetric detector consisting of a solenoid generating the $3.8$ T magnetic field, the inner trackers that allow to reconstruct the momentum of particles produced in the pseudorapidity range $|\eta|<2.5$ (where $\eta=-\log[\tan(\theta/2)]$ and $\theta$ is the polar angle with respect to the anticlockwise-beam direction) and the muon trackers located outside the solenoid Chatrchyan:2008aa .

The muon system is located outside the solenoid and covers the range $|\eta|<2.4$. It is a set of gaseous detectors sandwiched among the layers of the steel flux-return yoke. This allows for a muon to be detected along the track path at multiple points Sirunyan:2018fpa . The magnetic field in the muon system is not uniform, and goes from 2 T in the innermost part down to almost 0 T in the outer part CMS:1997iti .

Schematic drawing of the muon detector is shown in Fig. 2.

For the LHC Run 2, new reconstruction of muons has been introduced CMS_muonreco , the so-called displaced standalone muon reconstruction. This reconstruction is specifically designed to address cases when muons are produced in decays far away from the production vertex. New algorithm achieves an almost 100% reconstruction efficiency for the muon production radius up to about 3 m. This is a significant gain in the efficiency compared to the reconstruction which uses also inner tracker information, but at the same time, the momentum resolution deteriorates by about a factor of 10 and is in the range 10–60%.

The muon tracker can use two muon tracks to reconstruct a displaced vertex originating from the decay $X\to\mu\mu+\dots$. The reconstructed DV together with the production vertex that can be tagged by prompt decays products, e.g. a prompt lepton, and an underlying event produced together with the $X$ particle, is identified as a DV event. Due to the large distance between a PV and a reconstructed DV, we will call this scheme the “the long DV” scheme.

A presence of a prompt decay product in the event is essential for event triggering, so that it is recorded and can be analyzed offline. It should be noticed, that after the phase II upgrade, during the high-luminosity LHC phase, the possibility to use track-trigger in CMS will be introduced. This will enable a possibility to reconstruct and identify displaced tracks online CMS:2018lqx ; CMS:2018qgk ; Atlas:2019qfx , and hence will remove a need for a prompt lepton in the event. However, for the models discussed in this paper, current hardware configuration of the CMS allows to perform the searches with the already recorded data, as well with the data to be obtained during the Run 3 of the LHC.

At the same time, final states with a prompt, well identified, object in the event, as e.g. a prompt muon or electron, have much lower background rate. In this case the instrumental backgrounds and non-muon backgrounds from cosmic rays are reduced to a negligible level. The remaining cosmic-ray muon backgrounds can be suppressed by selections which do not impact signal efficiency, as described in Ref. Aad:2019kiz . The remaining sources of the background for the long DV scheme are processes with a presence of a prompt object (as e.g. W boson production) accompanied by decays of the SM particles into single muons, which give rise to combinatorial two-muon events, and two-muon decays of the SM particles (for example, $J/\psi,\rho,\omega$ mesons and the $Z$ boson). The most significant displacement of such DV appears in case of two muons originating for a heavy-flavor particle decay ($b$ or $c$ hadrons). As we do not carry out an experimental analysis in this paper, we assume that this background is negligible if one requires the transverse position of the displaced vertex to be as far as $l_{\text{DV}}>2\text{ cm}$ from the beam collision point, since most of the SM particles decay before reaching this displacement Sirunyan:2017nbv . Under this assumption we lose a part of the efficiency for LLPs with shorter lifetimes, but at the same time we provide a more robust estimate of the potential signal sensitivity. Because of the position of the muon trackers, the muon events can be reconstructed at the distances $l_{\text{DV}}<3\text{ m}$. The muons can be reconstructed with high efficiency and low misidentification probability if each of them has the transverse momentum $p_{T}>5\text{ GeV}$ CMS_mulowpt ; CMS_mulowptmisID .

To summarize, an event in the long DV search scheme should satisfy the following selection criteria:

• –

A prompt electron with $|\eta|<2.5,\ p_{T}>30\text{ GeV}$ or a prompt muon with $|\eta|<2.4,\ p_{T}>25\text{ GeV}$, which are required for an event to be recorded by the single lepton triggers;

• –

The minimal transverse displacement of the DV from the PV is $l_{\text{min},\perp}=2\text{ cm}$; the maximal transverse and longitudinal displacements are $l_{\text{max},\perp}=3\text{ m},\ l_{\text{max},l}=7\text{ m}$;

• –

Two displaced muon tracks, each with $|\eta|<2.4,\ p_{T}>5\text{ GeV}$.

The requirement of a large displacement of a DV from the PV helps to significantly reduce the background from SM processes. Therefore, even in the region with the invariant mass of two muons below 5 GeV (mass of $B$-mesons) the SM background is considered to be negligible. The scheme is presented in Fig. 3.

An event with prompt $\tau$ lepton can be tagged by its leptonic decays $\tau\to l\bar{\nu}_{l}\nu_{\tau}$, where the leptons $l=e/\mu$ satisfy the criteria for prompt leptons presented above. We do not consider the reconstruction of $\tau$ leptons by their hadronic decay products since the trigger threshold for $p_{T}$ of hadronic decay products is too high for efficient reconstruction.111Current trigger threshold is $p_{T}>180\text{ GeV}$. However, in the future it is wise to invest into the development of a dedicated multi-object trigger which would allow to bring down the prompt tau $p_{T}$ by including additional displaced leptons in the event.

In Drewes:2019fou a similar search scheme was discussed, albeit with less restrictive selection criteria $l_{\text{min},\perp}=0.5\text{ cm}$, $l_{\text{max},\perp}=4\text{ m}$, and $|\eta|<4$ for leptons.222After the HL-LHC upgrade the CMS will extend its pseudorapidity range to $|\eta|<4$. A wider range of muon pseudorapidities leads to the enlargement of the selection efficiency, while a smaller displacement between a DV and the PV lifts up the upper bound of the sensitivity and hence increases the maximal mass reach. However, we caution that the background-free hypothesis for the region with smaller DV displacements adopted in Drewes:2019fou has not been tested. Nevertheless, to demonstrate potential improvement from considering lower displacements we provide sensitivity for two scenarios: “realistic” for the selection criteria outlined above, and “optimistic”, defined according to Drewes:2019fou .

Estimation of the number of events. The number of decay events of a new particle $X$ that pass the selection criteria is

[TABLE]

where

• –

$N_{\rm parent}$ is the total number of parent particles that produce a particle $X$ at the LHC;

• –

$\mathrm{Br}_{\text{prod}}$ is the branching fraction of the production of a particle $X$ in decays of the parent particle;

• –

$P_{\mathrm{dec}}$ is the decay probability,

[TABLE]

with $\tau_{X}$ being the proper lifetime of the particle $X$, $\gamma_{X}$ is its $\gamma$ factor, and $f(p_{X},\gamma_{X})$ is the distribution function of the $X$ particle whose decay products satisfy the selection criteria;

• –

$\epsilon$ is the overall efficiency – the fraction of all decays of the $X$ particle that occurred in the decay volume between $l_{\mathrm{min}}$ and $l_{\mathrm{max}}$, have passed the selection criteria, and were successfully reconstructed.

The efficiency is a combination of several factors:

[TABLE]

where $\epsilon_{\text{sel}},\epsilon_{\text{rec}}$ are the efficiencies of the selection and subsequent reconstruction of an event correspondingly, and $\text{Br}_{X\to\mu\mu}$ is the branching ratio of the decay of the $X$ particle into two muons. Clearly, $\epsilon_{\text{rec}}$ does not depend on the nature of LLP. The reconstruction efficiency for leptons is well above 95% for muons with $p_{T}>5$ GeV CMS_mulowpt ; CMS_muonreco ; Sirunyan:2018fpa and for electrons with $p_{T}>30$ GeV Khachatryan:2015hwa . Therefore, for simplicity the reconstruction efficiency is taken to be equal to 1 ($\epsilon_{\text{rec}}=1$) in what follows.

We define the sensitivity curves by the condition $N_{\mathrm{events}}\simeq 3$, corresponding to the 95% exclusion limit under the assumption of zero background. The lower boundary can be easily rescaled to other $N_{\mathrm{events}}$.

Potential of the scheme. The main advantage of the long DV scheme is the large length of the fiducial decay volume $l_{\mathrm{max}}$, which exceeds the lengths of the decay volumes of other DV search schemes at the LHC (see, e.g., Cottin:2018nms ; Aaij:2014aba ) by $\simeq 10$ times. This has a benefit when searching for new particle with large decay lengths,

[TABLE]

Indeed, in this case the decay probability (2) is in the “linear regime”, $P_{\mathrm{dec}}\approx l_{\mathrm{max}}/l_{\mathrm{dec}}$, and as a result the number of events (1) is proportional to $l_{\mathrm{max}}$. For decay lengths that do not satisfy the condition (4) the decay probability does not depend on $l_{\mathrm{max}}$, and the improvement is lost (see Fig. 4).

In order to probe the domain (4) there must be sufficient production of the $X$ particles, i.e.

[TABLE]

where $N_{\text{prod}}=N_{\text{parent}}\cdot\text{Br}_{\text{prod}}$. The parameter space defined by the conditions (4), (5) is optimal for being probed by the long DV scheme. A toy example of the parameter space is given in Fig. 5.

III Examples of probed models

III.1 HNLs

Consider the model of heavy neutral lepton (HNL), which introduces a Majorana fermion singlet $N$ coupled to the gauge invariant operator $\bar{L}\tilde{H}$, where $L$ is the left lepton doublet and $\tilde{H}=i\sigma_{2}H^{*}$ is the Higgs doublet in conjugated representation. This coupling introduces the mass mixing between the HNL and active SM neutrino $\nu_{l}$ parametrized by the mixing angle $U_{l}$. We adopt the phenomenology of the HNLs from Bondarenko:2018ptm . The main production channel of the HNLs with masses in the range $m_{N}\gtrsim 5\text{ GeV}$ is the decay of the $W$ bosons. We use the value $\sigma_{W}\approx 190\text{ nb}$ for the total production cross-section of the $W$ bosons at the LHC at energies $\sqrt{s}=13\text{ TeV}$ Aad:2016naf . To estimate the parameter space defined by (4) and (5), we calculated the energy spectrum and geometric acceptance $\epsilon_{\text{geom}}$ of the HNLs in the pseudorapidity range $|\eta|<2.5$ in LO using the model HeavyN Degrande:2016aje . We found $\epsilon_{\text{geom}}\approx 0.5$ for the mass range $m_{N}\lesssim 20\text{ GeV}$ and $E_{N}\approx 80\text{ GeV}$.

In Fig. 6 we show the parameter space for the HNLs mixing with $\nu_{\mu}$ that can be optimally probed by the long DV scheme (see Sec. II).

We see that the domain where the long DV scheme has good potential corresponds to the masses $m_{N}<10\text{ GeV}$ and the mixing angles $U^{2}\gtrsim 10^{-9}$.

Simulations. To find the efficiency for the HNLs mixing with $\nu_{e/\mu}$, we used MadGraph5 Alwall:2014hca with the model HeavyN Degrande:2016aje . For simulating decays of $\tau$ lepton, we used taudecay_UFO model Hagiwara:2012vz . For the mixing with $\nu_{e/\mu}$ we simulated the process $p+p\to W,\ W\to l+N$, where $l=e$ for the mixing with $\nu_{e}$ and $l=\mu$ for the mixing with $\nu_{\mu}$, with subsequent decay $N\to\mu^{+}+\mu^{-}+\nu/\bar{\nu}_{l}$. In the case of the mixing with $\nu_{\tau}$, we simulated the process $p+p\to W,W\to\tau+N$ with subsequent decays $N\to\mu^{+}+\mu^{-}+\nu_{\tau}/\bar{\nu}_{\tau}$ and $\tau\to l+\bar{\nu}_{l}+\nu_{\tau}$, where $l=e/\mu$.

Using the selection criteria for the long DV scheme, we computed the selection efficiencies. They were found to be almost independent of the mass of the HNL in the mass range $1\text{ GeV}<m_{N}<20\text{ GeV}$. We give their values in Table 1.

The suppression of the efficiency for mixing with $\nu_{\tau}$ is due mainly to the reconstruction of the prompt $\tau$ event. Indeed, the amount of the leptons produced in the decay $\tau\to l\bar{\nu}_{l}\nu_{\tau}$ and passing the $p_{T}$ selection criterion for the prompt leptons is $\approx 0.1$.

For the average momentum we found $p_{N}\approx 70\text{ GeV}$ and $p_{N}\approx 180\text{ GeV}$ for the realistic and optimistic estimates correspondingly.

Comparison with other schemes. Let us compare the sensitivity of the long DV search scheme to the HNLs with a scheme from Cottin:2018nms ; Cottin:2018kmq that uses inner trackers at ATLAS to search for DVs events (c.f. Boiarska:2019jcw ). Owing to its smaller transverse displacement $l_{\mathrm{max}}=0.3\text{ m}$ we call it the “short DV scheme”. For the estimation of the sensitivity of the short DV scheme we use parameterized efficiencies $\epsilon(m_{N},U^{2})$ provided by the authors of Cottin:2018nms . The comparison of the sensitivities is given in Fig. 7. We show both optimistic and realistic estimate of the sensitivity of the long DV scheme. We also show the sensitivity of the SHiP experiment from SHiP:2018xqw that serves for an illustration of the sensitivity reach of Intensity Frontier experiments.

The long DV scheme allows to search for HNLs in the unexplored region of the parameter space that is not accessible to other Intensity Frontier experiments or other LHC searches. Its difference in the sensitivity with the short DV scheme is due to three reasons. First, for masses $m_{N}\lesssim 10\text{ GeV}$ the decay probability for both the schemes is in the linear regime (see Sec. II), and therefore the long DV scheme gets the benefit from the $10$ times larger length of the decay volume $l_{\mathrm{max}}$. Second, for the masses $5\text{ GeV}\lesssim m_{N}\lesssim 10\text{ GeV}$ there is a drop of the overall efficiency for the short DV scheme. This is caused by the selection criteria on the reconstructed invariant mass of the DV, $m_{\text{DV}}>5\text{ GeV}$, and the charged tracks, $N_{\text{trk}}\geqslant 4$, that are needed to remain in the background free region Aaboud:2017iio . Third, because of absence of the hadronic background the long DV scheme can probe the parameter space $m_{N}\lesssim 5\text{ GeV}$, which is not reachable by the short DV scheme.

Nevertheless, both the schemes are complementary to each other and provide a cross-check in the mass region $5\text{ GeV}<m_{N}<15\text{ GeV}$.

III.2 Chern-Simons portal

Chern-Simons portal introduces a vector particle $X$ interacting with pseudo-Chern-Simons current of the SM gauge bosons Antoniadis:2009ze ; Alekhin:2015byh :

[TABLE]

We can add the interaction of the $X$ boson with SM leptons in the form

[TABLE]

where $g_{Xll}$ is a dimensionless constant.333The coupling $g_{Xll}$ can be generated effectively by the interaction (6) or be an effect of new physics.

Let us consider the case when $c_{\gamma},c_{Z}\ll c_{W}$. Then the production of the $X$ particle in $pp$ collisions goes through the $XWW$ vertex, while the decay goes through the vertex (7) down to very small couplings $g_{Xll}^{2}\simeq 10^{-7}$ for the $X$ bosons as heavy as $m_{X}\simeq 40\text{ GeV}$, see Appendix A. These vertices are parametrically independent, and for particular values of $g_{Xll}$ it is possible to probe the parameter space in the optimal domain for the long DV scheme. The process of interest is

[TABLE]

The lepton $l$ produced in the $W$ decay can be triggered as a prompt lepton, while the muon pair from the decay of the $X$ boson can be reconstructed as displaced muons, which meets the selection criteria of a DV event within the long DV scheme.

To find the selection efficiency and the energy spectrum of the $W$ bosons, we implemented the model of the $X$ boson (6), (7) into the MadGraph using FeynRules Alloul:2013bka ; Christensen:2008py . The model is publicly available ChernSimonsFeynRules . We simulated the processes $p+p\to e^{+}/\mu^{+}+\nu_{e/\mu}+X$ (plus the charge conjugated final states) with subsequent decays $X\to\mu^{+}\mu^{-}$. We have found that the overall efficiency is $\epsilon\approx 2.3\cdot 10^{-2}$ for $m_{X}$ ranging from $1\text{ GeV}$ to $20\text{ GeV}$. The average momentum of the $X$ boson $p_{X}\approx 40\text{ GeV}$.

The sensitivity to the Chern-Simons portal is shown in Fig. 8. We conclude that the long DV scheme can probe masses up to $m_{X}\simeq 30\text{ GeV}$ and couplings down to $c_{W}^{2}\simeq 10^{-9}$. We note that the probed parameter space is well below the current experimental bound on $c_{W}$, which is $c_{W}^{2}\lesssim 10^{-3}(m_{X}/1\text{ GeV})^{2}$ Alekhin:2015byh .

IV Conclusion

In this paper we proposed a new method of searching for long-lived particles at LHC (“the long DV scheme”) that utilizes the muon tracker at the CMS experiment. It uses a prompt lepton and a displaced muon pair to reconstruct a displaced vertex event. The scheme is optimal for probing the parameter space of the LLPs with the decay lengths $l_{\mathrm{dec}}\gtrsim 3\text{ m}$. We demonstrated the potential of the scheme using two exemplary models: heavy neutral lepton (HNL) and Chern-Simons portal. For the HNLs we made a comparison between the long DV scheme and other planned searching schemes at ATLAS/CMS, see e.g. Cottin:2018nms ; Boiarska:2019jcw .

Our conclusions are the following:

• –

For the HNLs, the long DV scheme can probe the parameter space in the mass range $m_{N}\lesssim 20\text{ GeV}$ and down to the mixing angles $U^{2}\sim 10^{-8}$ (when mixing with $\nu_{\mu}$).

• –

The long DV scheme has a unique opportunity to probe the LLPs that decay predominantly into leptons, which is demonstrated by the example of the Chern-Simons portal;

• –

The long DV serach scheme has a sufficiently low SM background even for LLPs with the masses $m\lesssim 5\text{ GeV}$, which is unavailable for DV search schemes at the LHC that look for hadronic decay products. In the case of HNLs this gives a possibility to probe the parts of the parameter space that have not been probed by previous experiments and are outside the reach of the planned Intensity Frontier experiments.

Acknowledgements.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (GA 694896, 758316) and from the Netherlands Science Foundation (NWO/OCW).

Appendix A Chern-Simons portal

Decay width of the $W$ boson into $X$ boson.

The matrix element of the process shown in Fig. 9 is

[TABLE]

where $\epsilon(p)$ is the polarization vector. In the limit $m_{X,f,f^{\prime}}\ll m_{W}$ the decay width is

[TABLE]

Using this decay width, for the branching ratio of the process $W\to X+l+\nu_{l}$, where $l=e,\mu$ we obtain

[TABLE]

Tree-level decays generated by $c_{W}$ coupling. The vertex $c_{W}$ generates the tree level decay process $X\to ff^{\prime}f^{\prime\prime}f^{\prime\prime\prime}$. Based on dimensional grounds, we can estimate the corresponding decay width as

[TABLE]

For the ratio of this decay width to the decay width into two muons, $\Gamma_{X\to\mu\mu}\sim c_{W}^{2}g_{X\mu\mu}^{2}m_{X}/(2\pi)$, we have

[TABLE]

which means that for $m_{X}\lesssim 40\text{ GeV}$ the process $X\to ff^{\prime}f^{\prime\prime}f^{\prime\prime\prime}$ is not relevant for $g_{X\mu\mu}^{2}>10^{-7}$.