Improved bounds on the heavy neutrino productions at the LHC

The Majorana neutrino in the type-I seesaw and the pseudo-Dirac neutrinos in the inverse seesaw can have sizable mixings with the light neutrinos in the standard model, through which the heavy neutrinos can be produced at the LHC. In producing the heavy neutrinos, we study a variety of initial states such as quark-quark, quark-gluon and gluon-gluon as well as photon mediated processes. For the Majorana heavy neutrino production, we consider a same-sign dilepton plus dijet as the signal events. Using the recent ATLAS and CMS data at $\sqrt{s}=8\mathrm{TeV}$ with 20.3 and $19.7{\mathrm{fb}}^{-1}$ luminosities, respectively, we obtain direct upper bounds on the light-heavy neutrino mixing angles. For the pseudo-Dirac heavy neutrino production we consider the final sate with a trilepton plus missing energy as the signal events. Using the recent anomalous multilepton search by CMS at $\sqrt{s}=8\mathrm{TeV}$ with $19.5{\mathrm{fb}}^{-1}$ luminosity, we obtain upper bounds on the mixing angles. Taking the varieties of initial states into account, the previously obtained upper bounds on the mixing angles have been improved. We scale our results at the 8 TeV LHC to obtain a prospective search reach at the 14 TeV LHC with high luminosities.

Figure 1

Feynman diagram for $N\ell$ production from the $q\overline{q^{\prime }}$ annihilation.

Figure 2

Feynman diagrams for $N\ell j$ production from the $q\overline{q^{\prime }}$ annihilation.

Figure 3

Feynman diagrams for $N\ell j$ production from the $qg$ fusion.

Figure 4

The left panel shows the cross sections as a function of $m_N$ normalized by the square of the mixing angle for the $N\ell j$ final state at the $p_T^j>10$ (dashed), $p_T^j>20$ (dot-dashed) and $p_T^j>30\mathrm{GeV}$ (dotted) from the $q\overline{q^{\prime }}$ and $qg$ initial states and the $N\ell$ final state from the $qq$ initial states (solid) at the 8 TeV LHC. The right panel is the same as the left panel but at the 14 TeV LHC.

Figure 5

The decomposition of the cross section for the individual initial states for different $p_T^j$ cuts such that $p_T^j>10$ (solid), $p_T^j>20$ (dashed) and $p_T^j>30\mathrm{GeV}$ (dot-dashed). The cross sections at the 8 TeV LHC are shown in the left panel, whereas those at the 14 TeV LHC are shown in the right panel.

Figure 6

Sample Feynman diagrams for $N\ell jj$ production processes from the $q\overline{q^{\prime }}$ initial state.

Figure 7

Sample Feynman diagrams for $N\ell jj$ production processes from the $qg$ fusion.

Figure 8

Sample Feynman diagrams for $N\ell jj$ production processes from the $gg$ fusion.

Figure 9

The left panel shows the cross sections as a function of $m_N$ normalized by the square of the mixing angle for the $N\ell jj$ final state for $p_T^j>10\mathrm{GeV}$ (dashed), $p_T^j>20\mathrm{GeV}$ (dot-dashed) and $p_T^j>30\mathrm{GeV}$ (dotted) from the $q\overline{q^{\prime }}$, $qg$ and $gg$ initial states and the $N\ell$ final state from the $q\overline{q^{\prime }}$ initial state (solid) at the 8 TeV LHC. The right panel shows the results for the 14 TeV LHC.

Figure 10

The decomposition of the cross section for the individual initial states for different $p_T^j$ cuts such that $p_T^j>10$ (solid), $p_T^j>20$ (dashed) and $p_T^j>30\mathrm{GeV}$ (dot-dashed). The cross sections at the 8 TeV are shown in the left panel, whereas those at the 14 TeV are shown in the right panel.

Figure 11

The elastic or inelastic process for the $N\ell j$ final state.

Figure 12

The deep-inelastic processes for the $N\ell jj$ final state mediated by a photon.

Figure 13

The figure shows the production cross section of the heavy neutrino as a function of $m_N$ and normalized by the square of the mixing angle for the different photon mediated processes at the 14 TeV LHC. The solid line stands for the $N\ell$ final state for the $q\overline{q^{\prime }}$ initial state. The elastic process for different $p_T^j$ values are shown by the dashed lines. The inelastic processes are represented by the dotted lines. The deep-inelastic process (QED 2-jet) is depicted by the dot-dashed lines.

Figure 14

The first and second rows show the $p_T$ and $\eta$ distributions of the lepton produced in the $N\ell$ final state from the $q\overline{q^{\prime }}$ zero-jet processes. The third row shows the final state invariant mass $(m_{N\ell })$ distributions. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 15

The first and second rows show the $p_T$ and $\eta$ distributions of the lepton produced in the $N\ell j$ final state from the $q\overline{q^{\prime }}$ and $qg$ one-jet processes. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 16

The first and second rows show the $p_T$ and $\eta$ distributions of the jet produced in the $N\ell j$ final state from the $q\overline{q^{\prime }}$ and $qg$ one-jet processes. The third row shows the final state invariant mass $(m_{N\ell j})$ distributions. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 17

The first and second rows show the $p_T$ and $\eta$ distributions of the lepton produced in the $N\ell jj$ final state from the $q\overline{q^{\prime }}$, $qg$ and $gg$ initial states. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 18

The first and second rows show the $p_T$ and $\eta$ distributions of the nonleading jet produced in the $N\ell jj$ final state from the $q\overline{q^{\prime }}$, $qg$ and $gg$ initial states. The third and fourth rows show the same for the leading jet. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 19

The final state invariant mass $(m_{N\ell j_1{j}_2})$ distributions produced in the $N\ell jj$ final state from the $q\overline{q^{\prime }}$, $qg$ and $gg$ initial states. The left panel shows $m_N=100\mathrm{GeV}$, whereas the right one shows $m_N=500\mathrm{GeV}$.

Figure 20

The first and second rows show the $p_T$ and $\eta$ distributions of the lepton produced in the $N\ell j$ final state from the photon mediated elastic processes. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 21

The first and second rows show the $p_T$ and $\eta$ distributions of the jet produced in the $N\ell j$ final state from the photon mediated elastic processes. The third row shows the final state invariant mass $(m_{N\ell j})$ distributions. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 22

The first and second rows show the $p_T$ and $\eta$ distributions of the lepton produced in the $N\ell j$ final state from the photon mediated inelastic processes. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 23

The first and second rows show the $p_T$ and $\eta$ distributions of the jet produced in the $N\ell j$ final state from the photon mediated inelastic processes. The third row shows the final state invariant mass $(m_{N\ell }j)$ distributions. The left column stands for $m_N=100\mathrm{GeV}$, whereas the right one is for $m_N=500\mathrm{GeV}$.

Figure 24

The first and second rows show the $p_T$ and $\eta$ distributions of the lepton produced in the $N\ell jj$ final state from the photon mediated deep-inelastic processes. The left column is for $m_N=100\mathrm{GeV}$, whereas the right one stands for $m_N=500\mathrm{GeV}$.

Figure 25

The first and second rows show the $p_T$ and $\eta$ distributions of the nonleading jet produced in the $N\ell jj$ final state from photon mediated deep-inelastic processes. The third and fourth rows show the same for the leading jet. The left column is for $m_N=100\mathrm{GeV}$, whereas the right one stands for $m_N=500\mathrm{GeV}$.

Figure 26

The figure shows the final state invariant mass $(m_{N\ell j_1{j}_2})$ distributions produced in the $N\ell jj$ final state from the photon mediated deep-inelastic processes. The left panel shows $m_N=100\mathrm{GeV}$, whereas the right one is $m_N=500\mathrm{GeV}$.

Figure 27

The figure shows the upper bounds of the square on the mixing angles as a function of $m_N$ using the ATLAS data at the 8 TeV [18]. The zero-jet (0-jet8, $20.3{\mathrm{fb}}^{-1}$) result is compared with the ATLAS bounds (ATLAS8). The improved results with one jet [dashed, ($0+1$)-jet@8 TeV, $20.3{\mathrm{fb}}^{-1}$] and two jets [thick, solid, ($0+1+2$)-jet@8, $20.3{\mathrm{fb}}^{-1}$] are shown with respect to the bounds obtained by ATLAS [18]. These bounds are compared to (i) the ${\chi }^2$-fit to the LHC Higgs data [21] (Higgs); (ii) those from a direct search at LEP [22] (L3), valid only for the electron flavor; (iii) CMS limits from $\sqrt{s}=8\mathrm{TeV}$ LHC data [19] (CMS8), for a heavy Majorana neutrino of the muon flavor; and (iv) the indirect limit from a global fit to the electroweak precision data [23, 24, 25] (EWPD), for both electron (solid, EWPD-$e$) and muon (dotted, EWPD-$\mu$) flavors. The shaded region is excluded.

Figure 28

The figure shows the search reach for the square of the mixing angles as a function of $m_N$ at the 14 TeV LHC using the ATLAS data at 8 TeV [18]. In this plot, we give a prospective search reach for 14 TeV. The results with zero jets (0-jet@14 TeV, $20.3{\mathrm{fb}}^{-1}$), one jet [($0+1$)-jet@14 TeV, $20.3{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@14, $20.3{\mathrm{fb}}^{-1}$] are shown at $20.3{\mathrm{fb}}^{-1}$. The prospective results with zero jets (0-jet@14 TeV, $300{\mathrm{fb}}^{-1}$), one jet [($0+1$)-jet@14 TeV, $300{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@14 TeV, $300{\mathrm{fb}}^{-1}$] are also plotted at $300{\mathrm{fb}}^{-1}$ luminosity. The prospective results with zero jets (0-jet@14 teV, $1000{\mathrm{fb}}^{-1}$), one jet [($0+1$)-jet@14 TeV, $1000{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@14 TeV, $1000{\mathrm{fb}}^{-1}$] are plotted at $1000{\mathrm{fb}}^{-1}$ and compared to (i) the ${\chi }^2$-fit to the LHC Higgs data [21] (Higgs); (ii) those from a direct search at LEP [22] (L3), valid only for the electron flavor; (iii) CMS limits from $\sqrt{s}=8\mathrm{TeV}$ LHC data [19] (CMS8), for a heavy Majorana neutrino of the muon flavor; and (iv) the indirect limit from a global fit to the EWPD [23, 24, 25], for both electron (solid, EWPD-$e$) and muon (dotted, EWPD-$\mu$) flavors. The shaded region is excluded.

Figure 29

The figure shows the upper bounds on the square of the mixing angles as a function of $m_N$ using the CMS data at the 8 TeV [19]. The zero-jet (0-jet@8 TeV, $19.7{\mathrm{fb}}^{-1}$) result is compared with the CMS bounds (CMS8). The improved results with one jet [($0+1$)-jet@8 TeV, $19.7{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@8 TeV, $19.7{\mathrm{fb}}^{-1}$[ are shown with respect to the CMS data from Ref. [19]. The bounds are compared to (i) the ${\chi }^2$-fit to the LHC Higgs data [21] (Higgs); (ii) those from a direct search at LEP [22] (L3), valid only for the electron flavor; (iii) ATLAS limits from $\sqrt{s}=8\mathrm{TeV}$ LHC data [18] (ATLAS 8), for a heavy Majorana neutrino of the muon flavor; and (iv) the indirect limit from a global fit to the EWPD [23, 24, 25], for both electron (solid, EWPD-$e$) and muon (dotted, EWPD-$\mu$) flavors. The shaded region is excluded.

Figure 30

The figure shows the prospective search reach for the square of the mixing angles as a function of $m_N$ at the 14 TeV LHC using the CMS data at the 8 TeV [19]. Zero jets (0-jet@14 TeV, $20.3{\mathrm{fb}}^{-1}$), one jet [($0+1$)-jet@14 TeV, $20.3{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@14 TeV, $20.3{\mathrm{fb}}^{-1}$] are shown at the $20.3{\mathrm{fb}}^{-1}$. The prospective results with zero jets (0-jet@14 TeV, $300{\mathrm{fb}}^{-1}$), one jet [($0+1$)-jet@14 TeV, $300{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@14 TeV, $300{\mathrm{fb}}^{-1}$] are also plotted at $300{\mathrm{fb}}^{-1}$ luminosity. The prospective results with zero jets (0-jet@14 TeV, $1000{\mathrm{fb}}^{-1}$), one jet [($0+1$)-jet@14 TeV, $1000{\mathrm{fb}}^{-1}$] and two jets [($0+1+2$)-jet@14 TeV, $1000{\mathrm{fb}}^{-1}$] are plotted at $1000{\mathrm{fb}}^{-1}$ and compared to (i) the ${\chi }^2$-fit to the LHC Higgs data [21] (Higgs); (ii) those from a direct search at LEP [22] (L3), valid only for the electron flavor; (iii) CMS limits from $\sqrt{s}=8\mathrm{TeV}$ LHC data [19] (CMS8), for a heavy Majorana neutrino of the muon flavor; and (iv) the indirect limit from a global fit to the EWPD [23, 24, 25], for both electron (solid, EWPD-$e$) and muon (dotted, EWPD-$\mu$) flavors. The shaded region is excluded.

Figure 31

The 95% C.L. upper limits on the light-heavy neutrino mixing angles $|V_{\ell N}{|}^2$ as a function of the heavy Dirac neutrino mass $m_N$, derived from the CMS trilepton data at $\sqrt{s}=8\mathrm{TeV}$ LHC for $19.5{\mathrm{fb}}^{-1}$ luminosity [20]. The exclusion (shaded) regions are shown for two benchmark scenarios: (i) SF and (ii) FD, with two choices of the selection cut $m_{l^{+}{l}^{-}}<75\mathrm{GeV}$ (thick dotted) and $>105\mathrm{GeV}$ (thick solid). The previous results with the selection cut $m_{l^{+}{l}^{-}}<75\mathrm{GeV}$ (thick dot-dashed) and $>105\mathrm{GeV}$ (thick large-dashing) at the one-jet level are shown in this context from Ref. [28]. The corresponding conservative projected limits from $\sqrt{s}=14\mathrm{TeV}$ LHC data with $300{\mathrm{fb}}^{-1}$ integrated luminosity are shown by thin solid lines ($SF14_f^{105}$ and $FD14_f^{105}$) above the $Z$-pole. Some relevant existing upper limits (all at 95% C.L.) are also shown for comparison: (i) from a ${\chi }^2$-fit to the LHC Higgs data [21] (Higgs); (ii) from a direct search at LEP [22] (L3), valid only for the electron flavor; (iii) ATLAS limits from $\sqrt{s}=7\mathrm{TeV}$ LHC data [17] (ATLAS7) and $\sqrt{s}=8\mathrm{TeV}$ LHC data [18] (ATLAS8), valid for a heavy Majorana neutrino of the muon flavor; (iv) CMS limits from $\sqrt{s}=8\mathrm{TeV}$ LHC data [19] (CMS8), for a heavy Majorana neutrino of the muon flavor; and (v) the indirect limit from a global fit to the EWPD [23, 24, 25], for both electron (solid) and muon (dotted) flavors. The data for the one-jet case from Ref. [28] are shown by $S{F}_i^{75}$, $S{F}_i^{105}$, $F{D}_i^{75}$ and $F{D}_i^{105}$ (large dashed lines). The shaded region is excluded.