Dimension-seven operators in the standard model with right handed neutrinos

In this article, we consider the standard model extended by a number of (light) right-handed neutrinos, and assume the presence of some heavy physics that cannot be directly produced, but can be probed by its low-energy effective interactions. Within this scenario, we obtain all the gauge-invariant dimension-7 effective operators, and determine whether each of the operators can be generated at tree level by the heavy physics, or whether it is necessarily loop generated. We then use the tree-generated operators, including those containing right-handed neutrinos, to put limits on the scale of new physics $\mathrm{\Lambda }$ using low-energy measurements. We also study the production of same-sign dileptons at the Large Hadron Collider and determine the constraints on the heavy physics that can be derived from existing data, as well as the reach in probing $\mathrm{\Lambda }$ expected from future runs of this collider.

Figure 1

Leading Feynman diagrams that contribute to $pp\to \ell \ell jj$ at the LHC; the $eeWW$ vertex [Eq. (16)] is generated by ${\mathcal{O}}_{\ell \ell }$ in Eq. (17).

Figure 2

Production cross section for two same-sign leptons and two jets ($\ell \ell jj$) as a function of $\mathrm{\Lambda }$ (GeV) at LHC with $E_{\mathrm{CM}}=14\mathrm{TeV}$ (left) and 7,8 TeV (right) in green and blue, respectively.

Figure 3

Distributions of the invariant mass of leptons $M_{\ell \ell }$ (top) and transverse mass $H_T$ (bottom), for the $\ell \ell jj$ signal events at LHC with $E_{\mathrm{cm}}=14\mathrm{TeV}$ (left) and $E_{\mathrm{cm}}=8\mathrm{TeV}$ (right). We took $\mathrm{\Lambda }=100\mathrm{GeV}$ [see text and Eq. (18)]. Subprocesses $\overline{e}\overline{e}jj$ (red dots and lilac histograms) and $eejj$ (blue crosses and green histograms) are shown separately.

Figure 4

$E_{\cancel{T}}$ distribution for $t\overline{t}$ events at the LHC with two leptons (light green) and two leptons and two jets (red); dark green regions correspond to the overlap of the two distributions. Left: $E_{\mathrm{cm}}=14\mathrm{TeV}$. Right: $E_{\mathrm{cm}}=8\mathrm{TeV}$.

Figure 5

$M_{\ell \ell }$ distribution of the leptons for $t\overline{t}$ events at LHC. The distributions for $\ell \ell$ and $\ell \ell 2j$ events are shown in red and light green, respectively (dark green regions correspond to the overlap of the two distributions). Left: $E_{\mathrm{cm}}=14\mathrm{TeV}$. Right: $E_{\mathrm{cm}}=8\mathrm{TeV}$.

Figure 6

$H_T$ for $t\overline{t}$ events at LHC. The distributions for $\ell \ell$ and $\ell \ell 2j$ events are shown in red and light green, respectively (dark green regions correspond to the overlap of the two distributions). Left: $E_{\mathrm{cm}}=14\mathrm{TeV}$. Right: $E_{\mathrm{cm}}=8\mathrm{TeV}$.

Figure 7

Feynman diagrams generated by the operator ${\mathcal{O}}_{\ell \ell }$ and which contribute to the hadronically quiet trilepton channel $pp\to ee\overline{e}{\nu }_e$.

Figure 8

Tree-level graphs that can generate the operators ${\mathcal{O}}_1$ and ${\mathcal{O}}_3$ by the exchange of a heavy fermion (left) or scalar (right), both isotriplets with unit hypercharge (denoted by the thick internal lines).

Figure 9

Invariant mass distribution of the lepton with jets at LHC with $E_{\mathrm{cm}}=14\mathrm{TeV}$. The red dots (on the lilac histogram) correspond to the $\overline{e}\overline{e}jj$ final state; while the blue crosses (on the green histogram) correspond to the $eejj$ final state (the green area corresponds to regions where these distributions overlap).

Figure 10

$Z$-invisible decay limit on neutrino mass $m_{\nu }$ versus the new physics scale $\mathrm{\Lambda }$ plane derived from Eq. (28). The light red region and above is allowed by the operator $\overline{{\nu }^c}\cancel{Z}{P}_L\nu$, and the lilac region is allowed by $(\overline{{\nu }^c}{\sigma }^{\mu \nu }{P}_{L,R}\nu )Z_{\mu \nu }$.

Figure 11

$H$-invisible decay limit on neutrino mass $m_{\nu }$ versus the new physics scale $\mathrm{\Lambda }$ plane derived from Eq. (30). The shaded region is allowed by the operator $\overline{{\nu }^c}\nu |\varphi {|}^4$.

Figure 12

$W$-decay limit on neutrino mass $m_{\nu }$ versus the new physics scale $\mathrm{\Lambda }$ plane derived from Eq. (33). The yellow region and above is allowed by $W_{\mu }^{+}(\overline{{\nu }^c}{\partial }^{\mu }{P}_{R}e)$, the darker orange region and above is allowed by $(\overline{{\nu }^c}{\sigma }^{\mu \nu }{P}_{R}e){\partial }_{\mu }{W}_{\nu }^{+}$, and the orange region and above is allowed by $\overline{{\nu }^c}{\cancel{W}}^{+}{P}_{L}e$.

Figure 13

Shaded area: Region in the neutrino mass $m_{\nu }$ (GeV) versus the new physics scale $\mathrm{\Lambda }$ (GeV) plane allowed by the neutrino magnetic moment constraint [Eq. (35)].

Figure 14

Diagrams that generate operators of the form ${\psi }^2{D}^2{\phi }^2$ at tree level [thick lines denote particles with ($\mathrm{\Lambda }$) masses].

Figure 15

Tree-level graph that can generate operators of the form ${\psi }^{4}D$; the lines labeled “a” and “b” correspond to heavy particles (see text for details).