Phenomenology of TeV-scale scalar leptoquarks in the EFT

We examine new aspects of leptoquark (LQ) phenomenology using effective field theory (EFT). We construct a complete set of leading effective operators involving SU(2) singlets scalar LQ and the Standard Model fields up to dimension six. We show that, while the renormalizable LQ-lepton-quark interaction Lagrangian can address the persistent hints for physics beyond the Standard Model in the B-decays $\overline{B}\to D^{(*)}\tau \overline{\nu }$, $\overline{B}\to \overline{K}{\ell }^{+}{\ell }^{-}$ and in the measured anomalous magnetic moment of the muon, the LQ higher dimensional effective operators may lead to new interesting effects associated with lepton number violation. These include the generation of one-loop and two-loops sub-eV Majorana neutrino masses, mediation of neutrinoless $\mathrm{double}\text{−}\beta$ decay and novel LQ collider signals. For the latter, we focus on third generation LQ (${\varphi }_3$) in a framework with an approximate $Z_3$ generation symmetry and show that one class of the dimension five LQ operators may give rise to a striking asymmetric same-charge ${\varphi }_3{\varphi }_3$ pair-production signal, which leads to low background same-sign leptons signals at the LHC. For example, with $M_{{\varphi }_3}\sim 1\mathrm{TeV}$ and a new physics scale of $\mathrm{\Lambda }\sim 5\mathrm{TeV}$, we expect at the 13 TeV LHC with an integrated luminosity of $300{\mathrm{fb}}^{-1}$, about 5000 positively charged ${\tau }^{+}{\tau }^{+}$ events via $\mathit{p}\mathit{p}\to {\mathit{\varphi }}_{\mathbf{3}}{\mathit{\varphi }}_{\mathbf{3}}\to {\mathit{\tau }}^{+}{\mathit{\tau }}^{+}+\mathbf{2}·{\mathit{j}}_{\mathit{b}}$ ($j_b=b\text{−}\mathrm{jet}$), about 500 negatively charged ${\tau }^{-}{\tau }^{-}$ events with a signature $\mathit{p}\mathit{p}\to {\mathit{\varphi }}_{\mathbf{3}}{\mathit{\varphi }}_{\mathbf{3}}\to {\mathit{\tau }}^{-}{\mathit{\tau }}^{-}+\mathbf{4}·\mathit{j}+\mathbf{2}·{\mathit{j}}_{\mathit{b}}$ ($j=\mathrm{light}$ jet) and about 50 positively charged ${\ell }^{+}{\ell }^{+}$ events via $\mathit{p}\mathit{p}\to {\mathit{\ell }}^{+}{\mathit{\ell }}^{+}+\mathbf{2}·{\mathit{j}}_{\mathit{b}}+{\cancel{\mathit{E}}}_{\mathit{T}}$ for any of the three charged leptons, ${\ell }^{+}{\ell }^{+}=e^{+}{e}^{+},{\mu }^{+}{\mu }^{+},{\tau }^{+}{\tau }^{+}$. It is interesting to note that, in the LQ EFT framework, the expected same-sign lepton signals have a rate which is several times larger than the QCD LQ-mediated opposite-sign leptons signals, $gg,q\overline{q}\to {\varphi }_3{\varphi }_3^{*}\to {\ell }^{+}{\ell }^{-}+X$. We also consider the same-sign charged lepton signals in the LQ EFT framework at higher energy hadron colliders such as a 27 TeV HE-LHC and a 100 TeV FCC-hh.

Figure 1

Tree-level graphs in the underlying heavy theory that generate the dimension five effective operator $\overline{d}{d}^c{\varphi }^2$. $\mathrm{\Phi }$ and $\mathrm{\Psi }$ stand for a heavy scalar and heavy fermion, respectively, with quantum numbers $\mathrm{\Phi }(6,1,-\frac{2}{3})$ and $\mathrm{\Psi }(1,1,0)$ or $\mathrm{\Psi }(8,1,0)$ (see text).

Figure 2

Tree-level graphs in the underlying heavy theory that generate the dimension five effective operator $\overline{\ell }d\tilde{H}{\varphi }^{*}$. $\mathrm{\Phi }$ and $\mathrm{\Psi }$ stand for a heavy scalar and heavy fermion, respectively, with quantum numbers $\mathrm{\Phi }(3,2,\frac{1}{6})$ and $\mathrm{\Psi }(1,1,0)$, $\mathrm{\Psi }(1,3,0)$ or $\mathrm{\Psi }(3,2,-\frac{5}{6})$ (see text).

Figure 3

The one-loop and two-loops diagrams (a) and (b) which generates a Majorana mass term with the Yukawa-like LQ-quark-lepton interaction ($\propto y_{q\ell }^L$) and the dimension five operators $\overline{\ell }d\tilde{H}{\varphi }^{*}$ and $\overline{d}{d}^c{\varphi }^2$ (with the coupling strength $f_{\ell d\varphi H}$ and $f_{d^2{\varphi }^2}$, respectively). See also text.

Figure 4

Tree-level graph that generates neutrinoless double beta decay via the dimension five operator $\overline{d}{d}^c{\varphi }^2$. See also text.

Figure 5

Pair-production cross sections of the down-type LQ ${\varphi }_3$ at the 13 TeV LHC with ${\mathrm{\Lambda }}_{d^2{\varphi }^2}=5\mathrm{TeV}$: $pp\to {\varphi }_3{\varphi }_3$ (dashed line), $pp\to {\varphi }_3{\varphi }_3^{*}$ (solid line) and $pp\to {\varphi }_3^{*}{\varphi }_3^{*}$ (dashed-dot line) (see also text).

Figure 6

Pair-production cross sections of the down-type and up-type LQ, as a function of the LQ mass, for a NP scale $\mathrm{\Lambda }=5\mathrm{TeV}$, at a 27 TeV HE-LHC (upper plot) and a 100 TeV FCC-hh (lower plot): the QCD cross section via $gg,q\overline{q}\to {\varphi }_3{\varphi }_3^{*}$ (solid line), the same-charge up-type LQ pair-production cross section via $uu\to {\varphi }_3{\varphi }_3$ (dashed line) and the same-charge down-type LQ pair-production cross section via $dd\to {\varphi }_3{\varphi }_3$ (dashed-dotted line). See also text.

Figure 7

Same as Fig. 6 for $\mathrm{\Lambda }=10\mathrm{TeV}$.

Figure 8

Same as Fig. 6 for $\mathrm{\Lambda }=15\mathrm{TeV}$.