Quantitative study on helicity inversion in Majorana neutrino decays at the LHC

We report an analytical and numerical investigation into the impact of helicity inversion in LHC processes that do not conserve lepton number ($L$). As a case study, we focus on the production and decay of Majorana neutrinos ($N$) through on- and off-shell $W$ bosons in the phenomenological type I seesaw model. Using the Monte Carlo event generator madgraph5_amc@nlo in conjunction with the heavyn model libraries, we perform exact matrix element (ME) computations without the narrow width approximation. Despite helicity inversion appearing explicitly in MEs, we report the absence of helicity suppression of $L$-violating collider observables for $1\to 4$ and $2\to 4$ processes that are dominated by resonant $N$ production. We attribute this incongruity to the different scalings of 4-momenta and squared 4-momenta in MEs and squared MEs, with exact cancelations occurring in the latter when $N$ goes on-shell in the small-width limit. In off-shell regimes, total suppression/enhancement of $L$ violation can emerge. Implications for other neutrino mass models are discussed.

Figure 1

Born-level, diagrammatic representation of the (a) $L$-conserving process $u\overline{d}\to W^{+}\to N{\ell }_1^{+}\to {\ell }_1^{+}{\ell }_2^{-}{f}_1\overline{f_2}$, and (b) its $L$-violating analogue $u\overline{d}\to W^{+}\to N{\ell }_1^{+}\to {\ell }_1^{+}{\ell }_2^{+}\overline{f_1}{f}_2$. Interfering diagrams not shown. Drawn with jaxodraw [51].

Figure 2

The $W^{+}\to e_R^{+}{N}_R$ and $W^{+}\to e_R^{+}{N}_L$ branching ratio as a function of $m_N$ [GeV], as computed numerically from polarized matrix elements (solid) and analytically (dashed).

Figure 3

(a) Decay rate asymmetry between the $L$-conserving $W^{+}\to e_1^{+}N\to e_1^{+}{e}_2^{-}c\overline{s}$ $({\mathrm{\Gamma }}_{\mathrm{LNC}})$ and $L$-violating $W^{+}\to e_1^{+}N\to e_1^{+}{e}_2^{+}\overline{c}s$ $({\mathrm{\Gamma }}_{\mathrm{LNV}})$ processes as a function of heavy neutrino mass $m_N$ [GeV] for representative active-sterile neutrino mixing $|V_{eN}|$. (b) Same, but for the hadron-level, cross section asymmetry between the $L$-conserving $pp(u\overline{d})\to e_1^{+}N\to e_1^{+}{e}_2^{-}c\overline{s}$ $({\sigma }_{\mathrm{LNC}})$ and $L$-violating $pp(u\overline{d})\to e_1^{+}{e}_2^{+}\overline{c}s$ $({\sigma }_{\mathrm{LNV}})$ processes at $\sqrt{s}=13\mathrm{TeV}$. Also shown are statistical MC uncertainty bands ($\delta A_{\mathrm{MC}}$).

Figure 4

(a) Same as Fig. 3 but for a total width ${\mathrm{\Gamma }}_N$ that varies according to the Lagrangian given in Sec. 2 (default) as well as at fixed widths of ${\mathrm{\Gamma }}_N=100\mathrm{MeV}$ and 10 GeV. For all computations, $|V_{e4}{|}^2={10}^{-2}$ is assumed with $|V_{\mu 4}{|}^2,|V_{\tau 4}{|}^2=0$. (b) Same as (a) but for an extended mass range. (c,d) Same as Fig. 3 but for the assumptions of (a,b) respectively.