Rare few-body decays of the Standard Model Higgs boson

Updated manuscript after feedback from referees.

OLD: Precision tests of suppressed or forbidden processes in the SM ---such as flavour changing neutral currents (FCNC), or processes violating lepton flavour (LFV) or lepton flavour universality (LFUV)--- are powerful probes of BSM physics that have been mostly studied in b-quark decays so far~\cite{LHCb:2018roe,Belle-II:2018jsg}.
NEW: Precision tests of suppressed or forbidden processes in the SM ---such as flavour-changing neutral currents (FCNC), or processes violating lepton flavour (LFV) or lepton flavour universality (LFUV)--- are powerful probes of BSM physics. While highly competitive studies exist at low energies (e.g. in rare kaon decays, LFV searches with muons or taus, or electric dipole moment measurements), most investigations at multi-GeV mass scales have so far been mostly carried out exploiting b-quark decays at colliders~\cite{LHCb:2018roe,Belle-II:2018jsg}.

OLD: Our first result is that of the invisible two-body Higgs boson decay into a neutrino pair H→ν¯ν, which is infinitesimal in the SM (BR≈10−36) compared to the standard invisible (four-neutrino) H→ZZ⋆→4ν decay (BR≈0.1%)~\cite{Djouadi:2018xqq}. However, since the SM assumption of massless ν's is invalid, the H→ν¯ν decay can receive extra contributions depending on the mechanism of neutrino mass generation actually realized in nature.
NEW: Our first result concerns the invisible two-body Higgs boson decay into a neutrino pair, H→ν¯ν, proceeding via EW loops (Fig.~??? top left). In the SM with massless neutrinos, there is no tree-level Higgs-neutrino Yukawa coupling, and any amplitude for a scalar particle to decay into two massless fermions is forbidden by chirality (equivalently, a chirality flip is required and cannot be provided by massless fermions). However, in reality neutrinos are known to be massive, mν≲0.1~eV, and therefore such an amplitude is allowed in principle, although it is proportional to the tiny neutrino mass (a chirality flip) and further suppressed by the weak coupling and loop factors. We estimate this pure loop-induced branching ratio with MG5@NLO to be of order BR≈2×10−26, i.e., utterly negligible compared with the dominant invisible four-neutrino decay, H→ZZ⋆→4ν, which has a BR≈0.1%, obtained from BR(H→ZZ⋆)×BR(Z→ν¯ν)2~\cite{Djouadi:2018xqq}. For comparison, if neutrinos are Dirac fermions, a new right-handed neutrino field νR is added to the SM Lagrangian and they acquire mass via an ordinary Yukawa coupling (yν) through LYukawa∼yν¯L~HνR, where L is the lepton-handed lepton doublet and ~H is the hypercharge-conjugated Higgs field. After EW symmetry breaking, mν=yνv/√2 with v=246~GeV the Higgs vacuum expectation value, and the tree-level Higgs partial width into a neutrino pair can be derived with the usual fermionic formula, Γ(H→ν¯ν)=GFmHm2ν4√2π(1−4m2νm2H)3/2, which for mν≲0.1~eV yields Γ(H→ν¯ν)≲8.2×10−25~GeV, and therefore BR(H→ν¯ν)=Γ/ΓtotH≈2.0×10−22, using ΓtotH=4.1×10−3~GeV. Thus, a Dirac Yukawa-induced two-body decay (scaling as m2ν) is still larger than the loop-induced branching ratio quoted above, but anyway utterly negligible for phenomenology. The result scales as m2ν, so any smaller neutrino mass would further reduce the branching ratio. In an alternative case where neutrinos are Majorana fermions, and in the simplest assumption where the light Majorana masses arise from the Higgs mechanism so that the effective Higgs-neutrino coupling is still yν∝mν/v, the partial width has the same m2ν scaling but is reduced by a 1/2 symmetry factor relative to the Dirac formula because the two final-state Majorana neutrinos are identical. Hence ΓMajorana(H→ν¯ν)≈1/2ΓDirac(H→ν¯ν), and therefore Γ(H→ν¯ν)≲4.1×10−25~GeV and BR(H→ν¯ν)≲1×10−22. These estimates are valid for minimal Dirac- or Majorana-mass scenarios where the effective Higgs-neutrino coupling is proportional to mν/v. Non-minimal BSM constructions (new light mediators, large neutrino-Higgs mixing, or exotic operators) could (by construction) enhance H→ν¯ν, but such scenarios lie beyond the minimal SM-like Yukawa assumption and must be treated case by case.

OLD (Table 1 row):H→ν+¯¯¯ν7.2×10−36 (this work)
NEW (Table 1 row): H→ν+¯¯¯ν2.0×10−26(this work)

Fig. 3 left has been updated as suggested and, in addition, we have corrected the H→ν¯ν curve as per the discussion above. Also the right plot of Fig. 3 has been corrected so that the H→ν¯ν histogram matches the changes discussed above.

OLD: Table 3 last column: -- \; -- \; 1/10 \; -- \; -- \; 1/20 \; -- \; 1/10 \; 1/70 \; -- \; -- \; -- \; -- \;
NEW: Table 3 last column: --\; -- \; 1/100 \; -- \; -- \; 1/200 \; -- \; 1/100 \; 1/700 \; -- \; -- \; -- \; -- \;

OLD: A recent work~\cite{Martynenko:2024rfj} has computed higher-order corrections to these decays, finding consistent results with ours except for the H→γ+(e+e−)_1 channel that would have about 25 times larger decay rates.
NEW: A recent work~\cite{Martynenko:2024rfj} has computed higher-order corrections to these decays, finding consistent results with ours within a factor of three [footnote: Note that the value originally quoted in Ref.~\cite{Martynenko:2024rfj} had a typo that wrongly enhanced it by a factor of 25~\cite{MartinenkoPrivateComm}.]

OLD (Table 6 row): H→γ+(ee)_1 (3.5−88)×10−12
NEW (Table 6 row): H→γ+(ee)_1 (3.5−11)×10−12

OLD: with MG5@NLO using the SMEFT@NLO model~\cite{Degrande:2020evl}.
NEW: with MG5@NLO using the encoded loop-induced SM effective couplings of the SMEFT@NLO model~\cite{Degrande:2020evl}.