[P]resent estimates [8, 9], suggest that at the end of Run II the Higgs boson couplings to the vector bosons are expected to reach a ∼ 5% precision with 300 fb−1 luminosity, while the corresponding ones for the heavy fermions can reach ∼ 10 − 15% precision. Similar estimates for the end of the HL option indicate a reduction of these numbers by at least a factor ∼ 2.
The study of the trilinear (λ3) and quartic (λ4) Higgs self couplings in the scalar potential V (H) = m2 H 2 H2 + λ3vH3 + λ4H4 2 is in a completely different situation. In the SM, the potential is fully determined by only two parameters, v = (√ 2Gµ) −1/2 and λ, the coefficient of the (Φ†Φ)2 interaction Φ being the Higgs doublet field (m2 H = 2λv2 , λ3 = λ, λ4 = λ/4).
In the case of extended scalar sectors or in presence of new dynamics at higher scales the trilinear and quartic coupling become independent from the Higgs mass and their values can depart from the SM predictions [10,11].
At the Leading Order (LO) the cross sections corresponding to the main single Higgs production processes, i.e., gluon gluon fusion (ggF), vector boson fusion (VBF), W and Z associated production (ZH, V H) and production in association with a top quark pair (ttH¯ ), as well as the Higgs decay widths depend on the couplings of the Higgs boson to the other particles of the SM, yet they are insensitive to λ3 and λ4. Information on λ3 can be directly obtained at LO only from final states featuring at least two Higgs bosons. However, the cross sections corresponding to these processes are much smaller than those for single Higgs production due to the suppression induced by a heavier final state and an additional weak coupling.
At √ s = 13 TeV the single Higgs gluon-gluon-fusion production cross section in the SM is around 50 pb [12] while the double Higgs cross section is around 35 fb in the gluon-gluon-fusion channel [13–15] and even smaller in other production mechanisms [16, 17]. A plethora of perspective studies performed at √ s = 13 TeV suggest that it should be possible to detect the production of a Higgs pair via b ¯bγγ [16,18– 22], b ¯bτ τ¯ [16, 23], b ¯bW+W− [24] and b ¯bb¯b [25–27] final states. However, the ultimate precision with which λ3 could then be extracted is much less clear.
Even with an integrated luminosity of 3000 fb−1 , experimental analyses suggest that it will be possible to exclude at the LHC only values in the range λ3 < −1.3 λ SM 3 and λ3 > 8.7 λ SM 3 via the b ¯bγγ signatures [28] or λ3 < −4 λ SM 3 and λ3 > 12 λ SM 3 even including also b ¯bτ τ¯ signatures [29], i.e., a much more pessimistic perspective than the results reported in the phenomenological explorations.
The current experimental bounds on nonresonant Higgs pair production cross sections as obtained at 8 TeV are rather weak: ATLAS has been able to exclude only a signal up to 70 times larger than the SM one [30, 31], which we can be roughly translated to excluding λ3 < −12 λ SM 3 and λ3 > 17 λ SM 3 while CMS puts a 95% C.L. exclusion limit on λ3 < −17.5 λ SM 3 and λ3 > 22.5 λ SM 3 assuming changes only in the trilinear Higgs boson coupling, with all other parameters fixed to their SM values [32]. Thus, alternative strategies in the determination of the trilinear Higgs self coupling λ3 other than the constrains from Higgs pair production would be certainly helpful. Finally, the perspectives of determining the quartic Higgs self-coupling λ4 via measurements in triple Higgs production seems quite 3 bleak at the LHC [33, 34] due to the smallness of the corresponding cross section [14]. In this work we explore the possibility of constraining the trilinear Higgs self coupling with a different approach, namely, via precise measurements of processes featuring single Higgs production and decay at the LHC. Indeed, although single Higgs production does not depend on λ3 at LO or at higher orders in QCD, it does depend on it via weak loops, namely at Next-to-Leading (NLO) in the electroweak (EW) interactions. We therefore extract the λ3-dependent part from the corresponding NLO EW corrections for all phenomenologically relevant single Higgs production cross sections (ggF, VBF, W H, ZH, ttH¯ ) and branching ratios, (H → γγ, H → ZZ, WW → 4f, H → f ¯f, H → gg). By varying the value of λ3 we evaluate the impact of an anomalous trilinear Higgs self coupling on the predictions for the aforementioned cross sections and decay widths. A distinctive pattern of deformations of the SM predictions for the rates (σ(i) · BR(f)) is obtained that can be compared to the experimental data.
