Measuring the lower bound of the neutrino mass at the LHC in Higgs triplet model

We show in the framework of the Higgs triplet model that the lower bound of the neutrino mass is obtained if we can measure Γ(∆ −− →ee) Γ(∆→μμ) at the LHC. E-mail:[email protected] E-mail:[email protected] Neutrino phenomena have been the guiding force for physics beyond the standard model (SM) for the last two decades. Presently, observations of the Majorana nature of neutrinos and the absolute value of the neutrino mass would be strong evidence of particle physics. The Higgs triplet model (HTM) [1] is the simplest extension of the SM which invokes the new neutrino phenomena. In a previous paper [2] we showed that the HTM enables us to detect the Majorana property by the precise measurement of the usual muon decay. The interference term in muon decay due to the Majorana property was first discussed in [3], but the value was far beyond the present upper bound. On the contrary, the HTM gives a rather marginal value to the present precision order. In the present paper we discuss another urgent problem of the absolute value of the neutrino mass that may be solved in the observations at the CERN LHC if the HTM works well. The neutrino-Higgs coupling in the HTM is given by LHTM = LhM iτ2∆L+H. c. (1) Here neutrinos are required to be Majorana particles. The symmetric matrix hM is the coupling strength and τi(i = 1–3) denote the Pauli matrices. The triplet Higgs boson field with hypercharge Y = 2 can be parametrized by ∆ = ( ∆+/ √ 2 ∆++ v ∆ √ 2 +∆0 −∆+/ √ 2 ) , (2) where v∆ is the vacuum expectation value of the triplet Higgs boson. Mass eigenvalues of neutrinos are determined by diagonalization of mν = √ 2hMv∆. There is a tree-level contribution to the electroweak ρ parameter from the triplet vacuum expectation value as ρ ≈ 1 − 2v2 ∆/v. The CERN LEP precision results can give an upper limit v∆ . 5 GeV. There is no stringent bound from the quark sector on triplet Higgs bosons because they do not couple to quarks. The Yukawa interaction of the singly and the doubly charged Higgs boson is written as L∆ =− √ 2(hMU)lilLN c i ∆ − − (hM )ll′lLlL c ∆−− +H.c., (3) where hM = Um diag ν U T /( √ 2v∆) ≡ 〈mν〉ab /( √ 2v∆), (4) and Ni represent Majorana neutrinos which satisfy the conditions Ni = N c i = CNi T . The most stringent constraint on the triplet Yukawa coupling comes from μ → eeē through the tree-level contribution due to the doubly charged Higgs boson [4]. Thus the peculiar properties of the HTM appear in the processes of the doubly charged Higgs. Among them, we have a sizable cross section of ∆++ → lalb for m∆ = O(100) GeV, and the rate is given by Γ(∆ → l a l b ) = 1 4π(1 + f) |hab|m∆++, (5) where f = 1(0) for a = b (a 6= b). Searching for the neutrino mass in the HTM at the LHC was discussed in [5], where the event numbers were estimated at the scheduled energy and luminosity. Unfortunately, the LHC was forced to lower the energy scale to 10 TeV and the luminosity to 1033 cm−2s−1. The cross section for pp → ∆++∆−−, 99 fb for m∆++ = 200GeV 5.9 fb for m∆++ = 400GeV, (6) for √ s = 14TeV is reduced to 53 fb for m∆++ = 200GeV 2.6 fb for m∆++ = 400GeV, (7) for √ s = 10TeV [6]. The first 100-day run at low luminosity resulted in the integrated luminosity 10 fb−1. So we may have a sizable number of events even in this case, though the final number of ll events depends on Br(∆ → ll). In order to circumvent the ambiguous factors m∆ and v∆, let us consider the ratio Γ(∆−− → ee) Γ(∆−− → μμ) = ∣