PHYSICAL REVIEW D VOLUME 54, NUMBER 7 1 OCTOBER 1996 Possibility of searching for heavy neutrinos at accelerators D. Fargion,1,5,* Maxim Yu. Khlopov,2,3,† Rostislav V. Konoplich,2,4,5,6,‡ and R. Mignani4,5,§ 1 Dipartimento di Fisica, I Università di Roma ‘‘La Sapienza,’’ P.le A.Moro, 2, I-00185 Rome, Italy 2 Center for Cosmoparticle Physics ‘‘Cosmion,’’ Miusskaya Pl., 4, 125047 Moscow, Russia 3 Institute of Applied Mathematics by M. V. Keldysh, Miusskaya Pl., 4, 125047 Moscow, Russia 4 Dipartimento di Fisica ‘‘E. Amaldi,’’ III Università di Roma, Via della Vasca Navale, 84, I-00146 Roma, Italy 5 INFN, Sezione di Roma I, c/o Dipartimento di Fisica, I Università di Roma ‘‘La Sapienza,’’ P.le A.Moro 2, I-00185 Roma, Italy 6 Moscow Engineering Physics Institute, Kashirskoe sh., 31-114509 Moscow, Russia ~Received 5 December 1995! We discuss the possibility of searching for very heavy neutrinos of new generations in accelerator experiments ~by the process e 1 e 2 → nn̄ g !, which allow investigation in the region m n ;M Z /2, where it is difficult to get cosmological constraints on the neutrino mass. @S0556-2821~96!04017-9# PACS number~s!: 14.60.Pq, 13.10.1q It is well known that massive neutrinos play a basic role both in the theory of elementary particles ~in the choice of the most suitable unified scheme beyond the standard model! and in astrophysics and cosmology ~e.g., for solving the dark matter puzzle at galactic and cosmological scales!. Bounds on the possible values of the neutrino mass are obtained either from cosmological arguments ~based on estimates of the neutrino energy density in the universe! or from laboratory experiments. The latter ones provide the limits @1# m ~ n e ! ,5.1 eV, m ~ n m ! ,0.27 MeV, m ~ n t ! ,31 MeV for the masses of the three known neutrino species. Indeed, experiments @2# at the CERN e 1 e 2 collider LEP on Z-boson decay tell us that there are three lepton families. However, this constraint applies only to light neutrinos with mass M n ,M Z /2, where M Z is the mass of the Z boson, and therefore does not forbid the existence, within the framework of the standard model, of very heavy neutrinos, such that Z-boson decays into them are forbidden by phase space. In particular, the results of modern experiments are not inconsistent with the existence of heavy Dirac neutrinos with m n.44 GeV @3#. The role of very heavy neutrinos in astrophysics and cosmology is multifold: ~a! they are good candidates for cold dark matter, able to clusterize at small scales, contrary to light neutrinos, which might dominate only at larger scales ~extended galactic dark halos!; ~b! very heavy neutrinos can offer an earlier ‘‘gravitational seed’’ for galaxy formation; and ~c! their annihilation may ‘‘pollute’’ cosmic ray spectra at high energies. Therefore, the possible existence of such very massive neutrinos is urgent to be tested. The cosmological limit on a very heavy neutrino mass, 3 GeV,m n ,3 TeV, first obtained by Zeldovich, Dolgov, Lee, and Weinberg @4#, was improved a few years ago by taking into account the neutrino annihilation channel nn̄ →W 1 W 2 @5#. Moreover, in a recent paper @6# we carried out a detailed analysis of very heavy relic neutrino annihilation in the Galaxy, thus excluding the heavy neutrino mass range 60 GeV,m n,115 GeV. However, it is difficult to get cosmological constraints on m n in the region m n ,M Z /2. In this Brief Report we want, therefore, to briefly address the issue of a possible search for stable heavy neutrinos in accelerator experiments, which is indeed a quite uneasy task. It seems that, to this aim, the process e 1 e 2 → nn̄ g , with the detection of a single photon, could be more attractive. This process was suggested a while ago @7# as a neutrino-counting experiment, and we already discussed in a previous paper @8# the possibility of using it in order to investigate neutrino properties ~like their magnetic moment! in accelerators. We assume the standard electroweak model to be valid, including, however, one additional family of fermions. Then the heavy neutrino n and a heavy charged lepton L form a standard SU~2!L doublet. In order to ensure the stability of the heavy neutrino n, we assume that m n ,M L and that the heavy neutrino is a Dirac neutrino. There are five Feynman diagrams corresponding to the process ~1! and they are shown in Fig. 1. If the final state of the reaction ~1! contains heavy neutrinos of the new generation, then this process is described only by the two Feynman diagrams ~a! and ~b! corresponding to the s-channel Z-boson exchange. Using standard techniques, we calculate the differential cross section for the process ~1! with the heavy neutrinos in the final state: ds a ~ 12x/2! 2 1z 2 x 2 /4 2 2 2 5 G g 1g ! ~ V A dxdz 6 p 2 x ~ 12z 2 ! *Electronic address: FARGION@ROMA1.INFN.IT 3 @ 124m 2n /q 2 # 1/2M 4Z ~ q 2 2m 2n !@~ q 2 2M 2Z ! 2 † Electronic address: KHLOPOV@KHLOPOV.RC.AC.RU Electronic address: KONOPLIC@ROSTI.MEPHI.MSK.SU § Electronic address: MIGNANI@ROMA1.INFN.IT ‡ 0556-2821/96/54~7!/4684~3!/$10.00 ~1! 1M 2Z G 2 # 21 , 54 4684 ~2! © 1996 The American Physical Society BRIEF REPORTS 54 4685 FIG. 1. Feynman diagrams for the process e 1 e 2 → nn̄ g . where a51/137, x52 v / As, v is the photon energy, z5cos u, where u is the photon angle with respect to the direction of the electron beam, and q 2 5s(12x). In order to evaluate the total cross section, we integrate Eq. ~2! over z and x: FIG. 2. The total cross section for the process e 1 e 2 → nn̄ g . All values are in GeV. The value M̃ corresponds to the cutoff in photon energy, v,(124M̃ /s) As/2, for the background process with massless neutrinos. 2z 0 <z<z 0 , 2 v 0 / As<x<124m 2n /s, ~3! where u0 and v0 are the typical experimental cutoffs @9,10#, which define the acceptance region for the events. The results of numerical calculations of the total cross section for different neutrino masses at v051.5 GeV and u0530° are shown in Fig. 2. We plotted also the results for the process ~1! with the light ne , nm , and nt neutrinos in the final state ~the calculation for ne takes into account the charged current as well as the neutral one!. As we see from Fig. 2, the background process with the light neutrinos dominates over the process ~1! with heavy neutrinos ~due to the charged current! and therefore we can hope only for an investigation in the vicinity of the Z-boson peak: m n.50–100 GeV. In this mass region, assuming the experimental cuts ~3!, at a luminosity of the accelerator L51032 cm22 c 21, we could expect 30–300 events/yr with heavy neutrinos. Potential backgrounds to Eq. ~1! can arise from other e 1 e 2 radiative processes, cosmic rays, and beam-gas interactions. The dominant background to Eq. ~1! comes from radiative Bhabha scattering, when both electrons escape detection. We note that a typical overall efficiency for singlephoton experiments is about 60% @9,10#. In the conditions of the experiment @10# at LEP, the total cross section for the background processes was about 1 pb near the Z-boson peak at As.M Z . However, the upper cutoff ~3! on the photon energy allows one not only to reduce the contribution of massless neutrinos to the process ~1! with heavy neutrinos, but also to decrease, in the threshold region near the peak of the integrated cross section ~2!, the background contribution by about one order of magnitude to a more or less acceptable level ~see Fig. 2!. Let us stress again that experiments of this kind allow an investigation in the region m n ;M Z /2 where it is extremely difficult to obtain cosmological constraints on m n . The above analysis is based on the assumption of the absence of mixing between the hypothetical heavy neutrino and the light neutrinos. The existence of such a mixing ~without a special suppression! would lead to the instability of the heavy neutrinos and in this case a direct detection of neutrinos by their decay products would be possible. We note also that renormalization-group considerations restrict the number of quarks flavors to 16, since in this case QCD remains asymptotically free. Therefore it is possible to introduce only five additional neutrino generations within the framework of the standard model without violation of the asymptotic freedom. The analysis of the effective potential on the vacuum stability also allows for additional neutrino generations with masses of the order of a few hundred GeV 4686 BRIEF REPORTS ~if the origin of this mass is not connected with the Higgs mechanism of symmetry breaking!. Heavier neutrino masses ~*1 TeV! might be strongly constrained once again by astrophysical and cosmological bounds. This work was partially supported by the International Science Foundation ~Grant No. MB9000! and the Russian @1# Particle Data Group, L. Montanet et al., Phys. Rev. D 50, 1173 ~1994!. @2# D. Decamp et al., Phys. Lett. B 241, 435 ~1990!; B. Adeva et al., ibid. 237, 136 ~1990!; M. Z. 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