Constraints on fourth generation Majorana neutrinos

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1 Jornal of Physics: Conference Series Constraints on forth generation Majorana netrinos To cite this article: Alexaner Lenz et al 2010 J. Phys.: Conf. Ser Relate content - Lepton nmber, black hole entropy an copies of the Stanar Moel Sergey Kovalenko, Heinrich Päs an Ivan Schmit - An A4 moel for netrinos Earo Peinao - Type I Seesaw Mechanism, Lepton Flavor Violation an Higgs Decays Emiliano Molinaro View the article online for pates an enhancements. This content was ownloae from IP aress on 02/09/2018 at 18:37

2 Constraints on forth generation Majorana netrinos 1 Alexaner Lenz, Heinrich Päs an Dario Schalla Fakltät Physik, Technische Universiät Dortmn, Dortmn, Germany ario.schalla@t-ortmn.e Abstract. We investigate the possibility of a forth seqential generation in the lepton sector. Assming netrinos to be Majorana particles an starting from a recent - albeit weak - evience for a non-zero amixtre of a forth generation netrino from fits to weak lepton an meson ecays we iscss constraints from netrinoless oble beta ecay, raiative lepton ecay an like-sign i-lepton proction at haron colliers 1. Introction The aition of a forth family of fermions to the known three generations has recently become a poplar extension of the stanar moel (see [1, 2] for a review). Interesting featres an benefits of sch scenarios incle for example: weakening of the tension between irect an inirect bons on the Higgs mass, see e.g. [3, 4, 5], a sizeable enhancement of the measre of CP violation, see e.g. [6], gage copling nification [7], new strong ynamic effects e to large Ykawa coplings allowing for ynamical symmetry breaking, see e.g. [8, 9], a soltion of flavor problems like the observe 3.8 σ eviation of the measre vale of B - B s mixing from the stanar moel (SM3) preiction [10] which also enhances the imon asymmetry of the SM3 [11] towars the vale measre by the D0 collaboration [12]. In the following we consier the aition of a forth family ( ) ( ) t b t R b ν4 R l l 4R ν 4R, (1) 4 L while the gage an Higgs sector remains nchange compare to the SM 3. Natrally the aition of right-hane netrinos allows for both Dirac an Majorana mass terms for all for generations of netrinos. Moreover, tiny netrino masses are most natrally explaine for Majorana netrinos in a seesaw scheme, so we o not aopt lepton nmber conservation at this point. 1 Talk presente by Dario Schalla. L c 2010 Lt 1

3 A lower mass bon on SU(2) oblet forth generation netrinos can be obtaine by the invisible Z-ecay with [13]: N ν = ± (2) constraining the nmber of light netrinos with masses < M Z /2 to be three. Conseqently m 4 m Z GeV (3) provies a lower mass bon on forth generation netrinos. As the light mass eigenvales are bone from above by the Dirac masses at least in a typical seesaw moel, this provies a bon on the Dirac-type mass m D 4 as well. Assming pertrbativity of the forth generation netrino Ykawa coplings then constrains Dirac type netrino masses approximately to the interval 45 GeV < m D 4 < 1000 GeV. (4) Moreover, recent fits to electroweak precision ata in a for generation framework (SM 4) lea to the following constraints on the forth generation particle spectrm [14]: m t m b < 80 GeV m l4 m 4 < 140 GeV. (5) Finally a recent fit to a set of experimental ata in the SM4 framework has provie some evience for a non-zero amixtre of a forth generation netrino, reslting in a PMNS matrix [15] U P MNS = <0.089 >0.021 < < < < < < > (6) In the following we se this evience as weak as it may be as a starting point to reconsier bons on forth generation netrino masses. 2. Netrinoless oble beta ecay The most sensitive probe for netrino Majorana masses is generally netrinoless oble beta ecay (0νββ). 0νββ ecay can be realize by the exchange of a Majorana netrino (see Fig. 1). In the presence of aitional heavy netrino states the sal effective Majorana mass m ν has to be complemente by an effective heavy netrino mass m N 1 : T 0νββ 1/2 m ν = m e 3 i=1 U 2 eim i m N 1 = N The half-life of the ecay is then given by [16] [ ] ( ) 1 mν 2 = Cmm LL + ( mp m N ) 2 C NN mm + U 2 enm 1 N. (7) ( mν m e ) ( ) mp C NL m N mm, (8) where the C mm factors incle phase-space factors an nclear matrix elements [17, 18] an m p (m e ) the proton (electron) mass. Consiering only the heavy netrino contribtion an sing the PMNS matrix obtaine in Eq. (6) one obtains stringent bons on the allowe mass range from the crrent experimental lower half-life bon T1/2 Ge > years [19]. The allowe region is shown in Fig.2. This leas to the following mass bons for a single forth generation Majorana netrino Ue4 max = m max 4 = GeV (9) Ue4 min = m min 4 = GeV, (10) 2

4 T 1 2 years m N ev Figre 1. Feynman iagram of 0νββ Figre 2. Contribtion of heavy netrino ince by the exchange of a heavy forth on 0νββ half-life (thin lines) within the generation Majorana netrino. mixing region given by Eq. (6) an IGEX lower bon (tick line). The gray area inicates the allowe region. U e4 U e4 min U e4 U e4 max m N GeV 2.5 m N GeV m N GeV m N GeV 2.0 m N GeV m N GeV 2.0 m N GeV m N GeV Β 1.5 Β Α Α Figre 3. Masses that reproce the experimental 0νββ bon. α is the light an β the heavy netrino contribtion phase. which are far above the pertrbativity constraint of Eq. (4). Relative phases between light (α) an heavy (β) contribtions may cancel each other an ths loosen this bon (see Fig. for several phases α an β). Maximizing the light netrino contribtion by sing the largest possible allowe light netrino masses consistent with the large scale strctre of the niverse ( m ν < 0.66 ev) the mass region of the heavy netrino can be lowere to GeV < m 4 < GeV, (11) which remains several orers of magnite above the esire range (5). In principle there are three ifferent ways to save the possibility of a heavy forth generation netrino: (i) netrinos are Dirac particles an therefore 0νββ is forbien, which wol come at the cost of seesaw netrino mass sppression an leptogenesis as a sccessfl way to generate the baryon asymmetry of the niverse (ii) some other physics beyon the stanar moel is involve an cancels the heavy netrino contribtion, which wol reqire fine tning (iii) netrinos are pseo-dirac particles. 3

5 10 8 m ev m 4 ev Figre 4. Maximal mass splitting for heavy pseo-dirac netrinos. The pper (lower) crve correspons to the lower (pper) bon on U e4 accoring to Eq. (6). The marke area represents the allowe parameter space. In the following we will focs on the latter alternative which may provie sefl giance for ftre moel biling. Pseo-Dirac netrinos arise when the Majorana mass is small compare to the Dirac mass. The two reslting mass eigenstates (m +, m ) are nearly egenerate with tiny mass splitting δm an the active an sterile component exhibit practically maximal mixing. The 0νββ half-life of sch a netrino then reas [ T 0νββ 1/2 ] ( ) 1 2 ( ) 2 mp = Cmm NN mp Cmm NN. (12) m m + The allowe mass splittings are shown in Fig. 4 an vary from 32 kev to 350 MeV. 3. Raiative lepton ecays The analysis on netrino mixing se [15] is ominate by the raiative lepton flavor violating ecays of charge leptons. Here we shortly reconsier this bon for the case of pseo-dirac netrinos with masses in the 100 GeV range. The ecay with of these processes is given by [20]: G 2 F m5 l Γ l l γ = 1 2 (32π 2 ) 2 α U lαu l α 2 F 2 (x), (13) where F (x) is a fnction of the netrino masses. It is easy to see that the analysis hols for a pseo-dirac netrino as well. As the forth generation active an sterile states mix maximally an the masses are close to egenerate F (x) oes not change consierably compare to the pre Dirac case. As can be seen from Fig. 5, the ecay rate is sppresse by the tiny masses for the first three generations, while the contribtion of a forth heavy generation has to be sppresse e to small mixing. In the analysis [15] the netrino mass was fixe to 45 GeV. While a mass epenent sty is encorage, the conclsions of this work will remain nchange, as the size of the allowe region is anticipate to vary only slightly for ifferent netrino masses. The ecays of the τ lepton o not provie frther information as the experimental constraints in this channel are mch weaker [21, 22]. 4. Like-sign ilepton proction Finally, a process very similar to 0νββ is the proction of two charge leptons of the same charge at haron colliers: pp l + 1 l+ 2 X. (14) 4

6 F U Μ GeV GeV 500 GeV m Α GeV GeV e4 Figre 5. F 2 as a fnction of the mass of the exchange netrino. Figre 6. Constraint on the U µ4 U e4 parameter space obtaine from the bon on the branching ratio for µ eγ. Allowe is the region to the lower left. The bonaries of the intervalls plotte are given by the allowe vales for m 4 = 45 GeV accoring to Eq. (6) Σ fb Σ fb N N Figre 7. Cross section for like-sign Figre 8. Cross section for like-sign ilepton proction by an electroweak ilepton proction by an electroweak scale Majorana netrino withot 0νββ scale pseo-dirac netrino with 0νββ constraints. constraints. As shown in Fig. 9 a heavy Majorana netrino exchange rives the process whose cross section is [23]: σ ( pp l + 1 l+ 2 X) = G4 F m6 W (1 8π 5 12 ) δ l1l2 U l1 4U l2 4 2 F (E, m 4 ), (15) where F (E, m 4 ) is a fnction of beam energy an netrino mass. To escribe the exchange of a pseo-dirac netrino the cross section has to be moifie by introcing a sppression factor (12): pd 2 δm m 4. (16) Here the mass splitting δm follows from the 0νββ constraint an reslts in a sppression of the mass epenent cross section as shown in Fig. 7 an 8. The reslting cross sections are far to small to be observe at expecte LHC lminosities. 5

7 W + W + l + 1 W + N N l + W + 2 Figre 9. Feynman iagrams of like-sign ilepton proction l + 1 l Smmary In this note we have revisite bons on aitional Majorana netrinos, in orer to provie a sefl gie for forth generation netrino moel biling. We have shown that a forth generation Majorana netrino is not yet excle if it has a mass of several hnre GeV an the Majorana states pair p to form a pseo-dirac state. The mixing of sch a netrino is ominantly constraine by the raiative ecay of the mon. De to the pseo-dirac natre lepton nmber violating processes like like-sign ilepton proction trn ot to be strongly sppresse. Besies being potentially observable in next generation 0νββ experiments, the pseo-dirac netrinos col be irectly proce at the LHC, as iscsse in [24]. In this paper a 5 σ iscovery reach for heavy netrino masses p to 100 GeV was avocate with 30 fb 1. While for larger masses the proction cross section wol ecrease, new ecay channels open p once the heavy netrino mass exceeing the Higgs mass, which wol reqire a etaile simlation. References [1] Frampton P H, Hng P Q an Sher M 2000 Phys. Rept (Preprint hep-ph/ ) [2] Holom B et al PMC Phys. A3 4 (Preprint ) [3] Novikov V A, Rozanov A N an Vysotsky M I 2010 Phys. Atom. Ncl (Preprint ) [4] Kribs G D, Plehn T, Spannowsky M an Tait T M P 2007 Phys. Rev. D (Preprint ) [5] Chanowitz M S 2010 (Preprint ) [6] Ho W S, Mao Y Y an Shen C H 2010 (Preprint ) [7] Hng P Q 1998 Phys. Rev. Lett (Preprint hep-ph/ ) [8] Hng P Q an Xiong C 2009 (Preprint ) [9] Holom B 2006 JHEP (Preprint hep-ph/ ) [10] Lenz A et al (Preprint ) [11] Lenz A an Nierste U 2007 JHEP (Preprint hep-ph/ ) [12] Abazov V M et al. (D0) 2010 (Preprint ) [13] 2006 Phys. Rept (Preprint hep-ex/ ) [14] Eberhart O, Lenz A an Rohrwil J 2010 (Preprint ) [15] Lacker H an Menzel A 2010 (Preprint ) [16] Hirsch M, Klapor-Kleingrothas H V an Panella O 1996 Phys. Lett. B (Preprint hep-ph/ ) [17] Hirsch M an Klapor-Kleingrothas H V Prepare for International Workshop on Netrinoless Doble Beta Decay an Relate Topics, Trento, Italy, 24 Apr - 5 May 1995 [18] Mto K an Klapor H V IN *KLAPDOR, H.V. (ED.): NEUTRINOS* [19] Aalseth C E et al. (IGEX) 2002 Phys. Rev. D (Preprint hep-ex/ ) [20] Cheng T P an Li L F 1980 Phys. Rev. Lett [21] Brooks M L et al. (MEGA) 1999 Phys. Rev. Lett (Preprint hep-ex/ ) [22] Abert B et al. (BABAR) 2010 Phys. Rev. Lett (Preprint ) [23] Ali A, Borisov A V an Zamorin N B 2001 Er. Phys. J. C (Preprint hep-ph/ ) [24] el Agila F an Agilar-Saavera J A 2009 Phys. Lett. B (Preprint ) 6