Left-right symmetric models and long baseline neutrino experiments

Transcription

1 Left-right symmetric modes and ong baseine neutrino experiments Katri Huitu Hesinki Institute of Physics and Department of Physics, University of Hesinki, P. O. Box 64, FI University of Hesinki, Finand E-mai: Timo J. Kärkkäinen Hesinki Institute of Physics and Department of Physics, University of Hesinki, P. O. Box 64, FI University of Hesinki, Finand E-mai: Jukka Maaampi University of Jyvaskya, Department of Physics, P. O. Box 5, FI University of Jyvaskya, Finand E-mai: University of Jyvaskya, Department of Physics, P. O. Box 5, FI University of Jyvaskya, Finand E-mai: The Standard Mode has been the most successfu theory in the history of partice physics, but it fais to account for many important questions, such as the origin of neutrino mass. The so-caed eft-right symmetric modes provide an easy answer to these issues by adding a simpe extension to the Standard Mode gauge group, but it impies the existence of heavy right-handed neutrinos and additiona Higgs partices. In this work we discuss how the eft-right symmetry group woud affect neutrino osciations taking pace in ong baseine neutrino osciation experiments in the form of sterie neutrinos and non-standard neutrino interactions, using the Deep Underground Neutrino Experiment as our exampe. The 19th Internationa Workshop on Neutrinos from Acceerators-NUFACT September, 017 Uppsaa University, Uppsaa, Sweden Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercia-NoDerivatives 4.0 Internationa License (CC BY-NC-ND 4.0).

2 1. Introduction The ceebrated discovery of neutrino osciations proved that the Standard Mode (SM) gauge group SU() L U(1) Y is not abe to describe a partice physics phenomena, as it cannot expain the origin of neutrino mass. The existence of neutrino osciations is therefore a direct indication of physics beyond the SM. The present neutrino osciation experiments indicate that the neutrino masses m 1, m and m correspond to the two squared mass differences m 1 = m m ev and m 1 = m m ev. From these resuts it is obvious that there must be at east two neutrino masses that are different from zero. Thus far experiments have not yet determined neither the magnitude nor the ordering of the neutrino masses. At the same time, it is unknown why the neutrino masses are ight as compared with the other massive partices. One popuar method to tacke the ightness probem is the so-caed seesaw mechanism, where the suppression of neutrino masses foows from the existence of a new mass scae much higher than the eectroweak scae O(10 ) GeV. In Type I seesaw modes the neutrino masses are generated by heavy right-handed neutrinos, whereas in Type II seesaw modes a set of new scaars = ( ++, +, 0 ) is added to the SM partice content. In both types of modes, the SM partice content is extended with new partices, eading to potentiay testabe phenomena at the current and future partice physics experiments. In this proceeding, we focus on the so caed eft-right symmetric modes, where Type I and II seesaw modes occur naturay. In this cass of modes, the SM gauge group is extended to SU() C SU() L SU() R U(1) B L. In addition to expaining the sma neutrino masses via a Type I+II seesaw mechanism, the advantages of the eft-right symmetric modes incude the spontaneous breaking of the CP symmetry. Left-right symmetric modes have been studied vasty in the iterature, and its signatures of have been sought in e.g. high-energy proton-proton coision experiments. In this work, we investigate the prospects of probing scaar tripets of the eft-right symmetric modes in ong baseine neutrino experiments.. The eft-right symmetry Whie SM is very successfu in describing the interactions at the eectroweak scae, in addition to the emergence of neutrino masses, it does not expain the origin of parity vioation. Both of these mysteries are mitigated in eft-right symmetric modes (LRSM), which assume the fundamenta interactions are parity symmetric at high energies. This requires a arger partice content, consisting of right-handed neutrinos and gauge bosons and an extended scaar sector. In addition, LRSM can be thought of as an intermediate step between SM and SO(10) grand unified theory, which has a buit-in automatic B L gauge symmetry and right-handed neutrinos. The eectroweak part of LRSM has the gauge group G =SU() L SU() R U(1) B L, where the generator of U(1) group exhibits anomay-free quantum number B L. The eectric charge operator is given by Q = I L + I R + B L (.1) In addition to gauge transformations, LRSM is invariant under the parity transformation L R. 1

3 The right-handed fermions ν Ri and Ri form SU() R doubets L Ri = ( ν Ri Ri ) (1,, 1). To break the LRSM gauge group G to SM eectroweak gauge group, one has to introduce eft- and right-handed eptophiic scaar tripets L (,1,) and R (1,,), respectivey. This is the minima LRSM fied content. The Yukawa Lagrangian reevant to neutrino osciations is L = i, j=1 h i j L Li L R j + h i j L Li L R j +Y i j (L T LiC 1 σ L L L + L T RiC 1 τ R L R j ) + h.c. (.) where the SM Higgs fieds are presented as a bidoubet, and σ σ, with, (,,0). These terms generate ight neutrino masses via Type I+II seesaw mechanism (see Fig. 1). Simiary the scaar tripet are -matrices, defined L = i=1 1 σ i Li, R = i=1 The scaar sectors gain the foowing vacuum expectation vaues: L =, R = v L 0 v R 0 1 σ i Ri. (.), = k 0 0 k, (.4) where k + k = v. Let us denote 1 and. The scaar potentia of LRSM contains mixed L R terms i, j=1 γ i j Tr( L i R j ) + h.c., (.5) and assuming that right-handed scaar tripet is much more massive that L and SM Higgs, we may integrate out the right-handed scaar, eaving a effective triinear term (H is the SM Higgs doubet) N R L HH L = λ H T iσ LH. (.6) Figure 1: Tree-eve generation of neutrino masses in Type I (eft) and Type II (right) seesaw mechanisms, both of which are present in eft-right symmetric modes. In Type I neutrino masses originate from interactions with the right-handed neutrinos N R and in Type II in the scaar tripet.

4 . Impications on ong baseine neutrino experiments In this work, we estimate the phenomenoogica impications of the tripet scaar and heavy righthanded neutrino fieds in ong baseine neutrino experiments. Specificay, we cacuate the experimenta sensitivities for the future neutrino osciation faciities to measure the properties of the tripet Higgs bosons in presence of the heavy right handed neutrinos N i, where i = 1,,. We study the tripet in the imit where the mass of the tripet scaars M is assumed to be the same for 0, + and ++, and the momenta of the processes are negigibe with respect to the tripet mass. In this imit, the ampitudes of the reevant processes are described by the foowing effective Lagrangians [1]: L m ν = Y αβ λ v M ναr C ν βl = 1 (m ν) αβ ναr C ν βl, (.1) L NSI = Y σβ Y αρ ( ναl M γ µ ν βl ρl γ µ ) σl, (.) where m ν is the mass matrix that represents the eft-handed neutrinos, λ is the triinear couping strength from Eq. (.6), and v is the vacuum expectation vaue of the SM scaar Higgs fied. The Yukawa coupings are contained in the matrix Y. The NSI term of the effective Lagrangian in Eq. (.) describes the non-standard neutrino interactions (NSI) with eptons. These interactions arise from coupings with the scaar tripet. In neutrino osciations taking pace in ong baseine experiments the effective NSI Lagrangian can aso be written as L NSI = G F ε f f C αβ (ν αlγ µ ν βl )( f γ µ P C f ), (.) where P C refers to the chira projection operators P L and P R, G F is the Fermi couping constant, f and f are fermions of any type, and ε f f C αβ (α,β = e, µ,τ) are the NSI parameters to describe the strength of the NSI coupings. The NSI effects that emerge in neutrino propagation in matter are derived by soving the Yukawa couping Y αβ from the Majorana mass term in Eq. (.1), inserting it to Eq. (.), and comparing the resut with Eq. (.). This yieds the foowing expression: ε ρσ M αβ = 8 (m G F v 4 λ ν ) σβ (m ν) αρ, (.4) where α,β,ρ and σ are favor indices. The expression (.4) indicates the arger the ratio M /λ the stronger are the NSI of the ight neutrinos. Conversey, stricter bounds on ε ρσ αβ aso mean more stringent constraints on M /λ. In this work we interested in the NSI coupings with eectrons, which are parametrized as εαβ m = εee αβ, where α,β = e, µ,τ. In the iterature, these are often referred to as the matter NSI parameters. The ony background in probing the NSI effects caused by the scaar tripets is the presence of heavy right-handed neutrinos. In eft-right symmetric modes the heavy right-handed neutrino fieds give rise to three heavy neutrinos neutrinos with masses cose to the eectroweak scae. These neutrinos are too heavy to be kinematicay accessibe in neutrino osciation experiments, but they

5 do affect the osciation of ight neutrinos by making their mixing matrix non-unitary. There are severa methods to parametrize the ow energy effects of the non-unitarity, but in this work we choose the parametrization which was introduced in Ref. []. In this framework, mixing between the ight neutrinos is described with the non-unitary mixing matrix N = N NP U, where U is the conventiona unitary matrix and N NP is the trianguar matrix N NP = 1 α ee 0 0 α µe 1 α µµ 0 α τe α τµ 1 α ττ. (.5) Here α parametrize the deviations from unitarity, and since these deviations are known to be sma, one has α 1 and α 1. The parametrizations used for the tripet non-standard interactions in Eq. (.4) and the nonunitarity of the mixing matrix in Eq. (.5) do correate to some extent. In the eading order, the two ow energy parametrizations are reated as foows []: ε m ee = α ee ε m µµ = α µµ ε m ττ = α ττ ε m eµ = 1 α µe ε m eτ = 1 α τe ε m µτ = 1 α τµ. (.6) The non-unitarity of the ight neutrino mixing matrix and the matter NSI effects have both been studied in the iterature. The prospects of constraining the matter NSI parameters in DUNE were studied in detai in Ref. [] and the present experimenta constraints on the non-unitarity parameters are presented in Ref. []. 4. Numerica studies In this section we cacuate the avaiabe parameter vaues which DUNE wi be sensitive to regarding the tripet mass M and the triinear couping strength λ. We begin by estimating the upper bound for the ratio M / λ which DUNE can constrain in case no signa of matter NSI is found. First, we rewrite Eq. (.4) into the foowing forms: M λ M λ = 8 G F v 4 ε m αβ (m ν ) eβ (m ν) αe, (4.1) 8 G F v 4 (εαβ m = εm α β ) (m ν ) eβ (m ν) αe (m ν ) eβ (m, (4.) ν) α e where εαβ m = εee αβ and εm α β = ε ee α β for α,β,α,β = e, µ,τ. From the expressions in Eqs. (4.1) and (4.) we cacuate the upper imits for M /λ from the known 90% CL bounds for εαβ m and εm αβ εm α β. The eements of the ight neutrino mass matrix m ν are obtained from the equation m (m ν ) = U 0 m m 1 + ε U ee m εµµ m εeµ m εeτ m + A εeµ m 0 εµτ m εeτ m εµτ m εττ m εµµ m, (4.) 4

6 where U is the PMNS neutrino mixing matrix. We maximize the denominators of (Eq. 4.1) and (4.) by varying a reevant osciation parameters within their current experimenta imits. Using the current experimenta imits and the DUNE sensitivities avaiabe for ε m ee ε m µµ, ε m ττ ε m µµ, ε m eµ, ε m eτ and ε m µτ, one can obtain upper bounds for M / λ. See Ref. [4] for more detais. The presence of heavy right-handed neutrinos may cause simiar deviations from the standard three neutrino osciations as the matter NSI originating from interactions with the scaar tripet. The parameter vaues for which the non-unitarity due to the heavy right-handed neutrinos can be identified by converting the present experimenta constraints for the non-unitarity parameters [] into matter NSI parameters by using the reations in Eq. (.6). The resuts are presented in Fig.. The white region shows the parameter vaues which can be excuded by 90% confidence eve with the present experimenta data (see Ref. []). When the DUNE bounds are taken into account, the yeow region is excuded. The bue region represents the parameter vaues for which the non-unitarity caused by the heavy right-handed neutrinos can be mistaken as matter NSI from the scaar tripet. The green region shows the vaues which can not be probed by DUNE and are distinguishabe from the non-unitarity effect. The dashed, dot-dashed and dotted ines show where these 90% CL contours woud be if interted hierarchy was assumed. Finay, we cacuate which parameter vaues are aowed for λ when the present experimenta imits for M are taken into account. It is known from coider experiments that there are ower imits for the tripet mass M. We approximate this as a constraint M 750GeV and obtain the ower bounds for λ. See Ref. [4] for more detais. The resuts are presented in Fig.. Figure : The aowed vaues of M / λ at 90% CL, shown as function of the absoute neutrino mass scae. When the norma hierarchy is assumed, the yeow, green and bue regions correspond to the aowed vaues for the present experimenta imits, DUNE sensitivities, and the non-unitarity ambiguity, respectivey. The dashed, dot-dashed and dotted ines show the 90% CL contours for inverted hierarchy. See Ref. [4] for more detais. 5

7 Figure : The aowed vaues of ε m eτ and λ in (λ, ε m eτ )-pane. The bue region is excuded by the present experimenta imits, whereas the green region shows the parameter vaues which are avaiabe in DUNE. When M 750GeV, everything beow each m 1 contour is excuded. The contours are shown for m 1 =0, 0.1 and 0. ev. The dot-dashed ine shows the ε m eτ vaues which correspond to the Yukawa coupings Y αβ = 4π, where α,β = e, µ,τ. See Ref. [4] for more detais. References [1] M. Mainsky, T. Ohsson and H. Zhang, Non-Standard Neutrino Interactions from a Tripet Seesaw Mode, Phys. Rev. D 79 (009) [arxiv: [hep-ph]]. [] M. Bennow, P. Cooma, E. Fernandez-Martinez, J. Hernandez-Garcia and J. Lopez-Pavon, Non-Unitarity, sterie neutrinos, and Non-Standard neutrino Interactions, JHEP 04 (017) 15 [arxiv: [hep-ph]]. [] M. Bennow, S. Choubey, T. Ohsson, D. Pramanik and S. Raut, A combined study of source, detector and matter non-standard neutrino interactions at DUNE, JHEP 08 (016) 090 [arxiv: [hep-ph]]. [4] K. Huitu, T. Kärkkäinen, J. Maaampi and S. Vihonen, The effects of tripet Higgs bosons in ong baseine neutrino experiments, HIP TH (017) [arxiv: [hep-ph]]. 6