Neutrinoless Double-Β Decay with Nonstandard Majoron Emission

PHYSICAL REVIEW LETTERS 122, 181801 (2019) Neutrinoless Double-β Decay with Nonstandard Majoron Emission † ‡ ∥ Ricardo Cepedello,1,2,* Frank F. Deppisch,2,3, Lorena González,4,2, Chandan Hati,5,§ and Martin Hirsch1, 1AHEP Group, Instituto de Física Corpuscular—CSIC/Universitat de València Edificio de Institutos de Paterna, Apartado 22085, E–46071 València, Spain 2Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom 3Institut für Hochenergiephysik, Österreichische Akademie der Wissenschaften, Nikolsdorfer Gasse 18, 1050 Wien, Austria 4Department of Physics, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile 5Laboratoire de Physique de Clermont, CNRS/IN2P3 UMR 6533, Campus des Cézeaux, 4 Avenue Blaise Pascal, F-63178 Aubière Cedex, France (Received 13 November 2018; revised manuscript received 1 February 2019; published 7 May 2019) We present a novel mode of neutrinoless double-β decay with emission of a light Majoron-like scalar particle ϕ. We assume it couples via an effective seven-dimensional operator with a (V þ A) lepton current and (V Æ A) quark currents leading to a long-range contribution that is unsuppressed by the light neutrino mass. We calculate the total double-β decay rate and determine the fully differential shape for this mode. β Λ ≈ 1 We find that future double- decay searches are sensitive to scales of the order NP TeV for the effective operator and a light scalar mϕ < 0.2 MeV, based on ordinary double-β decay Majoron searches. The angular and energy distributions can deviate considerably from that of two-neutrino double-β decay, which is the main background. We point out possible ultraviolet completions where such an effective operator can emerge. DOI: 10.1103/PhysRevLett.122.181801 Introduction.—Double-β decay processes are sensitive just a charge-neutral scalar particle (Goldstone boson or probes of physics beyond the standard model (SM). not) or vector particle [3]. Originally considered to be The SM process of two-neutrino double-β (2νββ) decay massless, it may also be a light particle [4–6] that can is the rarest process ever observed with half-lives of order potentially be a dark matter candidate [7–9]. Searches for 2νββ ∼ 1021 β 0νββ extra particles in double-β decay are crucial in under- T1=2 yr. Neutrinoless double- ( ) decay, with no observation of any missing energy, is clearly the most standing neutrinos. Most importantly, violation of lepton important mode beyond the SM as it probes the Majorana number by two units and thus the Majorana nature of neutrinos can only be firmly established in the case of nature and mass mν of light neutrinos, with current 0νββ 2 26 0νββ decay. experiments sensitive as T ∼ ð0.1 eV=mνÞ × 10 yr. 1=2 Not all such emission modes have been discussed in the In general, it is a crucial test for any new physics scenario literature. Existing experimental searches so far focus on that violates lepton number by two units. the emission of one or two Majorons originating from the On the other hand, one or more exotic neutral particles intermediate neutrino exchanged in the process. The differ- may also be emitted, with a signature of anomalous missing ent Majoron scenarios have been classified into several 2νββ energy beyond that expected in decay. A well studied categories, all of which assume SM (V − A) charged set of theories involve the emission of a scalar particle, currents with the electrons and quarks. In this Letter, we called Majoron J. The first such proposed Majoron was a Goldstone boson associated with the spontaneous breaking of lepton number symmetry [1,2], coupling to a neutrino ν as gJννJ, cf. Fig. 1 (left). Current searches have a 0νββJ ∼ ð10−5 Þ2 1024 sensitivity of the order T1=2 =gJ × yr. The term Majoron has been used in a wider sense, implying Published by the American Physical Society under the terms of 0νββ the Creative Commons Attribution 4.0 International license. FIG. 1. Feynman diagrams for ordinary J Majoron decay 0νββϕ Further distribution of this work must maintain attribution to (left), decay triggered by an effective operator of the form Λ−3 ð¯O Þð¯OνÞϕ the author(s) and the published article’s title, journal citation, NP u d e (center), and possible ultraviolet completion and DOI. Funded by SCOAP3. of the latter in a left-right symmetric model (right). 0031-9007=19=122(18)=181801(6) 181801-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 122, 181801 (2019) instead consider 0νββϕ decay with emission of a light broken or conserved is of crucial importance for an under- neutral scalar ϕ from a single effective dimension-seven lying model (determined by the chosen lepton numbers for Λ−3 ð¯O Þð¯OνÞϕ ν ϕ operator of the form NP u d e , cf. Fig. 1 (center), R and ) but as far as the effective interactions in Eq. (1) are with the fermion currents having a different chiral structure concerned, this does not play a role in our calculations. The from that in the SM. In the following, we will refer to the proton mass mp is introduced in the exotic interactions as light scalar as “Majoron,” independent of its origin. We ϵϕ normalization to make the effective coupling constants RL determine the sensitivity to Λ and analyze the effect on ϕ NP and ϵ dimensionless, in analogy to the effective operator the energy and angular distributions in comparison with RR treatment of 0νββ decay [10,11]. In Eq. (1), we omit exotic 2νββ decay. We also comment on ultraviolet scenarios operators with left-handed lepton currents; as in the standard underlying the effective operator. long-range case, such contributions will be additionally Effective long-range interactions.—We are interested in suppressed by the small neutrino masses [11]. We instead processes where right- and left-handed electrons are emit- focus on the process depicted in Fig. 1 (center), where the ted along with a scalar ϕ considering as a first approach, SM (V − A) Fermi interaction, the first term in Eq. (1), meets only (V þ A) and (V − A) currents. The effective one of the exotic operators. In this case, the momentum part Lagrangian can then be written as in the numerator of the neutrino propagator contributes, θ ϵϕ ϵϕ rather than the mass. In Eq. (1) we consider the first L ¼ GF pcosffiffiffi C μ þ RL μ ϕ þ RR μ ϕ 0νββϕ jLJLμ jRJLμ jRJRμ generation electron and neutrino only. Generalizing to three 2 mp mp ϕ flavors amounts to promoting the ϵ couplings to 3 × 3 þ ð Þ RX H:c:; 1 ðϵϕ Þ α ¼ μ τ matrices in generation space, RX αi ( e, , , θ ¼ ν ν ν with the Fermi constant GF, the Cabbibo angle C, and the i 1; 2; 3).P The final decay rate will then be proportional μ ¼ ¯γμð1 ∓ γ Þν jϵϕ j2 → j ðϵϕ Þ j2 leptonic and hadronic currents jL;R e 5 and to RX i RX eiUei , where U is the SM lepton μ ¼ ¯γμð1 ∓ γ Þ ν JL;R u 5 d, respectively. Here, is a four-spinor mixing matrix. field of the light electron neutrino, either defined by ν ¼ Decay rate and distributions.—We base our calculation ν þ νc 0νββϕ L L (i.e., a Majorana spinor constructed from the SM of the decay rate and kinematic distributions on Doi active left-handed neutrino νL)orν ¼ νL þ νR (a Dirac et al. [12]. The details of the calculation are given in the spinor constructed from the SM νL and a new SM-sterile Supplemental Material A [13]; here we outline the main right-handed neutrino νR). Whether the light neutrinos are of features. Summing over all intermediate nuclear states N, 0þ → 0þ 0νββϕ Majorana or Dirac type and whether total lepton number is the amplitude of I F decay can be written as Z Z 2 X 3 ϕ ðG cos θ Þ d q M ¼ ϵ Fpffiffiffi C 3 3 ϕðyÞ iqðx−yÞ d xd y 2 e RX 2m 2π ω p N ρσ L ρσ R J ðx; yÞuρσðE1x;E2yÞ J ðx; yÞuρσðE1x;E2yÞ LX − XL − ð ↔ Þ ð Þ × 1 1 E1 E2 : 2 ω þ μN − 2 ðE1 − E2 − EϕÞ ω þ μN − 2 ðE1 − E2 þ EϕÞ ¼ ϵϕ ϵϕ μ ¼ − þ Here, X L, R correspond to RL, RR, N EN EI antisymmetry of the amplitude under the exchange of the Qββ=2 þ me with EI and EN the energies of the initial and two electrons. intermediate nucleus, respectively. The energies of the two In Eq. (2), the Majoron energy Eϕ is added or subtracted outgoing electrons and the Majoron are E1;2 and Eϕ, depending on whether the electron labeled 1 or 2 is being respectively, and the available kinetic energy release emitted from the exotic operator. The Majoron makes a Qββ. The nucleon and lepton currents are defined as crucial difference, as Eϕ goes together with ðE1 − E2Þ and not with the term proportional to the intermediate nuclei ρσ ðx yÞ¼h j ρ ðxÞj ih j σ ðyÞj i ¼ μ JYX ; F JY N N JX I ;X;Y L; R; energy N as for an ordinary Majoron. A dependence on Eϕ ð3Þ will thus appear through the matrix element in addition to that through the phase space. The differential decay rate for the 0þ → 0þ 0νββϕ decay can then be written as [12] 1 L;Rð x yÞ¼ μ ¯ð xÞγ γ γ ð1 ∓ γ Þ cð yÞ ð Þ uρσ E1 ;E2 2 q e E1 ρ μ σ 5 e E2 : 4 ð θ Þ4 2 Γ ¼ GF cos CgA me ½ ð Þ We consider that the internal neutrino propagates between d 7 2 a E1;E2 256π ðmpRÞ the interaction points x and y with momentum qμ ¼ðω; qÞ.

Load more