Double-Beta Decay from First Principles J. Engel April 23, 2020 Goal is set of matrix elements with real error bars by May, 2021 DBD Topical Theory Collaboration Lattice QCD Data Chiral EFT Similarity Renormalization Group Ab-Initio Many-Body Methods Harmonic No-Core Quantum Oscillator Basis Shell Model Monte Carlo Effective Theory Light Nuclei (benchmarking) DFT-Inspired Coupled Multi-reference In-Medium SRG Clusters In-Medium SRG for Shell Model Heavy Nuclei DFT Statistical Model Averaging (for EDMs) Shell Model Goal is set of matrix elements with real error bars by May, 2021 DBD Topical Theory Collaboration Haxton HOBET Walker-Loud McIlvain LQCD Brantley Monge- Johnson Camacho Ramsey- SM Musolf Horoi Engel EFT SM Cirigliano Nicholson Mereghetti "DFT" EFT LQCD QMC Carlson Jiao Quaglioni Vary SRG NC-SM Yao Papenbrock LQCD = Latice QCD Hagen EFT = Effective Field Theory Bogner QMC = Quantum Monte Carlo Morris Hergert DFT = Densty Functional Theory Sun Nazarewicz Novario SRG = Similarity Renormilazation Group More IM-SRG IM-SRG = In-Medium SRG Coupled Clusters DFT HOBET = Harmonic-Oscillator-Based Statistics Effective Theory NC-SM = No-Core Shell Model SM = Shell Model DBD Topical Theory Collaboration Haxton HOBET Walker-Loud McIlvain LQCD Brantley Monge- Johnson Camacho Ramsey- SM Musolf Horoi Engel EFT SM Cirigliano Nicholson Mereghetti "DFT" EFT LQCD QMC Carlson Jiao Quaglioni Vary Goal is set of matrixSRG elementsNC-SM with Yao real error bars by May, 2021 Papenbrock LQCD = Latice QCD Hagen EFT = Effective Field Theory Bogner QMC = Quantum Monte Carlo Morris Hergert DFT = Densty Functional Theory Sun Nazarewicz Novario SRG = Similarity Renormilazation Group More IM-SRG IM-SRG = In-Medium SRG Coupled Clusters DFT HOBET = Harmonic-Oscillator-Based Statistics Effective Theory NC-SM = No-Core Shell Model SM = Shell Model Part 0 0νββ Decay and neutrinos are their own antiparticles... n Example: 136Xe p can observe two neutrons turning Others: 76Ge, 130Te, 150Nd ... w into protons, emitting two electrons l e and nothing else. Different from already observed e two-neutrino process. wl n p Neutrinoless Double-Beta Decay . If energetics are right (ordinary beta decay forbidden)... Z+1, N-1 Z, N Z+2, N-2 and neutrinos are their own antiparticles... n p can observe two neutrons turning w into protons, emitting two electrons l e and nothing else. Different from already observed e two-neutrino process. wl n p Neutrinoless Double-Beta Decay . If energetics are right (ordinary beta decay forbidden)... Z+1, N-1 Z, N Z+2, N-2 Example: 136Xe Others: 76Ge, 130Te, 150Nd ... n Example: 136Xe p can observe two neutrons turning Others: 76Ge, 130Te, 150Nd ... w into protons, emitting two electrons l e and nothing else. Different from already observed e two-neutrino process. wl n p Neutrinoless Double-Beta Decay . If energetics are right (ordinary beta decay forbidden)... Z+1, N-1 Z, N and neutrinos are their own antiparticles... Z+2, N-2 Example: 136Xe Others: 76Ge, 130Te, 150Nd ... Different from already observed two-neutrino process. Neutrinoless Double-Beta Decay . If energetics are right (ordinary beta decay forbidden)... Z+1, N-1 Z, N and neutrinos are their own antiparticles... Z+2, N-2 n p can observe two neutrons turning w into protons, emitting two electrons l e and nothing else. ν e wl n p Example: 136Xe Others: 76Ge, 130Te, 150Nd ... Neutrinoless Double-Beta Decay . If energetics are right (ordinary beta decay forbidden)... Z+1, N-1 Z, N and neutrinos are their own antiparticles... Z+2, N-2 n p can observe two neutrons turning w into protons, emitting two electrons l e and nothing else. ν ν Different from already observed e two-neutrino process. wl n p 4 1 ] -2 [eV] a) NO, QRPA b) IO, QRPA β β m 10−1 − 1 10−2 probability density [eV − 10−1 − − 10 3 −4 −2 10 − − − − 10 10 5 10−4 10 3 10−2 10−1 1 10 5 10−4 10 3 10−2 10−1 1 m [eV] m [eV] − l l FIG. 1. Marginalized posterior distributionsAgostini, for mββ and Benato,ml for NO (a) Detweiler and IO (b). The solid lines show the allowed parameter Whateverspace assuming 3σ intervals the hierarchy, of the neutrino oscillation the Majorana observables from nu-fit mass [12]. The must plot is producedcome assuming from QRPA NMEs and the absence of mechanisms that drive ml or mββ to zero. The probability density is normalized by the logarithm of mββ somewhere,and of ml. and the Standard Model by itself doesn’t allow it. ] Its-1 presenceIO IO & Planck impliesIO & m =0 new particles, whichposterior distribution could make is slightly theshifted low to smaller values l for IO, and the discovery probability of future experi- 10 NO NO & Planck NO & ml=0 masses of neutrinos natural, and couldments remains also verychange high. In 0 NO,νββmββ israte. pushed below the reach of future experiments, and the discovery prob- abilities are driven to be very small as shown in FIG.2. 1 Using ml in the fit basis with a log-flat scale invariant probability density [eV prior would provide the same results as long as the cutoff on ml, required to have normalizable posterior distribu- tions, is set low enough to make the result independent 10−1 of the choice of cutoff. 1 0.8 III. EXPERIMENTAL SENSITIVITY 0.6 cumulative probability 0.4 The experimental search for 0νββ decay is a very ac- tive field. There is a number of isotopes that can undergo 0.2 0νββ decay and many detection techniques have been 0 developed and tested in recent years [49, 50]. Examples −3 −2 −1 10 10 10 are: high-purity Ge detectors [51, 52], cryogenic bolome- mββ [eV] ters [53, 54], loaded organic liquid scintillators [27], time- projection chambers [55, 56], and tracking chambers [57]. FIG. 2. Top: marginalized posterior distributions of mββ Various larger-scale experiments with the sensitivity to (solid line) for NO and IO, normalized by the logarithm of probe the full IO parameter space are being mounted m . Bottom: complementary cumulative distribution func- ββ or proposed for the near or far future. This work fo- tions for mββ . The band shows the deformation of the pos- 1terior distribution due to different assumptions on the NME. cuses on those projects considered recently by the U.S. The data from cosmology provide a somewhat stronger con- DOE/NSF Nuclear Science Advisory Committee’s Sub- straint on mββ than the current 0νββ decay experiments. committee on Neutrinoless Double Beta Decay [58]: CU- 3 The sharp peaks visible in the mββ distributions are due to a PID [59, 60], KamLAND-Zen [61], LEGEND [62, 63], volume effect dominated by Σ and the Majorana phases. For nEXO [64], NEXT [65], PandaX-III [66], SNO+ [67, 68], 2 NO with m = 0 there is negligible variation due to the NME. l and SuperNEMO [69, 70]. Most of these projects follow a staged-approach in which the target mass will be progres- sively increased. The various phases and parameters of change by only tens of percent. each project are summarized in TABLEI and discussed 4 When the fit is performed with Σ fixed to its mini- in AppendixC. We would like to caution the reader, how- mum allowed value (corresponding to ml = 0), the mββ ever, that many of these experiments are under rapid de- posterior distribution is constrained to lie within the hor- velopment, and the parameters publicly available during izontal bands that extend to m 0 in FIG.1. The m the snapshot of time in which this manuscript was pre- 10101010 1l → ββ Neutrino Physics in Neutrinoless Double-Beta Decay Diagram is proportional to n p effective “Majorana mass” WL e of light neutrinos, Õ 2 ν mββ = Uei mi ; i e WL so if 0νββ decay is seen neutrinos are their own n p antiparticles! And if mass hierarchy is inverted, or maybe even if it’s normal, next generation of experiments should be able to see the decay. #it{m_{#beta#beta}} [eV] 4 1 ] -2 [eV] a) NO, QRPA b) IO, QRPA β β m 10−1 − 1 10−2 probability density [eV − 10−1 − − 10 3 −4 −2 10 − − − − 10 10 5 10−4 10 3 10−2 10−1 1 10 5 10−4 10 3 10−2 10−1 1 m [eV] m [eV] − l l FIG. 1. Marginalized posterior distributions for mββ and ml for NO (a) and IO (b). The solid lines show the allowed parameter Whateverspace assuming 3σ intervals the hierarchy, of the neutrino oscillation the Majorana observables from nu-fit mass [12]. The must plot is producedcome assuming from QRPA NMEs and the absence of mechanisms that drive ml or mββ to zero. The probability density is normalized by the logarithm of mββ somewhere,and of ml. and the Standard Model by itself doesn’t allow it. ] Its-1 presenceIO IO & Planck impliesIO & m =0 new particles, whichposterior distribution could make is slightly theshifted low to smaller values l for IO, and the discovery probability of future experi- 10 NO NO & Planck NO & ml=0 masses of neutrinos natural, and couldments remains also verychange high. In 0 NO,νββmββ israte. pushed below the reach of future experiments, and the discovery prob- abilities are driven to be very small as shown in FIG.2. 1 Using ml in the fit basis with a log-flat scale invariant probability density [eV prior would provide the same results as long as the cutoff on ml, required to have normalizable posterior distribu- tions, is set low enough to make the result independent 10−1 of the choice of cutoff.