An electroweak basis for neutrinoless double $β$ decay
Michael L. Graesser
备注：
31 pages, 6 tables, 1 figure. v3 updated references and added extended introduction, conclusions unchanged from v2. v4: updated references; final published version
A discovery of neutrinoless double-$β$ decay would be profound, providing the first direct experimental evidence of $ΔL=2$ lepton number violating processes. While a natural explanation is provided by an effective Majorana neutrino mass, other new physics interpretations should be carefully evaluated. At low--energies such new physics could manifest itself in the form of color and $SU(2)_L \times U(1)_{Y}$ invariant higher dimension operators. Here we determine a complete set of electroweak invariant dimension--9 operators, and our analysis supersedes those that only impose $U(1)_{em}$ invariance. Imposing electroweak invariance implies: 1) a significantly reduced set of leading order operators compared to only imposing $U(1)_{em}$ invariance; and 2) other collider signatures. Prior to imposing electroweak invariance we find a minimal basis of 24 dimension-9 operators, which is reduced to 11 electroweak invariant operators at leading order in the expansion in the Higgs vacuum expectation value. We set up a systematic analysis of the hadronic realization of the 4-quark operators using chiral perturbation theory, and apply it to determine which of these operators have long-distance pion enhancements at leading order in the chiral expansion. We also find at dimension--11 and dimension--13 the electroweak invariant operators that after electroweak symmetry breaking produce the remaining $ΔL=2$ operators that would appear at dimension--9 if only $U(1)_{em}$ is imposed.
We demonstrate that in the process of deducing the constraint on the electroweak mixing angle $θ_{W}$ in our paper, we have indeed been working with three mass scales while implementing (331) model.
Fundamental mechanisms for Majoron emitting neutrinoless double beta decay in SU(3)_C x G_W x U(1) models, for electroweak flavor chiral extensions, G_W = SU(3)_L and SU(4)_L are pointed out. Both kinds of known Majoron emitting processes, charged Majoron emitting where the massless Nambu-Goldstone boson itself carries lepton charge, $L=-2$, and the ordinary Majoron emitting where the boson has a small mass are found possible. PACS numbers: 11.15.Ex, 12.60.Fr, 14.80.Cp
We point out that if the majoron-like scheme is implemented within a 331 model, there must exist at least three different mass scales for the scalar vacuum expectation values in the model.
In a class of left-right symmetric models for linear seesaw, a neutrinoless double beta decay induced by the left- and right-handed charged currents together will only depend on the breaking details of left-right and electroweak symmetries. This neutrinoless double beta decay can reach the experimental sensitivities if the right-handed charged gauge boson is below the 100 TeV scale.
We present a master formula describing the neutrinoless-double-beta decay ($0νββ$) rate induced by lepton-number-violating (LNV) operators up to dimension nine in the Standard Model Effective Field Theory. We provide an end-to-end framework connecting the possibly very high LNV scale to the nuclear scale, through a chain of effective field theories. Starting at the electroweak scale, we integrate out the heavy Standard Model degrees of freedom and we match to an $SU(3)_c\otimes U(1)_{\mathrm{em}}$ effective theory. After evolving the resulting effective Lagrangian to the QCD scale, we use chir…
We give the prediction on the effective Majorana mass for neutrinoless double $β$ decay in a simple extension of the Standard Model (nuMSM). The model adds three right-handed neutrinos with masses smaller than the electroweak scale, and explains dark matter of the Universe. This leads to constraints 1.3meV<m_{bb}^{NH}<3.4meV in normal neutrino mass hierarchy and 13meV<m_{bb}^{IH}<50meV in inverted hierarchy.
We consider a class of simplest Majoron models where neutrino- majoron couplings can be in the range $g \sim 10^{-5}-10^{-3}$ leading to the observability of neutrinoless double beta decay with majoron emission. The majoron is a singlet of the electroweak gauge symmetry, thus avoiding conflict with the LEP data on Z decay, which rules out the triplet and doublet majoron models.
We consider a model for the electroweak interactions with $SU(3)_L\otimes U(1)_N$ gauge symmetry. We show that, it is the conservation of $F=L+B$ which forbids massive neutrinos and the neutrinoless double beta decay, $(ββ)_{0ν}$. Explicit and spontaneous breaking of $F$ imply that the neutrinos have an arbitrary mass and $(ββ)_{0ν}$ proceeds also with some contributions that do not depend explicitly on the neutrino mass.
We calculate basis-space converged neutrinoless $ββ$ decay nuclear matrix elements for the lightest candidates: 48Ca, 76Ge and 82Se. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed $ββ$-decay operators. We find that the tensor component is non-negligible in 76Ge and 82Se, and resulting nuclear matrix elements are overall 25-45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires …
The problem of Majorana neutrino mass generated in Arkani-Hamed--Dimopoulos-Dvali model with n extra spatial dimensions is discussed. Taking into account constraints on neutrino masses coming from cosmological observations, it is possible to obtain lower limits on the size of extra dimensions as large as 10^{-6} mm. In the case of n=4 it is easy to lower the fundamental scale of gravity from the Planck energy to electroweak scale TeV without imposing any additional constraints. A link between the half-life of neutrinoless double beta decay and the size of extra dimensions is discussed.
We examine the pion realization of the short ranged supersymmetric (SUSY) mechanism of neutrinoless double beta decay. It originates from the R-parity violating quark-lepton interactions of the SUSY extensions of the standard model of the electroweak interactions. We argue that pions are dominant SUSY mediators in neutrinoless double beta decay. The corresponding nuclear matrix elements for various isotopes are calculated within the proton-neutron renormalized quasiparticle random phase approximation. We define those isotopes which are most sensitive to the SUSY signal and outlook the present …
We discuss the impact of the observation of neutrinoless double beta decay on the washout of lepton number in the early universe. Neutrinoless double beta decay can be triggered by a large number of mechanisms that can be encoded in terms of Standard Model effective operators which violate lepton number by two units. We calculate the contribution of such operators to the rate of neutrinoless double beta decay and correlate it with the washout of lepton number induced by the same operators in the early universe. We find that the observation of a non-standard contribution to neutrinoless double …
We explore the influence of the deformation on the nuclear matrix elements of the neutrinoless double beta decay (NME), concluding that the difference in deformation -or more generally in the amount of quadrupole correlations- between parent and grand daughter nuclei quenches strongly the decay. We correlate these differences with the seniority structure of the nuclear wave functions. In this context, we examine the present discrepancies between the NME's obtained in the framework of the Interacting Shell Model and the Quasiparticle RPA. We surmise that part of the discrepancy can be due to th…
We consider the contributions to the neutrinoless double beta decays in a $SU(3)_L\otimes U(1)_N$ electroweak model. We show that for a range of the parameters in the model there are diagrams involving vector-vector-scalar and trilinear scalar couplings which can be potentially as contributing as the light massive Majorana neutrino exchange one. We use these contributions to obtain constraints upon some mass scales of the model, like the masses of the new charged vector and scalar bosons. We also consider briefly the decay in which besides the two electrons a Majoron-like boson is emitted.
Physics beyond the standard model of electroweak interactions that violates lepton number will, in general, induce operators involving the quark and lepton fields that violate lepton number. I point out that some matrix elements of particular operators are known. In the limit of exact SU(3) flavor symmetry the operator overline{u} gamma_mu (1-gamma_5)d overline{u} gamma_mu (1-gamma_5)d is part of the ${\bf 27}$ representation responsible for Delta I=3/2 strangeness changing decays in the standard model. At leading order in the chiral expansion there is only one coupling constant that describes…
Ab initio calculations of two-neutrino and neutrinoless double-$\boldsymbolβ$ decay of $^{48}$Ca and related Gamow-Teller strength distributions
Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心极端物质研究所(EMMI)）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
We examine the pion exchange mode of neutrinoless double beta decay induced by the R-parity violating quark-lepton operators of the supersymmetric (SUSY) extensions of the standard model of the electroweak interactions. The corresponding nuclear matrix elements are evaluated within the renormalized quasiparticle random phase approximation with proton-neutron pairing, which includes the Pauli effect of fermion pairs and does not collapse for a physical value of the nuclear force strength. It is argued that the pion-exchange mode of neutrinoless double beta decay dominates over the conventional …
We discuss the contributions of lepton-number-violating sources to neutrinoless double beta decay ($0νββ$). Assuming that these sources arise at scales well above the electroweak scale, they can be described within an effective field theory. Here, we outline the steps required to express the $0νββ$ half-life in terms of the effective interactions, focusing on the dimension-five operator that induces a Majorana mass for the neutrinos. This process involves the evolution of the operators down to scales of a few GeV where they can be matched onto Chiral Perturbation Theory. The resulting Chiral L…
We discuss a class of left-right symmetric theories with a universal seesaw mechanism for fermion masses and mixing and the implications for neutrinoless double beta ($0νββ$) decay where neutrino masses are governed by natural type-II seesaw dominance. The scalar sector consists of left- and right-handed Higgs doublets and triplets, while the conventional Higgs bidoublet is absent in this scenario. We use the Higgs doublets to implement the left-right and the electroweak symmetry breaking. On the other hand, the Higgs triplets with induced vacuum expectation values can give Majorana masses to …
We comment on the recent claim for the experimental observation of neutrinoless double-beta decay. We discuss several limitations in the analysis provided in that paper and conclude that there is no basis for the presented claim.
We study in detail the contribution of heavy composite Majorana neutrinos to neutrino-less double beta decay. Our analysis confirms the result of a previous estimate by two of the authors. Excited neutrinos couple to the electroweak gauge bosons through a magnetic type effective Lagrangian. The relevant nuclear matrix element is related to matrix elements available in the literature and current bounds on the half-life of neutrino-less double beta decay are converted into bounds on the compositeness scale and/or the heavy neutrino mass. Our bounds are of the same order of magnitude as those ava…
We study in this letter the behavior of the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the Interacting Shell Model. We analize them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear structure models. In addition, it gives back the due protagonism in this process to the pairing interaction, the interaction which is responsible for the very existenc…
We analyze neutrinoless double beta decay ($0νββ$) within the framework of the Standard Model Effective Field Theory. Apart from the dimension-five Weinberg operator, the first contributions appear at dimension seven. We classify the operators and evolve them to the electroweak scale, where we match them to effective dimension-six, -seven, and -nine operators. In the next step, after renormalization group evolution to the QCD scale, we construct the chiral Lagrangian arising from these operators. We develop a power-counting scheme and derive the two-nucleon $0νββ$ currents up to leading order …
The neutrinoless double $β$-decay is reviewed. Model independent evidence in favor of neutrino masses and mixing is briefly summarized. The data of the recent experiments on the search for $0νββ$-decay are presented and some future experiments are discussed. The possible values of the effective Majorana mass, which can be predicted on the basis of the neutrino oscillation data under different assumptions on the pattern of the neutrino mass spectrum, are considered. A possible model independent test of the nuclear matrix element calculations is discussed.
Recently the evidence of the neutrinoless double $β$ ($0νββ$) decay has been announced. This means that neutrinos are Majorana particles and their mass hierarchy is forced to inverted mass hierarchy (Type B) or degenerate mass (Type C) patterns in the diagonal basis of charged lepton mass matrix. We estimate the magnitude of $0νββ$ decay in the degenerate neutrinos including the cosmological constraint of neutrino dark matter, since the inverted mass hierarchy pattern always satisfies the cosmological constraint. The absolute value of neutrino mass is constrained by $0νββ$ experiment or cosmol…
The process at the heart of neutrinoless double-beta decay, $nn \rightarrow p p\, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-lea…
Based on the observed neutrino mass-square differences and mixings, we derive a few general patterns for the neutrino mass matrix in the flavor basis, which can correctly describe the atmospheric and solar neutrino data. Upon the most recent result on the absolute neutrino mass bound from WMAP, we can rule out a large portion of the parameter space that claimed by the positive signal in the Heidelberg-Moscow $0νββ$ experiment. In the case when one of the majorana phases is $π$, the effective neutrino mass obtained is inconsistent with the claim.
The original Zee model can easily accommodate a bi-maximal mixing solution for the atmospheric and solar neutrino problems. From the most recent fit to the data we obtain a set of parameters for the Zee model. However, the recent claim on a positive signal observed in a neutrinoless double beta decay, which requires a nonzero $m_{ee}$, cannot be accounted for by the Zee model. Based on the observed neutrino mass-square differences and mixings, we derive a few general patterns for the neutrino mass matrix in the flavor basis, which can correctly describe the atmospheric, solar, and $0νββ$ data.…
Global Ab initio Neutrino Mass Limits from Neutrinoless Double-Beta Decay
TRIUMF；University of British Columbia（不列颠哥伦比亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心有限公司）；Massachusetts Institute of Technology（麻省理工学院）；McGill University（麦吉尔大学）
We discuss some phenomenological issues of the effective quark-lepton operators emerging from the bilinear lepton-Higgs couplings in the superpotential and in the soft supersymmetry (SUSY) breaking sector of the supersymmetric models without R-parity. The contribution of these operators to the neutrinoless double beta decay is derived. The corresponding nuclear matrix elements are calculated within the renormalized quasiparticle random phase approximation, which includes the Pauli effect of fermion pairs and does not collapse for the physical values of the nuclear force strength. On this basis…
The results of the HEIDELBERG-MOSCOW experiment which searches with 11 kg of enriched 76Ge for double beta decay in the GRAN Sasso underground laboratory are presented for the full running period August 1990 - May 2003. The duty cycle of the experiment was ~80%, the collected statistics is 71.7 kg y. The background achieved in the energy region of the Q value for double beta decay is 0.11 events/ kg y keV. The two-neutrino accompanied half-life is determined on the basis of more than 100 000 events. The confidence level for the neutrinoless signal has been improved to 4.2 sigma.
We consider the neutrinoless double beta ($0νββ$) decay in the so-called $ν$MSM, in which three right-handed neutrinos with masses below the electroweak scale are additionally introduced to the Standard Model. In this model there appear three heavy neutral leptons $N_1$, $N_2$, and $N_3$ corresponding to right-handed neutrinos. It has been known that the lightest one $N_1$ with keV mass, which is a candidate for dark matter, gives a negligible contribution to the $0 νββ$ decay. By contrast, the heavier ones $N_2$ and $N_3$, which are responsible to the seesaw mechanism of neutrino masses and b…
The relations between the effective Majorana mass of the electron neutrino, $m_{ee}$, responsible for neutrinoless double beta decay, and the neutrino oscillation parameters are considered. We show that for any specific oscillation pattern $m_{ee}$ can take any value (from zero to the existing upper bound) for normal mass hierarchy and it can have a minimum for inverse hierarchy. This means that oscillation experiments cannot fix in general $m_{ee}$. Mass ranges for $m_{ee}$ can be predicted in terms of oscillation parameters with additional assumptions about the level of degeneracy and the ty…
The experimental rate of neutrinoless double beta decay can be saturated by the exchange of virtual sterile neutrinos, that mix with the ordinary neutrinos and are heavier than 200 MeV. Interestingly, this hypothesis is subject only to marginal experimental constraints, because of the new nuclear matrix elements. This possibility is analyzed in the context of the Type I seesaw model, performing also exploratory investigations of the implications for heavy neutrino mass spectra, rare decays of mesons as well as neutrino-decay search, LHC, and lepton flavor violation. The heavy sterile neutrinos…
We consider a gauge model based on $SU(3)\otimes U(1)$ symmetry in which the lepton number is violated explicitly by charged scalar and gauge bosons, including a vector field with double electric charge. Although there exist in the literature several models based on a $SU(3)\otimes U(1)$ gauge symmetry, our model has a different representation content and a quite different new physics at an, in principle, arbitrary mass scale. This is possibly the simplest way to enlarge the gauge group $SU_L(2)\otimes U_Y(1)$ in order to have doubly charged gauge bosons, without losing the natural features of…
We study a type I see-saw scenario where the right-handed (RH) neutrinos, responsible for the light neutrino mass generation, lie at the electroweak scale. Under certain conditions, the strength of the charged and neutral current weak interactions of the Standard Model particles with the heavy RH neutrinos can be large enough to allow their production at the LHC, opening also the possibility of observing other low energy signatures of the new physics in the electroweak precision observables as well as in searches for rare leptonic decays or neutrinoless double beta decay. We argue that in this…
Complete UV Resonances of SMEFT Dim-9 Operators for Short-range Neutrinoless Double Beta Decay
School of Physics, Sun Yat-Sen University（中山大学物理学院）；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）；School of Science, Sun Yat-Sen University（中山大学科学学院）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；International Center for Theoretical Physics Asia-Pacific（亚太理论物理中心）
We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.
The standard model for electroweak interactions uses the concepts of weak hypercharge and local gauge invariance of the Lagrangian density under the gauge group SU(2) x U(1). Taylor has remarked that U(1), being a multiply-connected group, in general, should have different coupling strengths for singlets and doublets. But in the development of the standard model, even for U(1), the coupling strength has been taken to be the same for all the multiplets without a priori justification. Wilczek has pointed out that the assignment of hypercharge values to left- and right-handed leptons and quarks i…
We analyze the impact of the recently released CDF-II measurement of $W$ mass on the SMEFT analyses of the electroweak precision data as well as Higgs and electroweak diboson productions. We work in the Hagiwara, Ishihara, Szalapski, and Zeppenfeld basis in which eight generation-independent operators enter in the electroweak precision data at tree level and, unlike in the Warsaw basis, the analysis of that set of data constrains all the eight Wilson coefficients, without the need of combination with Higgs or electroweak diboson data results. We show that in the global analysis the determinati…
Neutrinoless double beta decay is the only realistic probe of the Majorana nature of the neutrino. In the standard picture, its rate is proportional to $m_{ee}$, the e-e element of the Majorana neutrino mass matrix in the flavor basis. I explore minimally allowed $m_{ee}$ values within the framework of mass matrix anarchy where neutrino parameters are defined statistically at low energies. Distributions of mixing angles are well defined by the Haar integration measure, but masses are dependent on arbitrary weighting functions and boundary conditions. I survey the integration measure parameter …
Recently the evidence of the neutrinoless double $β$ ($0νββ$) decay has been announced. This means that neutrinos are Majorana particles and their mass hierarchy is forced to certain patterns in the diagonal basis of charged lepton mass matrix. We estimate the magnitude of $0νββ$ decay in the classification of the neutrino mass hierarchy patterns as Type A, $m_{1,2} \ll m_{3}$, Type B, $m_1 \sim m_2 \gg m_3$, and Type C, $m_1 \sim m_2 \sim m_3$, where $m_{i}$ is the $i$-th generation neutrino absolute mass. The data of $0νββ$ decay experiment suggests the neutrino mass hierarchy pattern should…
There is a common belief that the main uncertainties in the theoretical analysis of neutrinoless double beta ($0νββ$) decay originate from the nuclear matrix elements. Here, we uncover another previously overlooked source of potentially large uncertainties stemming from non-perturbative QCD effects. Recently perturbative QCD corrections have been calculated for all dimension 6 and 9 effective operators describing $0νββ$-decay and their importance for a reliable treatment of $0νββ$-decay has been demonstrated. However, these perturbative results are valid at energy scales above $\sim 1$ GeV, wh…
We propose a new theory framework to study the electroweak radiative corrections in $K_{l3}$ decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important $\mathcal{O}(G_Fα)$ radiative corrections are described by a single tensor $T^{μν}$ involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special advantage in the $K_{l3}^{0}$ channel that it suffers the least imp…
The occurrence of the neutrinoless decay 0n-bb mode has fundamental consequences: first total lepton number is not conserved, and second, the neutrino is a Majorana particle. Further the effective mass measured allows to put an absolute scale of the neutrino mass spectrum. In addition, double beta experiments yield sharp restrictions also for other beyond standard model physics. These include SUSY models, leptoquarks (leptoquark-Higgs coupling),compositeness, left-right symmetric models (right-handed W boson mass), test of special relativity and of the equivalence principle in the neutrino sec…
As an important step towards a complete next-to-leading order (NLO) QCD analysis of the ratio $\varepsilon'/\varepsilon$ within the Standard Model Effective Field Theory (SMEFT), we present for the first time the NLO master formula for the BSM part of this ratio expressed in terms of the Wilson coefficients of all contributing operators evaluated at the electroweak scale. To this end we use the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. The relevant hadronic matrix elements of BSM operators at th…
Electroweak theory joins electromagnetism with the weak force in a single quantum field theory, ascribing the two fundamental interactions--so different in their manifestations--to a common symmetry principle. How the electroweak gauge symmetry is hidden is one of the most urgent and challenging questions facing particle physics. The provisional answer incorporated in the "standard model" of particle physics was formulated in the 1960s by Higgs, by Brout & Englert, and by Guralnik, Hagen & Kibble: The agent of electroweak symmetry breaking is an elementary scalar field whose self-interactions …
The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading order QCD. The results are presented for two common choices of the operator basis. This paves the way for a consistent matching of perturbatively evaluated Wilson coefficients and non-perturbative matrix elements evaluated by lattice simulations.
The matrix elements of electroweak currents which occur in exclusive decays of heavy hadrons are evaluated in the nonperturbative light-cone Fock representration. In general, each semileptonic exclusive decay amplitude receives two contributions, a diagonal $Δn = 0$ parton-number-conserving amplitude and a $Δn = -2$ contribution in which a quark and an antiquark from the initial hadron Fock state annihilate to the leptonic current. The general formalism can be used as a basis for systematic approximations to heavy hadron decay amplitudes such as hard perturbative QCD contributions. We illustra…
We discuss how the leading electroweak Higgs production processes at the LHC, namely vector-boson fusion and Higgs+W/Z associated production, can be characterized in generic extensions of the Standard Model by a proper set of pseudo-observables (PO). We analyze the symmetry properties of these PO and their relation with the PO set appearing in Higgs decays. We discuss in detail the kinematical studies necessary to extract the production PO from data, and present a first estimate of the LHC sensitivity on these observables in the high-luminosity phase. The impact of QCD corrections and the kine…
Universal Seesaw Model is a model which explains the mass hierarchy of the quark sector. This model introduces vector-like quarks. The top quark mass is generated in the electroweak scale and the other quark mass is generated using a seesaw-like mechanism. The invariant theory helps construct a weak-basis invariant. We study the weak-basis invariant (WBI) using Hilbert Series (HS) and apply it to the Universal Seesaw Model, particularly the one-generation case of the quark sector.
The observed phenomenon of neutrino oscillations is interpreted as the proof that neutrinos must have mass. As this is true for the neutrinos in the mass basis, the mass matrix in the flavor (weak) basis may still contain zeros. This can happen if the CP violating phases, usually neglected, come into play and result in suppression of processes which half-life depends on the masses of $ν_e$, $ν_μ$, or $ν_τ$. In the present paper we investigate the possibility of such suppression of the neutrinoless double beta decay ($0\nu2β$).
Models of Weakly Interacting Massive Particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computati…
We review the effective field theory approach to physics beyond the Standard Model using dimension-six operators. Topics include the choice of operator basis, electroweak boson pair production, precision electroweak physics (including one-loop contributions), and Higgs physics. By measuring the coefficients of dimension-six operators with good accuracy, we can hope to infer some or all of the features of the theory that lies beyond the Standard Model.
