Search

We investigate the impact of effective interactions of dimension-8 (dim-8) operators in the standard model effective field theory (SMEFT) on neutral meson mixing, focusing on the $K^0-\bar K^0$, $B_{d,s}-\bar B_{d,s}$, and $D^0-\bar D^0$ systems. Within the framework of the low energy effective field theory (LEFT), each system is governed by eight dim-6 operators, with four originating at tree level from dim-6 SMEFT operators and the other four from dim-8 SMEFT operators. Notably, in certain UV complete models those dim-8 operators instead of the dim-6 ones are generated at the leading order. Our analysis focuses on those dim-8 operators and includes their one-loop QCD renormalization group running effects. By leveraging the LEFT master formula we impose stringent constraints on the effective scales associated with these dim-8 operators. We find that neutral meson mixing can probe an effective scale up to 50 TeV for some operators, surpassing the constraints imposed on other dim-8 operators by other observables. Lastly, we present a UV complete model capable of generating dim-8 operators at the leading order, thus offering a unique perspective on the interplay between different operator dimensions in probing new physics phenomena., Comment: 20 pages, 4 figures

In this paper, we systematically investigate the general dark matter-electron interactions within the framework of effective field theories (EFT). We consider both the non-relativistic (NR) EFT and the relativistic EFT descriptions of the interactions with the spin of dark matter (DM) up to one, i.e., the scalar ($\phi$), fermion ($\chi$), and vector $(X)$ DM scenarios. We first collect the leading-order NR EFT operators describing the DM-electron interactions, and construct especially the NR operators for the vector DM case. Next, we consider all possible leading-order relativistic EFT operators including those with a photon field and perform the NR reduction to match them onto the NR EFT. Then we rederive the DM-bound-electron scattering rate within the NR EFT framework and find that the matrix element squared, which is the key input that encodes the DM and atomic information, can be compactly decomposed into three terms. Each term is a product of a DM response function $(a_{0,1,2})$, which is essentially a factor of Wilson coefficients squared, and its corresponding generalized atomic response function ($\widetilde W_{0,1,2}$). Lastly, we employ the electron recoil data from the DM direct detection experiments (including XENON10, XENON1T, and PandaX-4T) to constrain all the non-relativistic and relativistic operators in all three DM scenarios. We set strong bounds on the DM-electron interactions in the sub-GeV region. Particularly, we find that the latest PandaX-4T S2-only data provide stringent constraints on dark matter with a mass greater than approximately 20 MeV, surpassing those from the previous XENON10 and XENON1T experiments., Comment: 37 pages, 8 figures, minor corrections for several typos, and added one reference. Accepted by JHEP

We propose the nucleon consumption induced by dark matter as a new scenario to overcome the energy threshold of direct detection. It can be realized with proton ($\chi + p \rightarrow \chi + \ell^+$) or neutron ($\chi + n \rightarrow \chi + \nu$) target. Both effective operators and concrete models are provided to illustrate the idea. Since the initial DM and nucleon velocity is only $10^{-3}$ and $1/4$ of the speed of light, respectively, the cross section and hence event rate are determined by the involved particle masses and not affected by the nucleon Fermi motion. Of the two realizations, the proton consumption has richer phenomena with both charged lepton and the daughter nuclei de-excitation to allow double or even triple coincidence to significantly suppress the background. We also illustrate the projected sensitivities at DM and neutrino experiments such as PandaX-4T, DUNE, JUNO, and Hyper-K., Comment: 6 pages, 3 figures

In this letter we revisit general dark matter (DM)-bound-electron interactions studied previously in the influential work of [Catena et al., Phys. Rev. Res. 2, 033195 (2020)]. We derive the DM-electron response functions and find a crucial minus sign was missed for the second atomic response function $W_2$ defined in that work. The minus sign has significant phenomenological consequences when explaining experimental bounds on specific DM scenarios. Furthermore, for the most general DM-electron nonrelativistic or relativistic interactions for DM with spin up to one, we find there are three DM response functions ($a_{0,1,2}$) whose corresponding atomic response functions ($\widetilde W_{0,1,2}$) are linear combinations of the four response functions ($W_{1,2,3,4}$) given in that work, $$ \widetilde W_0 = W_1, \, \widetilde W_2 = |\mathbf{v}_0^\perp|^2 W_1+ W_3 - 2 {m_e\, \mathbf{q}\cdot \mathbf{v}_0^\perp \over \mathbf{q}^2} W_2,\, \widetilde W_3 = { (\mathbf{q}\cdot \mathbf{v}_0^\perp)^2 \over \mathbf{q}^2} W_1 + {m_e^2 \over \mathbf{q}^2}W_4 - 2 {m_e\, \mathbf{q}\cdot \mathbf{v}_0^\perp \over \mathbf{q}^2} W_2. $$ Due to the minus sign correction for $W_2$, there can be significant cancellations between the $W_2$ and $W_{3,4}$ terms, so that $\widetilde W_{2,3}$ are dominated by the usual response function $W_1$ in some cases. Ignoring the sign could thus result in misinterpretation of the experimental data in some DM scenarios. As an example, we show that the recent XENON1T constraint on the fermionic DM anapole moment is weakened by a factor of 2 or so. Many DM scenarios involving DM or electron axial-vector current can yield $W_2$ and thus are potentially affected by the sign., Comment: 6+2 pages, 4 figures

Recently Belle II reported the first measurement of $B^+\to K^++{\rm invisible (inv)}$, which is $2.7\sigma$ above the standard model (SM) prediction. If confirmed, this calls for new physics beyond SM. In the SM, the invisible particles are neutrino-anti-neutrino pairs. There are more possibilities when going beyond the SM. In this work, we focus on decays to dark matter (DM) and show that the $B\to K +\mathrm{inv}$ excess from Belle II and DM relic density can be simultaneously explained in a simple extension of the SM. The model introduces a real scalar singlet $\phi$ acting as a DM candidate, and two heavy vector-like quarks $Q,D$ with the same quantum numbers as the SM left-handed quark doublet and right-handed down-type quark singlet, respectively. All these new particles are odd under a $\mathbb{Z}_2$ symmetry while the SM particles are even. The model can successfully explain the Belle II anomaly and DM relic density for TeV-scale heavy quarks with hierarchical Yukawa couplings involving $b$ and $s$ quarks. At the same time, it can easily satisfy other flavour physics constraints. Direct detection searches utilizing the Migdal effect constrain some of the parameter space., Comment: v2: add the dark matter direct detection constraints due to the Migdal effect. To appear in JHEP

Effective field theory (EFT) provides a model-independent framework for interpreting the results of dark matter (DM) direct detection experiments. In this study, we demonstrate that the two fermionic DM-quark tensor operators, $(\bar{\chi} i\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$ and $(\bar{\chi} \sigma^{\mu\nu} \chi) (\bar{q} \sigma_{\mu\nu} q)$, can contribute to the DM electric and magnetic dipole moments via nonperturbative QCD effects, in addition to the well-studied contact DM-nucleon operators. We then investigate the constraints on these two operators by considering both the contact and the dipole contributions using the XENON1T nuclear recoil and Migdal effect data. We also recast other existing bounds on the DM dipole operators, derived from electron and nuclear recoil measurements in various direct detection experiments, as constraints on the two tensor operators. For $m_\chi \lesssim 1\,\rm GeV$, our results significantly extend the reach of constraints on the DM-quark tensor operators to masses as low as $5\,\rm MeV$, with the bound exceeding that obtained by the Migdal effect with only contact interactions by an order of magnitude or so. In particular, for the operator $(\bar{\chi} \sigma^{\mu\nu}i\gamma_5 \chi) (\bar{q} \sigma_{\mu\nu}q)$ with DM mass $m_\chi \gtrsim 10\,\rm GeV$, the latest PandaX constraint on the DM electric dipole moment puts more stringent bounds than the previous direct detection limit., Comment: v1: 19 pages, 4 figures; v2: We have updated discussion on nucleon form factors by using more recent numbers, without modifying our final numerical results; v3: Add comparisons with other constraints and provide a UV model for the generation of tensor operators from tree-level matching; To be published in CPC

Belle II has recently reported the new measurement ${\cal B}(B^+\to K^+\nu\bar\nu)=(2.3\pm0.7)\times 10^{-5}$ \cite{Belle-II:2023esi} which is two times larger than their previous result (although consistent within errors) and about $2.7\,\sigma$ higher than the SM prediction. We re-examine new physics scenarios we have discussed previously which can enhance this rate to determine if they can accommodate the higher value reported in the new measurement. We use consistency with existing bounds on $B\to K^*\nu\bar\nu$, $b\to s \ell^+\ell^-$, $B\to D^{(*)}\ell\bar\nu$ and $B_s$ mixing to limit possible explanations for the excess. For the case of LFV neutrino couplings, we find that only two leptoquarks remain viable requiring a large $C_{9^\prime}^{\tau\tau}=-C_{10^\prime}^{\tau\tau}$. For models with different types of light dark matter particle pairs (scalar, fermion, or vector), the preliminary $q^2$ distribution from Belle II, which shows that the excess appears mostly for bins with $3\leq q^2\leq7$ GeV$^2$ \cite{Belle-II:2023esi}, implies only the vector current operators with scalar or vector dark matter particles with masses in the hundreds of MeV can match the anomaly., Comment: Correct two typos

We introduce the effective field theory of two different light dark particles interacting with the standard model (SM) light states in a single vertex, termed dark sector effective field theory (DSEFT). We focus on the new light particles with spin up to 1 and being real in essence, namely, new real scalars $\phi$ and $S$, Majorana fermions $\chi$ and $\psi$, and real vectors $X_\mu$ and $V_\mu$. In the framework of low energy effective field theory with QED and QCD symmetry, the DSEFT can be classified into six categories, including the scalar-scalar-SM ($\phi S$-SM), fermion-fermion-SM ($\chi\psi$-SM), vector-vector-SM ($X V$-SM), scalar-fermion-SM ($\phi \chi$-SM), scalar-vector-SM ($\phi X$-SM), and fermion-vector-SM ($\chi X$-SM) cases. For each case, we construct the effective operator basis up to canonical dimension 7, which will cover most interesting phenomenology at low energy. As a phenomenological example, we investigate the longstanding neutron lifetime anomaly through the neutron dark decay modes $n \to \chi \phi \text{ or } \chi X$ from the effective interactions in the fermion-scalar-SM or fermion-vector-SM case. When treating the light fermion as a dark matter candidate, we also explore the constraints from DM-neutron annihilation signal at Super-Kamiokande. We find the neutron dark decay in each scenario can accommodate the anomaly, at the same time, without contradicting with the Super-Kamiokande limit., Comment: 33 pages, 4 figures, typos are corrected and several new references are included. To appear in JHEP

Fermionic dark matter can be pairly produced and hence searched with missing energy at colliders. We extend such probe to the associated production of a neutrino and a dark sector fermion at the future $e^+ e^-$ colliders such as CEPC, FCC-ee, ILC, and CLIC. Two typical processes, the mono-photon and electron-positron pair productions associated with missing energy, can serve the purpose. While the mono-photon search prevails at CEPC, FCC-ee, and ILC, the $e^+ e^- \met$ channel has more significant contributions at CLIC with much higher collision energy $\sqrt s$. The beam polarizations can help further suppressing the SM backgrounds to enhance the signal significance while differential cross sections can distinguish the Lorentz structure of various effective operators. The combined sensitivity can reach well above $1\tev$ at CEPC/FCC-ee and ILC while it further touches 30\,TeV at CLIC. Comparing with the updated results from the direct detection experiments (XENON1T, PandaX-II, PandaX-4T, LZ, and XENONnT), astrophysical $X/\gamma$-ray observations, and cosmological constraints for the sub-MeV absorption dark matter, the collider searches are actually more sensitive and hence can provide a complementary approach to addressing the dark fermions., Comment: 34pages, 17 captioned figures; v2: Title and text are improved

The scotogenic neutrino seesaw model is a minimal extension of the standard model with three $\mathbb{Z}_2$-odd right-handed singlet fermions $N$ and one $\mathbb{Z}_2$-odd Higgs doublet $\eta$ that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional matching formalism to the one-loop matching of the model onto the standard model effective field theory up to dimension seven for the case when all new states $N$ and $\eta$ are heavy to be integrated out. This is a realistic example which has no tree-level matching due to the $\mathbb{Z}_2$ symmetry. Using the matching results, we analyze their phenomenological implications for several physical processes, including the lepton number violating effect, the CDF $W$ mass excess, and the lepton flavor violating decays like $\mu\to e\gamma$ and $\mu\to 3e$., Comment: 28 pages, 2 figures, matched with the published version in JHEP

We consider decays of $B$ and $K$ mesons into a pseudo-scalar or vector meson plus missing energy. Within the SM, these modes originate from flavor changing neutral current (FCNC) processes with two neutrinos in the final state. In this paper we consider the experimental upper bounds on these modes and interpret the difference between these bounds and the SM prediction as a window into new light invisible particles. In particular we consider the case where some new symmetry requires the new particles to be produced in pairs. We first construct the general low energy effective Lagrangian coupling an FCNC with two dark sector particles of spin zero, one-half and one. We then present numerical estimates for the constraints that can be placed on these interactions, finding that an effective new physics scale from ${\cal O}(10)$-${\cal O}(10^{11})$ GeV can be probed, with the exact value strongly depending on the interaction structure as well as the mass of the invisible particle. For $K^+\to \pi^+ \displaystyle{\not} E$ we incorporate into our constraints the effect of using only the signal regions of NA62, and for $B^+\to K^+ \displaystyle{\not} E$ the $q^2$-dependent efficiency of Belle II., Comment: 40 pages, 42 figures, the consideration of Belle II efficiency is clarified and corrected, several new references are added, to appear in JHEP

We report a search on a sub-MeV fermionic dark matter absorbed by electrons with an outgoing active neutrino using the 0.63 tonne-year exposure collected by PandaX-4T liquid xenon experiment. No significant signals are observed over the expected background. The data are interpreted into limits to the effective couplings between such dark matter and electrons. For axial-vector or vector interactions, our sensitivity is competitive in comparison to existing astrophysical bounds on the decay of such dark matter into photon final states. In particular, we present the first direct detection limits for an axial-vector (vector) interaction which are the strongest in the mass range from 25 to 45 (35 to 50) keV/c$^2$.

We perform a systematic study of the fermionic DM absorption interactions on electron target in the context of effective field theory. The fermionic DM absorption is not just sensitive to sub-MeV DM with efficient energy release, but also gives a unique signature with clear peak in the electron recoil spectrum whose shape is largely determined by the atomic effects. Fitting with the Xenon1T and PandaX-II data prefers DM mass at $m_\chi = 59$keV and 105keV, respectively, while the cut-off scale is probed up to around 1TeV. The DM overproduction in the early Universe, the invisible decay effect on the cosmological evolution, and the astrophysical X(gamma)-ray from the DM visible decays are thoroughly explored to give up-to-date constraints. With stringent bounds on the tensor and pseudo-scalar operators, the other fermionic DM operators are of particular interest at tonne-scale direct detection experiments such as PandaX-4T, XENONnT, and LZ., Comment: 30 pages, 7 figures, and 1 table

We propose a new scenario of using the dark axion portal at one-loop level to explain the recently observed muon anomalous magnetic moment by the Fermilab Muon g-2 experiment. Both axion/axion-like particle (ALP) and dark photon are involved in the same vertex with photon. Although ALP or dark photon alone cannot explain muon $g-2$, since the former provides only negative contribution while the latter has very much constrained parameter space, dark axion portal can save the situation and significantly extend the allowed parameter space. The observed muon anomalous magnetic moment provides a robust probe of the dark axion portal scenario., Comment: 8 pages, 6 figures, match the EPJC version

We study the implication of $J/\psi$ decay into invisible particles for light sterile neutrino and sub-GeV dark matter (DM). The low-energy effective field theories (EFTs) are used for the description of general neutrino interactions and the Dirac fermion DM coupled to charm quark. For $J/\psi\to \gamma+{\rm invisible}$, we perform the likelihood fits for the individual neutrino and DM operators with distinct Lorentz structures and photon spectra. The limits on the decay branching fractions are obtained for different neutrino or DM scenarios and then converted to the lower bounds on the new energy scales. The most stringent bounds on the energy scale in neutrino and DM EFTs are 12.8 GeV and 11.6 GeV, respectively. The purely invisible decay $J/\psi\to {\rm invisible}$ provides complementary constraints on the effective operators. The relevant bound on the energy scale is above 100 GeV for the dipole operators. We also evaluate the limit on the DM-nucleon scattering cross section converted from $J/\psi$ data. The data of $J/\psi$ invisible decays are sensitive to the light DM mass range where the DM direct detection experiments cannot probe yet. The future Super Tau Charm Factory after one year run can push the limits down by two orders of magnitude., Comment: 24 pages, 5 figures, 1 table. version accepted by PRD

We continue our endeavor to investigate lepton number violating (LNV) processes at low energy in the framework of effective field theory (EFT). In this work we study the LNV tau decays $\tau^+\rightarrow \ell^-P_i^{+}P_j^{+}$, where $\ell=e,~\mu$ and $P^+_{i,j}$ are the lowest-lying charged pseudoscalars $\pi^+,~K^+$. We analyze the dominant contributions in a series of EFTs from high to low energy scales, namely, the standard model effective field theory (SMEFT), the low-energy effective field theory (LEFT), and the chiral perturbation theory ($\chi$PT). The decay branching ratios are expressed in terms of the Wilson coefficients of dimension-five and -seven operators in SMEFT and hadronic low energy constants. These Wilson coefficients involve the first and second generations of quarks and all generations of leptons and thus cannot be explored in low energy processes such as nuclear neutrinoless double decay or LNV kaon decays. Unfortunately, the current experimental upper limits on the branching ratios are too weak to set useful constraints on those coefficients. Or, if we assume the new physics scale is larger than 1 TeV, the branching ratios are well below the current experimental bounds. We also estimate hadronic uncertainties incurred in applying $\chi$PT to $\tau$ decays by computing one-loop chiral logarithms and attempt to improve convergence of chiral perturbation by employing dispersion relations in the short-distance part of the decay amplitudes., Comment: 16 pages, 4 figures, 4 tables

In this paper we systematically consider the baryon ($B$) and lepton ($L$) number violating dinucleon to dilepton decays ($pp\to \ell^+\ell^{\prime+}, pn\to \ell^+\bar\nu^\prime, nn\to \bar\nu\bar\nu^\prime$) with $\Delta B=\Delta L=-2$ in the framework of effective field theory. We start by constructing a basis of dimension-12 (dim-12) operators mediating such processes in the low energy effective field theory (LEFT) below the electroweak scale. Then we consider their standard model effective field theory (SMEFT) completions upwards and their chiral realizations in baryon chiral perturbation theory (B$\chi$PT) downwards. We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions, and express the decay rates in terms of the Wilson coefficients associated with the dim-12 operators in SMEFT and the low energy constants pertinent to B$\chi$PT. We find the current experimental limits push the associated new physics scale larger than $1-3$ TeV, which is still accessible to the future collider searches. Through weak isospin symmetry, we find the current experimental limits on the partial lifetimes of transitions $pp\to \ell^+\ell^{\prime+}, pn\to \ell^+\bar\nu^\prime$ imply stronger limits on $nn\to\bar\nu\bar\nu^\prime$ than their existing lower bounds, which are improved by $2-3$ orders of magnitude. Furthermore, assuming charged mode transitions are also dominantly generated by the similar dim-12 SMEFT interactions, the experimental limits on $pp\to e^+e^+,e^+\mu^+,\mu^+\mu^+$ lead to stronger limits on $pn\to \ell^+_\alpha\bar\nu_\beta$ with $\alpha,\beta=e,\mu$ than their existing bounds. Conversely, the same assumptions help us to set a lower bound on the lifetime of the experimentally unsearched mode $pp\to e^+\tau^+$ from that of $pn\to e^+\bar\nu_\tau$, i.e., $\Gamma^{-1}_{pp\to e^+\tau^+}\gtrsim 2\times 10^{34}~\rm yrs$., Comment: 55 pages, 2 figures, small revisions based on referee's constructive comments, typos are corrected and new references are added, version will appear in JHEP

We discuss the unique baryon number violation by two units neutron decay mode $n\to \bar p e^+\chi$, with $\chi$ being the standard model (SM) neutrino $\nu$ or antineutrino $\bar\nu$ or any beyond SM light fermion, in the framework of effective field theory. This mode is kinematically allowed but rarely discussed theoretically or searched for experimentally. We estimate the lower bound on its partial lifetime from that of the dinucleon decay $np\to e^+\chi$ per oxygen nucleus $^{16}$O set by the Super-Kamiokande experiment, with a conservative bound $\Gamma^{-1}_{n\to\bar pe^+\chi}>5.7\times 10^{39}~\rm yrs$. We also discuss its characteristic signature for the future experimental search and astrophysical implications., Comment: 6 pages, references updated, expanded discussion, version to appear in PLB

In this work we investigate the implication of low-energy precision measurements on the quark-lepton charged currents in general neutrino interactions with sterile neutrinos in effective field theories. The physics in low-energy measurements is described by the low-energy effective field theory extended with sterile neutrinos (LNEFT) defined below the electroweak scale. We also take into account renormalization group running and match the LNEFT onto the Standard Model (SM) effective field theory with sterile neutrinos (SMNEFT) to constrain new physics (NP) above the electroweak scale. The most sensitive low-energy probes are from leptonic decays of pseudoscalar mesons and hadronic tau lepton decays in terms of precise decay branching fractions, the lepton flavor universality and the Cabibbo-Kobayashi-Maskawa (CKM) unitarity. We also consider other constraints including nuclear beta decay. The constraints on charged current operators are generally stronger than the ones for quark-neutrino neutral current operators. We find that the most stringent bounds on the NP scale of lepton-number-conserving and lepton-number-violating operators in SMNEFT are 74 (110) TeV and 9.8 (13) TeV, respectively, for the operators with down (strange) quark., Comment: 34 pages, 12 tables. Version accepted by JHEP

We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $384|^{\Delta L=\pm 2}_{\Delta B=0}+10|^{\Delta L=0}_{\Delta B=\pm 2}+4|^{\Delta L=\pm3}_{\Delta B=\pm1}+236|^{\Delta L=\mp 1}_{\Delta B=\pm1}$ operators without referring to fermion generations, and $44874|^{\Delta L=\pm 2}_{\Delta B=0}+2862|^{\Delta L=0}_{\Delta B=\pm 2}+486|^{\Delta L=\pm3}_{\Delta B=\pm1}+42234|^{\Delta L=\pm 1}_{\Delta B=\mp1}$ operators when three generations of fermions are referred to, where $\Delta L,~\Delta B$ denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators., Comment: 31 pages, 10 tables; Section 3 is expanded with discussion on relevant phenomenologies; Typos are corrected; The version to be appear in JHEP

We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons. All operators are non-Hermitian and are classified according to their baryon ($\Delta B$) and lepton ($\Delta L$) numbers violated. Including Hermitian-conjugated operators, there are in total $3168$, $750$, $588$, $712$ operators with $(\Delta B,\Delta L)=(0,0)$, $(0,\pm 2)$, $(\pm 1,\mp 1)$, $(\pm 1,\pm 1)$ respectively. We perform the tree-level matching with the standard model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in both LEFT and SMEFT. As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 SMEFT operators. We compare the cross sections of various neutrino-photon scattering with their counterparts in the standard model and highlight the new features. Finally we illustrate how these effective interactions could arise from ultraviolet completion., Comment: version 1: 16 pages, 3 figures; version 2: minor changes, as published in the journal

Rare kaon decays with missing energy, $K\to\pi$+$E_{\rm miss}$, have received considerable attention because their rates can be calculated quite precisely within the standard model (SM), where the missing energy is carried away by an undetected neutrino-antineutrino pair. Beyond the SM, clean theoretical predictions can also be made regarding these processes. One such prediction is the so-called Grossman-Nir (GN) bound, which states that the branching fractions of the $K_L$ and $K^+$ modes must satisfy the relation $\mathcal{B}(K_L\to\pi^0$+$E_{\rm miss})\lesssim4.3\,\mathcal{B}(K^+\to\pi^+$+$E_{\rm miss})$ and applies within and beyond the SM, as long as the hadronic transitions change isospin by $\Delta I=1/2$. In this paper we extend the study of these modes to include new-physics scenarios where the missing energy is due to unobserved lepton-number-violating neutrino pairs, invisible light new scalars, or pairs of such scalars. The new interactions are assumed to arise above the electroweak scale and described by an effective field theory. We explore the possibility of violating the GN bound through $\Delta I=3/2$ contributions to the $K\to\pi$ transitions within these scenarios and find that large violations are only possible in the case where the missing energy is due to an invisible light new scalar., Comment: 30 pages, 5 figures, slightly expanded, typos corrected, matches publication

In this work we study the current bounds from the CE{\nu}NS process and meson invisible decays on generic neutrino interactions with sterile neutrinos in effective field theories. The interactions between quarks and left-handed SM neutrinos and/or right-handed neutrinos are first described by the low-energy effective field theory (LNEFT) between the electroweak scale and the chiral symmetry breaking scale. We complete the independent operator basis for the LNEFT up to dimension-6 by including both the lepton-number-conserving (LNC) and lepton-number-violating (LNV) operators involving right-handed neutrinos. We translate the bounds on the LNEFT Wilson coefficients from the COHERENT observation and calculate the branching fractions of light meson invisible decays. The bounds on LNEFT are then mapped onto the SM effective field theory with sterile neutrinos (SMNEFT) to constrain new physics above the electroweak scale. We find that the meson invisible decays can provide the only sensitive probe for {\tau} neutrino flavor component and s quark component in the quark-neutrino interactions involving two (one) active neutrinos and for the effective operators without any active neutrino fields. The CE{\nu}NS process places the most stringent bound on all other Wilson coefficients. By assuming one dominant Wilson coefficient at a time in SMNEFT and negligible sterile neutrino mass, the most stringent limits on the new physics scale are 2.7 - 10 TeV from corresponding dipole operator in LNEFT and 0.5 - 1.5 TeV from neutrino-quark operator in LNEFT., Comment: v2: 34 pages, 2 figures, 9 tables; discussion about UV completions and comparison to some other constraints added; version published in JHEP

The non-zero Dirac phases $\delta^q$ and $\delta^l$ in the CKM and PMNS mixing matrices signify CP violation. In general they are independent. Experimental data including recent T2K results show, however, that in the original KM parameterization for the mixing matrix, the sum $\delta^q_{\rm KM} + \delta^l_{\rm KM}$ is close to zero with $\delta^q_{\rm KM}$ to be approximately $\pi/2$. The KM parameterization may have provided some hints that these phases are actually related and CP is maximally violated. We show that this sum rule can be accommodated in models with spontaneous CP violation where both phases originate from a non-trivial common spontaneous CP violating maximized phase in the Higgs potential. We find some interesting phenomenological consequences for flavor changing neutral current and CP violation for such a model. In particular, data from $B_s - \bar B_s$ mixing provide very strong constraints on the mass scale for the new neutral scalars in the model, yet the model still allows the electric dipole moments of electron and neutron to reach to their current upper bounds. The model can be tested by near future experiments., Comment: 8 pages, figures are updated, T2K result was included which further enhanced the sum rule, matched to the version to be appeared in Physics Letters B

The ratio $\mathcal{B}(K_L\to\pi^0\nu\bar\nu)/\mathcal{B}(K^+\to\pi^+\nu\bar\nu)$ of the branching fractions of kaon decays $K_L\to\pi^0\nu\bar\nu$ and $K^+\to\pi^+\nu\bar\nu$ has a maximum of about 4.3 under the assumption that the underlying interactions change isospin by $\Delta I=1/2$. This is referred to as the Grossman-Nir (GN) bound, which is respected by the standard model (SM) and by many scenarios beyond it. Recent preliminary results of the KOTO and NA62 Collaborations searching for these kaon modes seem to imply a violation of this bound. The KOTO findings also suggest that $\mathcal{B}(K_L\to\pi^0\nu\bar\nu)$ could be much larger, by nearly two orders of magnitude, than that predicted in the SM. In this work we study the possibility of violating the GN bound in an effective field theory approach with only SM fields. We show that the bound holds, in addition to the original GN scenarios, whether or not the kaon decays conserve lepton number. We demonstrate that the inclusion of $\Delta I=3/2$ operators can lead to a violation of the GN bound and illustrate with an example of how the KOTO numbers may be reached with a new physics scale of order tens of GeV., Comment: 15 pages, 2 figures, minor changes for typos

This is a sequel to our recent work [1] in which we calculated the lepton number violating (LNV) $K^\pm$ decays due to contact dimension-9 (dim-9) quark-lepton effective interactions that are induced at a high energy scale. In this work we investigate the long-distance contribution to the decays arising from the exchange of a neutrino. These decays can probe LNV interactions involving the second generation of fermions that are not reachable in nuclear neutrinoless double-$\beta$ decays. Our study is completely formulated in the framework of effective field theories (EFTs), from the standard model effective field theory (SMEFT) through the low energy effective field theory (LEFT) to chiral perturbation theory. We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions and renormalization group effects, and express the decay branching ratios in terms of the Wilson coefficients associated with the dim-5 and dim-7 operators in SMEFT. Our result is general in that it does not depend on dynamical details of physics at a high scale that induce the effective interactions in SMEFT and in that it does not appeal to any hadronic models. We find that the long-distance contribution overwhelmingly dominates over the contact or short-distance one. Assuming the new physics scale to be around a TeV, the branching ratios are predicted to be below the current experimental upper bounds by several orders of magnitude., Comment: 16 pages, 2 figures, 1 table, 2 appendices

In this work we investigate the implication of $K\to \pi \nu \bar{\nu}$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu}$ decays provide the most sensitive probe for the operators with $\tau\tau$ component and point to a corresponding new physics scale of $\Lambda_{\rm NP} \in[47~\text{TeV},~72~\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to\pi\nu\bar{\nu}$ discrepancy with the SM prediction within a narrow range $\Lambda_{\rm NP}\in [19.4~\text{TeV},~21.5~\text{TeV}]$, which is consistent with constraints from Kaon invisible decays., Comment: 26 pages, 3 figures, version published in PRD

This is the first paper of our systematic efforts on lepton number violating (LNV) hadronic decays in the effective field theory approach. These decays provide information complementary to popular nuclear neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay in that they can probe LNV interactions involving heavier quarks and charged leptons. We may call them hadronic $0\nu\beta\beta$ decays in short, though $\beta$ refers to all charged leptons. In this work we investigate the decays $K^\pm\rightarrow\pi^\mp l^{\pm}l^{\pm}$ that arise from short-distance or contact interactions involving four quark fields and two charged lepton fields, which have canonical dimension nine (dim-9) at leading order in low energy effective field theory (LEFT). We make a complete analysis on the basis of all dim-9 operators that violate lepton number by two units, and compute their one-loop QCD renormalization effects. We match these effective interactions in LEFT to those in chiral perturbation theory ($\chi$PT) for pseudoscalar mesons, and determine the resulting hadronic low energy constants (LECs) by chiral symmetry and lattice results in the literature. The obtained decay rate is general in that all physics at and above the electroweak scale is completely parameterized by the relevant Wilson coefficients in LEFT and hadronic LECs in $\chi$PT. Assuming the standard model effective field theory (SMEFT) is the appropriate effective field theory between some new physics scale and the electroweak scale, we match our LEFT results to SMEFT whose leading effective interactions arise from LNV dim-7 operators. This connection to SMEFT simplifies significantly the interaction structures entering in the kaon decays, and we employ the current experimental bounds to set constraints on the relevant Wilson coefficients in SMEFT., Comment: 23 pages, 3 figures, 4 tables; v2: very minor changes and typos corrected; v3, version to appear in JHEP: added a para at end of sec 5 to show how relevant SMEFT operators may be induced in typical new physics models, more typos corrected

We showed in a previous publication that there are six independent dimension-seven operators violating both lepton and baryon numbers ($L=-B=1$) and twelve ones violating lepton but preserving baryon number ($L=2,~B=0$) in standard model effective field theory, and we calculated one-loop renormalization for the former six operators. In this work we continue our efforts on renormalization of the operators. It turns out this could become subtle because the operators are connected by nontrivial relations when fermion flavors are counted. This kind of relations does not appear in lower dimensional operators. We show how we can extract anomalous dimension matrix for a flavor-specified basis of operators from counterterms computed for the above flavor-blind operators without introducing singular inverse Yukawa coupling matrices. As a phenomenological application, we investigate renormalization group effects on nuclear neutrinoless double $\beta$ decay. We also discuss very briefly its analog in the meson sector, $K^\pm\to\pi^\mp\mu^\pm\mu^\pm$, and indicate potential difficulties to compute its decay width., Comment: v1: 18 pages, 2 figures, 5 tables. v2: 21 pages, 3 figures, 5 tables, to appear in jhep; minor revisions made without changing results: (1) corrected typos; (2) added clarifying statements and three refs; (3) Appendix expanded by an explicit example of calculation; (4) corrected an error in eq. (13), thanks to the referee; (5) replaced fig. 2 due to a numerical problem

We consider the feasibility of interpreting the $R_{K^{(*)}}$ anomaly in the colored Zee-Babu model. The model generates neutrino masses at two loops with the help of a scalar leptoquark $S\sim(3,3,-\frac{1}{3})$ and a scalar diquark $\omega\sim(6,1,-\frac{2}{3})$, and contributes to the transition $b\to s\ell\ell$ via the exchange of a leptoquark $S$ at tree level. Under constraints from lepton flavor violating (LFV) and flavor changing neutral current (FCNC) processes, and direct collider searches for heavy particles, we acquire certain parameter space that can accommodate the $R_{K^{(*)}}$ anomaly for both normal (NH) and inverted (IH) hierarchies of neutrino masses. We further examine the LFV decays of the $B$ meson, and find its strong correlation with the neutrino mass hierarchy, i.e., $\text{Br}(B^+ \to K^+ \mu^\pm\tau^\mp)\gtrsim\text{Br}(B^+ \to K^+ \mu^\pm e^\mp)\approx\text{Br}(B^+ \to K^+ \tau^\pm e^\mp)$ for NH, while $\text{Br}(B^+ \to K^+ \mu^\pm \tau^\mp)\ll\text{Br}(B^+ \to K^+ \mu^\pm e^\mp)\approx\text{Br}(B^+ \to K^+ \tau^\pm e^\mp)$ for IH. Among these decays, only $B^+ \to K^+ \mu^\pm e^\mp$ in the case of NH is promising at the LHCb RUN II, while for IH all LFV decays are hard to detect in the near future., Comment: 16 pages, 6 figures, accepted by NPB

We study two aspects of higher dimensional operators in standard model effective field theory. We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension. The power counting is determined by the number of loops and the difference of the indices of the two operators involved, which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power. Then we show that the operators with the lowest index are unique at each mass dimension $d$, i.e., $(H^\dagger H)^{d/2}$ for even $d\geq 4$, and $(L^T\epsilon H)C(L^T\epsilon H)^T(H^\dagger H)^{(d-5)/2}$ for odd $d\geq 5$. Here $H,~L$ are the Higgs and lepton doublet, and $\epsilon,~C$ the antisymmetric matrix of rank two and the charge conjugation matrix, respectively. The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting. We compute their anomalous dimensions at one loop for general $d$ and find that they are enhanced quadratically in $d$ due to combinatorics. We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights., Comment: 7 pages, 2 figures, 2 tables; v2: added a few refs and one sentence, without other changes; v3: minor rewording, published version

We revisit the effective field theory of the standard model that is extended with sterile neutrinos, $N$. We examine the basis of complete and independent effective operators involving $N$ up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and find seven redundant operators at dim-6, sixteen redundant operators and two new operators at dim-7. The correct numbers of operators involving $N$ are, without counting Hermitian conjugates, $16~(L\cap B)+1~(\slashed{L}\cap B)+2~(\slashed{L}\cap\slashed{B})$ at dim-6, and $47~(\slashed{L}\cap B)+5~(\slashed{L}\cap\slashed{B})$ at dim-7. Here $L/B~(\slashed L/\slashed B)$ stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for $n_f$ generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are $29~(1614)$ and $80~(4206)$ operators involving sterile neutrinos at dim-6 and dim-7 respectively for $n_f=1~(3)$., Comment: 14 pages, 0 figures, 4 tables

We study charged lepton flavor-violating (LFV) transitions in the color octet model that generates neutrino mass and lepton mixing at one loop. By taking into account neutrino oscillation data and assuming octet particles of TeV scale mass, we examine the feasibility to detect these transitions in current and future experiments. We find that for general values of parameters the branching ratios for LFV decays of the Higgs and $Z$ bosons are far below current and even future experimental bounds. For LFV transitions of the muon, the present bounds can be satisfied generally, while future sensitivities could distinguish between the singlet and triplet color-octet fermions. The triplet case could be ruled out by future $\mu-e$ conversion in nuclei, and for the singlet case the conversion and the decays $\mu\to 3e,~e\gamma$ play complementary roles in excluding relatively low mass regions of the octet particles., Comment: v1: 18 pages, 11 figures, 2 tables; v2: added one ref and corrected a typo, with no other changes

We study dimension-seven operators in standard model effective field theory. These operators are classified into two sets, one violating lepton number but preserving baryon number ($\Delta L=\pm 2$, $\Delta B=0$) and the other violating both but preserving their sum ($-\Delta L=\Delta B=\pm 1$). It has been found in the previous literature that there are respectively 13 and 7 such independent operators. We show that one operator is redundant in each set so that the complete list contains only 12 and 6 operators respectively. We accomplish this by using standard model equations of motion and various Fierz identities. We calculate the one-loop anomalous dimension matrix for the 6 operators in the second set, and illustrate its possible phenomenological implications by working out renormalization group running of the Wilson coefficients that could contribute to the type of proton decays with $-\Delta L=\Delta B=\pm 1$, such as $p\to\nu\pi^+$., Comment: v1: 11 pages, 2 figures, 1 table; v2: 12 pages, added a few refs, compared with previous work on counting of independent operators for general n generations, and added a few words on Fierz identities

We propose that the possible 750 GeV diphoton excess can be explained in the color-octet neutrino mass model extended with a scalar singlet $\Phi$. The model generally contains $N_s$ species of color-octet, electroweak doublet scalars $S$ and $N_f$ species of color-octet, electroweak triplet $\chi$ or singlet $\rho$ fermions. While both scalars and fermions contribute to the production of $\Phi$ through gluon fusion, only the charged members induce the diphoton decay of $\Phi$. The diphoton rate can be significantly enhanced due to interference between the scalar and fermion loops. We show that the diphoton cross section can be from 3 to 10 fb for O(TeV) color-octet particles while evading all current LHC limits., Comment: 12 pages, 4 figures; v2: 13 pages, 4 figures, version to appear in EPJC, clarified a few things, updated numerical analysis using the most recent bound on color-octet fermions but without changing conclusions, corrected a mistake when quoting the branching ratio to Z gamma, added some references missed in v1