<p>In this paper, we systematically investigate the general spin-1 dark matter–nucleus interactions within the framework of effective field theories (EFTs). We consider both the nonrelativistic (NR) and the relativistic EFT descriptions of the DM interactions with nucleons and quarks. In the NREFT framework, we present a complete list of NR operators for spin-1 DM coupling to nucleons and compute their contributions to the DM response functions. Next, we consider all possible leading-order relativistic EFT operators between DM and light quarks and the photon, and we perform NR reductions to match them onto the NREFT. We then derive the nuclear scattering rate from these interactions and employ recent DM direct detection data (from both the nuclear recoil and the Migdal effect) to constrain all these EFT operators and DM electromagnetic properties. We find that the elastic nuclear recoil data (from PandaX-4T, XENONnT, LZ, and DarkSide-50) set stringent bounds on the EFT coefficients for a DM mass above a few GeV, while the Migdal-effect datasets (from PandaX-4T, XENONnT, and DarkSide-50) can probe a DM mass region as small as 20 MeV. Lastly, we construct a UV-complete model that can provide a complex spin-1 DM candidate, and at the same time generate DM-quark/photon operators discussed in this work.</p>

China

Jin-Han Liang

Yi Liao

Xiao-Dong Ma

Hao-Lin Wang

Systematic investigation on vector dark matter-nucleus scattering in effective field theories

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 $$ {K}^0-{\overline{K}}^0 $$ , $$ {B}_{d,s}-{\overline{B}}_{d,s} $$ , and $$ {D}^0-{\overline{D}}^0 $$ 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 80 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.

Probing dimension-8 SMEFT operators through neutral meson mixing

Most studies on baryon number violating (BNV) processes in the literature focus on free or bound nucleons in nuclei, with limited attention given to the decay of bound atoms. Given that hydrogen is the most abundant atom in the universe, it is particularly intriguing to investigate the decay of hydrogen atom as a means to probe BNV interactions. In this study, for the first time, we employ a robust effective field theory (EFT) approach to estimate the decay widths of two-body decays of hydrogen atom into standard model particles, by utilizing the constraints on the EFT cutoff scale derived from conventional nucleon decay processes. We integrate low energy effective field theory (LEFT), chiral perturbation theory (ChPT), and standard model effective field theory (SMEFT) to formulate the decay widths in terms of the LEFT and SMEFT Wilson coefficients (WCs), respectively. By applying the bounds on the WCs from conventional nucleon decays, we provide a conservative estimate on hydrogen BNV decays. Our findings indicate that the bounds on the inverse partial widths of all dominant two-body decays exceed 10 <sup>44</sup> years. Among these modes, the least constrained diphoton decay <math altimg='si1.svg'><mi mathvariant='normal'>H</mi><mo stretchy='false'>&#8594;</mo><mi>&#947;</mi><mi>&#947;</mi></math> might be astrophysically interesting, although the monochromatic photon signal from our Sun is difficult to detect with current near-Earth telescopes.

Wei-Qi Fan

Baryon number violating hydrogen decay

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   $(\bar{\chi} {\rm{i}}\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$   and   $(\bar{\chi} {\rm{i}}\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$   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 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   $(\bar{\chi} {\rm{i}}\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$  , our results significantly extend the reach of constraints on the DM-quark tensor operators to masses as low as   $(\bar{\chi} {\rm{i}}\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$  , with the bound exceeding that obtained by the Migdal effect with only contact interactions by approximately an order of magnitude. In particular, for the operator   $(\bar{\chi} {\rm{i}}\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$   with DM mass   $(\bar{\chi} {\rm{i}}\sigma^{\mu\nu} \gamma^5 \chi) (\bar{q} \sigma_{\mu\nu}q)$  , the latest PandaX constraint on the DM electric dipole moment puts more stringent bounds than the previous direct detection limit. We also briefly discuss the constraints obtained from experiments other than direct detection.

Comprehensive constraints on fermionic dark matter-quark tensor interactions in direct detection experiments  

In this Letter we revisit general dark matter (DM)-bound-electron interactions studied previously in the influential work [R. Catena et al., Atomic responses to general dark matter-electron interactions, Phys. Rev. Res. 2, 033195 (2020)]. For the most general DM-electron nonrelativistic or relativistic interactions for DM with spin up to 1, we find the average ionization matrix element squared can be organized into three terms, each of which is a product of a DM response function (<math><msub><mi>a</mi><mrow><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math>) and a linear combination (<math><msub><mover><mi>W</mi><mo>˜</mo></mover><mrow><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math>) of the four atomic response functions (<math><msub><mi>W</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></math>) given in that work, <math><mrow><msub><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mn>0</mn></msub><mo>=</mo><msub><mrow><mi>W</mi></mrow><mn>1</mn></msub></mrow></math>, <math><mrow><msub><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mn>1</mn></msub><mo>=</mo><mo>|</mo><msubsup><mrow><mi>v</mi></mrow><mn>0</mn><mrow><mo>⊥</mo></mrow></msubsup><msup><mrow><mo>|</mo></mrow><mn>2</mn></msup><msub><mrow><mi>W</mi></mrow><mn>1</mn></msub><mo>−</mo><mn>2</mn><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow></msub><mi>q</mi><mo>·</mo><msubsup><mrow><mi>v</mi></mrow><mn>0</mn><mrow><mo>⊥</mo></mrow></msubsup></mrow><mrow><msup><mrow><mi>q</mi></mrow><mn>2</mn></msup></mrow></mfrac><msub><mrow><mi>W</mi></mrow><mn>2</mn></msub><mo>+</mo><msub><mrow><mi>W</mi></mrow><mn>3</mn></msub></mrow></math>, <math><mrow><msub><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mo>(</mo><mi>q</mi><mo>·</mo><msubsup><mrow><mi>v</mi></mrow><mn>0</mn><mrow><mo>⊥</mo></mrow></msubsup><msup><mrow><mo>)</mo></mrow><mn>2</mn></msup></mrow><mrow><msup><mrow><mi>q</mi></mrow><mn>2</mn></msup></mrow></mfrac><msub><mrow><mi>W</mi></mrow><mn>1</mn></msub><mo>−</mo><mn>2</mn><mfrac><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow></msub><mi>q</mi><mo>·</mo><msubsup><mrow><mi>v</mi></mrow><mn>0</mn><mrow><mo>⊥</mo></mrow></msubsup></mrow><mrow><msup><mrow><mi>q</mi></mrow><mn>2</mn></msup></mrow></mfrac><msub><mrow><mi>W</mi></mrow><mn>2</mn></msub><mo>+</mo><mfrac><mrow><msubsup><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow><mn>2</mn></msubsup></mrow><mrow><msup><mrow><mi>q</mi></mrow><mn>2</mn></msup></mrow></mfrac><msub><mrow><mi>W</mi></mrow><mn>4</mn></msub></mrow></math>. Furthermore, we find a crucial minus sign was missed for the calculation of <math><msub><mi>W</mi><mn>2</mn></msub></math> in that work, which has significant phenomenological consequences when explaining experimental bounds on specific DM scenarios. Due to the corrected sign, there can be significant cancellations between the <math><msub><mi>W</mi><mn>2</mn></msub></math> and <math><msub><mi>W</mi><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></msub></math> terms, so that <math><msub><mover><mi>W</mi><mo>˜</mo></mover><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math> are dominated by the usual response function <math><msub><mi>W</mi><mn>1</mn></msub></math> in some cases. Many DM scenarios involving DM or electron axial-vector current can yield <math><msub><mi>W</mi><mn>2</mn></msub></math> and thus are potentially affected by the sign. 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. We also present a complete list of NR operators for spin-1 DM and compute their contributions to the DM response functions.

Revisiting general dark matter-bound-electron interactions

In this paper, we systematically investigate the general dark matter-electron interactions within the framework of effective field theories (EFTs). 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 (ϕ), fermion (χ), 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   <math> <mfenced> <msub> <mover> <mi>W</mi> <mo>~</mo> </mover> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mfenced> </math>  $$ \left({\overset{\sim }{W}}_{0,1,2}\right) $$ . 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.

A systematic investigation on dark matter-electron scattering in effective field theories

With the method of the background field expansion, we investigate the one-loop quantization of the Euclidean nonlocal f (R) model in the de-Sitter universe. We obtain the ghost-free condition (GFC) based on the transformation from the Jordan frame to the Einstein frame and the classical stability condition (CSC) satisfied  $${f}_{RR}^{\left(0\right)}-{\phi }_{0}{F}_{RR}^{\left(0\right)}&lt;0$$ . We present the on-shell and off-shell one-loop effective action and quantum stability condition (QSC) by utilizing the generalized zeta-function. We find that under the fulfillment of GFC, CSC and QSC are inconsistent.

Haiyuan Feng

Rong-Jia Yang

Stability of the de-Sitter universe: one-loop nonlocal f (R) gravity

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 ϕ and S, Majorana fermions χ and ψ, and real vectors X  μ  and V  μ . 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 (ϕS-SM), fermion-fermion-SM (χψ-SM), vector-vector-SM (XV-SM), scalar-fermion-SM (ϕχ-SM), scalar-vector-SM (ϕX-SM), and fermion-vector-SM (χX-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 → χϕ or χX 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.

Dark sector effective field theory

The scotogenic neutrino seesaw model is a minimal extension of the standard model with three ℤ 2-odd right-handed singlet fermions N and one ℤ 2-odd Higgs doublet η 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 η are heavy to be integrated out. This is a realistic example which has no tree-level matching due to the 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 μ → eγ and μ → 3e.

One-loop matching of scotogenic model onto standard model effective field theory up to dimension 7

We continue our endeavor to investigate lepton number violating (LNV) processes at low energies 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   $ \tau^+\rightarrow \ell^-P_i^{+}P_j^{+} $   and   $ \tau^+\rightarrow \ell^-P_i^{+}P_j^{+} $   denote the lowest-lying charged pseudoscalars   $ \tau^+\rightarrow \ell^-P_i^{+}P_j^{+} $  . We analyze the dominant contributions in a series of EFTs from high to low energy scales, namely the standard model EFT (SMEFT), the low-energy EFT (LEFT), and the chiral perturbation theory (   $ \tau^+\rightarrow \ell^-P_i^{+}P_j^{+} $  ). The decay branching ratios are expressed in terms of the Wilson coefficients of dimension-five and -seven operators in SMEFT and the hadronic low-energy constants. These Wilson coefficients involve the first and second generations of quarks and all generations of leptons; thus, they cannot be explored in low-energy processes such as nuclear neutrinoless double beta decay or LNV kaon decays. Unfortunately, the current experimental upper bounds on the branching ratios are too weak to set useful constraints on these coefficients. Alternatively, 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 the hadronic uncertainties incurred in applying   $ \tau^+\rightarrow \ell^-P_i^{+}P_j^{+} $   to   $ \tau^+\rightarrow \ell^-P_i^{+}P_j^{+} $   decays by computing one-loop chiral logarithms and attempt to improve the convergence of chiral perturbation by employing dispersion relations in the short-distance part of the decay amplitudes.