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.

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 44 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

We propose the nucleon consumption induced by dark matter (DM) as a new scenario to overcome the energy threshold of direct detection. It can be realized with proton (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>χ</mi><mo>+</mo><mi>p</mi><mo stretchy="false">→</mo><mi>χ</mi><mo>+</mo><msup><mo>ℓ</mo><mo>+</mo></msup></math>) or neutron (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>χ</mi><mo>+</mo><mi>n</mi><mo stretchy="false">→</mo><mi>χ</mi><mo>+</mo><mi>ν</mi></math>) target. Both effective operators and concrete models are provided to illustrate the idea. Since the initial DM and nucleon velocity is only <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>4</mn></math> 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 deexcitation 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.

Shao-Feng Ge

Nucleon consumption and mass-energy conversion induced by dark matter

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

Recently Belle II reported the first measurement of B + → K + + invisible(inv), which is 2.7σ 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 → K + 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 ϕ 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 ℤ2 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.

Xiao-Gang He

Australia

Michael Schmidt

German Valencia

Raymond Volkas

Scalar dark matter explanation of the excess in the Belle II B + → K ++ invisible measurement

Belle II recently reported the new measurement <math><mi>B</mi><mo>(</mo><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover><mo>)</mo><mo>=</mo><mo>(</mo><mn>2.3</mn><mo>±</mo><mn>0.7</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> [I. Adachi et al. (Belle-II Collaboration), arXiv:2311.14647] which is two times larger than their previous result (although consistent within errors) and about <math><mn>2.7</mn><mi>σ</mi></math> higher than the SM prediction. We reexamine new physics scenarios we 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 <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mo>*</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math>, <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>, <math><mi>B</mi><mo>→</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math>, and <math><msub><mi>B</mi><mi>s</mi></msub></math> mixing to limit possible explanations for the excess. For the case of lepton flavor violating neutrino couplings, we find that only two leptoquarks remain viable requiring a large <math><msubsup><mi>C</mi><msup><mn>9</mn><mo>′</mo></msup><mrow><mi>τ</mi><mi>τ</mi></mrow></msubsup><mo>=</mo><mo>−</mo><msubsup><mi>C</mi><mrow><msup><mn>10</mn><mo>′</mo></msup></mrow><mrow><mi>τ</mi><mi>τ</mi></mrow></msubsup></math>. For models with different types of light dark matter particle pairs (scalar, fermion, or vector), the preliminary <math><msup><mi>q</mi><mn>2</mn></msup></math> distribution from Belle II, which shows that the excess appears mostly for bins with <math><mn>3</mn><mo>≤</mo><msup><mi>q</mi><mn>2</mn></msup><mo>≤</mo><mn>7</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math> [I. Adachi et al. (Belle-II Collaboration), arXiv:2311.14647], implies only the vector current operators with scalar or vector dark matter particles with masses in the hundreds of MeV can match the anomaly.

Taiwan

Revisiting models that enhance <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> in light of the new Belle II measurement

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.