Complete EFT operator bases for dark matter and weakly-interacting light particle

Recently, the Belle II collaboration announced the first measurement of the branching ratio $$ \mathcal{B}\left({B}^{+}\to {K}^{+}\nu \overline{\nu}\right) $$ B B + → K + ν ν ¯ , which is found to be about 2.7σ higher than the Standard Model (SM) prediction. We decipher the data with two new physics scenarios: the underlying quark-level $$ b\to s\nu \overline{\nu} $$ b → sν ν ¯ transition is, besides the SM contribution, further affected by heavy new mediators that are much heavier than the electroweak scale, or amended by an additional decay channel with undetected light final states like dark matter or axion-like particles. These two scenarios can be most conveniently analyzed in the SM effective field theory (SMEFT) and the dark SMEFT (DSMEFT) framework, respectively. We consider the flavour structures of the resulting effective operators to be either generic or satisfy the minimal flavour violation (MFV) hypothesis, both for the quark and lepton sectors. In the first scenario, once the MFV assumption is made, only one SM-like low-energy effective operator induced by the SMEFT dimension-six operators can account for the Belle II excess, whose parameter space is, however, excluded by the Belle upper bound of the branching ratio $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}\nu \overline{\nu}\right) $$ B B 0 → K ∗ 0 ν ν ¯ . In the second scenario, it is found that the Belle II excess can be accommodated by 22 of the DSMEFT operators involving one or two scalar, fermionic, or vector dark matters as well as axion-like particles. These operators also receive dominant constraints from the B0 → K*0 + inv and Bs → inv decays. Once the MFV hypothesis is assumed, the number of viable operators is reduced to 14, and the B+ → π+ + inv and K+ → π+ + inv decays start to put further constraints on them. Within the parameter space allowed by all the current experimental data, the q2 distributions of the B → K(*) + inv decays are then studied for each viable operator. We find that the resulting prediction of the operator $$ {\mathcal{Q}}_{q\chi}=\left({\overline{q}}_p{\gamma}_{\mu }{q}_r\right)\left(\overline{\chi}{\gamma}^{\mu}\chi \right) $$ Q qχ = q ¯ p γ μ q r χ ¯ γ μ χ with a fermionic dark matter mass mχ ≈ 700 MeV can closely match the Belle II event distribution in the bins 2 ≤ q2 ≤ 7 GeV2. In addition, we, for the first time, calculate systematically the longitudinal polarization fraction FL of K* in the B → K* + inv decays within the DLEFT. By combining the decay spectra and FL, almost all the DSMEFT operators are found to be distinguishable from each other. Finally, the future prospects at Belle II, CEPC and FCC-ee are also discussed for some of these FCNC processes.

Deciphering the Belle II data on $$ B\to K\nu \overline{\nu} $$ decay in the (dark) SMEFT with minimal flavour violation

Hou,

Li,

Shen

et al. 2024

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

Liang,

Liao,

et al. 2024

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 (a0,1,2), which is essentially a factor of Wilson coefficients squared, and its corresponding generalized atomic response function $$ \left({\overset{\sim }{W}}_{0,1,2}\right) $$ 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.

Complete CP eigen-bases of mesonic chiral Lagrangian up to p8-order

Li,

Sun,

Tang

et al. 2024

Chiral perturbation theory systematically describes the low energy dynamics of meson and baryons using nonlinear Nambu-Goldstone fields. Using the Young tensor technique, we construct the pure mesonic effective operators up to p8-order, one-to-one corresponding to contact amplitudes with the on-shell Adler zero condition. The off-shell external sources, non-vanishing under equation-of-motion conditions, are also added to the operator bases. We also show the invariant tensor bases using the Young tableau is equivalent to the trace bases with Cayley-Hamilton relations. Separated into different CP eigenstates, at $$ \mathcal{O}\left({p}^8\right) $$ O p 8 we obtain the operator lists of the 567 C+P+ operators, 483 C+P- operators, 376 C-P+ operators, and 408 C-P- operators for SU(2) case, while there are 1959 C+P+ operators, 1809 C+P- operators, 1520 C-P+ operators, and 1594 C-P- operators for SU(3) case, consistent with results using the Hilbert series.