Low-Energy Effective Field Theory below the Electroweak Scale: dimension-8 operators

In the present paper, we carry out a systematic study of the flavor invariants and their renormalization-group equations (RGEs) in the leptonic sector with three generations of charged leptons and massive Majorana neutrinos. First, following the approach of the Hilbert series from the invariant theory, we show that there are 34 basic flavor invariants in the generating set, among which 19 invariants are CP-even and the others are CP-odd. Any flavor invariants can be expressed as the polynomials of those 34 basic invariants in the generating set. Second, we explicitly construct all the basic invariants and derive their RGEs, which form a closed system of differential equations as they should. The numerical solutions to the RGEs of the basic flavor invariants have also been found. Furthermore, we demonstrate how to extract physical observables from the basic invariants. Our study is helpful for understanding the algebraic structure of flavor invariants in the leptonic sector, and also provides a novel way to explore leptonic flavor structures.

Section: Jhep09(2021)053 B Invariant Theory and Hilbert Seriesmentioning

confidence: 99%

Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos

Wang

Zhou

2021

“…The SMEFT contains all the SM fields to construct the effective Lagrangians and respects the SM gauge symmetry SU(3) C × SU(2) W × U(1) Y . After integrating out the massive gauge bosons W ± , Z, the top quark t and the Higgs boson h, the low energy effective field theory (LEFT) [10][11][12][13] describes all possible physics below the electroweak scale, regarding to the gauge symmetry SU(3) C × U(1) EM .…”

Section: Introductionmentioning

confidence: 99%

Operator bases in effective field theories with sterile neutrinos: d ≤ 9

Ren

Xiao

et al. 2021

We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos (νSMEFT) and low energy effective field theory with light sterile neutrinos (νLEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the νSMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile neutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation of fermions, while 24, 5223, 3966, 25425, 789426 independent operators in the νLEFT for two generations of up-type quarks and three generations of all other fermions.

“…where L dim≤4 is the renormalizable terms, and the Wilson coefficientsĈ d,i together with the heavy scale Λ encode informations about the presumed fundamental physics. The systematic enumeration of operator bases up to dim 9 have been figured out in [31][32][33][34].…”

Section: Left Operatorsmentioning

confidence: 99%

An EFT toolbox for baryon and lepton number violating dinucleon to dilepton decays

2021

In this paper we systematically consider the baryon (B) and lepton (L) number violating dinucleon to dilepton decays (pp → ℓ+ℓ′+, pn → $$ {\mathrm{\ell}}^{+}\overline{\nu}^{\prime } $$ ℓ + ν ¯ ′ , nn → $$ \overline{\nu}\overline{\nu}^{\prime } $$ ν ¯ ν ¯ ′ ) with ∆B = ∆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 (BχPT) 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 the SMEFT and the low energy constants pertinent to BχPT. 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 lifetime of transitions pp → ℓ+ℓ′+, pn → $$ {\mathrm{\ell}}^{+}\overline{\nu}^{\prime } $$ ℓ + ν ¯ ′ imply stronger limits on nn → $$ \overline{\nu}\overline{\nu}^{\prime } $$ ν ¯ ν ¯ ′ 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 → e+e+, e+μ+, μ+μ+ lead to stronger limits on pn → $$ {\mathrm{\ell}}_{\alpha}^{+}{\overline{\nu}}_{\beta } $$ ℓ α + ν ¯ β with α, β = e, μ than their existing bounds. Conversely, the same assumptions help us to set a lower bound on the lifetime of the experimentally unsearched mode pp → e+τ+ from that of pn → $$ {e}^{+}{\overline{\nu}}_{\tau } $$ e + ν ¯ τ , i.e., $$ {\Gamma}_{pp\to {e}^{+}{\tau}^{+}}^{-1}\gtrsim 2\times {10}^{34} $$ Γ pp → e + τ + − 1 ≳ 2 × 10 34 yr.