What is Leading Order for LFV in SMEFT?

Abstract

Upcoming searches for lepton flavour change (LFV) aim to probe New Physics (NP) scales up to ΛNP ∼ 104 TeV, implying that they will be sensitive to NP at lower scales that is suppressed by loops or small couplings. We suppose that the NP responsable for LFV is beyond the reach of the LHC and can be parametrised in Effective Field Theory, introduce a small power-counting parameter λ (à la Cabibbo-Wolfenstein), and assess whether the existing dimension six operator basis and one-loop RGEs provide a good approximation for LFV. We find that μ ↔ e observables can be sensitive to a few dozen dimension eight operators, and to some effects of two-loop anomalous dimensions, for ΛNP ≲ 20 − 100 TeV. We also explore the effect of some simplifying assumptions in the one-loop RGEs, such as neglecting flavour-changing effects.

Z lepton flavour violation as a probe for new physics at future $$e^+e^-$$ colliders

“…Such an effective theory is known as the Standard Model Effective Field Theory (SMEFT) [17,18] (for a recent review see [19]) and provides the optimal framework for a model-independent analysis. In this context, LFV processes could be induced by dimension 6 effective operators, as discussed in detail in [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In this article we will employ the SMEFT framework to study low-energy constraints on LFVZD.…”

The sensitivity of $μ\to e$ processes to $τ$ flavour change

“…At all scales, the doublet and singlet leptons are in the low energy mass eigenstate basis, so the lepton Yukawa matrix [y e ] can have off-diagonal entries, in the presence of the operator O eH (see equations 17 and 70). We follow [23] in choosing this basis, because it defines lepton flavour in the presence of LFV, so it simplifies our calculations(as mentioned at the end of section 2.4). The Yukawa matrix eigenvalue of fermion f is written y f .…”

“…Complete bases of on-shell dimension eight operators have appeared recently [26,27], and our dimension eight operators are in these lists. However in reality, we are only interested in the subset of dimension eight µ ↔ e operators to which experiments could be sensitive, which was given in [23]. Finally, some operators in eq.…”

Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

“…For example, dimensionsix interactions do not provide the dominant contribution to some observables [15] or even they do not arise at tree level in concrete ultraviolet (UV) completions of the SM [16,17]. It can be also that relatively low values of Λ are favoured by data in some interactions, and therefore corrections involving higher powers of E/Λ are not negligible [16,18]; or simply that some observables are so well measured (or constrained) that they are sensitive to higherdimensional operators [18][19][20].…”

“…(Dimension-seven interactions [21,22] are also LNV.) This has been in fact the approach adopted in a number of recent theoretical works [16,[18][19][20][23][24][25][26][27][28], but so far mostly at tree level. Our goal is to make a first step forward towards the renormalisation of the SMEFT to order E 4 /Λ 4 .…”