We study implications of the four-fermion semileptonic operators at the low-energy and at electroweak (EW) scale in the framework of Standard Model Effective Field Theory (SMEFT). We show how the renormalization group (RG) running effects can play an important role in probing the \emph{generic flavour structure} of such operators. It is shown that at the 1-loop level, through RG running, depending upon the flavour structure, these operators can give rise to sizable effects at low energy in the electroweak precision (EWP) observables, the leptonic, quark, as well as the $Z$ boson flavour violating decays. To this end, we isolate the phenomenological relevant terms in the full anomalous dimension matrices (ADMs) and discuss the impact of the QED+QCD running in the Weak effective field theory (WET) and the SMEFT running due to gauge and Yukawa interactions on the dim-4 and dim-6 operators at the low energy. Considering all the relevant processes, we derive lower bounds on the new physics (NP) scale $Λ$ for each semileptonic operator, keeping a generic flavour structure. In addition, we also report the allowed ranges for the Wilson coefficients at a fixed value of $Λ=3$ TeV.
We consider the Drell-Yan processes $pp \to \ell \ell^{(\prime)}$ and $pp\to \ell \barν$ at high-$p_T$ as probes of New Physics effects in semileptonic transitions. For this purpose, we describe the $2\to2$ scattering amplitudes in terms of general form-factors which we match to the SMEFT at $\mathcal{O}(1/Λ^{4})$ including corrections from dimension-$8$ operators and to tree-level mediators with $\mathcal{O}$(TeV) masses arising from ultraviolet models. By using the latest LHC run-II data from monolepton and dilepton production channels, we derive constraints on the SMEFT and on leptoquark mo…
We revisit electroweak radiative corrections to Standard Model Effective Field Theory (SMEFT) operators which are relevant for the $B$-meson semileptonic decays. The one-loop matching formulae onto the low-energy effective field theory are provided without imposing any flavor symmetry. The on-shell conditions are applied especially in dealing with quark-flavor mixings. Also, the gauge independence is shown explicitly in the $R_ξ$ gauge.
We present for the first time NLO QCD Renormalization Group (RG) evolution matrices for non-leptonic $ΔF=2$ transitions in the Standard Model Effective Field Theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM operators in the so-called BMU basis into the ones in the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. This allows us subsequently to find the two-loop QCD ADMs for the SMEFT non-leptonic $ΔF=2$ operators in the Warsaw basis. Ha…
Using background-field method and super-heat-kernel expansion, we derive a master formula for the one-loop UV divergences of the bosonic dimension-6 operators in Standard Model Effective Field Theory (SMEFT). This approach reduces the calculation of all the UV divergences to algebraic manipulations. Using this formula we corroborate results in the literature for the one-loop anomalous dimension matrix of SMEFT obtained via diagrammatic methods, considering contributions from the operators $X^3, ϕ^6, ϕ^4 D^2, X^2 ϕ^2$ of the Warsaw basis. The formula is derived in a general way and can be appli…
We study nuclear electric dipole moments induced by $ΔF=1$ effective operators in the Standard Model Effective Field Theory. Such contributions arise through renormalization group evolutions and matching conditions at the electroweak symmetry breaking scale. We provide one-loop formulae for the matching conditions. We also discuss correlations of these effects with $ΔF=2$ observables such as $ε_K$ and $ΔM_{B_d}$.
When looking for heavy ($\mathcal{O}$(few TeV)) New Physics, the most efficient way to benefit from both high and low-energy measurements simultaneously is the use of the Standard Model Effective Field Theory (SMEFT). In this talk I highlight the importance of semileptonic $τ$ decays in complementing, in this respect, the traditional low-energy precision observables and high-energy measurements. This is yet another reason for considering hadronic tau decays as golden channels at Belle-II beyond the unquestionable interest of the CP violation anomaly in $τ\to K_Sπν_τ$ decays, that I also discus…
We describe the on-shell method to deriving the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examp…
We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole …
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure f…
The Standard Model Effective Field Theory (SMEFT) provides a systematic and model-independent framework to study neutrino non-standard interactions (NSIs). We study the constraining power of the on-going neutrino oscillation experiments T2K, NO$ν$A, Daya Bay, Double Chooz and RENO in the SMEFT framework. A full consideration of matching is provided between different effective field theories and the renormalization group running at different scales, filling the gap between the low-energy neutrino oscillation experiments and SMEFT at the UV scale. We first illustrate our method with a top-down a…
QCD contributions to the $b \to u \ell^- \barν_\ell$ decay rate, which are known to two-loop order in the $\bar{MS}$ scheme, exhibit sufficient dependence on the renormalization mass $μ$ to compromise phenomenological predictions for inclusive semileptonic $B \to X_u$ processes. Such scale dependence is ameliorated by the renormalization-group (RG) extraction and summation of all leading and RG-accessible subleading logarithms occurring subsequent to two-loop order in the perturbative series. This optimal RG-improvement of the known portion of the perturbative series virtually eliminates $μ$-d…
The calculation of the moments in inclusive B meson semileptonic decays is upgraded to O(alphas^2). The first three moments of the lepton energy and invariant hadronic mass distributions are computed for arbitrary cuts on the lepton energy and in various renormalization schemes, finding in general small deviations from the O(alphas^2 beta0) calculation. I also review the relation between MSbar and kinetic heavy quark masses.
The Standard Model Effective Field Theory (SMEFT) offers a powerful theoretical framework for parameterizing the low-energy effects of heavy new particles with masses far above the scale of electroweak symmetry breaking. Additional light degrees of freedom extend the effective theory. We show that light new particles that are weakly coupled to the SM via non-renormalizable interactions induce non-zero Wilson coefficients in the SMEFT Lagrangian via renormalization-group evolution. For the well-motivated example of axions and axion-like particles (ALPs) interacting with the SM via classically s…
We investigate the high-$p_T$ tails of the $pp\to \ell ν$ and $pp \to \ell \ell$ Drell-Yan processes as probes of New Physics in semileptonic interactions with an arbitrary flavor structure. For this purpose, we provide a general decomposition of the $2\to2$ scattering amplitudes in terms of form-factors that we match to specific scenarios, such as the Standard Model Effective Field Theory (SMEFT), including all relevant operators up to dimension-$8$, as well as ultraviolet scenarios giving rise to tree-level exchange of new bosonic mediators with masses at the TeV scale. By using the latest L…
The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group invariant quantities. This technique is applied to the inclusive semileptonic process $b\to u \barν_\ell\ell^-$ (explicitly known to two-loop order) to obtain bounds on the three- and four-loop perturbative coefficients that are not accessible via the renormalization group. Using the principle of minimal sensitivity, an estimate is obtained for the perturbative con…
The perturbative QCD corrections to the semileptonic decay width of the tau lepton are evaluated in the next-next-to-leading order from the contour integral representation in various renormalization schemes, using numerical solution of the renormalization group equation for complex energies. A quantitative estimate of the ambiguities resulting from the freedom of choice of the renormalization scheme is obtained by taking into account predictions in all schemes that do not involve large cancellations in the expression for the scheme invariant combination of the expansion coefficients. The probl…
The QCD corrections to the moments of the invariant mass distribution in the semileptonic $τ$ decays are considered. The effect of the renormalization scheme dependence on the fitted values of alpha_s(m^2_tau) and the condensates is discussed, using a simplified approach where the nonperturbative contributions are approximated by the dimension six condensates. The fits in the vector and the axial-vector channel are investigated in the next-to-leading and the next-to-next-to-leading order. The next-to-next-to-leading order results are found to be relatively stable with respect to change of the …
We present a model-independent anatomy of the $ΔF=2$ transitions $K^0-\bar K^0$, $B_{s,d}-\bar B_{s,d}$ and $D^0-\bar D^0$ in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude $\big[M_{12} \big]_\text{BSM}$. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale $μ_\text{ew}$ and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale $Λ$. The coefficients $P_a^{ij}$ entering these formulae contain all the information below the …
After reviewing how the renormalization group equation can be used to sum logarithmic corrections to the decay rate for the semi-leptonic process b->u when using minimal subtraction, we consider renormalization scheme dependence for this calculation when employing this renor- malization scheme. In this calculation, an ambiguity resides in the running strong coupling and in the running b quark mass. The ambiguity usually associated with the renormalization mass scale mu is shown to cancel. It is demonstrated how in one renormalization scheme, there are only leading-log contributions to this dec…
Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS} scheme works favorably in the b \to u case whereas the pole mass scheme shows better convergence in the b \to c case. Upon the inclusion of the estimated three-loop contribution, we find the full perturbative decay rate to be 192π^3Γ(b\to u\barν_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm GeV^5} and 192π^3Γ(b\to c\ell^-\barν_\ell)/(G_F^2|V_{cb}|^2)= 992 \pm 198 {\rm GeV…
We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of th…
We study Yukawa Renormalization Group (RG) running effects in the context of the Standard Model Effective Theory (SMEFT).The Yukawa running being flavour dependent leads to RG-induced off-diagonal entries, so that initially diagonal Yukawa matrices at the high scale have to be rediagonalized at the electroweak (EW) scale. Performing such flavour rotations can lead to flavour violating operators which differ from the ones obtained through SMEFT RG evolution. We show, that these flavour rotations can have a large impact on low-energy phenomenology. In order to demonstrate this effect, we compare…
We explore the interplay of New Physics (NP) effects in $(g-2)_\ell$ and $h \to \ell^+ \ell^-$ within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and $SU(2)_L$ gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimen…
Standard Model Neutrino Effective Field Theory (SMNEFT) is an effective theory with Standard Model (SM) gauge-invariant operators constructed only from SM and right-handed neutrino fields. For the full set of dimension-six SMNEFT operators, we present the gauge coupling terms of the one-loop anomalous dimension matrix for renormalization group evolution (RGE) of the Wilson coefficients between a new physics scale and the electroweak scale. We find that the SMNEFT operators can be divided into five subsets which are closed under RGE. Our results apply for both Dirac and Majorana neutrinos. We a…
The question of the renormalization scheme dependence of the $τ$ semileptonic decay rate is revisited in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this dependence and the actual selection of a subset of ``acceptable'' renormalization schemes. It is argued that a reasonable universal measure of the renormalization scheme dependence can be formulated, which gives encouraging results when applied to various physical quantities, including the semileptonic $τ$ decay rate.
