Standard Model Effective Field Theory And Its Applications

In this thesis we discuss some aspects of the Standard Model effective field theory(SMEFT)and its applications.We start by taking a quick review of the basic concepts and some important results in the literature,including the operator basis,the method of matching,the anomalous dimension matrix and mapping the Wilson coefficients to observables.Then we discuss some general features of the helicity amplitudes in the effective field theory(EFT),at both tree level and one-loop level.We first classify the operators at different dimensions and the helicity amplitudes they correspond to.Then we make a map showing the general patterns of the tree level amplitudes of different numbers of external legs in the EFT,as well as the patterns of how the operators renormalize each other.We further discuss the rationality of a class of one-loop amplitudes in the EFT,which is a generalization of the non-renormalizaiton theorems in the literature.We also find some interesting vanishing one-loop amplitudes which leads to the non-interference between the renormalizable theory and the EFT at both tree level and one-loop.Lastly we make a classification of the operators as tree-level generated and loop-level generated up to dimension 8,which helps further our understanding of beyond the Standard Model(BSM)effects.We apply the covariant derivative expansion(CDE)method to integrate out the neutralinos and charginos in the minimal supersymmetric standard model(MSSM).The results are presented as set of pure bosonic dimension six operators in SMEFT.Nontrivial chirality dependence in the fermionic CDE is discussed carefully.The results are checked by computing the/hγγ effective coupling and the elec-troweak oblique parameters,both using the SMEFT with our effective operators and via a direct loop calculation.In global fits to the proposed lepton collider constraint projections,special phenomenolog-ical emphasis is placed on the gaugino mass unification scenario(M2(?)2M1)and anomaly mediation scenario(Mi(?)3.3M2).These results show that precision measurements at future lepton colliders will provide a very useful complementary probes of the electroweakino sector,in particular filling the gap of the soft lepton plus missing ET channel search left by the traditional collider,where the neutralino as the lightest supersymmetric particle is closely degenerate with the next-to-lightest chargino/neutralino.We present the results of the first complete one-loop matching calculation between the real singlet scalar extension of the Standard Model and SMEFT at dimension six.Beyond their immediate rele-vance to the precision calculation of observables in singlet extensions of the Standard Model,our results illustrate a variety of general features of one-loop matching.We explore the interplay between non-supersymmetric non-renormalization theorems,the logarithmic dependence of Wilson coefficients,and the relevance of mixed diagrams in theories with large scale separation.In addition,we highlight some of the subtleties involved in computing observables at next-to-leading order in SMEFT by mapping our results to the T parameter at one-loop.