SUSY Breaking Mechanism And The Flavor Structure Of Low Energy Supersymmetry

The Standard Model(SM)of particle physics is undoubtable the most successful theory in particle physics.The discovery of 125 GeV Higgs,in particular,fills the last missing piece of the SM.However,the standard model,which is in good agreement with almost all the electroweak(EW)measurements,also has many theoretical and aesthetical problems,such as the hierarchy problem(the quadratic divergence problem for the Higgs mass,or fine tuning problem),dark matter puzzle,the gauge coupling unification problem,neutrino mass problem and flavor puzzle,etc.In order to solve these problems,many new physical models have been proposed,such as supersymmetry(SUSY),which is one of the most beautiful new physical theories.SUSY is a maximal extension of space-time symmetry with fermionic generators,which connects bosons and fermions.In the Minimal Supersymmetric Standard Model(MSSM),each standard Model particle has a superpartner with a spin difference of 1/2.Since no supersymmetric particles have been observed so far,SUSY must be broken.In order to avoid the reintroduction of the hierarchy problem,the SUSY broken parameters introduced are required to be soft.An UV-completed SUSY model in generally contains three parts:the invisible supersymmetric breaking sector,the visible low-energy supersymmetric standard model sector and the meditation mechanism to transfer the SUSY broken effects to the visible sector.Depending on the way that the visible sector "feels" the SUSY breaking effects in the hidden sector,the SUSY breaking mechanisms can be classified into gravity mediation,gauge mediation,anomaly mediation scenarios,etc.Our first work is based on the generalized deflected mirage mediation.Mirage mediation is a mixed modulus-anomaly mediation.With certain assumptions on the Yukawa couplings and the modular weights,the change of the SUSY breaking contributions(from the inputs)by the renormalization group evolution(RGE)and the anomaly mediation contributions could cancel each other at a ’mirage’ scale,leading to an apparent pure modulus mediation scenario(similar with gravity mediation).Such a mixed modulus-anomaly mediation SUSY breaking mechanism is dubbed as ’mirage mediation’.Because the anomaly mediation is the essential component of the mirage mediation,the mirage mediation also possibly has the " tachyonic slepton" problem.We try to deflect the RGE trajectory by introducing additional Yukawa contribution to generate a realistic soft SUSY breaking parameters,just similar to that in the deflected anomaly mediation.General approach in previous studies always adopts the total contributions from the modular mediation and anomaly mediation as input at the grand unified(GUT)scale.After RGE evolution from the GUT scale to the messenger scale,the contributions from the messengers are added at the messenger scale before final evolution from the messenger scale to the EW scale.We propose that we can obtain the soft SUSY input at the messenger scale through the Wilsonian effective action approach by integrating out the heavy fields.In order to avoid the μ-bμ problem and accommodate easily the 125 GeV SM-like Higgs mass,this work is carried out in the framework of the next minimal supersymmetric standard model(NMSSM).Through numerical analysis,we find that the NMSSM spectrum can be successfully obtained by our generalized deflected mirage mediation mechanism with additional gauge or Yukawa mediation contribution.Besides,our model can mitigate the stringent constraints from 125GeV Higgs and successful EWSB.Tiny neutrino mass can be the obtained from the seesaw mechanisms.The Froggatt-Nielsen mechanism,discrete flavor symmetry and modular flavor symmetry are widely used to explain the flavor problems of the Standard Model.Our second and third works are based on the modular flavor symmetry.Modular flavor symmetry can be realized from typical compactification of extra dimension theories and is always closely related to SUSY.Supermultiplets with different representations of finite discrete modular ΓN and different modular weight can transform non-trivially under the finite modular group.After selecting proper modular weights and irreducible representations of the modular group for different flavor supermultiplets,the form of the Yukawa coupling matrix can be determined by modular invariance of the superpotential.The modular flavor symmetry can explain fairly well the flavor structure of the matter field.Meanwhile,the SUSY partners,which share the same superpotential with quarks and leptons,are also constrained by the flavor structure obtained from the modular flavor symmetry.Therefore,constraints from the collider and dark matter can also be used to constrain the allowed parameters for the modular field in the modular supersymmetric model.In our second work,we firstly discuss the possibility to realize the S3 modular field at fixed points of the T2/ZN orbifold,especially T2/Z2.Secondly,we take the simplest UV-complete S3 modular symmetric SU(5)grand unified model with the most economical generalized gravity mediation mechanism as an example to discuss the potential supersymmetry breaking effects on the modular flavor models.Experimental data from the collider,the dark matter etc are used to constrain the allowed values of the modulus field in the modular GUT models.Flipped SU(5)GUT can naturally accommodate the economical missing-partner mechanism to solve the notorious doublet-triplet splitting problem of GUT and efficiently suppress the dimension-five proton decay rate.Besides,the flipped SU(5)GUT naturally include the right-handed neutrinos and can be further unified into SO(10)GUT.It can also be embedded in string theory and explain some cosmological puzzles.In our third work,we construct the A4 modular flipped SU(5)GUT models extended by inverse seesaw mechanism for neutrinos.All possible choices of the quantum numbers for the fields and the resultant mass spectrums are discussed.We check if such choices can best-fit the mass structures of matter fields(including neutrinos)and the flavor mixing parameters.Besides,we discuss the RGE evolution effects for general forms of Yukawa couplings.Especially in the grand unified model with modular flavor symmetry extended by inverse seesaw mechanism,the effects from non-diagonal elements cannot be ignored.In particular,the hierarchical mass structure of SM matter contents and flavor mixing parameters can be fitted successfully in the most economical case with all matter supermultiplets fitted in the triplet represention of A4.