Flavor and Dark Matter Issues in Supersymmetric Models
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The Standard Model of particle physics attempts to unify the fundamental forces in the Universe (except gravity). Over the years it has been tested in numerous experiments. While these experimental results strengthen our understanding of the SM, they also point out directions for physics beyond the SM. In this thesis we assume supersymmetry (SUSY) to be the new physics beyond the SM. We have tried to analyze the present status of low energy SUSY after the recent results from direct (collider) and indirect (flavor, dark matter) searches .We have tried to see the complementarity between these apparently different experimental results and search strategies from the context of low energy SUSY. We show that such complementarity does exist in well-defined models of SUSY breaking like mSUGRA, NUHM etc. The first chapter outlines the present status of the SM and discusses about the unanswered questions in SM. Keeping SUSY as the new physics beyond the SM, we also detail about its present experimental status. Chapter1 ends with the motivation and comprehensive description about each chapter of the thesis. In chapter2, we present an introduction to formal structure of SUSY algebra and the structure of MSSM. One of the such complementarities we have studied is between flavor and dark matter. In general flavor violation effects are not considered when studying DM regions in minimal SUSY models like mSUGRA. If however flavor violation does get generated through non-minimal SUSY breaking sector, one of the most susceptible regions would be the co-annihilation region for neutralino DM. In chapter 3 we consider flavor violation in the sleptonic sector and study its implications on the stau co-annihilation region. In this work we have taken flavor violation between the right-handed smuon (˜µR) and stau (˜τR). Due to this flavor mixing the lightest slepton (ĺ1) is a ﬂavor mixed state. We have studied the effect of such ĺ11’s in the ‘stau co-annihilation’ region of the parameter space, where the relic density of the neutralinos gets depleted due to efficient co-annihilation with the staus. Limits on the flavor violating insertion in the right-handed sleptonic sector mainly comes from BR(τ → µγ). These limits are weak in some regions of the Parameter space where cancellations happen with in the amplitudes. We look for overlaps in parameter space where both the co-annihilation condition as well as the cancellations with in the amplitudes occur. We have shown that in models with non-universal Higgs boundary conditions (NUHM) overlap between these two regions is possible. The effect of flavor violation is two fold: (a) It shifts the co-annihilation regions towards lighter neutralino masses and (b) the co-annihilation cross sections would be modified with the inclusion of flavor violating diagrams which can contribute significantly. In the overlap regions, the flavor violating cross sections become comparable and in some cases even dominant to the flavor conserving ones. A comparison among the different flavor conserving and flavor violating channels, which contribute to the neutralino annihilation cross-section, is presented. One of the challenges of addressing quantitatively the complementarity problems is the lack of proper spectrum generator (numerical tools which computes SUSY sparticle spectrum in the presence of flavor violation in the sfermionic sector). For the lack of a publicly available code which considers general flavor violating terms in the renormalization group equations (RGE) we have developed a SUSY spectrum calculator, named as SuSeFLAV .It is a code written in FORTRAN language and calculates SUSY particle spectrum (with in the context of gravity mediation) in type I seesaw, in the presence of heavy right handed neutrinos (RHN). SuSeFLAV also calculates the SUSY spectrum in other type of SUSY breaking mechanisms (e.g. gauge mediation). The renormalization group (RG) flow of soft-SUSY breaking terms will generate large off-diagonal terms in the slepton sector in the presence of this RHNs, which will give rise to sizable amount of flavor violating (LFV) decays at the weak scale. Hence, in this code we also calculate the different rare LFV decays like, µ → eγ, τ → µγ etc. In SuSeFLAV the user has the freedom to choose the scale of the RHNs as well as the mixing matrix in neutrino sector. It is also possible to choose the values of the SUSY breaking input parameters at the user defined scale. The details of this package is discussed in chapter 4. Many of the present studies of complementarity between the direct and indirect searches are inadequate to address realistic scenarios, where SUSY breaking could be much more general compared to the minimal models. The work in this thesis is a step to wards this direction. Having said that, in the present thesis we have considered modifications of popular models with either explicit flavor violating terms (in some sectors) or sources of flavor violation through new particles and new couplings motivated by strong phenomenological reasons like neutrino masses. It should be noted however, the numerical tool which has been developed during the thesis can be used to address more complicated problems like with complete flavor violation in models of SUSY breaking. One of the popular mechanisms of neutrino mass generation is the so called Seesaw Mechanism. Depending on the extra matter sector present in the theory there are three basic types of them. The type I seesaw, which has singlet bright-handed neutrinos, the type II seesaw contains scalar triplets and type III seesaw has additional fermionic triplets. One of the implications of the seesaw mechanism is flavor violation in the sfermionic sector even in the presence of flavor universal SUSY breaking. This leads to a complementarity between flavor experiments and direct SUSY searches at LHC. With the announcement of the results from the reactor neutrino oscillation experiments, the reactor mixing angle (θ13) in the neutrino mixing matrix (PMNS matrix) gets fixed to a rather large non-zero value. In SO (10) GUT theories neutrino Yukawa couplings of type I seesaw gets related to the up-type fermion sector of the SM. In chapter 5 we update the status of SUSY type I seesaw assuming SO (10)- like relations for neutrino Dirac Yukawa couplings and two cases of mixing, one large, PMNS-like, and another small, CKM-like, are considered. It is shown that for the large mixing case, only a small range of parameter space with moderate tan β is still allowed. It is shown that the renormalization group induced flavor violating slepton mass terms are highly sensitive to the Higgs boundary conditions. Depending on the choice of the parameters, they can either lead to strong enhancements or cancellations with in the flavor violating terms. We have shown that in NUHM scenario there could be possible cancellations which relaxes the severe constraints imposed by lepton flavor violation compared to mSUGRA. We further updated the flavor consequences for the type II seesaw in SUSY theories. As mentioned previously in type II seesaw neutrino mass gets generated due to exchange of heavy SU (2) L triplet Higgs field. The ratio of lepton flavor violating branching ratios (e.g. BR(τ → µγ) /BR (µ → eγ) etc.) are functions of low energy neutrino masses ans mixing angles. In chapter 6 we have analyzed how much these ratios become, after the experimental measurement of θ13, in the whole SUSY parameter space or in other words how much these ratios help to constrain the SUSY parameter space. We compute different factors which can affect this ratios. We have shown that the cMSSM-like scenarios, in which slepton masses are taken to be universal at the high scale, predict 3.5 BR(τ → µγ) / BR(µ → eγ) 30 for normal hierarchical neutrino masses. We Show that the current MEG limit puts severe constraints on the light sparticle spectrum in cMSSM-like model for seesaw scale with in1013 - 1015 GeV. These constraints can be relaxed and relatively light sparticle spectrum can be still allowed by MEG result in a class of models in which the soft mass of triplet scalar is taken to be non-universal at the GUT scale. In chapter 7 we have analyzed the effect of largen eutrino Yukawa couplings on the supersymmetric lightest Higgs mass. In July 2012, ATLAS and CMS collaboration have updated the Higgs search in LHC and found an evidence of a scalar particle having mass around 125 GeV. The one-loop contribution to Higgs mass mainly depends on the top trilinear couplings (At), the SUSY scale and the top Yukawa (Yt). Thus in models with extra large Yukawa couplings at the high scale like the seesaw mechanism ,the renormalization scaling of the At parameter can get significantly affected. This in turn can modify the light Higgs mass at the weak scale for the same set of SUSY parameters. We have shown in type I seesaw with (Yν ~ 3Yu) the light Higgs mass gets reduced by 2 - 3 GeV in most of the parameter rspace. In other words the SUSY scale must be pushed high enough to achieve similar Higgs mass compared to the cMSSM scenario. We have got similar effect in SUSY type III seesaw scenario with (Yν ~Yu) at the GUT scale. In chapter 8 we summarize the results of the thesis and discuss the possible future directions.
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