We discuss the issue of precision gauge unification in the MSSM. We find that a comparably light gluino, as it emerges in certain patterns of soft supersymmetry breaking, can be a key ingredient for ensuring precision gauge unification without relying on the presence of extra particles around the scale of grand unification. In particular, the so-called mirage pattern for gaugino masses can naturally lead to precision gauge unification. There is also an interesting correlation with reduced fine-tuning, due to rather light gluinos.
We investigate gauge coupling unification at 2-loops for theories with 5 extra vectorlike SU(5) fundamentals added to the MSSM. This is a borderline case where unification is only predicted in certain regions of parameter space. We establish a lower bound on the scale for the masses of the extra flavors, as a function of the sparticle masses. Models far outside of the bound do not predict unification at all (but may be compatible with unification), and models outside but near the boundary cannot reliably claim to predict it with an accuracy comparable to the MSSM prediction. Models inside the …
Motivated by the coupling unification problem, we propose a novel extension of the Minimal Supersymmetric Standard Model. One of the predictions of this extension is existence of new states neutral under SU(3)_c X SU(2)_w but charged under U(1)_Y. The mass scale for these new states can be around the mass scale of the electroweak Higgs doublets. This suggests a possibility of their detection in the present or near future collider experiments. Unification of gauge couplings in this extension is as precise (at one loop) as in the MSSM, and can occur in the TeV range.
We study gauge and Yukawa coupling unification in the simplest extension of the Minimal Supersymmetric Standard Model (MSSM) which incorporates R-Parity violation through a bilinear superpotential term. Contrary to what happens in the MSSM, we show that bottom-tau unification at the scale M_GUT where the gauge couplings unify can be achieved for any value of tan(beta) by choosing appropriately the sneutrino vacuum expectation value. In addition, we show that bottom-tau-top unification occurs in a slightly wider tan(beta) range than in the MSSM.
Talk given at PASCOS 2012, Merida, Mexico describing work in progress in collaboration with Archana Anandakrishnan, Christopher Plumberg and Akin Wingerter.
I briefly summarize the main features related to the unification of gauge and Yukawa couplings in the MSSM, emphasizing the predictions derived in this framework, which are of special interest in the light of present and near--future experiments
We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $\rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $\rm{SU}(5)$ or Pati-Salam only extra matter $\mathbf{16}$ supermultiplet of $SO(10)$ can appear at TeV scale, apart from MSSM spectrum.
We examine unification of gauge couplings in four dimensional renormalizable gauge theories inspired by the latticized (deconstructed) SM or MSSM in five dimensions. The models are based on replicated gauge groups, spontaneously broken to the diagonal subgroup. The analysis is performed at one-loop level, with the contribution from the heavy vector bosons included, and compared with the analogous results in the SM or MSSM. Unification at or above the diagonal breaking scale is discussed. We find that in the considered class of extensions of the SM(MSSM) unification is possible for a wide range…
It is well-known that in scenarios with direct gauge mediation of supersymmetry breaking the messenger fields significantly affect the running of Standard Model couplings and introduce Landau poles which are difficult to avoid. This appears to remove any possibility of a meaningful unification prediction and is often viewed as a strong argument against direct mediation. We propose two ways that Seiberg duality can circumvent this problem. In the first, which we call "deflected-unification", the SUSY-breaking hidden sector is a magnetic theory which undergoes a duality to an electric phase, wit…
Study of the MSSM in large tan$β$ regime has to include correlations between the constraints presented by the low energy values of the b quark mass and $BR(b\to sγ)$. Both quantities receive SUSY contributions enhanced by tan$β$ and have a major impact on the MSSM analysis. Here we summarize the results of such a study constrained by minimal SO(10) unification. We show the best fits, in the $(m_0,M_{1/2})$ plane, obtained in the global analysis spanned over the gauge, Yukawa and SUSY parameter space at the unification scale. Two distinct fits describe the available low-energy data very well. T…
We consider non-canonical embeddings of the MSSM in high-dimensional orbifold GUTs based on the gauge symmetry SU(N), N=5,6,7,8. The hypercharge normalization factor k_Y can either have unique non-canonical values, such as 23/21 in a six-dimensional SU(7) model, or may lie in a (continuous) interval. Gauge coupling unification and gauge-Yukawa unification can be realized in these models by introducing new particles with masses in the TeV range which may be found at the LHC. In one such example there exist color singlet fractionally charged states.
We consider the constrained minimal supersymmetric standard model which emerges from one theory with a small deviation from Yukawa unification which is adequate for $μ>0$. We show that this model possesses a wide and natural range of parameters which is consistent with the data on $b\to sγ$, the muon anomalous magnetic moment, the cold dark matter abundance in the universe, and the Higgs boson masses.
For the weakly coupled heterotic string (WCHS) there is a well-known factor of twenty conflict between the minimum string coupling unification scale, Lambda_H ~5x10^(17) GeV, and the projected MSSM unification scale, Lambda_U ~ 2.5x10^(16) GeV, assuming an intermediate scale desert (ISD). Renormalization effects of intermediate scale MSSM-charged exotics (ISME) (endemic to quasi-realistic string models) can resolve this issue, pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected Lambda_U unification under ISD is accidental. If the …
We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge …
Low-energy supersymmetric models such as MSSM, NMSSM and MSSM with vectorlike fermion are consistent with perturbative unification. While the non-minimal extensions naturally explain Higgs mass and dark matter in the low energy region, it is unclear how seriously they are constrained in the ultraviolet region. Our study shows that $i)$, In the case of embedding MSSM into $\rm{SU}(5)$, the fit to SM fermion masses requires a singlet $S$, which leads to unviable embedding of NMSSM into $\rm{SU}(5)$ because such $S$ feeds singlet $N$ a mass of order unification scale as well. $ii)$, Similar resul…
In the light of the gathering evidence for $ν_μ-ν_τ$ neutrino oscillations, coming in particular from the Super-Kamiokande data on atmospheric neutrinos, we re-analyze the unification of gauge and Yukawa couplings within the minimal supersymmetric extension of the Standard Model (MSSM). Guided by a range of different grand-unified models, we stress the relevance of large mixing in the lepton sector for the question of bottom-tau Yukawa coupling unification. We also discuss the dependence of the favoured value of $\tanβ$ on the characteristics of the high-energy quark and lepton mass matrices. …
We make a complete analysis of the Yukawa coupling unification in SU(5) extensions of the MSSM in the framework of the radiative symmetry breaking scenario. Both logarithmic and finite threshold corrections of sparticles have been included in the determination of the gauge and Yukawa couplings at M_Z. The effect of the heavy masses of each model in the renormalization group equations is also included. We find that in the minimal SU(5) model b-tau Yukawa unification can be achieved for too large a value of alpha_s. On the other hand the Peccei-Quinn version of the Missing Doublet model, with th…
In the MSSM extended by a complete vectorlike family, precise top, bottom and tau Yukawa coupling unification can be achieved assuming SUSY threshold corrections which are typical for comparable superpartner masses. Furthermore, the unification is possible with a large unified coupling, implying that all three fermion masses can be simultaneously close to their IR fixed points. Assuming unified Yukawa couplings of order one or larger, the preferred common scale of new physics (superpartners and vectorlike matter) is in the 3 TeV to 30 TeV range, with larger couplings favoring smaller scales. S…
In warped supersymmetric grand unification, XY gauge particles appear near the TeV scale along with Kaluza-Klein towers of the standard model gauge fields. In spite of this exotic low-energy physics, MSSM gauge coupling unification is preserved and proton decay is naturally suppressed. In this paper we study in detail the low-lying mass spectrum of superparticles and GUT particles in this theory, taking supersymmetry breaking to be localized to the TeV brane. The masses of the MSSM particles, Kaluza-Klein modes, and XY states are all determined by two parameters, one which fixes the strength o…
We calculate ~$\sin^2θ(M_Z)$ ~in the MSSM in terms of ~ $α_{EM}$, ~$G_F$, ~$m_t$, ~$\tanβ$ ~and SUSY mass parameters with the same accuracy as the present calculations of ~$\sin^2θ(M_Z)$ ~in the SM. We compare the results with the standard leading logarithmic approximation used for SUSY threshold corrections and find important differences in the case of light sparticles. We give approximate formulae connecting coupling constants in the SM and in the MSSM and comment on process dependence of such formulae. The obtained values of the MSSM couplings ~$α_i(M_Z)$ ~are used to investigate gauge coup…
We construct four dimensional gauge theories in which the successful supersymmetric unification of gauge couplings is preserved but accelerated by N-fold replication of the MSSM gauge and Higgs structure. This results in a low unification scale of $10^{13/N}$ TeV.
Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tan…
We show that in the CMSSM with the non-holomorphic soft SUSY breaking terms, the Yukawa coupling unification of the third family fermions at the GUT scale, called $ t-b-τ$ Yukawa unification (YU), is possible under the recent collider and Dark Matter results. The YU parameter can also be found $ R_{tbτ} \approx 1 $, called perfect unification. We find that the squark masses exceed 3 TeV while the stau can be considerably lighter. In the case of YU, the $ \tanβ$ is in the interval $ [46,55] $. We obtain bino-like dark matter (DM) of mass in the range of $ 0.6$ TeV $ \lesssim m_{χ_{1}^{0}} \less…
We analyze the implications of the infrared quasi fixed point solution for the top quark mass in the Minimal Supersymmetric Standard Model. This solution could explain in a natural way the relatively large value of the top quark mass and, if confirmed experimentally, may be suggestive of the onset of nonperturbative physics at very high energy scales. In the framework of grand unification, the expected bottom quark - tau lepton Yukawa coupling unification is very sensitive to the fixed point structure of the top quark mass. For the presently allowed values of the electroweak parameters and the…
We study the predictions for M_top, tan(beta) and V_cb in a popular texture ansatze for the fermion mass matrices. We do this both for the Minimal Supersymmetric Standard Model (MSSM) and for the simplest model (MSSM-BRpV) where a bilinear R-Parity violating term is added to the superpotential. We find that taking the experimental values for M_top and V_cb at 99 % C.L. and the GUT relations h_b=h_tau and (V_cb)^2=h_c/h_t within 5 %, the large tan(beta) solution, characteristic in the MSSM with bottom--tau unification, becomes disallowed. In contrast the corresponding allowed region for the MSS…
In order to achieve gauge unification at the string scale M_X sim 5.10^17 GeV in the minimal supersymmetric standard model (MSSM) it is necessary to add extra gauge non-singlet representations at an intermediate scale M_I<M_X, leading to a class of models which we refer to as MSSM+X models. We perform a detailed analysis of a large class of MSSM+X models and find that the number of (3,1) representations added must be greater than the total of the number of (3,2) and (1,2) representations. Predictions of M_I, M_X and alpha(M_X) are obtained for models with up to 5 extra vector representations t…
We discuss whether the (MSSM) unification of gauge couplings can be accommodated in string theories with a low (TeV) string scale. This requires either power law running of the couplings or logarithmic running extremely far above the string scale. In both cases it is difficult to arrange for the multiplet structure to give the MSSM result. For the case of power law running there is also enhanced sensitivity to the spectrum at the unification scale. For the case of logarithmic running there is a fine tuning problem associated with the light closed string Kaluza Klein spectrum which requires gau…
We calculate the weak scale MSSM spectrum starting from a heterotic string theory compactified on an anisotropic orbifold. Supersymmetry breaking is mediated by vector-like exotics that arise naturally in heterotic string theories. The messengers that mediate SUSY breaking come in incomplete GUT multiplets and give rise to non-universal gaugino masses at the GUT scale. Models with non-universal gaugino masses at the GUT scale have the attractive feature of allowing for precision gauge coupling unification at the GUT scale with negligible contributions from threshold corrections near the unific…
We study the Minimal Supersymmetric Standard Model (MSSM) constrained by unification assuming mSUGRA SUSY breaking. In particular this means that the three gauge couplings are unified at a {\it per cent} level, third generation yukawa couplings are unified at a $10 $% level, and at the unification scale $M_U\approx 10^{16}$ the SUSY breaking masses of squarks and sleptons are universal up to specific D-term contributions. At $M_U$ we also include right-handed neutrinos that are decoupled at their three respective scales. In a top-down global analysis we then find that there are two distinct be…
These lectures begin with a brief introduction to the minimal supersymmetric standard model (MSSM) and the various mechanisms for hidden sector supersymmetry breaking and go on to provide a pedagogical discussion of the various kinds of supersymmetric unified theories beyond the MSSM including SUSY GUTs. Their implications for proton decay, R-parity violation, doublet triplet splitting etc. are discussed. Exhaustive discussion of SU(5) and SO(10) models is given. Other GUT models such as those based on $E_6$, $SU(5)\times SU(5)$, flipped SU(5) and SU(6) are also presented.
We review recent progress in embedding the supersymmetric standard model into string theory. We discuss how, with the incorporation of certain aspects of grand unification, a search strategy can be developed that allows to efficiently find rather large numbers of promising string vacua. Global string-derived models with the following features are discussed: (i) exact MSSM spectrum below the unification scale; (ii) R parity; (iii) hierarchical Yukawa couplings with non-trivial mixing; (iv) solution to the mu problem; (v) see-saw suppressed neutrino masses.
String compactification with fluxes yields MSSM soft SUSY breaking terms that receive comparable contributions from modulus and anomaly mediation whose relative strength is governed by a phenomenological parameter $α$. Gaugino and first/second generation (and sometimes also Higgs and third generation) scalar mass parameters unify at a mirage unification scale $Q \not= M_{\rm GUT}$, determined by the value of $α$. The ratio of scalar to gaugino masses at this mirage unification scale depends directly on the scalar field modular weights, which are fixed in turn by the brane or brane intersection…
We examine the issue of fine tuning in the MSSM with GUT-scale boundary conditions. We identify specific unification patterns and mass relations that can lead to a significant lowering of the fine tuning due to gauginos, scalars, and the μ parameter, relative to the simplest unification conditions. We focus on a phenomenologically interesting region that is favored by the Higgs mass and the relic density where the dark matter is a nearly pure higgsino with mass given by μ~1 TeV while the scalars and gauginos have masses in the multi-TeV regime. There, we find that the fine tuning can be reduce…
The unification of gauge coupling constants in the minimal supersymmetric model (MSSM) is unaffected at the one-loop level by the inclusion of additional mass-degenerate SU(5) multiplets. Perturbativity puts an upper limit on the number of additional fields. We analyse the evolution of the gauge coupling constants in all models satisfying these criteria using two-loop $β$ functions and including low energy threshold effects. We find that similarly to the minimal supersymmetric model (MSSM) unification takes place within the theoretical and experimental errors. The dominant proton decay mode is…
This is a pedagogical review article surveying the various approaches towards understanding gauge coupling unification within string theory. As is well known, one of the major problems confronting string phenomenology has been an apparent discrepancy between the scale of gauge coupling unification predicted within string theory, and the unification scale expected within the framework of the Minimal Supersymmetric Standard Model (MSSM). In this article, I provide an overview of the different approaches that have been taken in recent years towards reconciling these two scales, and outline some o…
We investigate supersymmetric SU(5) grand-unified theories (GUTs) realized in 5 space-time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S^1/(Z_2 x Z_2') orbifold with two 3-branes. The doublet-triplet splitting problem is entirely avoided by locating the MSSM Higgs doublets on the brane on which SU(5) is not a good symmetry. An extremely simple model is then described in which the MSSM matter is also located on this SU(5)-violating brane. Although this model does not unify the MSSM matter within SU(5) multiplets, it explains gauge coupling unification. A s…
We show that large string threshold corrections can reconcile the string and MSSM unification scales in fermionic strings. This requires at least three moduli with large VEVs which are different from each other and MSSM states arising in an unconventional manner from the string spectrum. The former is easily achieved by supersymmetry breaking by both hidden gaugino and matter condensation whereas the latter needs to be seen in explicit string models.
This paper introduces a random statistical scan over the high-energy initial parameter space of the minimal SUSY $B-L$ model--denoted as the $B-L$ MSSM. Each initial set of points is renormalization group evolved to the electroweak scale--being subjected, sequentially, to the requirement of radiative $B-L$ and electroweak symmetry breaking, the present experimental lower bounds on the $B-L$ vector boson and sparticle masses, as well as the lightest neutral Higgs mass of $\sim$125 GeV. The subspace of initial parameters that satisfies all such constraints is presented, shown to be robust and to…
We show that in some SU(N) type GUTs with the complementary pairs of the conjugated fermion multiplets there naturally appear the relatively light ($M\ll M_{GUT}$) vectorlike fermions which considerably modify the desert physics. In the non-SUSY case they can provide for the unification of the standard coupling constant $α_1$, $α_2$ and $α_S$ whereas in the SUSY case they can increase the unification point up to the string unification limit and decrease $α_S(M_Z)$ down to the value predicted from the low energy physics.
The recent conjecture of possible equivalence between the string scale $M_S$ and the minimal supersymmetric standard model unification scale M_U ~ 2.5 x 10^{16} GeV is considered in the context of string models. This conjecture suggests that the observable gauge group just below the string scale should be SU(3)_C x SU(2)_L x U(1)_Y and that the SU(3)_C x SU(2)_L x U(1)_Y-charged spectrum of the observable sector should consist solely of the MSSM spectrum. We demonstrate that string models can actually be constructed that possess these observable features. Two aspects generic to many classes of…
Gauge coupling unification is studied in the MSSM with non-universal soft supersymmetry breaking terms. If gaugino masses are sufficiently smaller than scalar soft masses and the scalar soft masses have also certain types of non-universality, gauge coupling unification scale can be larger than $3\times 10^{16}$~GeV even within the MSSM contents. String unification may not need a large threshold correction or a large modulus value. We also discuss the relation to the string model building.
Motivated by the fact that the string scale can be many orders of magnitude lower than the Planck mass, we investigate the required modifications in the MSSM $β$--functions in order to achieve intermediate ($10^{10-13}$GeV) scale unification, keeping the traditional logarithmic running of the gauge couplings. We present examples of string unified models with the required extra matter for such a unification while we also check whether other MSSM properties (such as radiative symmetry breaking) are still applicable.
The approximate unification of gauge couplings is the best indirect evidence for low-energy supersymmetry, although it is not perfect in its simplest realizations. Given the experimental evidence for small non-zero neutrino masses, it is plausible to extend the MSSM with three right-handed neutrino chiral multiplets, with large Majorana masses below the unification scale, so that a see-saw mechanism can be implemented. In this extended MSSM, the unification prediction for the strong gauge coupling constant at M_Z can be lowered by up to \sim 5%, bringing it closer to the experimental value at …
We study $3$rd family Yukawa unification in the context of supersymmetric (SUSY) $\mathrm{SO}(10)$ GUTs and $\mathrm{SO}(10)$-motivated boundary conditions for the SUSY-breaking soft terms. We consider $μ<0$ such that the SUSY loop-threshold effects enable a good fit to all third family masses of the charged Standard Model (SM) fermions. We find that fitting the third family masses together with the mass of the SM-like Higgs particle, the scenario predicts the masses of the superpartner particles and of the extra Higgs states of the MSSM: while the sparticles are predicted to be comparatively …
We investigate the possibility of generating the $μ$-term in the MSSM by the condensation of a field that is a singlet under the SM gauge group but charged under an additional family-independent $U(1)_X$ gauge symmetry. We attempt to do so while preserving the gauge coupling unification of the MSSM. For this, we find that SM non-singlet exotics must be present in the spectrum. We also prove that the pure $U(1)_X$ anomalies can always be solved with rationally charged fields, but that a large number of SM singlets are often required. For $U(1)_X$ charges that are consistent with an embedding of…
We investigate gauge coupling unification for F-theory respectively Type IIB orientifold constructions of SU(5) GUT theories with gauge symmetry breaking via non-trivial hypercharge flux. This flux has the non-trivial effect that it splits the values of the three MSSM gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way.
The commonly accepted notion of a weak unified coupling $α_X \approx 0.04$, based on the assumption of the MSSM--spectrum, is questioned. It is suggested that the four--dimensional unified string coupling should very likely have an intermediate value $(\sim 0.2-0.3$, say) so that it may be large enough to stabilize the dilaton but not so large as to disturb the coupling--unification relations. Bearing this in mind, as well as the smallness of the MSSM unification scale $M_X$ compared to the string scale, the consequences of a previously suggested extension of the MSSM spectrum are explored. Th…
We explore the extent to which string theories with higher-level gauge symmetries and non-standard hypercharge normalizations can reconcile the discrepancy between the string unification scale and the GUT scale extrapolated from the Minimal Supersymmetric Standard Model (MSSM). We determine the phenomenologically allowed regions of (k_Y,k_2,k_3) parameter space, and investigate the proposal that there might exist string models with exotic hypercharge normalizations k_Y which are less than their usual value k_Y=5/3. For a broad class of heterotic string models (encompassing most realistic strin…
We investigate the possibility of satisfying the $SU(5)$ boundary condition $\mathbf{Y}^d=\mathbf{Y}^{e\,T}$ at the GUT scale within the renormalizable $R$-parity conserving Minimal Supersymmetric Standard Model (MSSM). Working in the super-CKM basis, we consider non-zero flavour off-diagonal entries in the soft SUSY-breaking mass matrices and the $A$-terms. At the same time, the diagonal $A$-terms are assumed to be suppressed by the respective Yukawa couplings. We show that a non-trivial flavour structure of the soft SUSY-breaking sector can contribute to achieving precise Yukawa coupling uni…
When realizing the Minimal Supersymmetric Standard Model (MSSM) within a (simple) Grand Unified Theory (GUT), the predicted ranges for the strong coupling and the ratio of two Higgs doublet expectation values are strongly correlated with the weak angle and the $t$-quark mass. (The latter are extracted from precision data.) We spell out those relations and point out the implication for the mass of the light MSSM (CP even) Higgs boson.
We study gauge extensions of the MSSM that contain non-decoupling D-terms, which contribute to the Higgs boson mass. These models naturally maintain gauge coupling unification and raise the Higgs mass without fine-tuning. Unification constrains the structure of the gauge extensions, limiting the Higgs mass in these models to roughly less than 150 GeV. The D-terms contribute to the Higgs mass only if the extended gauge symmetry is broken at energies of a few TeV, leading to new heavy gauge bosons in this mass range.
In this letter, we study collider phenomenology in the supersymmetric Standard Model with a certain type of non-universal gaugino masses at the gauge coupling unification scale, motivated by the little hierarchy problem. In this scenario, especially the wino mass is relatively large compared to the gluino mass at the unification scale, and the heavy wino can relax the fine-tuning of the higgsino mass parameter, so-called $μ$-parameter. Besides, it will enhance the lightest Higgs boson mass due to the relatively large left-right mixing of top squarks through the renormalization group (RG) effec…
We consider a particular class of threshold corrections to Yukawa couplings and mass relations in the MSSM and supersymmetric grand unified models. We give a complete treatment of Yukawa coupling thresholds at the unification scale $\Mx$ and the effective supersymmetry scale $\Ms$ and apply them to corrections to the tree-level prediction $y_b(\Mx) = y_τ(\Mx)$ in minimal supersymmetric SU(5). We apply both gauge and Yukawa coupling thresholds to gauge unification and the above Yukawa unification condition to find predictions for the top quark mass, $M_t$, the superheavy vector boson mass $\Mv$…
In the context of the Grand Unified MSSM, we investigate the fermion mass matrices at GUT scale. We note that from the experimental mass pattern the determinants of the Yukawa matrices at this scale can be unified with good precision. Taking the unification o determinants as an hypothesis, it gives two model independent predictions that in the MSSM turns out to determine an appropriate value for the product m_d m_s and tan(beta)~7-10 in the favored range. We then review a predictive model of SU(3) flavour in the context of supersymmetric SO(10) that nicely implements this mechanism, while expl…
The minimal supersymmetry standard model (MSSM) extended with vector-like theories have long been discussed. If we extend the vector-like MSSM theory into NMSSM and let the vector-like particles couple with the singlet (S), we find out a natural way to generate the vector-like particle masses near 1TeV through the breaking of the Z_3 group. Compared with MSSM+vectorlike models, vector-like models extended into NMSSM contain more yukawa couplings and can help us adjust the renormalization group (RG) trajectories of the gauge couplings in order to unify the intersections. They can also help pres…
In this talk, I present a family unification in $Z_3$ orbifolded $E_8\times E_8^\prime$ heterotic strings. It is argued that trinification is a plausible candidate toward supersymmetric standard model at low energy.
We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken supersymmetric gauge theory with a non-simple gauge group containing an abelian factor, and present the associated beta-function through three loops. We also include in an appendix the result for several abelian factors. We specialise to the case of the minimal supersymmetric standard model (MSSM), and investigate the behaviour of the Fayet-Iliopoulos coupling for various boundary conditions at the unification scale. We focus particularly on the case of non-standard soft supersymmetry breaking couplings, for whic…
We show that contrary to first expectations realistic three generation supersymmetric intersecting brane world models give rise to phenomenologically interesting predictions about gauge coupling unification. Assuming the most economical way of realizing the matter content of the MSSM via intersecting branes we obtain a model independent relation among the three gauge coupling constants at the string scale. In order to correctly reproduce the experimentally known values of sin^2[theta_W(M_z)] and alpha_s(M_z) this relation leads to natural gauge coupling unification at a string scale close to t…
We discuss the unification of gauge couplings within the framework of a wide class of realistic free-fermionic string models which have appeared in the literature, including the flipped SU(5), SO(6)xSO(4), and various SU(3)xSU(2)xU(1) models. If the matter spectrum below the string scale is that of the Minimal Supersymmetric Standard Model (MSSM), then string unification is in disagreement with experiment. We therefore examine several effects that may modify the minimal string predictions. First, we develop a systematic procedure for evaluating the one-loop heavy string threshold corrections i…
We present an orbifold GUT model in which the NMSSM Higgs trilinear couplings are unified with the three Standard Model gauge couplings. The model is constructed as an N=2 supersymmetric SU(8) gauge theory in six dimensions, which is reduced to the NMSSM with extra U(1) factors upon compactification. Such an unification is in good agreement with experiments. The predicted upper limit for the lightest CP-even neutral Higgs boson is somewhat larger than in the MSSM, and can be tested in the upcoming Large Hadron Collider.
Supersymmetric Gauge-Higgs Unification is a well-motivated new physics scenario, both in heterotic model building and from the perspective of higher-dimensional Grand Unified Theories. When combined with radion mediated supersymmetry breaking, it allows for very specific predictions concerning the high-scale parameters of the MSSM. Using an appropriately modified version of a standard RGE evolution code (SuSpect), we derive low-scale predictions which can be tested at the LHC. The phenomenological success of our setting depends crucially on the 5d Chern-Simons term, which has not been used in …
