Radiative corrections with new heavy particles coupling to Higgs doublets destabilize the electroweak scale and require an ad-hoc counterterm cancelling the large loop contribution. If the mass scale m1 of these new particles in in the TeV range, this feature constitutes the "little fine-tuning problem". We consider the case that the new-physics spectrum has a little hierarchy with two particle mass scales m1, m2 and m2 = O(10 m1) and no tree-level couplings of the heavier particles to Higgs doublets. As a concrete example we study the (next-to-)minimal supersymmetric standard model ((N)MSSM) for the case that the gluino mass M3 is significantly larger than the stop mass parameters m_{L,R} and show that the usual one-loop fine-tuning analysis breaks down. If m_{L,R} is defined in the dimensional-reduction (DR-bar) or any other fundamental scheme, corrections enhanced by powers of M3^2/m_{L,R}^2 occur in all higher loop orders. After resumming these terms we find the fine-tuning measure substantially improved compared to the usual analyses with M3 <~ m_{L,R}. In our hierarchical scenario the stop self-energies grow like M3^2, so that the stop masses m_{L,R}^{OS} in the on-shell (OS) scheme are naturally much larger than their DR-bar counterparts m_{L,R}^{DR-bar}. This feature permits a novel solution to the little fine-tuning problem: DR-bar stop masses are close to the electroweak scale, but radiative corrections involving the heavy gluino push the OS masses, which are probed in collider searches, above their experimental lower limits. As a byproduct, we clarify which renormalization scheme must be used for squark masses in loop corrections to low-energy quantities such as the B-B-bar mixing amplitude.
In models with low-energy supersymmetry breaking, an anomalous Abelian horizontal gauge symmetry can simultaneously explain the fermion mass hierarchy and the values of the $μ$ and $B$ terms. We construct an explicit model where the anomaly is cancelled by the Green-Schwarz mechanism at the string scale. We show that with our charge assignments, the breaking of the horizontal symmetry generates the correct order of magnitude and correct hierarchy for all Yukawa couplings.
Supersymmetric scenarios with inverted mass hierarchy can be hard to observe at a hadron collider, particularly for the non-strongly interacting sector. We show how the production of stau-pairs via gauge boson fusion, along with hard jets in the high rapidity region, can be instrumental in uncovering the signatures of such scenarios. We demonstrate this both in a model-independent way and with reference to some specific, well-motivated models.
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce extra vector-like heavy fields in the extra dimensions, and the suitable fermion mass hierarchies and flavor mixings are generated by integrating out these heavy fields. We consider gaugino mediation and gauge mediation supersymmetry breaking mechanisms and their flavor structures. The experimental constraints of small flavor changing neutral currents sugge…
We propose an attractor mechanism which generates the "more minimal" supersymmetric standard model from a broad class of supersymmetry breaking boundary conditions. The hierarchies in the fermion masses and mixings are produced by the same dynamics and a natural weak scale results from gaugino mediation. These features arise from augmenting the standard model with a new SU(3) gauge group under which only the third generation quarks are charged. The theory flows to a strongly interacting fixed point which induces a negative anomalous dimension for the third generation quarks and a positive anom…
In supersymmetric models with scalar sequestering, superconformal strong dynamics in the hidden sector suppresses the low-energy couplings of mass dimension two, compared to the squares of the dimension one parameters. Taking into account restrictions on the anomalous dimensions in superconformal theories, I point out that the interplay between the hidden and visible sector renormalizations gives rise to quasi-fixed point running for the supersymmetric Standard Model squared mass parameters, rather than driving them to 0. The extent to which this dynamics can ameliorate the little hierarchy pr…
We present a scenario wherein the anomalous U(1) D-term of string origin triggers supersymmetry breaking and generates naturally a Split Supersymmetry spectrum. When the gaugino and the Higgsino masses (which are of the same order of magnitude) are set at the TeV scale, we find the scalar masses to be in the range (10^6 - 10^8) GeV. The U(1) D-term provides a small expansion parameter which we use to explain the mass and mixing hierarchies of quarks and leptons. Explicit models utilizing exact results of N = 1 suersymmetric gauge theories consistent with anomaly constraints, fermion mass hiera…
It is suggested that various hierarchy problems in supersymmetric standard model, i.e. the Yukawa hierarchies, the μproblem, and the suppression of dangerous baryon and/or lepton number (B/L) violating couplings, are resolved altogether in the framework of horizontal U(1) symmetry whose spontaneous breaking results in the appearance of one expansion parameter (the Cabibbo angle). Within a reasonable range of U(1) charges, there exist a few models compatible with experiments. The specific sizes of B/L violating couplings of these models are calculated and several phenomenological consequences a…
Warped compactifications with branes provide a new approach to the hierarchy problem and generate a diversity of four-dimensional thresholds. We investigate the relationships between these scales, which fall into two classes. Geometrical scales, such as thresholds for Kaluza-Klein, excited string, and black hole production, are generically determined soley by the spacetime geometry. Dynamical scales, notably the scale of supersymmetry breaking and moduli masses, depend on other details of the model. We illustrate these relationships in a class of solutions of type IIB string theory with imagin…
Within the minimal supersymmetric extension of the Standard Model, the mass of the light CP-even Higgs boson is computed to three-loop accuracy, taking into account the next-to-next-to-leading order effects from supersymmetric Quantum Chromodynamics. We consider two different scenarios for the mass hierarchies of the supersymmetric spectrum. Our numerical results amount to corrections of about 500 MeV which is of the same order as the experimental accuracy expected at the CERN Large Hadron Collider (LHC).
We extend the work of Carone, Chaurasia and Vasquez on non-supersymmetric models of flavor based on the double tetrahedral group. Three issues are addressed: (1) the sector of flavor-symmetry-breaking fields is simplified and their potential studied explicitly, (2) a flavorful axion is introduced to solve the strong CP problem and (3) the model is extended to include the neutrino sector. We show how the model can accommodate the strong hierarchies manifest in the charged fermion Yukawa matrices, while predicting a qualitatively different form for the light neutrino mass matrix that is consiste…
We use supersymmetry to address the little hierarchy problem in Randall-Sundrum models by naturally generating a hierarchy between the IR scale and the electroweak scale. Supersymmetry is broken on the UV brane which triggers the stabilization of the warped extra dimension at an IR scale of order 10 TeV. The Higgs and top quark live near the IR brane whereas light fermion generations are localized towards the UV brane. Supersymmetry breaking causes the first two sparticle generations to decouple, thereby avoiding the supersymmetric flavour and CP problems, while an accidental R-symmetry protec…
The current experimental lower bound on the Higgs mass significantly restricts the allowed parameter space in most realistic supersymmetric models, with the consequence that these models exhibit significant fine-tuning. We propose a solution to this `supersymmetric little hierarchy problem'. We consider scenarios where the stop masses are relatively heavy - in the 500 GeV to a TeV range. Radiative stability of the Higgs soft mass against quantum corrections from the top quark Yukawa coupling is achieved by imposing a global SU(3) symmetry on this interaction. This global symmetry is only appro…
The little Higgs mechanism provides an alternative solution to the hierarchy problem, arguably fitting better into the phenomenological hint of the "little hierarchy" which may cause some fine-tuning for the case of supersymmetry. We discuss an aspect of little Higgs physics lacking proper attention -- the construction of an interesting and consistent chiral fermionic sector and its phenomenological implications. At least for the kind of example models to be discussed, the gauge and top sector structure of a model largely dictates, through gauge anomaly cancellation conditions, a specific chir…
We argue that in certain models with family symmetries the implementation of the alignment mechanism for the supression of the flavor changing neutral currents requires mass matrices with holomorphic zeros in the down quark sector. Holomorphic zeros typically open flat directions that potentially spoil the uniqueness of the supersymmetric vacuum. We then present an anomalous U(1) model without holomorphic zeros in the quark sector that can reproduce the fermion mass hierarchies, provided that $\tanβ$ is of order one. To avoid undesired flavor changing neutral currents we propose a supersymmetr…
From a theoretical point of view it is not hard to imagine gaugino masses being much lighter than scalar masses. The dominant contributions to gaugino masses are then their anomaly-mediated values. Given current lower bounds on gauginos, which are near the W-mass scale, considering a little hierarchy between weak-scale gauginos and much heavier scalars requires suspending normal intuition on finetuning and naturalness of the Higgs potential. Nevertheless, tantalizing perks come from the hypothesis: lessened flavor and CP violation problems, more compatibility with gauge coupling unification an…
With the aim of uncovering viable regions of parameter space in deflected mirage mediation (DMM) models of supersymmetry breaking, we study the landscape of particle mass hierarchies for the lightest four non-Standard Model states for DMM models and compare the results to that of minimal supergravity/constrained MSSM (mSUGRA/CMSSM) models, building on previous studies of Feldman, Liu, and Nath. Deflected mirage mediation is a string-motivated scenario in which the soft terms include comparable contributions from gravity mediation, gauge mediation, and anomaly mediation. DMM allows a wide varie…
We compare theoretical and experimental predictions of two main classes of models addressing fermion mass hierarchies and flavour changing neutral currents (FCNC) effects in supersymmetry: Froggatt-Nielsen (FN) U(1) gauged flavour models and Nelson-Strassler/extra dimensional models with hierarchical wave functions for the families. We show that whereas the two lead to identical predictions in the fermion mass matrices, the second class generates a stronger suppression of FCNC effects. We prove that, whereas at first sight the FN setup is more constrained due to anomaly cancelation conditions,…
The supersymmetric flavor problem may be solved if the first and second generation scalars are heavy (with multi-TeV masses) and scalars with large Higgs couplings are light (with sub-TeV masses). We show that such an inverted spectrum may be generated radiatively; that is, from initial conditions where all scalar masses are multi-TeV at some high scale, those with large Higgs couplings may be driven asymptotically to the weak scale in the infra-red. The lightness of third generation scalars is therefore a direct consequence of the heaviness of third generation fermions, and fine-tuning is avo…
There are compelling reasons to think that new physics will appear at or below the TeV-scale. It is not known what form this new physics will take, however. Although The Large Hadron collider is very likely to discover new particles associated with the TeV-scale, it may be difficult for it to determine the nature of those particles, whether superpartners, Kaluza-Klein modes or other states. In this article, we consider how direct and indirect dark matter detection experiments may provide information complementary to hadron colliders, which can be used to discriminate between supersymmetry, mod…
The little Higgs idea is an alternative to supersymmetry as a solution to the gauge hierarchy problem. In this note, I review various little Higgs models and their phenomenology with emphases on the precision electroweak constraints in these models.
A possible resolution of the flavor puzzle is that the fermion mass hierarchy can be dynamically generated through the coupling of the first two generation fields to a strongly coupled sector, which is approximately conformally invariant and leads to large anomalous dimensions for the first two generation fields over a large range of energies. We investigate the possibility of using the same sector to also break supersymmetry. We show that this automatically gives an "inverted hierarchy" in which the first two generation squarks and sleptons are much heavier than the other superpartners. Imple…
We study the neutrino mass matrix in supersymmetric models in which the quark and charged lepton mass hierarchies and also the suppression of baryon or lepton number violating couplings are all explained by horizontal $U(1)_X$ symmetry. It is found that the neutrino masses and mixing angles suggested by recent atmospheric and solar neutrino experiments arise naturally in this framework which fits in best with gauge-mediated supersymmetry breaking with large $\tanβ$. This framework highly favors the small angle MSW oscillation of solar neutrinos, and determine the order of magnitudes of all the…
We study the little hierarchy between mass parameters in the Higgs sector and other SUSY breaking masses. This type of spectrum can relieve the fine-tuning problem in the MSSM Higgs sector. Our scenario can be realized by superconformal dynamics. The spectrum in our scenario has significant implications in other phenomenological aspects like the relic abundance of the lightest neutralino and relaxation of the unbounded-from-below constraints.
TeV scale mirage mediation has been proposed as a supersymmetry breaking scheme reducing the fine tuning for electroweak symmetry breaking in the minimal supersymmetric extension of the standard model. We discuss a moduli stabilization set-up for TeV scale mirage mediation which allows an extra-dimensional interpretation for the origin of supersymmetry breaking and naturally gives an weak-scale size of the Higgs B-parameter. The set-up utilizes the holomorphic gauge kinetic functions depending on both the heavy dilaton and the light volume modulus whose axion partners are assumed to be periodi…
In this thesis we try to discuss certain phenomenological aspects of an R-parity violating non-minimal supersymmetric model, called $μν$SSM. We show that $μν$SSM can provide a solution to the $μ$-problem of supersymmetry and can simultaneously accommodate the existing three flavour global data from neutrino experiments even at the tree level with the simple choice of flavour diagonal neutrino Yukawa couplings. We show that it is also possible to achieve different mass hierarchies for light neutrinos at the tree level itself. In $μν$SSM, the effect of R-parity violation together with a seesaw m…
Dynamical breaking of supersymmetry was long thought to be an exceptional phenomenon, but recent developments have altered this view. A question of great interest in the current framework is the value of the underlying scale of supersymmetry breaking. The "little hierarchy" problem suggests that supersymmetry should be broken at low energies. Within one class of models, low energy breaking be achieved as a consequence of symmetries, without requiring odd coincidences. The low energy theories are distinguished by the presence or absence of $R$ symmetries; in either case, and especially the latt…
In the context of gauge/gravity dualities, we calculate the scalar and tensor mass spectrum of the boundary theory defined by a special 8-scalar sigma-model in five dimensions, the background solutions of which include the 1-parameter family dual to the baryonic branch of the Klebanov-Strassler field theory. This provides an example of a strongly-coupled, multi-scale system that yields a parametrically light mass for one of the composite scalar particles: the dilaton. We briefly discuss the implications of these findings towards identifying a satisfactory solution to both the big and little hi…
We stress that the lack of direct evidence for supersymmetry forces the soft mass parameters to lie very close to the critical line separating the broken and unbroken phases of the electroweak gauge symmetry. We argue that the level of criticality, or fine-tuning, that is needed to escape the present collider bounds can be quantitatively accounted for by assuming that the overall scale of the soft terms is an environmental quantity. Under fairly general assumptions, vacuum-selection considerations force a little hierarchy in the ratio between m_Z^2 and the supersymmetric particle square masses…
We extend a model of the Dirac gauginos, which originate from N=2 supersymmetry (SUSY) for the gauge sector, such that the N=2 SUSY is imposed also to the sfermion sector but only for the 3rd generation squarks and sleptons. In addition to the N=2 supersymmetry, our model is constructed based on the SU(3)c times SU(3)L times U(1)' gauge symmetry. By this extension, the dominant source of radiative correction to the Higgs mass squared coming from the stop loop becomes controllable based on the enhanced symmetry. Then it becomes a viable model which provides a solution to the little hierarchy pr…
We construct an extension of the MSSM in which scalar superpartners can naturally be as heavy as 1 TeV. In the MSSM, the most significant fine tuning stems from the logarithmically enhanced top-stop loop contribution to the soft Higgs mass. We combine supersymmetry with the "simplest little Higgs" to render this loop finite, thereby removing the large logarithm even in models in which superpartner masses are generated at high scales such as in supergravity. Our model predicts an extended Higgs sector, superpartner masses near a TeV and little Higgs partners at a few TeV.
We consider a supersymmetric model that uses partial compositeness to explain the fermion mass hierarchy and predict the sfermion mass spectrum. The Higgs and third-generation matter superfields are elementary, while the first two matter generations are composite. Linear mixing between elementary superfields and supersymmetric operators with large anomalous dimensions is responsible for simultaneously generating the fermion and sfermion mass hierarchies. After supersymmetry is broken by the strong dynamics, partial compositeness causes the first- and second-generation sfermions to be split fro…
When an abelian gauge theory with integer charges is spontaneously broken by the expectation value of a charge Q field, there remains a Z_Q discrete symmetry. In a supersymmetric theory, holomorphy adds additional constraints on the operators that can appear in the effective superpotential. As a result, operators with the same mass dimension but opposite sign charges can have very different coupling strengths. In the present work we characterize the operator hierarchies in the effective theory due to holomorphy, and show that there exist simple relationships between the size of an operator and…
Little Higgs models represent an alternative to Supersymmetry as a solution to the Hierarchy Problem. After introducing the main physical ideas of these models, we present the fine-tuning associated to the electroweak breaking in Little Higgs scenarios. Taking into account the most general properties of this scenarios and focusing on two representative ``Little Higgs'' models, we find that the fine-tuning is much higher than suggested by the rough estimates usually made. The main sources that increase the fine-tuning in these models are identified, then they can be taken into account in order …
We study the interplay between the spontaneous breaking of a global symmetry of the Higgs sector and gauge-mediated supersymmetry breaking, in the framework of a supersymmetric model with global SU(3) symmetry. In addition to solving the supersymmetric flavour problem and alleviating the little hierarchy problem, this scenario automatically triggers the breaking of the global symmetry and provides an elegant solution to the mu/Bmu problem of gauge mediation. We study in detail the processes of global symmetry and electroweak symmetry breaking, including the contributions of the top/stop and ga…
Sparticle mass hierarchies contain significant information regarding the origin and nature of supersymmetry breaking. The hierarchical patterns are severely constrained by electroweak symmetry breaking as well as by the astrophysical and particle physics data. They are further constrained by the Higgs boson mass measurement. The sparticle mass hierarchies can be used to generate simplified models consistent with the high scale models. In this work we consider supergravity models with universal boundary conditions for soft parameters at the unification scale as well as supergravity models with …
We consider an SO(10) grand unified theory in which the ratio of the SU(2)_W and SU(3)_c gaugino masses satisfy M_2/M_3 \approx 3, which results in the realization of natural supersymmetry. In the MSSM parameter space this relation looks artificial, but in the SO(10) case it results from a field with a designated vacuum expectation value. We consider two models, namely M_1:M_2:M_3=-1/5:3:1 (Case I), and M_1:M_2:M_3=-5:3:1 (Case II). Focusing on ameliorating the little hierarchy problem, we explore the parameter space of these models which yield small fine-tuning measuring parameters (natural s…
Little Higgs theories, in which the Higgs particle is realized as the pseudo-Goldstone boson of an approximate global chiral symmetry have generated much interest as possible alternatives to weak scale supersymmetry. In this paper we analyze precision electroweak observables in the Minimal Moose model and find that in order to be consistent with current experimental bounds, the gauge structure of this theory needs to be modified. We then look for viable regions of parameter space in the modified theory by calculating the various contributions to the S and T parameters.
We apply a model-independent, agnostic approach to the collider phenomenology of supersymmetry (SUSY), in which all mass parameters are taken as free inputs at the weak scale. We consider the gauginos, higgsinos, and the first two generations of sleptons and squarks, and analyze all possible mass hierarchies among them ($4\times 8!=161,280$ in total) in which the lightest superpartner is neutral, leading to missing energy. In each case, we identify the full set of the dominant (i.e. least suppressed by phase space, small mixing angles or Yukawa couplings) decay chains originating from the ligh…
The little hierarchy problem encountered in the constrained minimal supersymmetric model (CMSSM) can be ameliorated in supersymmetric models based on the gauge symmetry G_{422} \equiv SU(4)_c x SU(2)_L x SU(2)_R. The standard assumption in CMSSM (and in SU(5) and SO(10)) of universal gaugino masses can be relaxed in G_{422}, and this leads to a significant improvement in the degree of fine tuning required to implement radiative electroweak breaking in the presence of a characteristic supersymmetry breaking scale of around a TeV. Examples of Higgs and sparticle mass spectra realized with 10% fi…
We demonstrate that natural supersymmetry is readily realized in the framework of SU(4)_c \times SU(2)_L \times SU(2)_R with non-universal gaugino masses. Focusing on ameliorating the little hierarchy problem, we explore the parameter space of this model which yields small fine-tuning measuring parameters (natural supersymmetry) at the electroweak scale (Δ_{EW}) as well as at high scale (Δ_{HS}). It is possible to have both Δ_{EW} and Δ_{HS} less than 100 in these models, (2 % or better fine-tuning), while keeping the light CP-even (Standard Model-like) Higgs mass in the 123 GeV-127 GeV range.…
We compute the leading QCD corrections to K-Kbar mixing in the supersymmetric standard model with general soft supersymmetry-breaking parameters. We construct the ΔS=2 effective Lagrangian for three hierarchies of supersymmetric particle masses, namely, when the gluino mass is comparable to, much greater than, or much less than the masses of the first two generation squarks. We find that the QCD corrections tighten the limits on squark mass splittings by more than a factor of two.
We investigate the little hierarchy between Z boson mass and the SUSY breaking scale in the context of landscape of electroweak symmetry breaking vacua. We consider the radiative symmetry breaking and found that the scale where the electroweak symmetry breaking conditions are satisfied and the average stop mass scale is preferred to be very close to each other in spite of the fact that their origins depend on different parameters of the model. If the electroweak symmetry breaking scale is fixed at about 1 TeV by the supersymmetry model parameters then the little hierarchy seems to be preferred…
We consider minimal models of gauge mediated supersymmetry breaking with an extra $U(1)$ factor in addition to the Standard Model gauge group. A $U(1)$ charged, Standard Model singlet is assumed to be present which allows for an additional NMSSM like coupling, $λH_u H_d S$. The U(1) is assumed to be flavour universal. Anomaly cancellation in the MSSM sector requires additional coloured degrees of freedom. The $S$ field can get a large vacuum expectation value along with consistent electroweak symmetry breaking. It is shown that the lightest CP even Higgs boson can attain mass of the order of 1…
In this paper we consider a set of soft supersymmetry breaking terms within the NMSSM which leads to a small hierarchy between the supersymmetry breaking scale and the electroweak scale. Specifically only the gaugino masses and the soft term in the Higgs sector are non-vanishing at the GUT scale. This pattern can be found in gaugino mediated models and in higher-dimensional orbifold GUTs. We study the phenomenology of this scenario and find different low energy spectra depending on the Yukawa coupling $λ$ of the NMSSM singlet. In particular, for low values of $λ$ the singlet is the lightest sc…
We propose the gravitino dark matter in the gravity mediated supersymmetry breaking scenario. The mass hierarchies between the gravitino and other superparticles can be achieved by the nontrivial Kähler metric of the supersymmetry breaking field. As a concrete model, we consider the five-dimensional supergravity model in which moduli are stabilized, and then one of the moduli induces the slow-roll inflation. It is found that the relic abundance of the gravitino and the Higgs boson mass reside in the allowed range without a severe fine-tuning.
Supersymmetry combined with little-Higgs can render the Higgs vev super-little, providing models of electroweak symmetry breaking free from fine-tunings. We discuss the difficulties that arise in implementing this idea and propose one simple successful model. Thanks to appropriately chosen Higgs representations, D-terms give no tree-level mass term to the Goldstone. The fermion representations are anomaly free, generation independent and embeddable into an SU(6) GUT. A simple mechanism provides the large top quark mass.
We examine the use of modified Higgs sectors to address the little hierarchy problem of supersymmetry. Such models reduce weak-scale fine-tuning by allowing lighter stops, but they retain some fine-tuning independent of the Higgs. The modified Higgs sector can also introduce model-dependent tunings. We consider the model-independent constraints on naturalness from squark, gluino, chargino and neutralino searches, as well as the model-dependent tuning in the PQ- and R-symmetric limits of the NMSSM, where cascade decays or additional quartic interactions can hide a Higgs without relying on heavy…
A brief review is given of the implications of a 126 GeV Higgs boson for the discovery of supersymmetry. Thus a 126 GeV Higgs boson is problematic within the Standard Model because of vacuum instability pointing to new physics beyond the Standard Model. The problem of vacuum stability is overcome in the SUGRA GUT model but the 126 GeV Higgs mass implies that the average SUSY scale lies in the several TeV region. The largeness of the SUSY scale relieves the tension on SUGRA models since it helps suppress flavor changing neutral currents and CP violating effects and also helps in extending the p…
We present a unified picture of flavor and electroweak symmetry breaking based on a nonlinear sigma model spontaneously broken at the TeV scale. Flavor and Higgs bosons arise as pseudo-Goldstone modes. Explicit collective symmetry breaking yields stable vacuum expectation values and masses protected at one loop by the little-Higgs mechanism. The coupling to the fermions generates well-definite mass textures--according to a U(1) global flavor symmetry--that correctly reproduce the mass hierarchies and mixings of quarks and leptons. The model is more constrained than usual little-Higgs models be…
We propose a new dynamical relaxation mechanism of the little hierarchy problem, based on a singlet extension of the minimal supersymmetric standard model (MSSM). In this scenario, the small soft mass parameter of an MSSM singlet is responsible for the electroweak symmetry breaking and the non-zero Higgs vacuum expectation value, whereas the effect of the large soft mass parameter of the Higgs boson, -m_{h_u}^2 is dynamically compensated by a flat direction of the MSSM singlets. The small singlet's soft mass and the Z boson mass can be protected, even if the stop mass is heavier than 10 or 20 …
The Littlest Seesaw (LS) model involves two right-handed neutrinos and a very constrained Dirac neutrino mass matrix, involving one texture zero and two independent Dirac masses, leading to a highly predictive scheme in which all neutrino masses and the entire PMNS matrix is successfully predicted in terms of just two real parameters. We calculate the renormalisation group (RG) corrections to the LS predictions, with and without supersymmetry, including also the threshold effects induced by the decoupling of heavy Majorana neutrinos both analytically and numerically. We find that the predictio…
If physics at the Planck scale requires new conceptions of space-time, then generic renormalizable field theories predict observable violations of Lorentz invariance in the low energy sector. The little recognized ``Lorentz Fine Tuning Problem'' comes from logarithmic loop corrections which are not suppressed to the enormous extent commonly assumed. Fine-tuning of parameters at the Planck scale is one possible but unpalatable solution. Here we show that violation of Lorentz invariance is highly suppressed in a supersymmetric theory, the Wess-Zumino model. We conjecture that supersymmetry may b…
Little Higgs theories are an attempt to address the little hierarchy problem, i.e., the tension between the naturalness of the electroweak scale and the precision measurements showing no evidence for new physics up to 5-10 TeV. In little Higgs theories, the Higgs mass-squareds are protected to the one-loop order from the quadratic divergence. This allows the cutoff to be raised up to \~10 TeV, beyond the scales probed by the precision data. However, strong constraints can still arise from the contributions of the new TeV scale particles and hence re-introduces the fine-tuning problem. In this …
It is proposed that supersymmetry (SUSY) maybe used to understand fermion mass hierarchies. A family symmetry Z_{3L} is introduced, which is the cyclic symmetry among the three generation SU(2) doublets. SUSY breaks at a high energy scale ~ 10^{11} GeV. The electroweak energy scale ~ 100 GeV is unnaturally small. No additional global symmetry, like the R-parity, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values which are about (10^0-10^{-2}). Under the family symmetry, only the third generation charged fermions get their masses. This family symmetr…
Experiments are once again under way at the LHC. This time around, however, the mood in the high-energy physics community is pessimistic. There is a growing suspicion that naturalness arguments that predict new physics near the weak scale are faulty and that prospects for a new discovery are limited. We argue that such doubts originate from a misunderstanding of the foundations of naturalness arguments. In spite of the first run at the LHC, which aggravated the little-hierarchy problem, there is no cause for doubting naturalness or natural theories. Naturalness is grounded in Bayesian probabil…
We study the consequences of combining SUSY with a pseudo Nambu-Goldstone boson Higgs coming from an SO(5)/SO(4) coset and partial compositeness. In particular, we focus on how electroweak symmetry breaking and the Higgs mass are reproduced in models where the symmetry SO(5) is linearly realized. The global symmetry forbids tree-level contributions to the Higgs potential coming from D-terms, differently from what happens in most of the SUSY little-Higgs constructions. While the stops are generally heavy, light fermion top partners below 1 TeV are predicted. In contrast to what happens in non-S…
The invention of supersymmetry, almost exactly 25 years ago, changed the face of high-energy physics. The idea that the observed low-energy gauge groups appear due to the process of spontaneous breaking of a single unifying group $G$ is also quite popular. The synthesis of these two elements results in supersymmetric grand unification. I present (perturbatively) exact results regarding the supersymmetric evolution of the gauge couplings from the scale of their unification to lower scales. In particular, it is shown how the heavy mass thresholds can be properly taken into account to all orders.
