Supersymmetric Mass Term Research Articles

Supersymmetric Wormholes in String Theory.

We construct a large family of Euclidean supersymmetric wormhole solutions of type IIB supergravity which are asymptotically AdS_{5}×S^{5}. The solutions are constructed using consistent truncation to maximally gauged supergravity in five dimensions which is further truncated to a four scalar model. Within this model we perform a full analytic classification of supersymmetric domain wall solutions with flat Euclidean domain wall slices. On each side of the wormhole, the solution asymptotes to AdS_{5} dual to N=4 supersymmetric Yang-Mills deformed by a supersymmetric mass term.

Effects of localized μ-terms at the fixed points in magnetized orbifold models

We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called μ-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. The zero-mode degeneracy to be identified as the generation in four-dimensional (4D) effective theories is determined by the magnetic fluxes. It is known that multiple Higgs zero-modes appear in general in magnetized orbifold models. We derive the analytic form of the μ-term matrix in the 4D effective theory generated by the localized sources on T2/Z2 orbifold fixed points, and find that this matrix can lead to a distinctive pattern of the eigenvalues that yields hierarchical μ-terms for the multiple Higgs fields. The lightest ones can be exponentially suppressed due to the localized wavefunctions of zero-modes determined by the fluxes, while the others are of the order of the compactification scale, which can provide a dynamical origin of the electroweak scale as well as a simultaneous decoupling of extra Higgs fields. We also show that a certain linear combination of the lightest Higgs fields could generate the observed mass ratios of down-type quarks through their Yukawa couplings determined by the wavefunctions.

Naturalizing supersymmetry with a two-field relaxion mechanism

AbstractWe present a supersymmetric version of a two-field relaxion model that naturalizes tuned versions of supersymmetry. This arises from a relaxion mechanism that does not depend on QCD dynamics and where the relaxion potential barrier height is controlled by a second axion-like field. During the cosmological evolution, the relaxion rolls with a nonzero value that breaks supersymmetry and scans the soft supersymmetric mass terms. Electroweak symmetry is broken after the soft masses become of order the supersymmetric Higgs mass term and causes the relaxion to stop rolling for superpartner masses up to ∼ 109 GeV. This can explain the tuning in supersymmetric models, including split-SUSY models, while preserving the QCD axion solution to the strong CP problem. Besides predicting two very weakly-coupled axion-like particles, the supersymmetric spectrum may contain an extra Goldstino, which could be a viable dark matter candidate.

Witten index for noncompact dynamics

Among gauged dynamics motivated by string theory, we find many with gapless asymptotic directions. Although the natural boundary condition for ground states is $L^2$, one often turns on chemical potentials or supersymmetric mass terms to regulate the infrared issues, instead, and computes the twisted partition function. We point out how this procedure generically fails to capture physical $L^2$ Witten index with often misleading results. We also explore how, nevertheless, the Witten index is sometimes intricately embedded in such twisted partition functions. For $d=1$ theories with gapless continuum sector from gauge multiplets, such as non-primitive quivers and pure Yang-Mills, a further subtlety exists, leading to fractional expressions. Quite unexpectedly, however, the integral $L^2$ Witten index can be extracted directly and easily from the twisted partition function of such theories. This phenomenon is tied to the notion of the rational invariant that appears naturally in the wall-crossing formulae, and offers a general mechanism of reading off Witten index directly from the twisted partition function. Along the way, we correct early numerical results for some of $\mathcal N=4,8,16$ pure Yang-Mills quantum mechanics, and count threshold bound states for general gauge groups beyond $SU(N)$.

Light Higgsino as the tail of theμ−Bμsolution

Gauge mediation predicts 10 TeV or heavier squarks because such a heavy stop is required to explain the observed 125 GeV Higgs boson mass without a large trilinear soft mass term in the minimal supersymmetric standard model. Although such a high scale cannot be searched by the LHC directly, gauge mediation also predicts a hierarchy $\mu^2 \ll B_\mu$ by a simple and naive solution of the $\mu$ problem. We point out that this simple and naive way of generating the $\mu$ ($B_\mu$) term works in the case of 10 TeV or heavier squarks with a slight breaking of a GUT relation among messenger B-terms (or supersymmetric mass terms). Furthermore, the upper bound on the Higgsino mass is obtained from the observed Higgs boson mass, perturbativity of a relevant coupling, and conditions avoiding tachyonic sneutrinos and stop. It turns out that the light Higgsino of O(100) GeV is a promising signal of gauge mediation.

Chaotic inflation from nonlinear sigma models in supergravity

We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry — making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU(3)/SU(2)×U(1), with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E7/SO(10)×U(1)×U(1) which incorporates the first two generations of (light) quarks as the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten–Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.

Singlet Extensions of the MSSM withZ4RSymmetry

We discuss singlet extensions of the MSSM withZ4Rsymmetry. We show that holomorphic zeros can avoid a potentially large coefficient of the term linear in the singlet. The emerging model has both an effectiveμterm and a supersymmetric mass term for the singletμNwhich are controlled by the gravitino mass. Theμterm turns out to be suppressed againstμNby about one or two orders of magnitude. We argue that this class of models might provide us with a solution to the little hierarchy problem of the MSSM.

SUPERSYMMETRIC UNIFICATION AND R SYMMETRIES

We review the role of R symmetries in models of supersymmetric unification in four and more dimensions, and in string theory. We show that, if one demands anomaly freedom and fermion masses, only R symmetries can forbid the supersymmetric Higgs mass term μ. We then review the proof that R symmetries are not available in conventional grand unified theories (GUTs) and argue that this prevents natural solutions to the doublet–triplet splitting problem in four dimensions. On the other hand, higher-dimensional GUTs do not suffer from this problem. We briefly comment on an explicit string-derived model in which the μ and dimension-5 proton decay problems are solved simultaneously by an order four discrete R symmetry. We also comment on the higher-dimensional origin of this symmetry.

Solving the little hierarchy problem with a light singlet and supersymmetric mass terms

A generalization of the Next-to-Minimal Supersymmetric Model (NMSSM) is studied in which an explicit μ-term as well as a small supersymmetric mass term for the singlet superfield are incorporated. We study the possibility of raising the Standard Model-like Higgs mass at tree level through its mixing with a light, mostly-singlet, CP-even scalar. We are able to generate Higgs boson masses up to 145 GeV with top squarks below 1.1 TeV and without the need to fine tune parameters in the scalar potential. This model yields light singlet-like scalars and pseudoscalars passing all collider constraints.

The lightest scalar in theories with broken supersymmetry

We study the scalar mass matrix of general supersymmetric theories with local gauge symmetries, and derive an absolute upper bound on the lightest scalar mass. This bound can be saturated by suitably tuning the superpotential, and its positivity therefore represents a necessary and sufficient condition for the existence of metastable vacua. It is derived by looking at the subspace of all those directions in field space for which an arbitrary supersymmetric mass term is not allowed and scalar masses are controlled by supersymmetry-breaking splitting effects. This subspace includes not only the direction of supersymmetry breaking, but also the directions of gauge symmetry breaking and the lightest scalar is in general a linear combination of fields spanning all these directions. We present explicit results for the simplest case of theories with a single local gauge symmetry. For renormalizable gauge theories, the lightest scalar is a combination of the Goldstino partners and its square mass is always positive. For more general non-linear sigma models, on the other hand, the lightest scalar can involve also the Goldstone partner and its square mass is not always positive.

Cosmological vacuum selection and metastable susy breaking

We study gauge mediation in a wide class of O'Raifeartaigh type models where supersymmetry breaking metastable vacuum is created by gravity and/or quantum corrections. We examine their thermal evolution in the early universe and the conditions under which the susy breaking vacuum can be selected. It is demonstrated that thermalization typically makes the metastable supersymmetry breaking cosmologically disfavoured but this is not always the case. Initial conditions with the spurion displaced from the symmetric thermal minimum and a small coupling to the messenger sector can result in the realization of the susy breaking vacuum even if the reheating temperature is high. We show that this can be achieved without jeopardizing the low energy phenomenology. In addition, we have found that deforming the models by a supersymmetric mass term for messengers in such a way that the susy breaking minimum and the susy preserving minima are all far away from the origin does not change the conclusions. The basic observations are expected to hold also in the case of models with an anomalous U(1) group.

Gauge-mediated embedding of the singlet extension of the minimal supersymmetric standard model

We embed the S-MSSM -- a singlet extension of the minimal supersymmetric standard model with an explicit mu-term and supersymmetric mass term -- in a gauge-mediated supersymmetry breaking scheme. We find that by absolving the singlet of its responsibility for solving the mu-problem, we are instead able to solve the little hierarchy problem naturally. Specifically, we find that even with a minimal embedding of the S-MSSM into a gauge-mediated scheme, we can easily raise the lightest Higgs mass above 114 GeV, while keeping top squarks below the TeV scale, maintaining perturbative unification of the gauge couplings, and without tuning the other parameters of the model.

Electric dipole moments in pseudo-Dirac gauginos

The SUSY CP problem is one of serious problems in construction of realistic supersymmetric standard models. We consider the problem in a framework in which adjoint chiral multiplets are introduced and gauginos have Dirac mass terms induced by a U ( 1 ) gauge interaction in the hidden sector. This is realized in hidden sector models without singlet chiral multiplets, which are favored from a recent study of the Polonyi problem. We find that the dominant contributions to electron and neutron electric dipole moments (EDMs) in the model come from phases in the supersymmetric adjoint mass terms. When the supersymmetric adjoint masses are suppressed by a factor of ∼100 compared with the Dirac ones, the electron and neutron EDMs are suppressed below the experimental bound even if the SUSY particle masses are around 1 TeV. Thus, this model works as a framework to solve the SUSY CP problem.

A chiral supersymmetric standard model

We propose a supersymmetric extension of the Standard Model with an extra U(1) gauge symmetry, so that all supersymmetric mass terms, including the μ-term, are forbidden by the gauge symmetries. Supersymmetry is broken dynamically which results in U(1) breaking and generation of realistic μ term and soft breaking masses. The additional fields required to cancel the U(1) anomalies are identified with the messengers of supersymmetry breaking. The gaugino masses arise as in the usual gauge mediated scenario, while squarks and sleptons receive their masses from both the U(1) D-term and the two-loop gauge mediation contributions. The scale of supersymmetry breaking in this model can be below 10 6 GeV, yielding collider signatures with decays to goldstinos inside the detector.

Feynman rules in N = 2 projective superspace (II).Massive hypermultiplets

Manifest N = 2 supersymmetric hypermultiplet mass terms can be introduced in the projective N = 2 superspace formalism. In the case of complex hypermultiplets, where the gauge covariantized spinor derivatives have an explicit representation in terms of gauge prepotentials, it is possible to interpret such masses as vacuum expectation values of an Abelian vector multiplet. The duality transformation that relates the N = 2 off-shell projective description of the hyper-multiplet to the on-shell description involving two N = 1 chiral superfields allows us to obtain the massive propagators of the N = 1 complex linear fields in the projective hypermultiplet. The N = 1 massive propagators of the component superfields in the projective hypermultiplet suggest a possible ansatz for the N = 2 massive propagator, which agrees with an explicit calculation in N = 2 superspace.

Algebraic renormalization of N = 1 supersymmetric gauge theories with supersymmetry breaking masses

We provide N = 1 super Yang-Mills theory in the Wess-Zumino gauge with mass terms for the supersymmetric partners of the gauge fields and of the matter fields, together with a supersymmetric mass term for the fermionic matter fields. All mass terms are chosen in such a way as to induce soft supersymmetry breakings at most, while preserving gauge invariance to all orders of perturbation theory. The breakings are controlled through an extended Slavnov-Taylor identity. The renormalization analysis, both in the ultraviolet and in the infrared region, is performed.

Conditions on supersymmetry soft-breaking terms from GUTs

We study the effect of integrating out the heavy fields in a supersymmetric GUT which does not contain small mass parameters in the limit of exact supersymmetry. The trilinear ( A) and bilinear ( B) coefficients of the supersymmetry soft-breaking terms of the low-energy effective theory are related in a simple and model-independent way to those of the underlying theory. From these relations, we obtain the bound | B| ⩾ 2, which, together with the requirements of stability of the potential and electroweak symmetry breaking, imposes severe constraints on the space of allowed supersymmetric parameters. In models based on supergravity with a flat Kähler metric, we obtain B = 2, instead of the relation B = A − 1 usually used in phenomenological applications. The low-energy theory contains also a supersymmetric mass term μ for the two Higgs doublets, which is of the order of the supersymmetry-breaking scale.

Higgs bosons in supersymmetric models (I)

We describe the properties of Higgs bosons in a class of supersymmetric theories. We consider models in which the low-energy sector contains two weak complex doublets and perhaps one complex gauge-singlet Higgs field. Supersymmetry is assumed to be either softly or spontaneously broken, thereby imposing a number of restrictions on the Higgs boson parameters. We elucidate the Higgs boson masses and present Feynman rules for their couplings to the gauge bosons, fermions and scalars of the theory. We also present Feynman rules for vertices which are related by supersymmetry to the above couplings. Exact analytic expressions are given in two useful limits — one corresponding to the absence of the gauge-singlet Higgs field and the other corresponding to the absence of a supersymmetric Higgs mass term.

Gauge boson/Higgs boson unification: The Higgs bosons as superpartners of massive gauge bosons

We show how one can use massive gauge superfields to describe, simultaneously, gauge bosons (W ±, Z,…) and Higgs bosons (w ±,z,…) together with their spin- 1 2 partners (pairs of winos, zinos,…), despite their different electroweak properties. This provides a manifestly supersymmetric formulation of spontaneously broken supersymmetric gauge theories, and makes explicit the relations between massive gauge bosons and Higgs bosons. It raises, however, the following question: if the gauge bosons W ± and Z and the Higgs bosons w ± and z are related by supersymmetry, how is it possible that the former couple to leptons and quarks proportionately to g or g′, and the latter proportionately to G F 1 2 m (fermions)? The paradox is solved as follows: when the Higgs bosons are described by massive gauge superfields, the lagrangian density is non-polynomial and field redefinitions have to be performed, in particular: lepton or quark field → lepton or quark field + (∼ G F 1 2 Higgs field) (lepton or quark field). They automatically regenerate, from the lepton and quark supersymmetric mass terms, the correct Yukawa couplings of Higgs bosons proportional to fermion masses. We also apply this method to the case in which an extra U(1) group is gauged, the standard Higgs boson h 0 being then the superpartner of the new neutral gauge boson U.

Nonrenormalizable interactions from supergravity, quantum corrections and effective low energy theories

We investigate the effects of quantum corrections involving nonrenormalizable interactions suppressed by powers of the Planck scale Mp in supersymmetric theories. Assuming a cutoff of O(Mp) and taking soft supersymmetry breaking into account, we derive the corresponding power counting rules with the help of superspace methods. We find that supersymmetric mass terms proportional to the soft supersymmetry breaking scale m and one point functions for gauge singlet fields proportional to mMp can be generated radiatively.