Higgs as a pseudo-Goldstone boson, the mu problem and gauge-mediated supersymmetry breaking
Anna Kaminska, Stephane Lavignac
备注：
19 pages, 6 figures. New section 3.3 on the mu/Bmu problem, more detailed analytic computation in section 4.1, error in Fig. 5 corrected, significant redactional changes (including abstract, introduction and conclusion) in order to better emphasize the main results of the paper. Title changed in journal. Final version to appear in Eur. Phys. J. C
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 gauge-Higgs sectors to the one-loop effective potential of the pseudo-Goldstone Higgs boson. While the joint effect of supersymmetry and of the global symmetry allows in principle the electroweak symmetry to be broken with little fine-tuning, the simplest version of the model fails to bring the Higgs mass above the LEP bound due to a suppressed tree-level quartic coupling. To cure this problem, we consider the possibility of additional SU(3)-breaking contributions to the Higgs potential, which results in a moderate fine-tuning. The model predicts a rather low messenger scale, a small tan beta value, a light Higgs boson with Standard Model-like properties, and heavy higgsinos.
We consider supersymmetric models in which a (pseudo) Goldstone supermultiplet plays the role of the messenger of supersymmetry breaking. Such models lead to a highly predictive form of flavor and CP conserving soft terms, particularly the soft scalar masses and trilinear couplings vanish at the scale where the (approximate) global symmetry is spontaneously broken. We discuss also the possibility for realizing this scheme in supergravity models derived from string theories.
We study the breaking of supersymmetry in models with anomalous U(1). These models are simple to construct and contain natural candidates for being the messengers of gauge-mediated supersymmetry breaking. When some of the ordinary matter fields transform under the anomalous U(1), we find a hybrid scenario in which the U(1) and the gauge interactions mediate the breaking of supersymmetry. This leads to a hierarchy of soft masses between the charged and neutral fields and provides a solution to the $μ$-problem. Among these models, we present a scenario in which the Higgs arises as a pseudo-Golds…
In certain mild extensions of the Standard Model, spin-independent long range forces can arise by exchange of two very light pseudoscalar spin--0 bosons. In particular, we have in mind models in which these bosons do not have direct tree level couplings to ordinary fermions. Using the dispersion theoretical method, we find a $1/r^{3}$ behaviour of the potential for the exchange of very light pseudoscalars and a $1/r^{7}$ dependence if the pseudoscalars are true massless Goldstone bosons.
We propose a possibility of the 125 GeV Higgs being a pseudo-Goldstone boson in supersymmetry with extra vector-like fermions. Higgs mass is obtained from loops of top quark and vector-like fermions from the global symmetry breaking scale f at around TeV. The mu, Bmu/mu \sim f are generated from the dynamics of global symmetry breaking and the Higgs quartic coupling vanishes at f as tan beta \simeq 1. The relation of msoft \sim $4πM_Z$ with f \sim mu \sim m_soft \sim TeV is obtained and large mu does not cause a fine tuning for the electroweak symmetry breaking. The Higgs to di-photon rate can…
We point out that a sector required to set the cosmological constant to zero in gauge-mediated supersymmetry-breaking models naturally produces a supersymmetry-invariant mass ($μ$ term) for Higgs doublets of the order of the electroweak scale. Since this new sector preserves the supersymmetry, it does not generate supersymmetry-breaking masses for the Higgs doublets and thus the $μ$ problem is solved.
Diagnostic signals of the minimal model of anomaly mediated supersymmetry breaking are discussed in the context of a $\sqrt{s}$ = 1 TeV $e^+e^-$ linear collider.
We explore two distinct resolutions to the tachyonic slepton puzzle in the Anomaly Mediated Supersymmetry Breaking scenario. Both are based on extending the MSSM by an anomaly free U(1) symmetry, and in both cases exact RG invariance is preserved.
We show the usefulness of an $e^-γ$ collider with backscattered laser photons in unveiling the signatures of Gauge-Mediated Supersymmetry Breaking models, with a right selectron as the next LSP. We also show how the signal can be distinguished from the Standard Model background as well as from signals of minimal supersymmetry.
We study in detail the particle spectrum in anomaly mediated supersymmetry breaking models in which supersymmetry breaking terms are induced by the super-Weyl anomaly. We investigate the minimal anomaly mediated supersymmetry breaking models, gaugino assisted supersymmetry breaking models, as well as models with additional residual nondecoupling D-term contributions due to an extra U(1) gauge symmetry at a high energy scale. We derive sum rules for the sparticle masses in these models which can help in differentiating between them. We also obtain the sparticle spectrum numerically, and compare…
Recently, it has been demonstrated that radion mediated supersymmetry breaking gives the same spectrum as Scherk-Schwarz supersymmetry breaking, and can be interpreted as a dynamical realization of it. We make this connection explicit by exhibiting the direct transformation from one theory to the other. We then use the extreme UV softness of Scherk-Schwarz theories to calculate the one-loop soft masses of matter fields. We do not find any cutoff sensitive ``Kaluza-Klein mediated'' contributions.
Recent progress in the gauge-mediated supersymmetry breaking is reviewed, with emphasis on the theoretical problems which gauge-mediated models so successfully solve, as well as those problems which are endemic to the models themselves and still beguile theorists today.
We study the novel features in a model with Gauge Mediated Supersymmetry Breaking. If the messenger fields have positive R-parity, there will be new sources of flavor violations. We show that the dimension-5 operators will be quite important. When dressing these operators by wino-loops, the constraints on them by the present data are given.
We study the signatures of minimal anomaly mediated supersymmetry breaking in an e^- gamma collider. We demonstrate that the associated production of a sneutrino with the lightest chargino leads to a substantially large signal size. The background is negligibly small, though. Even more interestingly, a measurement of the fundamental supersymmetry breaking parameters could be possible.
We consider constraints on gauge mediated supersymmetry breaking models imposed by the requirement of grand unification. In particular, we demonstrate several ways to reduce the number of parameters coming from the dynamical supersymmetry breaking sector. One of approaches exploits nonperturbative unification of gauge couplings in multi-messenger models.
We reinterpret anomaly-mediated supersymmetry breaking from a field-theoretic perspective in which superconformal anomalies couple to either the chiral compensator or the $U(1)_R$ vector superfield. As supersymmetry in the hidden sector is spontaneously broken by non-vanishing vacuum expectation values of the chiral compensator F-term and/or the $U(1)_R$ vector superfield D-term, the soft breakdown of supersymmetry emerges in the visible sector. This approach is physically more understandable compared with the conventional approach where the chiral compensator is treated on the same footing as…
We consider the proton decay involving a light gravitino or axino in gauge-mediated supersymmetry breaking models to derive constraints on the $R$ parity and baryon number violating Yukawa couplings. Bounds on all nine coupling constants are obtained by considering the decay amplitudes at one-loop order.
By considering the constraints from nucleon decay we obtain upper limits on tan beta in generalized supersymmetric SU(5) grand unified theories with gauge-mediated supersymmetry breaking. We find that the predicted values of tan beta in these models are mostly inconsistent with the constraints from nucleon decay.
We discuss gauge-mediated models which employ a tree-level mass term in the superpotential. We give explicit composite realizations in which the mass terms are not fundamental. Instead, they arise as effective terms in the superpotential from confining gauge dynamics.
We point out that, in a class of gauge mediation models using metastable supersymmetry breaking vacua, the minimum of the supersymmetry breaking field in the early universe is dynamically deviated from the one in the low energy. The deviation induces coherent oscillations of the supersymmetry breaking field, which decays into the gravitinos. For certain parameters, it can produce a right amount of the gravitinos to account for the observed dark matter.
We explore, in the MSSM context, an extension of the Anomaly Mediated Supersymmetry Breaking solution for the soft scalar masses that is possible if the underlying theory has a gauged R-symmetry. The slepton mass problem characteristic of the scenario is resolved, and a context for the explanation of the fermion mass hierarchy provided.
The question of naturalness is addressed in the context of gauge-mediated supersymmetry breaking models. Requiring that $M_Z$ arises naturally imposes upper limits on the right-handed selectron mass in these models that are stronger than in the Minimal Supersymmetric Standard Model and are interesting from the point of view of searches at the current and future colliders.
The R-parity non-conservation phenomenology within the minimal supersymmetric standard model with gauge mediated supersymmetry breaking has been studied. New constraints on the lepton number violating constant $λ_{111}^\prime$ were imposed by non-observability of the neutrinoless double beta decay. We find that $λ_{111}^\prime$ depends strongly on the effective supersymmetry breaking scale $Λ$ only and deduce limits which are much stronger than those previously found in literature.
We study gauge-mediated theories containing several messengers with the most general SU(5)-invariant mass and supersymmetry-breaking parameters. We show that these theories are predictive, containing only two relevant parameters more than the minimal gauge-mediated model. Hypercharge D-terms can contribute significantly to the right-handed charged sleptons and bring them closer in mass to the left-handed sleptons. The messenger masses must be invariant under either SU(5) or a ``messenger parity" to avoid spontaneous breaking of charge conservation.
We present a detailed analysis of how a mixed-anomaly-free U(1) symmetry can be used to both resolve the slepton mass problem associated with Anomaly Mediated Supersymmetry Breaking and generate the fermion mass hierarchy via the Froggatt-Nielsen mechanism. Flavour changing neutral currents problems are evaded by a specific form of the Yukawa textures.
The messenger sector of existing models of gauge-mediated supersymmetry breaking may be simplified by using a non-renormalizable superpotential term to couple the vector-like quark and lepton messenger fields to a chiral gauge-invariant of the supersymmetry-breaking sector. This eliminates the need for a fundamental singlet and for an additional gauge sector needed to generate appropriate expectation values for the singlet component fields. This scenario is more natural if the supersymmetry-breaking sector itself involves a non-renormalizable superpotential. Several examples are constructed ba…
We point out that in supersymmetric theories with extra dimensions, radius stabilization can give rise to a VEV for the $F$ component of the radius modulus. This gives an important contribution to supersymmetry breaking of fields that propagate in the bulk. A particularly attractive class of models is obtained if the standard-model gauge fields propagate in the bulk, while the quark and lepton fields are localized on a brane. This leads to gaugino mediated supersymmetry breaking without the need for singlets in the hidden sector. We analyze a simple explicit model in which this idea is realize…
We investigate effects of D-term contributions to the mixed modulus-anomaly mediated supersymmetry breaking scenario. In the original scenario, the tachyonic slepton problem in the pure anomaly mediated supersymmetry breaking is cured by modulus contributions. We generalize the scenario so as to include contributions from the D-terms of U(1)_Y and the gauged U(1)_{B-L} which is motivated in a grand unified theory based on a higher rank gauge group such as SO(10). As a consequence of additional $D$-term contributions to scalar masses, we obtain various soft supersymmetry breaking mass spectra, …
The general form of soft supersymmetry breaking terms at one loop for effective supergravity models based on the weakly-coupled heterotic string are presented, with special emphasis on those terms arising from the superconformal anomaly. The standard "anomaly-mediated" soft terms are observed to be a special case of a more general class of models. Some phenomenological consequences are considered and a comparison is made with scenarios involving universal soft terms.
We consider the branching ratio of $b \to sγ$ in gauge mediated supersymmetry breaking theories. Useful bounds on the parameter space of these models are derived from the experimental bounds on $b \to sγ$. Constraints on masses of NLSP are presented as a function of $tanβ$ and $M/Λ$ for $μ<0$ and $μ>0$.
Moduli are generic in string (M) theory. In a large class of gauge-mediated Supersymmetry breaking models, the fermionic components of such fields have very light masses, around the eV scale, and non-negligible mixing with active neutrinos, of order $10^{-4}$. Consequently, these fermions could play the role of sterile neutrinos to which active neutrinos oscillate, thus affecting measurements of solar neutrinos or of atmospheric neutrinos. They could also provide warm dark matter, thus affecting structure formation.
We show that in a minimal extension of the MSSM by means of an extra U(1) gauge group, the negative mass-squared problem characteristic of the Anomaly Mediated Supersymmetry Breaking scenario is naturally solved by means of Fayet-Iliopoulos D-terms. We derive a set of sum rules for the sparticle masses which are consequences of the resulting framework.
A supersymmetric model which naturally accommodates MeV tau neutrino within the framework of gauge mediated supersymmetry breaking is described. The lepton number violation is originally introduced in the messenger sector of the theory. A large slepton-Higgs mixing mass and a small lepton-higgsino mixing mass are generated at one-loop. Scalar tau neutrino has non-vanishing vacuum expectation value. These result in a non-zero ν_τ mass which is in the range of (1-10) MeV.
Using the facts that in Gauge-Mediated Supersymmetry Breaking schemes, masses of the right and the left sfermions can differ widely, and the gravitino is the Lightest Supersymmetric Particle, we show that it is possible to obtain unambiguous signatures of such schemes in a high energy $e^+e^-$ collider if one looks at the asymmetries in the cross-sections for certain final states with left-and right-polarized beams.
Spontanous symmetry breaking usually gives spin 0 Goldstone bosons for the case of internal symmetries and spin 1/2 fermions for the supersymmetry. The spontaneous breaking of higher dimensional Lorentz symmetry can give vector Goldstone boson in 4-dimension.
We discuss a framework for communicating supersymmetry breaking to the visible sector where the radius modulus, which determines the size of extra dimensions, has an auxiliary vacuum expectation value. The modulus couplings generate mass splitting in Kaluza-Klein supermultiplets and they act as messengers of supersymmetry breaking. The soft masses are expressed in terms of renormalization-group functions and the sparticle spectrum is determined by what kind of field propagates in the bulk. This framework also provides new possibilities for solving the supersymmetric flavor problem.
When the strong CP problem is solved by spontaneous breaking of an anomalous global symmetry in theories with gauge-mediated supersymmetry breaking, the pseudo Goldstone fermion (the axino) is a good candidate of a light sterile neutrino. Its mixing with neutrinos relevant for current neutrino experiments can arise in the presence of R-parity violation. The realistic four neutrino mass matrix is obtained when the see-saw mechanism is brought in, and an ansatz for the right-handed neutrino mass is constructed.
We present the predictions for the mass $M_h$ of the lightest Higgs boson in models with gauge-mediated supersymmetry breaking as a function of the SUSY-breaking scale. We include all radiative corrections up to two loops and point out that if the CDF e+ e- two-photon event is interpreted in terms of these models, then the lightest Higgs boson should be lighter than 110 GeV.
We provide a simple solution to the $μ$ and strong CP problems in the context of gauge mediated supersymmetry breaking. The generic appearance of R symmetry in dynamical supersymmetry breaking is used to implement Peccei-Quinn symmetry. Acceptable $μ$ and $B$ terms as well as the large symmetry breaking scale are induced in the presence of nonrenormalizable interactions. Cosmological consequences of this scheme turn out to yield constraints on the PQ symmetry breaking scale and the number of the messenger/heavy quarks. Complexity in introducing non-R Peccei-Quinn symmetry is contrasted with th…
Supersymmetric models with broken R-parity provide mechanisms that allow to generate Majorana neutrino masses and magnetic moments through virtual particle-sparticle loops. This constitutes an attractive alternative to the see-saw mechanism. In this paper we present a detailed calculation of the transition magnetic moments of a Majorana neutrino in gauge mediated supersymmetry breaking MSSM without R-parity. We base our analysis on the renormalization group evolution of the MSSM parameters, which are unified at the GUT scale.
Within the MSSM framework and with purely anomaly mediated supersymmetry breaking the slepton masses turn out to be tachyonic. We resolve this problem by introducing an anomaly free U(1) gauge symmetry which provides positive $D$-term contributions to sparticle masses squared that are flavor conserving at one loop. Two realistic examples based on SU(5) are presented. With U(1) spontaneously broken at a scale $\sim 10^{16}$ GeV, the right handed neutrinos acquire masses $\stackrel{<}{_\sim}10^{14}$ GeV. This breaking scale of U(1) also plays an important role in the proposed resolution of the M…
Collisions of non-topological solitons, Q-balls, are considered in the Minimal Supersymmetric Standard Model where supersymmetry has been broken at a low energy scale via a gauge mediated mechanism. Q-ball collisions are studied numerically on a two dimensional lattice for a range of Q-ball charges. Total cross-sections, as well as fusion and geometrical cross-sections are calculated. The total and geometrical cross-sections appear to converge with increasing charge. The fusion cross-section has been estimated to be larger than 60% of the geometrical cross-section for large balls.
We study various modifications to the minimal models of gauge mediated supersymmetry breaking. We argue that, under reasonable assumptions, the structure of the messenger sector is rather restricted. We investigate the effects of possible mixing between messenger and ordinary squark and slepton fields and, in particular, violation of universality. We show that acceptable values for the $μ$ and $B$ parameters can naturally arise from discrete, possibly horizontal, symmetries. We claim that in models where the supersymmetry breaking parameters $A$ and $B$ vanish at tree level, $\tanβ$ could be l…
We estimate the upper bound of the Higgs mass and allowed parameter region in the anomaly mediated supersymmetry breaking models. There has been a difficulty that the parameter region cannot be determined precisely in almost SUSY models. However, we succeed to give strict constraints on the parameters from the recent results of the precision measurements of the muon g-2 (anomalous magnetic dipole moment). Especially, the upper bound of the Higgs mass is obtained as a function of only $\tanβ$, and is estimated less than about 123 (GeV) for all the range of $\tanβ<60$ .
We study the deflected anomaly-mediated supersymmetry breaking (AMSB) scenario in the light of the recent result of the muon g-2 from Brookhaven E821 experiment. The E821 result suggests the deviation from the SM prediction, though there remain unsettled uncertainties. We find that the supersymmetric contribution to the muon g-2 can be \mathcal{O}(10^{-9}), large enough to fill the deviation, with other experimental constraints satisfied. In particular, the Higgs mass and b \to s γput severe constraints on the model and large \tanβis favored to enhance the muon g-2.
The sliding singlet mechanism is one of the most interesting solutions of the triplet-doublet splitting problem. We analyze this mechanism in the gauge mediated supersymmetry breaking scenario. We show that the sliding singlet mechanism does not work in the naive gauge mediation scenario because of the singlet linear terms derived from the gravity, although $F$ term is much smaller than the one in the gravity mediation scenario. We also consider the extension in order for the sliding singlet mechanism to work.
We present a combined study of the muon anomalous magnetic moment, $a_μ \equiv (g-2)_μ /2$, and $b \to s γ$ decay in the minimal supersymmetric standard model with gauge-mediated supersymmetry-breaking. Combining new experimental data on $a_μ$ and the branching ratio for $b \to s γ$, useful limits on the parameter space of these models are derived. Bounds on supersymmetric particle masses as a function of $\tan β$ are also presented.
It is well known that Zee type neutrino mass matrix can provide bi-maximal neutrino mixing for three neutrinos. We study the reconciliation of this model with the gauge mediated supersymmetry breaking scenario, which naturally suppresses the large flavor changing neutral current and CP violation in the supersymmetric standard model. When the messenger fields have suitable B-L charges, the radiative correction naturally induces the Zee neutrino mass matrix, which provides tiny neutrino masses and large lepton flavor mixings. Our numerical results are consistent with the neutrino oscillation exp…
We consider the phenomenology of GMSB models where the lighter stau is the next to lightest supersymmetric particle. In this situation, the dominant signals for supersymmetry are events with two or three high p_T tau leptons accompanied by large missing transverse energy. We find that the inclusive two tau jets signature could be observable at the Tevatron's Run II, while the inclusive three tau jets signature could be important at Run III.
Left-Right symmetry including supersymmetry presents an important class of gauge models which may possess natural solutions to many issues of phenomenology. Cosmology of such models indicates a phase transition accompanied by domain walls. Such walls must be unstable in order to not conflict with standard cosmology, and can further be shown to assist with open issues of cosmology such as dilution of unwanted relic densities and leptogenesis. In this paper we construct a model of gauge mediated supersymmetry breaking in which parity breaking is also signalled along with supersymmetry breaking a…
We explore the phenomenology of supersymmetric SO(10) grand unified theories with gauge mediated supersymmetry breaking. We show that if SO(10) breaking proceeds through intermediate left-right symmetric gauge groups which are broken at the supersymmetry breaking scale, then perturbative unification allows the existence of only a few consistent models with very similar phenomenological consequences. We list and discuss some distinctive signatures of these theories. The most remarkable feature of the class of theories introduced here is that, unlike in models with simpler symmetry breaking chai…
In theories with gauge mediated supersymmetry breaking, the scalar tau, (${\tilde τ_1}$) is the lightest superpartner for a large range of the parameter space. At the large electron positron collider (LEP 2) this scenario can give rise to events with four $τ$ leptons and large missing energy. Two of the $τ$'s ( coming from the decays of ${\tilde τ_1}$'s ) will have large energy and transverse momentum, and can have similar sign electrical charges. Such events are very different from the usual photonic events that have been widely studied, and could be a very distinct signal for the discovery o…
Recently we have proposed a simple hadronic axion model within gauge-mediated supersymmetry breaking. In this paper we discuss various cosmological consequences of the model in great detail. A particular attention is paid to a saxion, a scalar partner of an axion, which is produced as a coherent oscillation in the early universe. We show that our model is cosmologically viable, if the reheating temperature of inflation is sufficiently low. We also discuss the late decay of the saxion which gives a preferable power spectrum of the density fluctuation in the standard cold dark matter model when …
We explore, in the context of the MSSM generalised to admit massive neutrinos, an extension of the Anomaly Mediated Supersymmetry Breaking solution for the soft scalar masses to incorporate Fayet-Iliopoulos D-terms. The slepton mass problem characteristic of the scenario is resolved, and the fermion mass hierarchy is explained via the Froggatt-Nielsen mechanism. FCNC problems are evaded by a combination of universal doublet charges and Yukawa textures which are diagonalised by transforming the left-handed fields only.
Excited Q-balls are studied by numerical simulations in the Minimal Supersymmetric Standard Model with supersymmetry broken by a gravity mediated mechanism. It is found that there is a suppression factor of $\cO(10^{-2})$ in the rate at which a Q-ball can emit their excess energy compared to the rate set by the dynamical scale of the field, $m$. Furthermore, it is noted that a Q-ball can withstand a large amount of excess energy without losing a significant amount of its charge. The cosmological importance of these properties are considered for Q-balls in the thermal bath of the early universe…
The lighter neutral scalar Higgs mass is examined in gauge-mediated supersymmetry-breaking models in which the messenger sector responsible for SUSY breaking is allowed to involve more general sets of $SU(3) \otimes SU(2) \otimes U(1)$ multiplets than those contained in the SU(5) $5 + \bar{5}$ or $10 + \bar{10}$ multiplets. The largest mass for the lighter scalar Higgs is found to be 132 GeV when the breaking parameter $Λ$ is taken to be 100 TeV\@. Thus the predictions for the lightest Higgs mass can be tested at the upgraded Tevatron runs for these general classes of GMSB models.
We propose a novel supersymmetric unified scenario of the triplet seesaw mechanism where the exchange of the heavy triplets generates both neutrino masses and soft supersymmetry breaking terms. Our framework is very predictive since it relates neutrino mass parameters, lepton flavour violation in the slepton sector, sparticle and Higgs spectra and electroweak symmetry breakdown. The phenomenological viability and experimental signatures in lepton flavor violating processes are discussed.
We construct hadronic axion models in the framework of the anomaly-mediated supersymmetry breaking scenario. If the Peccei-Quinn symmetry breaking is related to the supersymmetry breaking, mass spectrum of the minimal anomaly-mediated scenario is modified, which may solve the negative slepton mass problem in the minimal anomaly-mediated model. We find several classes of phenomenologically viable models of axion within the framework of the anomaly mediation and, in particular, we point out a new mechanism of stabilizing the axion potential. In this class of models, the Peccei-Quinn scale is rel…
Gauge-mediated supersymmetry breaking is known to greatly suppress flavor changing neutral current effects. However, we show that gauge mediation in the context of leptogenesis implies potentially large lepton flavor violating signals. If the heavy right-handed neutrinos that participate in leptogenesis are lighter than the messenger scale of gauge mediation, they will induce flavor off-diagonal masses to the sleptons which in turn can induce large effects in mu to e gamma, tau to mu gamma, and mu-e conversion in nuclei. We demonstrate this result and compute numerically the lepton-flavor viol…
