Search

Direct CP asymmetry in semi-leptonic $τ$ decays is an intriguing hint for new physics beyond the standard model. We investigate the CP asymmetry in $τ^- \to K_S^0 π^- ν_τ$ and $τ^- \to K^- π^0 ν_τ$ decays in non-minimal SU(5) model, with 45-dimensional Higgs multiplet. We show that the associate color-triplet scalar is a natural example of a scalar leptoquark that mediates the transition $τ\to s \bar u ν_τ$, and accounts for the 2.8 $σ$ discrepancy between the $A_{\rm CP}(τ^- \to K_S^0 π^- ν_τ)$ experimental results and the SM expectation. Furthermore, it predicts a sizable $A_{\rm CP}(τ^- \to K^- π^0 ν_τ)$, of order ${\cal O}(10^{-3})$, which can be accessible in current and near future experiments., 10 pages, 3 figures

The early Universe was characterized by the presence of heavy particles that decoupled at different temperatures leading to different phases of the Universe. This had a consequences on the time evolution of the thermodynamic and the cosmological parameters characterizing each phase of the early Universe. In this study, we derive the analytic expressions of the equations governing the time evolution of these parameters in the early eras of the Universe namely, the radiation era, the quark-gluon plasma era, the hadron era and the mixed era. The parameters under concern include the energy density, the entropy density, the temperature, the pressure in addition to Hubble parameter and the scale factor. Having these expressions allows us to give estimations of the times corresponding to the beginning and ending of each era of the Universe as will be presented in this work., Comment: 23 pages, 4 figures

A general analysis of possible violation of CP in processes like $\tau \to K\pi \nu$, for unpolarized $\tau$ is presented. In this paper, we derive the new contributions to the effective Hamiltonian governs $\vert\Delta S \vert=1$ semileptonic tau decays in the framework of two Higgs doublet model with generic Yukawa structure and Leptoquarks models. Within these models, we list all operators, in the effective Hamiltonian and provide analytical expression for their corresponding Wilson coefficients. Moreover, we analyze the role of the different contributions, originating from the scalar, vecor and tensor hadronic currents, in generating direct CP asymmetry in the decay rate of $\tau^-\to K^-\pi^0\nu_\tau$. We show that non vanishing direct CP asymmetry in the decay rate of $\tau^-\to K^-\pi^0\nu_\tau$ can be generated due to the presence of both, the weak phase in the Wilson coefficient corresponding to the tensor operator and the strong phase difference resulting from the interference between the form factors expressing the matrix elements of the vector and tensor hadronic currents. After taking into account all relevant constraints, we find that the generated direct CP asymmetry is of order $10^{-8}$ which is several orders of magnitude larger than the standard model prediction. We show also that, in two Higgs doublet model with generic Yukawa structure , direct local or non integrated CP violation can be as large as $0.3$ % not far from experimental possibilities. This kind of asymmetry can be generated due to the interference between vector and scalar contributions with different weak phases which is not the case in the SM., Comment: 31 pages, 2 figures. Accepted version for journal publication

In this paper we investigate CP violation in charged decays of D meson. Particularly, we study the direct CP asymmetry of the Cabibbo favored non-leptonic ${D}^{+}\to {\overline{K}}^{0}{\pi }^{+}$ and the doubly Cabibbo-suppressed decay mode ${D}^{+}\to {K}^{0}{\pi }^{+}$ within standard model, two Higgs doublet model with generic Yukawa structure and left right symmetric models. In the standard model, we first derive the contributions from box and di-penguin diagrams contributing to their amplitudes which are relevant to the generation of the weak phases essential for non-vanishing direct CP violation. Then, we show that the generated phases are so tiny leading to null direct CP asymmetries of both decay modes. Regarding the two Higgs doublet model with generic Yukawa structure, after taking into account all constraints on the parameter space of the model, we show that the weak phases of the amplitudes can be enhanced compared to the standard model ones. However, the enhancement is still not enough to have sizable direct CP asymmetries. Finally, within left right symmetric models, we find that $|{A}_{\mathrm{CP}}^{SM+LR}\left({D}^{+}\to {\overline{K}}^{0}{\pi }^{+}\right)|\lesssim O\left({10}^{-3}\right)$ after respecting all relevant constraints on the parameter space of the model.

This is the written version of a talk given by S.K. at the $10^{th}$ International Conference on High Energy and Astroparticle, Constantine, Algeria. We briefly review the Standard Model (SM) and the major evidences and main direction of physics beyond the SM (BSM). We introduce supersymmetry, as one of the well-motivated BSM. Basic introduction to Minimal Supersymmetric Standard Model (MSSM) is given. We analyze the thermal relic abundance of lightest neutralino, which is the Lightest Supersymmetric Particle (LSP) in the MSSM. We show that the combined Large Hadron Collider (LHC) and relic abundance constraints rule out most of the MSSM parameter space except a very narrow region. We also review non-minimal SUSY model, based on the gauge group $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_{B-L}$ (BLSSM), where an Inverse Seesaw mechanism of light neutrino mass generation is naturally implemented. The phenomenological implications of this type of model at the Large Hadron Collider (LHC) are analyzed., Comment: 20 pages, 12 figures, presented at the $10^{th}$ International Conference on High Energy and Astroparticle, Constantine, Algeria

Violation of charge conjugation-parity ( $CP$ ) symmetry plays a major rule in the dominance of matter in our universe. A kind of $CP$ violation results from the asymmetry of the life time measured in ${M}^{0}$ and ${\overline{M}}^{0}$ , here M is a heavy meson, decays to final states which is referred in the literature as ${A}_{\Gamma }^{f}$ . In this paper, we give an estimation of the upper bound on $|{A}_{\Gamma }^{f}|$ for the Cabibbo Favored ${D}^{0}\to {K}^{-}{\pi }^{+}$ decay process in different models. We show that in the standard model, $|{A}_{\Gamma }^{f}|\lesssim O\left({10}^{-10}\right)$ . Recently a bound on ${A}_{\Gamma }^{f}$ has been obtained: ${\left({A}_{\Gamma }^{f}\right)}^{Exp.}=\left(1.6±1\right)×{10}^{-4}$ . This result motivates further studies on ${A}_{\Gamma }^{f}$ in beyond standard model physics. In the framework of two Higgs doublet model with generic Yukawa structure, we show that $|{A}_{\Gamma }^{f}|\lesssim O\left({10}^{-7}\right)$ which is several orders of magnitude smaller than the current experimental value. Finally, in the framework of left-right symmetric models in which the mixing between the left and the right gauge bosons is allowed and the left-right symmetry is not manifest at unification scale, we find that ${A}_{\Gamma }^{f}$ can be as large as $|{A}_{\Gamma }^{f}|\lesssim O\left({10}^{-5}\right)$ which is one order of magnitude smaller than the experimentally measured value by LHCb collaborators.

In this paper we investigate CP violation in charged decays of $D$ meson. Particularly, we study the direct CP asymmetry of the Cabibbo favored non-leptonic $D^+ \rightarrow \bar K^0 ��^+$ and the doubly Cabibbo-suppressed decay mode $D^+ \rightarrow K^0 ��^+$ within standard model, two Higgs doublet model with generic Yukawa structure and left right symmetric models. In the standard model, we first derive the contributions from box and di-penguin diagrams contributing to their amplitudes which are relevant to the generation of the weak phases essential for non-vanishing direct CP violation. Then, we show that these phases are so tiny leading to a direct CP asymmetry of order $10^{-11}$ in both decay modes. Regarding the two Higgs doublet model with generic Yukawa structure and after taking into account all constraints on the parameter space of the model, we show that the enhanced direct CP asymmetries can be 6 and 7 orders of magnitudes larger than the standard model prediction for $D^+ \rightarrow \bar K^0 ��^+$ and $D^+ \rightarrow K^0 ��^+$ respectively. Finally, within left right symmetric models, we find that sizable direct CP asymmetry of ${\mathcal O } (10^{-3})$ can be obtained for the decay mode $D^+ \rightarrow \bar K^0 ��^+$ after respecting all relevant constraints., 20 pages, 2 figures. arXiv admin note: text overlap with arXiv:1710.00413

The anomalous results of recent measurements on various $b\to s{\mu }^{+}{\mu }^{-}$ processes could be initial evidence of physics beyond the standard model (SM). Assuming this to be the case, we entertain the possibility that the underlying new physics also affects the rare nonleptonic decays of the ${\overline{B}}_{s}^{0}$ meson. We consider in particular new physics arising from the interactions of a heavy ${Z}^{\prime }$ boson and investigate their influence on the decay modes ${\overline{B}}_{s}^{0}\to \left(\eta ,{\eta }^{\prime },\varphi \right)\omega $, which receive sizable QCD- and electroweak-penguin contributions. These decays are not yet observed, and their rates are estimated to be relatively small in the SM. Taking into account the pertinent constraints, we find that the ${Z}^{\prime }$ effects can greatly increase the rates of ${\overline{B}}_{s}^{0}\to \left(\eta ,\varphi \right)\omega $, by as much as two orders of magnitude, with respect to the SM expectations. We have previously shown that ${\overline{B}}_{s}^{0}\to \left(\eta ,\varphi \right){\pi }^{0}$, with similarly suppressed SM rates, could also undergo substantial ${Z}^{\prime }$-induced enhancement. These rare modes can therefore serve as complementary probes of the potential new physics which may be responsible for the $b\to s{\mu }^{+}{\mu }^{-}$ anomalies.

A general analysis of possible violation of CP in processes like $��\to K����$, for unpolarized $��$ is presented. In this paper, we derive the new contributions to the effective Hamiltonian governs $\vert��S \vert=1$ semileptonic tau decays in the framework of two Higgs doublet model with generic Yukawa structure and Leptoquarks models. Within these models, we list all operators, in the effective Hamiltonian and provide analytical expression for their corresponding Wilson coefficients. Moreover, we analyze the role of the different contributions, originating from the scalar, vecor and tensor hadronic currents, in generating direct CP asymmetry in the decay rate of $��^-\to K^-��^0��_��$. We show that non vanishing direct CP asymmetry in the decay rate of $��^-\to K^-��^0��_��$ can be generated due to the presence of both, the weak phase in the Wilson coefficient corresponding to the tensor operator and the strong phase difference resulting from the interference between the form factors expressing the matrix elements of the vector and tensor hadronic currents. After taking into account all relevant constraints, we find that the generated direct CP asymmetry is of order $10^{-8}$ which is several orders of magnitude larger than the standard model prediction. We show also that, in two Higgs doublet model with generic Yukawa structure , direct local or non integrated CP violation can be as large as $0.3$ % not far from experimental possibilities. This kind of asymmetry can be generated due to the interference between vector and scalar contributions with different weak phases which is not the case in the SM., 31 pages, 2 figures. Accepted version for journal publication

The anomalous results of recent measurements on various $b\to s��^+��^-$ processes could be initial evidence of physics beyond the standard model (SM). Assuming this to be the case, we entertain the possibility that the underlying new physics also affects the rare nonleptonic decays of the $\bar B_s^0$ meson. We consider in particular new physics arising from the interactions of a heavy $Z'$ boson and investigate their influence on the decay modes $\bar B_s^0\to(��,��',��)��$, which receive sizable QCD- and electroweak-penguin contributions. These decays are not yet observed, and their rates are estimated to be relatively small in the SM. Taking into account the pertinent constraints, we find that the $Z'$ effects can greatly increase the rates of $\bar B_s^0\to(��,��)��$, by as much as two orders of magnitude, with respect to the SM expectations. We have previously shown that $\bar B_s^0\to(��,��)��^0$, with similarly suppressed SM rates, could also undergo substantial $Z'$-induced enhancement. These rare modes can therefore serve as complementary probes of the potential new physics which may be responsible for the $b\to s��^+��^-$ anomalies., 16 pages, 4 figures, slightly expanded, matches publication

The present data on a number of observables in b → sμ + μ − processes manifest some tensions with the standard model (SM). Assuming that these anomalies have a new physics origin, we consider the possibility that a Z ′ boson is responsible for them. We further assume that its interactions with quarks also affect rare nonleptonic decays of the B ¯ s 0 meson which are purely isospin-violating and tend to be dominated by electroweak-penguin contributions, namely B ¯ s 0 → η , η ′ , ϕ π 0 ρ 0 . Most of these decays are not yet observed, and their rates are expected to be relatively small in the SM. Taking into account constraints from various measurements, including the evidence for B ¯ s 0 → ϕ ρ 0 recently seen by LHCb, we find that the Z ′ effects on B ¯ s 0 → η ϕ π 0 can make their rates bigger than the SM predictions by up to an order of magnitude. For B ¯ s 0 → η ′ π 0 , η η ′ ρ 0 , the enhancement factors are at most a few. Since the Z ′ contributions to the different channels depend on different combinations of its couplings, observations of more of these decays in future experiments, along with improved b → sμ + μ − data, will probe this Z ′ scenario more thoroughly.

The decay modes B¯s→π0(ρ0)η(′) are dominated by electroweak penguins that are small in the standard model. In this work we investigate the contributions to these penguins from a model with an additional U(1)′ gauge symmetry and show there effects on the branching ratios of B¯s→π0(ρ0)η(′) . In a scenario of the model, where Z′ couplings to the left-handed quarks vanish, we show that the maximum enhancement occurs in the branching ratio of B¯s0→π0η′ where it can reach 6 times the SM prediction. On the other hand, in a scenario of the model where Z′ couplings to both left-handed and right-handed quarks do not vanish, we find that Z′ contributions can enhance the branching ratio of Bs0→ρ0η up to one order of magnitude comparing to the SM prediction for several sets of the parameter space where both ΔMBs and Sψϕ constraints are satisfied. This kind of enhancement occurs for a rather fine-tuned point where the ΔMBs constraint on ∣SSM(Bs)+SZ′(Bs)∣ is fulfilled by overcompensating the SM via SZ′(Bs)≃-2SSM(Bs) .

In this paper we study the direct CP asymmetry of the doubly Cabibbo-suppressed decay mode $D^0 \to K^+ ��^- $ within standard model and two Higgs doublet model with generic Yukawa structure. In the standard model we derive the corrections to the tree level amplitude, generated from the box and di-penguin diagrams, required for generating the weak CP violating phases. We show that these phases are so tiny leading to a direct CP asymmetry of order $10^{-9}$. Regarding the two Higgs doublet model with generic Yukawa structure we derive the Wilson coefficients relevant to $D^0 \to K^+ ��^- $. After taking into account all constraints on the parameter space of the model we show that charged Higgs couplings to quarks can lead to a direct CP asymmetry of order $10^{-3}$ which is $6$ orders of magnitude larger than the standard model prediction., 17 pages

This is a report on our newly proposed model of dynamical supersymmetry breaking with some details of the analysis involved. The model in the simplest version has only a chiral superfield (multiplet), with a strong four-superfield interaction in the K\"ahler potential that induces a real two-superfield composite with vacuum condensate. The latter has supersymmetry breaking parts, which we show to bear nontrivial solution following basically a standard nonperturbative analysis for a Nambu--Jona-Lasinio type model on a superfield setting. The real composite superfield has a spin one component but is otherwise quite unconventional. We discuss also the parallel analysis for the effective theory with the composite. Plausible vacuum solutions are illustrated and analyzed. The supersymmetry breaking solutions have generated soft mass(es) for the scalar avoiding the vanishing supertrace condition for the squared-masses of the superfield components. We also present some analysis of the resulted low energy effective theory with components of the composite become dynamical. The determinant of the fermionic modes is shown to be zero illustrating the presence of the expected Goldstino. The model gives the possibility of constructing a supersymmetric standard model with all (super)symmetry breaking masses generated dynamically and directly without the necessity of complicated hidden or mediating sectors., Comment: 40 pages, 17 figures

Violation of charge conjugation-parity ($\rm CP$) symmetry plays a major rule in the dominance of matter in our universe. A kind of $\rm CP$ violation results from the asymmetry of the life time measured in $M^0$ and $\bar M^0$, here $M$ is a heavy meson, decays to final states which is referred in the literature as $A_{\Gamma}^f$. In this paper, we give an estimation of the upper bound on $|A_{\Gamma}^f|$ for the Cabibbo Favored $D^0 \rightarrow K^- \pi^+$ decay process in different models. We show that in the standard model, $|A_{\Gamma}^f| \lesssim\mathcal{O} (10^{-10})$. Recently a bound on $A_{\Gamma}^f$ has been obtained: $(A^f_{\Gamma})^{Exp.}= (1.6 \pm 1)\times 10^{-4}$. This result motivates further studies on $A_{\Gamma}^f$ in beyond standard model physics. In the framework of two Higgs doublet model with generic Yukawa structure, we show that $|A_\Gamma^{f}|\lesssim \mathcal{O} (10^{-7})$ which is several orders of magnitude smaller than the current experimental value. Finally, in the framework of left-right symmetric models in which the mixing between the left and the right gauge bosons is allowed and the left-right symmetry is not manifest at unification scale, we find that $A_{\Gamma}^f$ can be as large as $|A_{\Gamma}^f|\lesssim\mathcal{O} (10^{-5})$ which is one order of magnitude smaller than the experimentally measured value by LHCb collaborators., Comment: 17 pages, no figures, accepted for publication

In this paper, we study the Cabibbo favored three body non-leptonic D^+ \rightarrow K^- ��^+ ��^+ decay. We show that the corresponding direct CP asymmetry is so tiny in the framework of the Standard Model and is out of the experimental range. Motivated by this result we extend the study of the CP asymmetry to include a toy model with CP violating weak phase equals 20 degrees in a_2, a model with extra gauge bosons within Left-Right Grand Unification models and a model with charged Higgs boson. We show that the toy model can strongly improve the SM prediction of the CP asymmetry to be about 30%. The largest CP asymmetry can be achieved in the non-manifest Left-Right models where a CP asymmetry up to 25% can be reached. For the two Higgs doublets models the CP asymmetry is of order 10^{-3}., 20 pages, 3 figures

The decay modes $\bar{B}_s \rightarrow ��^0(��^0 )\,��^{(')} $ are dominated by electroweak penguins that are small in the standard model. In this work we investigate the contributions to these penguins from a model with an additional $U(1)'$ gauge symmetry and show there effects on the branching ratios of $\bar{B}_s \rightarrow ��^0(��^0 )\,��^{(')} $. In a scenario of the model, where $Z^\prime$ couplings to the left-handed quarks vanish, we show that the maximum enhancement occurs in the branching ratio of $\bar B^0_s\to \,��^0\,��'$ where it can reach $6$ times the SM prediction. On the other hand, in a scenario of the model where $Z^\prime$ couplings to both left-handed and right-handed quarks do not vanish, we find that $Z^\prime$ contributions can enhance the branching ratio of $B^0_s\to\,��^0\,��$ up to one order of magnitude comparing to the SM prediction for several sets of the parameter space where both $ ��M_{B_s}$ and $S_{����}$ constraints are satisfied. This kind of enhancement occurs for a rather fine-tuned point where $ ��M_{B_s}$ constraint on $\mid S_{SM} (B_s) + S_{Z'} (B_s)\mid $ is fulfilled by overcompensating the SM via $S_{Z'} (B_s) \simeq -2 S_{SM} (B_s)$., 25 pages, 7 figures. Version accepted for publication in European Physical Journal C

We study the decay modes $\bar{B}_s\to ����^0$ and $\bar{B}_s\to ����^0$ within the frameworks of two-Higgs doublet models type-II and typ-III. We adopt in our study Soft Collinear Effective Theory as a framework for the calculation of the amplitudes. We derive the contributions of the charged Higgs mediation to the weak effective Hamiltonian governing the decay processes in both models. Moreover we analyze the effect of the charged Higgs mediation on the Wilson coefficients of the electrowek penguins and on the branching ratios of $\bar{B}_s\to ����^0$ and $\bar{B}_s\to ����^0$ decays. We show that wthin two-Higgs doublet models type-II and type-III the Wilson coefficients corresponding to the electroweak penguins can be enhanced due to the contributions from the charged Higgs mediation leading into enhancement in the branching ratios of $ \bar{B}_s\to ����^0$ and $\bar{B}_s\to ����^0 $ decays. We find that, within two-Higgs doublet models type-II, the enhancement in the branching ratio of $\bar{B}_s\to ����^0$ can not exceed $18\%$ with respect to the SM predictions. For the branching ratio of $\bar{B}_s\to ����^0$, we find that the charged Higgs contribution in this case is small where the branching ratio of $\bar{B}_s\to ����^0$ can be enhanced or reduced by about $4\% $ with respect to the SM predictions. For the case of the two-Higgs doublet models type-III we show that the branching ratio of $\bar{B}_s\to ����^0$ can be enhanced by about a factor $2$ of its value within two-Higgs doublet models type-II. However no sizable enhancement with respect to the SM predictions can be obtained for both $\bar{B}_s\to ����^0$ and $\bar{B}_s\to ����^0$ decays., 22 pages,4 figures. Accepted version for publication in Physics Letters B

In this paper, we study the Cabibbo favored non-leptonic $D^0$ decays into $K^- ��^+$ decays. First we show that, within the Standard Model, the corresponding CP asymmetry is strongly suppressed and out of the experimental range even taking into account the large strong phases coming from final state Interactions. We show also that although new physics models with extra sequential generation can enhance the CP asymmetry by few orders of magnitude however the resulting CP asymmetry is still far from experimental range. The most sensitive New Physics Models to this CP asymmetry comes from no-manifest Left-Right models where a CP asymmetry up to 10% can be reached and general two Higgs models extension of SM where a CP asymmetry of order $10^{-2}$ can be obtained without being in contradiction with the experimental constraints on these models., 33 pages, 5 figures

We study the decay modes $\bar{B}_s\to ����^0$ and $\bar{B}_s\to ����^0$ using Soft Collinear Effective Theory. Within Standard Model and including the error due to the SU(3) breaking effect in the SCET parameters we find that BR $\bar{B}_s\to ����^0 =7_{-1-2}^{+1+2}\times 10^{-8} $ and BR $\bar{B}_s\to ����^0=9_{-1-4}^{+1+3}\times 10^{-8}$ corresponding to solution 1 and solution 2 of the SCET parameters respectively.For the decay mode $\bar{B}_s\to ����^0$, we find that BR $\bar{B}_s\to ����^0 = 20.2^{+1+9}_{-1-12}\times 10^{-8} $ and BR $ \bar{B}_s\to ����^0 = 34.0^{+1.5 + 15}_{-1.5-22}\times 10^{-8} $ corresponding to solution 1 and solution 2 of the SCET parameters respectively. We extend our study to include supersymmetric models with non-universal A-terms where the dominant contributions arise from diagrams mediated by gluino and chargino exchanges. We show that gluino contributions can not lead to an enhancement of the branching ratios of $\bar{B}_s\to ����^0$ and $\bar{B}_s\to ����^0$. In addition, we show that SUSY contributions mediated by chargino exchange can enhance the branching ratio of $\bar{B}_s\to ����^0$ by about 14% with respect to the SM prediction. For the branching ratio of $\bar{B}_s\to ����^0$, we find that SUSY contributions can enhance its value by about 1% with respect to the SM prediction., 25 pages,5 figures, version accepted for publication

Exploring hints of New Physics in the decay modes B -> pi K^* and B -> rho K can shed light on the B -> K pi puzzle. In this talk we discuss supersymmetric contributions to the direct CP asymmetries of the decays B -> pi K^* and B -> rho K within Soft Collinear Effective Theory. We consider non-minimal flavor SUSY contributions mediated by gluino exchange and apply the Mass Insertion Approximation in the analysis. We show that gluino contributions can enhance the CP asymmetries and accommodate the experimental results., 7 pages, 5 figures, Invited talk at YongPyong-2011 Conference, South Korea, February 21-26, 2011

A non-universal axigluon in generalized chiral color models leads to flavor changing neutral currents (FCNCs) at tree level. We analyze phenomenologically the new contributions to $B_{q}$ (q=d, s) mixing and the related CP asymmetries (CPAs) that are generated by axigluon exchange. We find that although $\Delta m_{B_q}$ can give a strict constraint on the parameters of $b\to q$ transition, the precise measurement of $\sin2\beta_{J/\Psi K^0}$ can further exclude the parameter space of $b\to d$ transition. The axigluon-mediated effects can enhance the like-sign dimuon charge asymmetry ${\cal A}^{b}_{s\ell}$ by one order of magnitude larger than the standard model prediction. Accordingly, large CPA $\sin2\beta^{J/\Psi \phi}_s$ and CPA difference $\sin2\beta_{J\Psi K^0}-\sin2\beta_{\phi K^0}$ are achieved., Comment: pages 1+18, 8 figures, figures added, discussions extended and references added and updated, version to be published in Physics Letters B

We introduce a simple model of dynamical supersymmetry breaking. It is like a supersymmetric version of a Nambu--Jona-Lasinio model with a spin one composite. The simplest version of the model as presented here has a single chiral superfield (multiplet) with a four-superfield interaction. The latter has the structure of the square of the superfield magnitude square. A vacuum condensate of the latter is illustrated to develop giving rise to supersymmetry breaking with a soft mass term for the superfield. We report also the effective theory picture with a real superfield composite, illustrating the matching effective potential analysis and the vacuum solution conditions for the components. The nature of its fermionic part as the Goldstone mode is presented. Phenomenological application to the supersymmetric standard model is plausible., Comment: 14 pages, 3 figures