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Naturalness in low-scale SUSY models and "non-linear" MSSM.

Antoniadis I, Babalic EM, Ghilencea DM - Eur Phys J C Part Fields (2014)

Bottom Line: This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce [Formula: see text].In the present case [Formula: see text] is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio [Formula: see text] of the visible to the hidden sector SUSY breaking scales.By increasing the hidden sector scale [Formula: see text] one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.

View Article: PubMed Central - PubMed

Affiliation: CERN Theory Division, 1211 Geneva 23, Switzerland.

ABSTRACT

In MSSM models with various boundary conditions for the soft breaking terms ([Formula: see text]) and for a Higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning [Formula: see text] to [Formula: see text] for the constrained MSSM and [Formula: see text] for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector ([Formula: see text]) to few TeV, which we show to restore naturalness to more acceptable levels [Formula: see text] for the most conservative case of low [Formula: see text] and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce [Formula: see text]. In the present case [Formula: see text] is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio [Formula: see text] of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale [Formula: see text] one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.

No MeSH data available.


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The diagrams that generate the new quartic effective Higgs couplings in V, Eq. (9). The coefficients  are generated by , .  is the auxiliary component of  that breaks SUSY. The left (right) diagrams are generated by D (F) terms in the action, while the middle one is a mixture of both. These interactions are important in low-scale SUSY breaking models while in the MSSM they are strongly suppressed since  is large)
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getmorefigures.php?uid=PMC4383770&req=5

Fig1: The diagrams that generate the new quartic effective Higgs couplings in V, Eq. (9). The coefficients are generated by , . is the auxiliary component of that breaks SUSY. The left (right) diagrams are generated by D (F) terms in the action, while the middle one is a mixture of both. These interactions are important in low-scale SUSY breaking models while in the MSSM they are strongly suppressed since is large)

Mentions: The Lagrangian of the “non-linear MSSM” model can be written as [6–9]2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}=\mathcal{L}_0+\mathcal{L}_X+\mathcal{L}_1+\mathcal{L}_2; \end{aligned}$$\end{document}L=L0+LX+L1+L2; is the usual MSSM SUSY Lagrangian which we write below to establish the notation:3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_0&= \sum _{\Phi , H_{1,2}} \int \mathrm{d}^4\theta \Phi ^\dagger e^{V_i}\Phi +\bigg \{\int \mathrm{d}^2\theta \Big [\mu H_1H_2+ H_2QU^c\nonumber \\&+QD^cH_1+LE^cH_1\Big ]+\hbox {h.c.}\bigg \} \nonumber \\&+\sum _{i=1}^3\frac{1}{16g_i^2\kappa } \int \mathrm{d}^2\theta \text{ Tr }[W^\alpha W_\alpha ]_i\nonumber \\&+\hbox { h.c.}, \quad \Phi :Q,D^c,U^c,E^c,L, \end{aligned}$$\end{document}L0=∑Φ,H1,2∫d4θΦ†eViΦ+{∫d2θ[μH1H2+H2QUc+QDcH1+LEcH1]+h.c.}+∑i=13116gi2κ∫d2θTr[WαWα]i+h.c.,Φ:Q,Dc,Uc,Ec,L, is a constant canceling the trace factor, and the gauge coupling is , for , , and , respectively. Further, is the Lagrangian of the goldstino superfield that breaks SUSY spontaneously and whose Weyl component is “eaten” by the gravitino (super-Higgs effect [52, 53]). can be written as [8, 9]4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_X\!=\!\int \mathrm{d}^4\theta X^\dagger X \!+\!\Big \{\int \mathrm{d}^2\theta fX\!+\!\hbox {h.c.}\Big \}\quad \mathrm{with}\ X^2\!=\!0.\quad \end{aligned}$$\end{document}LX=∫d4θX†X+{∫d2θfX+h.c.}withX2=0.The otherwise interaction-free when endowed with a constraint [8–11] describes (on-shell) the Akulov–Volkov Lagrangian of the goldstino [54]; see also [55–61], with non-linear SUSY. The constraint has a solution that projects (integrates) out the sgoldstino field which becomes massive and is appropriate for a low energy description of SUSY breaking. Further, fixes the SUSY breaking scale () and the breaking is transmitted to the visible sector by the couplings of to the MSSM superfields, to generate the usual SUSY breaking (effective) terms in (see below). These couplings are commonly parametrized (on-shell) in terms of the spurion field where is a generic notation for the soft masses (later denoted , ); however, this parametrization obscures the dynamics of (off-shell effects) relevant below that generates additional Feynman diagrams mediated by (Fig. 1). Such effects are not seen in the leading order (in ) in the spurion formalism. The off-shell couplings are easily recovered by the formal replacement [8, 9]5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} S\rightarrow \frac{m_\mathrm{soft}}{f} X. \end{aligned}$$\end{document}S→msoftfX.In this way one obtains the SUSY breaking couplings that are indeed identical to those obtained by the equivalence theorem [1–5] from a theory with the corresponding explicit soft breaking terms and in which the goldstino fermion couples to the derivative of the supercurrent of the initial theory. These couplings are generated by the D-terms below:6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_{1}&= \sum _{i=1,2} c_i \int \mathrm{d}^4\theta X^\dagger X H_i^\dagger e^{V_i}H_i \nonumber \\&+\sum _{\Phi } c_\Phi \int \mathrm{d}^4\theta X^\dagger X\Phi ^\dagger e^V \Phi . \end{aligned}$$\end{document}L1=∑i=1,2ci∫d4θX†XHi†eViHi+∑ΦcΦ∫d4θX†XΦ†eVΦ.and by the F-terms:7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_{2}&= \sum _{i=1}^3 \frac{1}{16 g^2_i\kappa } \frac{2m_{\lambda _i}}{f} \int \mathrm{d}^2\theta X\text{ Tr }[W^\alpha W_\alpha ]_i \nonumber \\&+c_3\int \mathrm{d}^2\theta XH_1H_2+\frac{A_u}{f}\int \mathrm{d}^2\theta XH_2QU^c\nonumber \\&+ \frac{A_d}{f}\int \mathrm{d}^2\theta XQD^c H_1 +\frac{A_e}{f}\int \mathrm{d}^2\theta XLE^cH_1+\hbox {h.c.}\nonumber \\ \end{aligned}$$\end{document}L2=∑i=13116gi2κ2mλif∫d2θXTr[WαWα]i+c3∫d2θXH1H2+Auf∫d2θXH2QUc+Adf∫d2θXQDcH1+Aef∫d2θXLEcH1+h.c.with8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&c_{j}=-\frac{m_j^2}{f^2},\quad j=1,2;\qquad c_3=-\frac{m_3^2}{f}, \qquad c_\Phi =-\frac{m_\Phi ^2}{f^2},\nonumber \\&\qquad \Phi : Q, U^c, D^c, L, E^c, \end{aligned}$$\end{document}cj=-mj2f2,j=1,2;c3=-m32f,cΦ=-mΦ2f2,Φ:Q,Uc,Dc,L,Ec,In the UV one can eventually take , () for all gaugino masses, ( in the UV) and these define the “constrained” version of the “non-linear” MSSM, discussed later. For simplicity, Yukawa matrices are not displayed; to recover them just replace above any pair of fields , , ; similar for the fermions and auxiliary fields, with matrices.


Naturalness in low-scale SUSY models and "non-linear" MSSM.

Antoniadis I, Babalic EM, Ghilencea DM - Eur Phys J C Part Fields (2014)

The diagrams that generate the new quartic effective Higgs couplings in V, Eq. (9). The coefficients  are generated by , .  is the auxiliary component of  that breaks SUSY. The left (right) diagrams are generated by D (F) terms in the action, while the middle one is a mixture of both. These interactions are important in low-scale SUSY breaking models while in the MSSM they are strongly suppressed since  is large)
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4383770&req=5

Fig1: The diagrams that generate the new quartic effective Higgs couplings in V, Eq. (9). The coefficients are generated by , . is the auxiliary component of that breaks SUSY. The left (right) diagrams are generated by D (F) terms in the action, while the middle one is a mixture of both. These interactions are important in low-scale SUSY breaking models while in the MSSM they are strongly suppressed since is large)
Mentions: The Lagrangian of the “non-linear MSSM” model can be written as [6–9]2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}=\mathcal{L}_0+\mathcal{L}_X+\mathcal{L}_1+\mathcal{L}_2; \end{aligned}$$\end{document}L=L0+LX+L1+L2; is the usual MSSM SUSY Lagrangian which we write below to establish the notation:3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_0&= \sum _{\Phi , H_{1,2}} \int \mathrm{d}^4\theta \Phi ^\dagger e^{V_i}\Phi +\bigg \{\int \mathrm{d}^2\theta \Big [\mu H_1H_2+ H_2QU^c\nonumber \\&+QD^cH_1+LE^cH_1\Big ]+\hbox {h.c.}\bigg \} \nonumber \\&+\sum _{i=1}^3\frac{1}{16g_i^2\kappa } \int \mathrm{d}^2\theta \text{ Tr }[W^\alpha W_\alpha ]_i\nonumber \\&+\hbox { h.c.}, \quad \Phi :Q,D^c,U^c,E^c,L, \end{aligned}$$\end{document}L0=∑Φ,H1,2∫d4θΦ†eViΦ+{∫d2θ[μH1H2+H2QUc+QDcH1+LEcH1]+h.c.}+∑i=13116gi2κ∫d2θTr[WαWα]i+h.c.,Φ:Q,Dc,Uc,Ec,L, is a constant canceling the trace factor, and the gauge coupling is , for , , and , respectively. Further, is the Lagrangian of the goldstino superfield that breaks SUSY spontaneously and whose Weyl component is “eaten” by the gravitino (super-Higgs effect [52, 53]). can be written as [8, 9]4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_X\!=\!\int \mathrm{d}^4\theta X^\dagger X \!+\!\Big \{\int \mathrm{d}^2\theta fX\!+\!\hbox {h.c.}\Big \}\quad \mathrm{with}\ X^2\!=\!0.\quad \end{aligned}$$\end{document}LX=∫d4θX†X+{∫d2θfX+h.c.}withX2=0.The otherwise interaction-free when endowed with a constraint [8–11] describes (on-shell) the Akulov–Volkov Lagrangian of the goldstino [54]; see also [55–61], with non-linear SUSY. The constraint has a solution that projects (integrates) out the sgoldstino field which becomes massive and is appropriate for a low energy description of SUSY breaking. Further, fixes the SUSY breaking scale () and the breaking is transmitted to the visible sector by the couplings of to the MSSM superfields, to generate the usual SUSY breaking (effective) terms in (see below). These couplings are commonly parametrized (on-shell) in terms of the spurion field where is a generic notation for the soft masses (later denoted , ); however, this parametrization obscures the dynamics of (off-shell effects) relevant below that generates additional Feynman diagrams mediated by (Fig. 1). Such effects are not seen in the leading order (in ) in the spurion formalism. The off-shell couplings are easily recovered by the formal replacement [8, 9]5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} S\rightarrow \frac{m_\mathrm{soft}}{f} X. \end{aligned}$$\end{document}S→msoftfX.In this way one obtains the SUSY breaking couplings that are indeed identical to those obtained by the equivalence theorem [1–5] from a theory with the corresponding explicit soft breaking terms and in which the goldstino fermion couples to the derivative of the supercurrent of the initial theory. These couplings are generated by the D-terms below:6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_{1}&= \sum _{i=1,2} c_i \int \mathrm{d}^4\theta X^\dagger X H_i^\dagger e^{V_i}H_i \nonumber \\&+\sum _{\Phi } c_\Phi \int \mathrm{d}^4\theta X^\dagger X\Phi ^\dagger e^V \Phi . \end{aligned}$$\end{document}L1=∑i=1,2ci∫d4θX†XHi†eViHi+∑ΦcΦ∫d4θX†XΦ†eVΦ.and by the F-terms:7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \mathcal{L}_{2}&= \sum _{i=1}^3 \frac{1}{16 g^2_i\kappa } \frac{2m_{\lambda _i}}{f} \int \mathrm{d}^2\theta X\text{ Tr }[W^\alpha W_\alpha ]_i \nonumber \\&+c_3\int \mathrm{d}^2\theta XH_1H_2+\frac{A_u}{f}\int \mathrm{d}^2\theta XH_2QU^c\nonumber \\&+ \frac{A_d}{f}\int \mathrm{d}^2\theta XQD^c H_1 +\frac{A_e}{f}\int \mathrm{d}^2\theta XLE^cH_1+\hbox {h.c.}\nonumber \\ \end{aligned}$$\end{document}L2=∑i=13116gi2κ2mλif∫d2θXTr[WαWα]i+c3∫d2θXH1H2+Auf∫d2θXH2QUc+Adf∫d2θXQDcH1+Aef∫d2θXLEcH1+h.c.with8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned}&c_{j}=-\frac{m_j^2}{f^2},\quad j=1,2;\qquad c_3=-\frac{m_3^2}{f}, \qquad c_\Phi =-\frac{m_\Phi ^2}{f^2},\nonumber \\&\qquad \Phi : Q, U^c, D^c, L, E^c, \end{aligned}$$\end{document}cj=-mj2f2,j=1,2;c3=-m32f,cΦ=-mΦ2f2,Φ:Q,Uc,Dc,L,Ec,In the UV one can eventually take , () for all gaugino masses, ( in the UV) and these define the “constrained” version of the “non-linear” MSSM, discussed later. For simplicity, Yukawa matrices are not displayed; to recover them just replace above any pair of fields , , ; similar for the fermions and auxiliary fields, with matrices.

Bottom Line: This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce [Formula: see text].In the present case [Formula: see text] is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio [Formula: see text] of the visible to the hidden sector SUSY breaking scales.By increasing the hidden sector scale [Formula: see text] one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.

View Article: PubMed Central - PubMed

Affiliation: CERN Theory Division, 1211 Geneva 23, Switzerland.

ABSTRACT

In MSSM models with various boundary conditions for the soft breaking terms ([Formula: see text]) and for a Higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning [Formula: see text] to [Formula: see text] for the constrained MSSM and [Formula: see text] for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector ([Formula: see text]) to few TeV, which we show to restore naturalness to more acceptable levels [Formula: see text] for the most conservative case of low [Formula: see text] and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce [Formula: see text]. In the present case [Formula: see text] is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio [Formula: see text] of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale [Formula: see text] one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.

No MeSH data available.


Related in: MedlinePlus