Bottom-Up Approach to Moduli Dynamics in Heavy Gravitino Scenario : Superpotential, Soft Terms and Sparticle Mass Spectrum

TL;DR

This work analyzes moduli dynamics in a heavy gravitino setting, showing that CP conservation in gaugino masses from anomaly mediation restricts the moduli superpotential to two forms (KKLT-type and racetrack). By deriving the full soft-term structure and MSSM mass spectrum under combined moduli- and anomaly-mediated SUSY breaking, the authors find that the two mediation channels contribute comparably, producing near-degenerate gaugino masses at the electroweak scale and a lightest neutralino with substantial higgsino content. The moduli are stabilized with large masses, solving the cosmological moduli problem, while the heavy gravitino helps avert gravitino-induced cosmological issues; cosmological and dark-matter implications, including possible non-thermal production, are discussed. The scenario makes distinctive predictions for collider phenomenology and dark matter detection, notably a higgsino–bino mixed LSP and nonuniversal gaugino masses, offering testable signals in future experiments.

Abstract

The physics of moduli fields is examined in the scenario where the gravitino is relatively heavy with mass of order 10 TeV, which is favored in view of the severe gravitino problem. The form of the moduli superpotential is shown to be determined, if one imposes a phenomenological requirement that no physical CP phase arise in gaugino masses from conformal anomaly mediation. This bottom-up approach allows only two types of superpotential, each of which can have its origins in a fundamental underlying theory such as superstring. One superpotential is the sum of an exponential and a constant, which is identical to that obtained by Kachru et al (KKLT), and the other is the racetrack superpotential with two exponentials. The general form of soft supersymmetry breaking masses is derived, and the pattern of the superparticle mass spectrum in the minimal supersymmetric standard model is discussed with the KKLT-type superpotential. It is shown that the moduli mediation and the anomaly mediation make comparable contributions to the soft masses. At the weak scale, the gaugino masses are rather degenerate compared to the minimal supergravity, which bring characteristic features on the superparticle masses. In particular, the lightest neutralino, which often constitutes the lightest superparticle and thus a dark matter candidate, is a considerable admixture of gauginos and higgsinos. We also find a small mass hierarchy among the moduli, gravitino, and superpartners of the standard-model fields. Cosmological implications of the scenario are briefly described.

Figures (10)

• Figure 1: Gaugino masses at the unification scale for the standard model gauginos: gluino $\tilde{g}$, wino $\tilde{W}$, and bino $\tilde{B}$. Here we fix the moduli contribution $F_X/X_R$. The region for small values of $bX_R$ is described by the extrapolation, and the gaugino masses become universal at $bX_R=0$ where the moduli contribution dominates the spectrum.
• Figure 2: Gaugino masses at the electroweak scale for the standard model gauginos: gluino $\tilde{g}$, wino $\tilde{W}$, and bino $\tilde{B}$. Here we fix the anomaly contribution $F_\phi$ and assume that the gaugino masses are mediated at the unification scale ($=2\times10^{16}$ GeV). For a larger value of $R_{bX}$, the gaugino mass hierarchy decreases.
• Figure 3: Typical sparticle masses at the electroweak scale for $n=1$ moduli. We assume the universal Kähler terms for visible and hidden sector fields; that is, $l={}^\forall m_i=1/3$ in Eq. (\ref{['fXZQ']}). The horizontal axis denotes the ratio of two $F$-term contributions: $R_{bX}\equiv F_\phi/(F_X/2X_R)$. In the figure, $\tan\beta=10$, and $F_\phi$ is fixed to be 20 TeV as an example, but the spectrum is scaled by $F_\phi$. The gaugino masses are given by the solid (black) lines, and the two-dotted-dashed line is the higgsino mass parameter $\mu$. We show the mass of the lightest neutralino ($\tilde{\chi}^0_1$) by two-dotted line. The dotted (green) and dotted-dashed (blue) lines represent left- and right-handed squarks of the first two generations, respectively. We show, in particular, the mass of right-handed scalar tau by dashed (red) line, which is the lightest among sfermions.
• Figure 4: Constant contours of the mass of the lightest neutral Higgs boson for $n=1$ moduli. We assume the universal Kähler terms for visible and hidden sector fields; that is, $l={}^\forall m_i=1/3$ in Eq. (\ref{['fXZQ']}). The dotted-dashed line denotes the current experimental bound from LEP II. In the figure, we take $\tan\beta=10$ and the top quark pole mass $M_t=178$ GeV.
• Figure 5: Typical sparticle masses at the electroweak scale for $n=3$ moduli. We assume the sequestered Kähler potential for visible and hidden sector fields; that is, $l={}^\forall m_i=0$ in Eq. (\ref{['fXZQ']}). The horizontal axis denotes the ratio of two $F$-term contributions: $R_{bX}\equiv F_\phi/(F_X/2X_R)$. In the figure, $\tan\beta=10$, and $F_\phi$ is fixed to be 20 TeV as an example, but the spectrum is scaled by $F_\phi$. The gaugino masses are given by the solid (black) lines, and the two-dotted-dashed line is the higgsino mass parameter $\mu$. We show the mass of the lightest neutralino ($\tilde{\chi}^0_1$) by two-dotted line. The dotted (green) and dotted-dashed (blue) lines represent left- and right-handed squarks of the first two generations, respectively. We show, in particular, the mass of right-handed scalar tau by dashed (red) lines, which is the lightest supersymmetric particle in a wide range of parameter space for vanishing universal corrections to scalar masses ($m_0=0$). Also shown is the mass of right-handed scalar tau for $m_0=1.5 \times 10^{-2} |F_{\phi}|$.