Modulus-dominated SUSY-breaking soft terms in F-theory and their test at LHC

TL;DR

The paper analyzes modulus-dominated SUSY breaking in Type IIB/F-theory frameworks, showing that gaugino masses arise at leading order only when MSSM fields live on D7-branes or their F-theory relatives, and that a single local Kahler modulus $t$ governs the MSSM soft terms through modular weights. It identifies three viable 7-brane configurations—A-A-$\phi$, I-I-A, and I-I-I—constrained by Yukawa couplings and phenomenology; among them, the intersecting-branes pattern I-I-I (and closely related I-I-A) can satisfy radiative electroweak symmetry breaking and DM requirements, while the bulk A-A-$\phi$ setup is disfavored due to a charged LSP and lack of viable DM. The resulting MSSM spectrum is highly structured, with soft terms $M=F_t/t$, $m_\alpha^2=(1-\xi_\alpha)|M|^2$, and trilinears $A_{\alpha\beta\gamma}$ determined by the modular weights; subleading flux corrections can tune the B-term and DM abundance. The work further shows that LHC can test these patterns, predicting testable regions with characteristic gaugino-squark spectra and neutralino-stau coannihilation features, thereby providing a direct probe of the underlying string compactification.

Abstract

We study the general patterns of SUSY-breaking soft terms arising under the assumption of Kahler moduli dominated SUSY-breaking in string theory models. Insisting that all MSSM gauginos get masses at leading order and that the top Yukawa coupling is of order the gauge coupling constant identifies the class of viable models. These are models in which the SM fields live either in the bulk or at the intersection of local sets of Type IIB D7-branes or their F-theory relatives. General arguments allow us to compute the dependence of the Kahler metrics of MSSM fields on the local Kahler modulus of the brane configuration in the large moduli approximation. We illustrate this study in the case of toroidal/orbifold orientifolds but discuss how the findings generalize to the F-theory case which is more naturally compatible with coupling unification. Only three types of 7-brane configurations are possible, leading each of them to very constrained patterns of soft terms for the MSSM. We study their consistency with radiative electroweak symmetry breaking and other phenomenological constraints. We find that essentially only the configuration corresponding to intersecting 7-branes is compatible with all present experimental constraints and the desired abundance of neutralino dark matter. The obtained MSSM spectrum is very characteristic and could be tested at LHC. We also study the LHC reach for the discovery of this type of SUSY particle spectra.

Figures (7)

• Figure 1: Different origin of matter fields in $D7/D3$ configurations. a) States from reduction of gauge fields A within the $D7$ worldvolume; b) From reduction of D=8 fields $\phi$ parametrizing the $D7$ position; c) From two intersecting $D7$-branes; d) From open strings between a $D3$ and a $D7$; e) From open strings starting and ending on $D3$ branes.
• Figure 2: The SM $7$-branes wrap local 4-cycles of size $t$ in a CY whose (larger) volume is controlled by $t_b$.
• Figure 3: Low-energy supersymmetric spectrum as a function of $\tan\beta$ for $\xi_H=1/2,$ (left) and $\xi_H=1$ (right) with $M=400\ {\rm GeV}$ and $\mu<0$. From bottom to top, the solid lines represent the masses of the lightest neutralino, the lightest chargino, and the gluino. Dashed lines display the masses of the lightest stau and lightest sneutrino. Dot-dashed lines correspond to the stop and sbottom masses. Finally, the lightest Higgs mass, the pseudoscalar Higgs mass and the absolute value of the $\mu$ parameter are displayed by means of dotted lines. The ruled area for large $\tan\beta$ is excluded by the occurrence of tachyons in the slepton sector.
• Figure 4: Effect of the various experimental constraints on the $(M,\,\tan{\beta})$ plane for cases with $\xi_H=0.5,\,0.6,\,0.8$, and $1$, from left to right and top to bottom. Dark grey regions correspond to those excluded by any experimental bound. Namely, the area below (and to the left of) the thin dashed line is ruled out by the lower constraint on the lightest Higgs mass. The region below the thin dotted lines is excluded by the lower bounds on the stau and chargino masses. The area below the thick dashed line is excluded by $b\to s\gamma$. The region below the double dot-dashed line is excluded by $B_s^0\to\mu^+\mu^-$. The thin dot-dashed lines correspond, from top to bottom, to the lower and upper constraint on $a^{\rm SUSY}_\mu$. The area contained within solid lines corresponds to the region in which the stau is the LSP, and is depicted in light grey when experimental constraints are fulfilled. In the remaining white area the neutralino is the LSP. The thin black area, in the vicinity of the region with stau LSP, corresponds to the region where the neutralino relic density is in agreement with the WMAP bound.
• Figure 5: Left) Resulting $B(M_{GUT})/M$ as a function of $\tan\beta$ for the case with $\xi_H=0.5$. The dotted, dashed, dot-dashed, and solid lines correspond to $M=300,\,500,\,1000$, and $1500\,{\rm GeV}$, respectively, for both signs of the $\mu$ parameter. The boundary condition $B=-M$ is indicated with a horizontal dotted line. Right) The same, but for the cases with $\xi_H=0.5,\,0.6,\,0.7,\,0.8,\,0.9$, and $1$, from bottom to top, with $\mu<0$ and $M=1000\,{\rm GeV}$. The corresponding boundary conditions for $B$ are represented with horizontal dotted lines, and the solid circles indicate the values of $\tan\beta$ consistent with these.