[Paper Review] Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM

Anthony Ashmore, Sebastian Dumitru+1 more|arXiv (Cornell University)|Dec 20, 2020

Black Holes and Theoretical PhysicsPhysics and Astronomy129 references9 citations

TL;DR

This paper proposes a realistic mechanism for explicit soft supersymmetry breaking in the heterotic M-theory B−L MSSM via gaugino condensation in a strongly coupled heterotic vacuum. By analyzing a specific line bundle L = OX(2,1,3) that yields a low condensation scale (~1–10 TeV), the authors compute moduli-dependent soft terms and demonstrate that a substantial subset of initial conditions—designated as "red" points—yield phenomenologically viable low-energy physics satisfying all experimental constraints, including the quadratic Higgs-Higgs conjugate term bound.

ABSTRACT

The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the $B-L$ MSSM theory is reviewed, including a discussion of the "bundle" constraints that both the observable sector $SU(4)$ vector bundle and the a hidden sector bundle induced from a line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of K\"ahler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent $F$-terms due to a gaugino superpotential - which spontaneously break $N=1$ supersymmetry in this sector - is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in K\"ahler moduli space that satisfy all "bundle" constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.

Motivation & Objective

• To construct a realistic hidden sector bundle in strongly coupled heterotic M-theory that supports gaugino condensation with a low enough scale to be compatible with LHC energy scales.
• To compute the moduli-dependent F-terms and soft supersymmetry breaking parameters in the observable sector arising from spontaneous N = 1 SUSY breaking in the hidden sector.
• To determine whether the resulting soft terms yield phenomenologically viable low-energy physics, satisfying all experimental constraints including the quadratic Higgs-Higgs conjugate term.
• To identify a region in Kähler moduli space where all bundle constraints are satisfied and the soft terms lead to realistic renormalization group evolution outcomes.

Proposed method

• Review the heterotic M-theory vacuum for the B−L MSSM, including the observable SU(4) vector bundle and hidden sector line bundle constraints on a Schoen Calabi–Yau threefold.
• Identify the line bundle L = OX(2,1,3) as the unique one yielding a low condensation scale (~1–10 TeV), compatible with LHC energy scales.
• Compute the moduli-dependent F-terms from the gaugino superpotential, which spontaneously break N = 1 supersymmetry in the hidden sector.
• Derive explicit expressions for the moduli-dependent coefficients of all soft terms: gravitino mass, scalar masses, cubic couplings, and the holomorphic quadratic term.
• Perform a statistical scan over the Kähler moduli space to evaluate the resulting soft terms via renormalization group evolution (RGE) analysis.
• Classify initial conditions as "black" points (phenomenologically viable) or "red" points (also satisfying the Higgs-Higgs conjugate term constraint).

Experimental results

Research questions

• RQ1 Which hidden sector line bundle in the strongly coupled heterotic M-theory B−L MSSM vacuum yields a gaugino condensation scale compatible with LHC energy scales?
• RQ2 How do the moduli-dependent soft supersymmetry breaking parameters in the observable sector arise from spontaneous N = 1 SUSY breaking via gaugino condensation?
• RQ3 What fraction of initial conditions in Kähler moduli space lead to phenomenologically viable low-energy physics after renormalization group evolution?
• RQ4 Do any of these initial conditions also satisfy the additional constraint on the coefficient of the holomorphic quadratic Higgs-Higgs conjugate soft term?
• RQ5 What is the range of the soft SUSY breaking scale msusy that yields viable phenomenological outcomes in this framework?

Key findings

• The line bundle L = OX(2,1,3) is identified as the unique hidden sector bundle that yields a gaugino condensation scale within the range [1 TeV, 10 TeV], compatible with LHC energy scales.
• A substantial subset of initial conditions in Kähler moduli space—designated as "red" points—produce soft terms that satisfy all low-energy phenomenological constraints, including the Higgs-Higgs conjugate term bound.
• The region of viable "black" points forms a strip within the green subregion of Kähler moduli space where msusy ∈ [1 TeV, 105 TeV], with the most promising region for realism being msusy ∈ [1 TeV, 10 TeV].
• No "black" points are produced when msusy ≲1 TeV due to sparticle masses violating experimental lower bounds, and none are produced when msusy > ∼105 TeV due to Higgs mass being inconsistent with experimental bounds.
• The RGE solutions for b and µ are derived for both the "right-side-up" and "upside-down" hierarchies, with the system simplified by neglecting small Yukawa couplings (yb, yτ) at high scales.
• The final constraint on the coefficient of the holomorphic quadratic term is satisfied by a substantial subset of the initial conditions, confirming that "red" points are physically viable.