[Paper Review] Supersymmetry with composite bosons

Alejandro Rivero|ArXiv.org|Dec 5, 2005

Particle physics theoretical and experimental studies10 references3 citations

TL;DR

This paper proposes a novel realization of supersymmetry in which composite bosons—diquarks in the quark sector and mesons in the lepton sector—serve as superpartners to fermions, naturally forming charged supermultiplets for three generations. The exact match in degrees of freedom between diquarks/mesons and charged fermions (quarks and leptons) provides a dynamical mechanism to address the hierarchy problem, with the model uniquely stabilized at three generations and one top quark unable to form mesons.

ABSTRACT

We note that hadronic susy (empirical quark-diquark) symmetry can be expanded into the lepton sector, and that for three generations the counting of degrees of freedom is the one we need to build charged supermultiplets. For this to cure hierarchy, Higgs modeling becomes restricted.

Motivation & Objective

• To explore whether hadronic supersymmetry (quark-diquark) can be extended to include leptons, forming a unified composite supersymmetry.
• To resolve the hierarchy problem by using composite bosons (diquarks and mesons) to cancel fermionic loop contributions to the Higgs self-energy.
• To explain the observed coincidence in particle counts between charged fermions and composite bosons in three generations.
• To provide a dynamical explanation for Koide's formula in leptons via their composite supersymmetric partners.
• To investigate the breaking mechanism of this composite supersymmetry, particularly in relation to the top quark and electroweak symmetry breaking.

Proposed method

• Construct all possible diquark and meson pairings using quark flavors, classifying them by electric charge to identify potential superpartners.
• Count the number of charged and neutral composite states (diquarks and mesons) and compare them to the number of charged fermions (quarks and leptons) in three generations.
• Use group theory and representation counting to verify that diquarks and mesons provide exactly 6 charged bosonic states per generation, matching the 6 charged fermions.
• Apply the condition that the Higgs must couple with equal strength to quarks and diquarks to ensure loop cancellation for the hierarchy problem.
• Analyze the role of the 4/3 charge diquarks as spurious states and propose mechanisms to suppress their interactions.
• Explore the possibility of supersymmetry restoration at a critical value of the strong coupling constant, based on the preservation of Koide’s formula.

Experimental results

Research questions

• RQ1 Can quark-diquark supersymmetry be consistently extended to include leptons via mesonic superpartners?
• RQ2 Why is the number of composite bosons (diquarks and mesons) exactly sufficient to form supermultiplets with three generations of charged fermions?
• RQ3 How can the hierarchy problem be addressed if composite diquarks and mesons cancel fermionic loop contributions to the Higgs self-energy?
• RQ4 What is the role of the 4/3 charge diquarks, and can they be rendered harmless through coupling suppression?
• RQ5 Can the observed Koide’s formula for charged leptons be explained by their composite supersymmetric partners?

Key findings

• For three generations of quarks and leptons, diquarks provide exactly 6 charged bosons with +1/3 and -2/3 charge, matching the 6 charged fermions (up-type quarks and charged leptons).
• Mesons provide exactly 6 charged bosons with +1 charge, which can serve as superpartners to the 6 charged leptons, completing the supermultiplets.
• The model uniquely requires three generations and one top quark (which cannot form mesons), as shown by solving the system D×U = 2N and D(D+1)/2 = 2N, with minimal solution N=3.
• The number of neutral composite states (13) is sufficient to potentially include neutrino superpartners, though the exact count depends on model-specific group theory constraints.
• The Higgs coupling must be equal to the quark-diquark coupling to cancel one-loop corrections, a condition realizable in composite Higgs models.
• The 4/3 charge diquarks are identified as spurious states, and their suppression is essential to avoid breaking the model’s consistency.