Baryon stability on the Higgs dissolution edge: threshold corrections and suppression of baryon violation in the NMSGUT

Superheavy threshold corrections to the matching condition between matter Yukawa couplings of the effective Minimal Supersymmetric Standard Model (MSSM) and the New Minimal Supersymmetric ( <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">SO</mi></mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> ) GUT (NMSGUT) provide a novel and generic mechanism for reducing the long standing and generically problematic operator dimension 5 baryon decay rates. In suitable regions of the parameter space strong wave function renormalization of the effective MSSM Higgs doublets due to the large number of heavy fields can take the wave function renormalization of the MSSM Higgs field close to the dissolution value ( <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>Z</mi></mrow><mrow><mi>H</mi><mo>,</mo><mover accent="true"><mrow><mi>H</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msub><mo>=</mo><mn>0</mn></math> ). Rescaling to canonical kinetic terms lowers the <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">SO</mi></mrow><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> Yukawas required to match the MSSM fermion data. Since the same Yukawas determine the dimension 5 B violation operator coefficients, the associated rates can be suppressed to levels compatible with current limits. Including these threshold effects also relaxes the constraint <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>y</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>−</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo>≃</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>−</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>μ</mi></mrow></msub></math> operative between 10 – 120 -plet generated tree level MSSM matter fermion Yukawas <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>y</mi></mrow><mrow><mi>f</mi></mrow></msub></math> . We exhibit accurate fits of the MSSM fermion mass-mixing data in terms of NMSGUT superpotential couplings and 5 independent soft Susy breaking parameters specified at <math altimg="si5.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mn>10</mn></mrow><mrow><mn>16.25</mn></mrow></msup><mtext> </mtext><mtext>GeV</mtext></math> with the claimed suppression of baryon decay rates. As before, our s-spectra are of the mini split supersymmetry type with large <math altimg="si6.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">|</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy="false">|</mo><mo>,</mo><mi>μ</mi><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>H</mi><mo>,</mo><mover accent="true"><mrow><mi>H</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></msub><mo>&gt;</mo><mn>100</mn><mtext> </mtext><mtext>TeV</mtext></math> , light gauginos and normal s-hierarchy. Large <math altimg="si7.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mi>μ</mi></math> and soft masses allow significant deviation from the canonical GUT gaugino mass ratios and ensure vacuum safety. Even without optimization, prominent candidates for BSM discovery such as the muon magnetic anomaly, <math altimg="si8.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo stretchy="false">→</mo><mi>s</mi><mi>γ</mi></math> and leptogenesis CP violation emerge in the preferred ball park