Symmergent Gravity, Seesawic New Physics, and Their Experimental Signatures

The standard model of elementary particles (SM) suffers from various problems, such as power-law ultraviolet (UV) sensitivity, exclusion of general relativity (GR), and absence of a dark matter candidate. The LHC experiments, according to which the TeV domain appears to be empty of new particles, started sidelining TeV-scale SUSY and other known cures of the UV sensitivity. In search for a remedy, in this work, it is revealed that affine curvature can emerge in a way restoring gauge symmetries explicitly broken by the UV cutoff. This emergent curvature cures the UV sensitivity and incorporates GR as symmetry-restoring emergent gravity ( symmergent gravity , in brief) if a new physics sector (NP) exists to generate the Planck scale and if SM+NP is Fermi-Bose balanced. This setup, carrying fingerprints of trans-Planckian SUSY, predicts that gravity is Einstein (no higher-curvature terms), cosmic/gamma rays can originate from heavy NP scalars, and the UV cutoff might take right value to suppress the cosmological constant (alleviating fine-tuning with SUSY). The NP does not have to couple to the SM. In fact, NP-SM coupling can take any value from zero to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msubsup></mml:math> if the SM is not to jump from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">500</mml:mn><mml:mo> </mml:mo><mml:mo> </mml:mo><mml:mi mathvariant="normal">G</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">V</mml:mi></mml:math> to the NP scale <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>. The zero coupling, certifying an undetectable NP, agrees with all the collider and dark matter bounds at present. The seesawic bound <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msubsup></mml:math>, directly verifiable at colliders, implies that (i) dark matter must have a mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mo>≲</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>M</mml:mi></mml:mrow></mml:msub></mml:math>, (ii) Higgs-curvature coupling must be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mo>≈</mml:mo><mml:mn mathvariant="normal">1.3</mml:mn><mml:mi mathvariant="normal">%</mml:mi></mml:math>, (iii) the SM RGEs must remain nearly as in the SM, and (iv) right-handed neutrinos must have a mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mo>≲</mml:mo><mml:mn mathvariant="normal">1000</mml:mn><mml:mo> </mml:mo><mml:mo> </mml:mo><mml:mi mathvariant="normal">T</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">V</mml:mi></mml:math>. These signatures serve as a concise testbed for symmergence.

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