Solving the strong CP problem with massless grand-color quarks

A bstract We propose a solution to the strong CP problem that specifically relies on massless quarks and has no light axion. The QCD color group SU(3) c is embedded into a larger, simple gauge group (grand-color) where one of the massless, colored fermions enjoys an anomalous chiral symmetry, rendering the strong CP phase unphysical. The grand-color gauge group G GC is Higgsed down to SU(3) c × $$ {G}_{c^{\prime }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:msup> <mml:mi>c</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> </mml:math> , after which $$ {G}_{c^{\prime }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:msup> <mml:mi>c</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> </mml:math> eventually confines at a lower scale, spontaneously breaking the chiral symmetry and generating a real, positive mass to the massless, colored fermion. Since the chiral symmetry has a $$ {G}_{c^{\prime }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:msup> <mml:mi>c</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> </mml:math> anomaly, there is no corresponding light Nambu-Goldstone boson. The anomalous chiral symmetry can be an accidental symmetry that arises from an exact discrete symmetry without introducing a domain wall problem. Potential experimental signals of our mechanism include vector-like quarks near the TeV scale, pseudo Nambu-Goldstone bosons below the 10 GeV scale, light dark matter decay, and primordial gravitational waves from the new strong dynamics.