Phenomenology of non-Abelian gauge and Goldstone bosons in a U(2) flavor model

We investigate the phenomenological implications of the bosons associated with the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:msub> <a:mo stretchy="false">)</a:mo> <a:mi>F</a:mi> </a:msub> </a:math> subgroup in a simple and realistic <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>2</e:mn> <e:msub> <e:mo stretchy="false">)</e:mo> <e:mi>F</e:mi> </e:msub> </e:math> flavor model. While the Nambu-Goldstone boson of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>U</i:mi> <i:mo stretchy="false">(</i:mo> <i:mn>1</i:mn> <i:msub> <i:mo stretchy="false">)</i:mo> <i:mi>F</i:mi> </i:msub> </i:math> factor behaves as a standard QCD axion (an axiflavon) with suppressed flavor-violating couplings, the three degrees of freedom from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>S</m:mi> <m:mi>U</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>2</m:mn> <m:msub> <m:mo stretchy="false">)</m:mo> <m:mi>F</m:mi> </m:msub> </m:math> have not been studied before. This work focuses on these states, considering both the case where <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>S</q:mi> <q:mi>U</q:mi> <q:mo stretchy="false">(</q:mo> <q:mn>2</q:mn> <q:msub> <q:mo stretchy="false">)</q:mo> <q:mi>F</q:mi> </q:msub> </q:math> is a global symmetry, yielding pseudo-Nambu-Goldstone bosons (PNGBs), and the case where it is a gauge symmetry with a potentially small coupling, yielding a triplet of (possibly) light gauge bosons. In both scenarios, these new bosons naturally feature unsuppressed flavor-violating couplings to Standard Model fermions in the mass basis. We derive the resulting predictions for flavor-changing neutral currents and lepton flavor violation, including exotic decays of mesons and leptons. Our analysis shows that processes like <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>K</u:mi> <u:mo stretchy="false">→</u:mo> <u:mi>π</u:mi> <u:mi>X</u:mi> </u:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>μ</x:mi> <x:mo stretchy="false">→</x:mo> <x:mi>e</x:mi> <x:mi>X</x:mi> </x:math> place the most stringent constraints, probing the flavor symmetry breaking scale <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>v</ab:mi> <ab:mi>ϕ</ab:mi> </ab:msub> </ab:math> up to <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mrow> <cb:msup> <cb:mrow> <cb:mn>10</cb:mn> </cb:mrow> <cb:mrow> <cb:mn>11</cb:mn> </cb:mrow> </cb:msup> <cb:mi>–</cb:mi> <cb:msup> <cb:mrow> <cb:mn>10</cb:mn> </cb:mrow> <cb:mrow> <cb:mn>12</cb:mn> </cb:mrow> </cb:msup> <cb:mtext> </cb:mtext> <cb:mtext> </cb:mtext> <cb:mi>GeV</cb:mi> </cb:mrow> </cb:math> for light bosons, while heavier states are tested in <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>B</eb:mi> </eb:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>τ</gb:mi> </gb:math> decays, as well as by <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>K</ib:mi> <ib:mtext>−</ib:mtext> <ib:mover accent="true"> <ib:mi>K</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> </ib:math> mixing and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>μ</mb:mi> <mb:mo stretchy="false">→</mb:mo> <mb:mi>e</mb:mi> <mb:mi>γ</mb:mi> </mb:math> . We demonstrate that low-energy flavor experiments provide a powerful probe of this framework, capable of testing ultrahigh symmetry breaking scales that surpass the limits set by astrophysical observations.