Flavor anomalies in leptoquark model with gauged <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>τ</mml:mi></mml:msub></mml:mrow></mml:msub></mml:math>

Abstract

In addition to anomalies associated with the muon <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>g</a:mi><a:mo>−</a:mo><a:mn>2</a:mn></a:math> and the branching ratio (BR) of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>B</c:mi><c:mo stretchy="false">→</c:mo><c:msup><c:mrow><c:mi>D</c:mi></c:mrow><c:mrow><c:mo stretchy="false">(</c:mo><c:mo>*</c:mo><c:mo stretchy="false">)</c:mo></c:mrow></c:msup><c:mi>τ</c:mi><c:mover accent="true"><c:mrow><c:mi>ν</c:mi></c:mrow><c:mrow><c:mo stretchy="false">¯</c:mo></c:mrow></c:mover></c:mrow></c:math>, Belle II recently observed an unexpectedly large BR in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>B</j:mi><j:mo>+</j:mo></j:msup><j:mo stretchy="false">→</j:mo><j:msup><j:mi>K</j:mi><j:mo>+</j:mo></j:msup><j:mi>ν</j:mi><j:mover accent="true"><j:mi>ν</j:mi><j:mo stretchy="false">¯</j:mo></j:mover></j:math> decay. To resolve the anomalous excesses in these observables, we propose a framework involving a leptoquark, denoted by <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>S</o:mi><o:mn>1</o:mn></o:msub></o:math>, which has the feature that down-type quarks merely couple to neutrinos but not the charged leptons, avoiding the strict constraint from the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>B</q:mi><q:mi>s</q:mi></q:msub><q:mo stretchy="false">→</q:mo><q:msup><q:mi>μ</q:mi><q:mo>−</q:mo></q:msup><q:msup><q:mi>μ</q:mi><q:mo>+</q:mo></q:msup></q:math> decay. With the introduction of the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>U</t:mi><t:mo stretchy="false">(</t:mo><t:mn>1</t:mn><t:msub><t:mo stretchy="false">)</t:mo><t:mrow><t:msub><t:mi>L</t:mi><t:mi>μ</t:mi></t:msub><t:mo>−</t:mo><t:msub><t:mi>L</t:mi><t:mi>τ</t:mi></t:msub></t:mrow></t:msub></t:math> gauge symmetry, the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>Z</x:mi><x:mo>′</x:mo></x:msup></x:math> with light mass not only resolves the muon <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>g</z:mi><z:mo>−</z:mo><z:mn>2</z:mn></z:math> anomaly, but also ensures that <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>S</bb:mi><bb:mn>1</bb:mn></bb:msub></bb:math> couples exclusively to the third-generation leptons so that only <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>τ</db:mi><db:msub><db:mover accent="true"><db:mi>ν</db:mi><db:mo stretchy="false">¯</db:mo></db:mover><db:mi>τ</db:mi></db:msub></db:math> and <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>τ</hb:mi></hb:math>-neutrino modes are involved in the processes <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mi>b</jb:mi><jb:mo stretchy="false">→</jb:mo><jb:mi>c</jb:mi><jb:mo>ℓ</jb:mo><jb:mover accent="true"><jb:mi>ν</jb:mi><jb:mo stretchy="false">¯</jb:mo></jb:mover></jb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>b</ob:mi><ob:mo stretchy="false">→</ob:mo><ob:mi>s</ob:mi><ob:mi>ν</ob:mi><ob:mover accent="true"><ob:mi>ν</ob:mi><ob:mo stretchy="false">¯</ob:mo></ob:mover></ob:math>, respectively. Under the dominant constraints from <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mo stretchy="false">|</tb:mo><tb:mi mathvariant="normal">Δ</tb:mi><tb:mi>F</tb:mi><tb:mo stretchy="false">|</tb:mo><tb:mo>=</tb:mo><tb:mn>2</tb:mn></tb:math> processes, we find that the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msub><yb:mi>S</yb:mi><yb:mn>1</yb:mn></yb:msub></yb:math> contributions to the BRs of <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi>B</ac:mi><ac:mo stretchy="false">→</ac:mo><ac:msup><ac:mi>K</ac:mi><ac:mrow><ac:mo stretchy="false">(</ac:mo><ac:mo>*</ac:mo><ac:mo stretchy="false">)</ac:mo></ac:mrow></ac:msup><ac:mi>ν</ac:mi><ac:mover accent="true"><ac:mi>ν</ac:mi><ac:mo stretchy="false">¯</ac:mo></ac:mover></ac:math> and <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"><hc:msub><hc:mi>K</hc:mi><hc:mi>L</hc:mi></hc:msub><hc:mo stretchy="false">→</hc:mo><hc:msup><hc:mi>π</hc:mi><hc:mn>0</hc:mn></hc:msup><hc:mi>ν</hc:mi><hc:mover accent="true"><hc:mi>ν</hc:mi><hc:mo stretchy="false">¯</hc:mo></hc:mover></hc:math> can be factorized into the same multiplicative factor multiplying the standard model predictions, and the enhancement can be up to a factor of 2. In particular, <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:mi mathvariant="script">B</mc:mi><mc:mo stretchy="false">(</mc:mo><mc:msup><mc:mi>K</mc:mi><mc:mo>+</mc:mo></mc:msup><mc:mo stretchy="false">→</mc:mo><mc:msup><mc:mi>π</mc:mi><mc:mo>+</mc:mo></mc:msup><mc:mi>ν</mc:mi><mc:mover accent="true"><mc:mi>ν</mc:mi><mc:mo stretchy="false">¯</mc:mo></mc:mover><mc:mo stretchy="false">)</mc:mo></mc:math> can reach the upper <uc:math xmlns:uc="http://www.w3.org/1998/Math/MathML" display="inline"><uc:mn>1</uc:mn><uc:mi>σ</uc:mi></uc:math> error of the experimental value, i.e., <wc:math xmlns:wc="http://www.w3.org/1998/Math/MathML" display="inline"><wc:mo>≃</wc:mo><wc:mn>15.4</wc:mn><wc:mo>×</wc:mo><wc:msup><wc:mn>10</wc:mn><wc:mrow><wc:mo>−</wc:mo><wc:mn>11</wc:mn></wc:mrow></wc:msup></wc:math>. We also show that the model can fit the new world averages of <yc:math xmlns:yc="http://www.w3.org/1998/Math/MathML" display="inline"><yc:mi>R</yc:mi><yc:mo stretchy="false">(</yc:mo><yc:msup><yc:mi>D</yc:mi><yc:mrow><yc:mo stretchy="false">(</yc:mo><yc:mo>*</yc:mo><yc:mo stretchy="false">)</yc:mo></yc:mrow></yc:msup><yc:mo stretchy="false">)</yc:mo></yc:math> and contribute significantly to the <ed:math xmlns:ed="http://www.w3.org/1998/Math/MathML" display="inline"><ed:mi>τ</ed:mi></ed:math> polarization in the <gd:math xmlns:gd="http://www.w3.org/1998/Math/MathML" display="inline"><gd:mi>B</gd:mi><gd:mo stretchy="false">→</gd:mo><gd:mi>D</gd:mi><gd:mi>τ</gd:mi><gd:mover accent="true"><gd:mi>ν</gd:mi><gd:mo stretchy="false">¯</gd:mo></gd:mover></gd:math> decay and <ld:math xmlns:ld="http://www.w3.org/1998/Math/MathML" display="inline"><ld:mi mathvariant="script">B</ld:mi><ld:mo stretchy="false">(</ld:mo><ld:msub><ld:mi>B</ld:mi><ld:mi>c</ld:mi></ld:msub><ld:mo stretchy="false">→</ld:mo><ld:mi>τ</ld:mi><ld:mover accent="true"><ld:mi>ν</ld:mi><ld:mo stretchy="false">¯</ld:mo></ld:mover><ld:mo stretchy="false">)</ld:mo></ld:math>. Published by the American Physical Society 2024

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