Discriminating tauphilic leptoquark explanations of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>B</mml:mi> </mml:math> anomalies via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">

Leptoquark models are prime candidates for new physics (NP) explanations of the longstanding anomalies in semileptonic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>B</a:mi> </a:math> decays; <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>b</c:mi> <c:mo stretchy="false">→</c:mo> <c:mi>c</c:mi> <c:mi>τ</c:mi> <c:mover accent="true"> <c:mi>ν</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> </c:math> [encoded in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>R</h:mi> <h:mo stretchy="false">(</h:mo> <h:msup> <h:mi>D</h:mi> <h:mrow> <h:mo stretchy="false">(</h:mo> <h:mo>*</h:mo> <h:mo stretchy="false">)</h:mo> </h:mrow> </h:msup> <h:mo stretchy="false">)</h:mo> </h:math> ] and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>b</n:mi> <n:mo stretchy="false">→</n:mo> <n:mi>s</n:mi> <n:mo>ℓ</n:mo> <n:mover accent="true"> <n:mo>ℓ</n:mo> <n:mo stretchy="true">¯</n:mo> </n:mover> <n:mo stretchy="false">(</n:mo> <n:mo>ℓ</n:mo> <n:mo>=</n:mo> <n:mi>e</n:mi> <n:mo>,</n:mo> <n:mi>μ</n:mi> <n:mo stretchy="false">)</n:mo> </n:math> transitions. Furthermore, Belle II and NA62 reported weaker-than-expected limits on <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>B</u:mi> <u:mo>+</u:mo> </u:msup> <u:mo stretchy="false">→</u:mo> <u:msup> <u:mi>K</u:mi> <u:mo>+</u:mo> </u:msup> <u:mi>ν</u:mi> <u:mover accent="true"> <u:mi>ν</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> </u:math> and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msup> <z:mi>K</z:mi> <z:mo>+</z:mo> </z:msup> <z:mo stretchy="false">→</z:mo> <z:msup> <z:mi>π</z:mi> <z:mo>+</z:mo> </z:msup> <z:mi>ν</z:mi> <z:mover accent="true"> <z:mi>ν</z:mi> <z:mo stretchy="false">¯</z:mo> </z:mover> </z:math> , respectively. While the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>R</eb:mi> <eb:mo stretchy="false">(</eb:mo> <eb:msup> <eb:mi>D</eb:mi> <eb:mrow> <eb:mo stretchy="false">(</eb:mo> <eb:mo>*</eb:mo> <eb:mo stretchy="false">)</eb:mo> </eb:mrow> </eb:msup> <eb:mo stretchy="false">)</eb:mo> </eb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>b</kb:mi> <kb:mo stretchy="false">→</kb:mo> <kb:mi>s</kb:mi> <kb:mo>ℓ</kb:mo> <kb:mover accent="true"> <kb:mo>ℓ</kb:mo> <kb:mo stretchy="true">¯</kb:mo> </kb:mover> </kb:math> measurements can be explained with NP contributions at the <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:mi mathvariant="script">O</pb:mi> <pb:mo stretchy="false">(</pb:mo> <pb:mn>10</pb:mn> <pb:mo>%</pb:mo> <pb:mo stretchy="false">)</pb:mo> </pb:math> level, the neutrino channels suggest that the NP effect could be comparable in size to the Standard Model one. In this context, we consider the two types of leptoquark models with minimal sets of the couplings that can best describe the semileptonic <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mi>B</ub:mi> </ub:math> anomalies and lead at the same time to effects in the neutrino modes, the singlet-triplet scalar leptoquark model ( <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"> <wb:msub> <wb:mi>S</wb:mi> <wb:mn>1</wb:mn> </wb:msub> <wb:mo>+</wb:mo> <wb:msub> <wb:mi>S</wb:mi> <wb:mn>3</wb:mn> </wb:msub> </wb:math> ) and the singlet vector leptoquark model ( <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:msub> <yb:mi>U</yb:mi> <yb:mn>1</yb:mn> </yb:msub> </yb:math> ). More specifically, the neutrino channels pose nontrivial constraints on the parameter space, and we find that large effects (i.e., accounting for the current central value) in <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> are only possible in the <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"> <hc:msub> <hc:mi>S</hc:mi> <hc:mn>1</hc:mn> </hc:msub> <hc:mo>+</hc:mo> <hc:msub> <hc:mi>S</hc:mi> <hc:mn>3</hc:mn> </hc:msub> </hc:math> setup, while both models can account for the central value of <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"> <jc:msup> <jc:mi>K</jc:mi> <jc:mo>+</jc:mo> </jc:msup> <jc:mo stretchy="false">→</jc:mo> <jc:msup> <jc:mi>π</jc:mi> <jc:mo>+</jc:mo> </jc:msup> <jc:mi>ν</jc:mi> <jc:mover accent="true"> <jc:mi>ν</jc:mi> <jc:mo stretchy="false">¯</jc:mo> </jc:mover> </jc:math> .