SMEFT predictions for semileptonic processes

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>L</a:mi></a:msub><a:mo>×</a:mo><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mi>Y</a:mi></a:msub></a:math> invariance of the Standard Model effective field theory (SMEFT) predicts multiple restrictions in the space of Wilson coefficients of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:msub><g:mo stretchy="false">)</g:mo><g:mrow><g:mi>e</g:mi><g:mi>m</g:mi></g:mrow></g:msub></g:math> invariant effective Lagrangians such as the low-energy effective field theory (LEFT), used for low-energy flavor physics observables, or the Higgs effective field theory (HEFT) in unitary gauge, appropriate for weak-scale observables. In this work, we derive and list all such predictions for semileptonic operators up to dimension 6. These predictions can be expressed as linear relations among the HEFT/LEFT Wilson coefficients (WCs), that are completely independent of any assumptions about the alignment of the mass and flavor bases. We find seven sets of relations among the WCs of vector operators, nine sets with scalar and tensor operators, and two sets with the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>Z</k:mi><k:mo>,</k:mo><k:msup><k:mi>W</k:mi><k:mo>±</k:mo></k:msup></k:math> couplings. These correspond to 2223 linear relations among the complex WCs when the quark and lepton generation indices are included. They connect diverse experimental searches such as rare meson decays, high-<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>p</m:mi><m:mi>T</m:mi></m:msub></m:math> dilepton searches, top decays, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>Z</o:mi></o:math>-pole observables, charged lepton flavor violating observables, and nonstandard neutrino interaction searches. We demonstrate how these relations can be used to derive strong indirect constraints on multiple WCs that are currently either weakly constrained from direct experiments or have no direct bound at all. They also imply, in general, that evidence for new physics in a particular search channel must be accompanied by correlated anomalies in other channels. For example, the observed excess in <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>B</q:mi><q:mo stretchy="false">→</q:mo><q:mi>K</q:mi><q:mi>ν</q:mi><q:mover accent="true"><q:mi>ν</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:math> would imply possible anomalies in <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>B</v:mi><v:mo stretchy="false">→</v:mo><v:msup><v:mi>D</v:mi><v:mrow><v:mo stretchy="false">(</v:mo><v:mo>*</v:mo><v:mo stretchy="false">)</v:mo></v:mrow></v:msup><v:mo>ℓ</v:mo><v:msub><v:mi>ν</v:mi><v:mo>ℓ</v:mo></v:msub></v:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>B</ab:mi><ab:mo stretchy="false">→</ab:mo><ab:msup><ab:mi>K</ab:mi><ab:mrow><ab:mo stretchy="false">(</ab:mo><ab:mo>*</ab:mo><ab:mo stretchy="false">)</ab:mo></ab:mrow></ab:msup><ab:msup><ab:mo>ℓ</ab:mo><ab:mo>+</ab:mo></ab:msup><ab:msup><ab:mo>ℓ</ab:mo><ab:mo>−</ab:mo></ab:msup></ab:math>, <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msub><fb:mi>B</fb:mi><fb:mi>q</fb:mi></fb:msub><fb:mo stretchy="false">→</fb:mo><fb:mi>τ</fb:mi><fb:msub><fb:mi>ν</fb:mi><fb:mi>τ</fb:mi></fb:msub></fb:math>, <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>B</ib:mi><ib:mi>s</ib:mi></ib:msub><ib:mo stretchy="false">→</ib:mo><ib:msup><ib:mi>τ</ib:mi><ib:mo>+</ib:mo></ib:msup><ib:msup><ib:mi>τ</ib:mi><ib:mo>−</ib:mo></ib:msup></ib:math>, <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msub><lb:mi>D</lb:mi><lb:mi>s</lb:mi></lb:msub><lb:mo stretchy="false">→</lb:mo><lb:msup><lb:mi>τ</lb:mi><lb:mo>+</lb:mo></lb:msup><lb:msub><lb:mi>ν</lb:mi><lb:mi>τ</lb:mi></lb:msub></lb:math>, <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>t</ob:mi><ob:mo stretchy="false">→</ob:mo><ob:mi>c</ob:mi><ob:msup><ob:mo>ℓ</ob:mo><ob:mo>+</ob:mo></ob:msup><ob:msup><ob:mo>ℓ</ob:mo><ob:mo>−</ob:mo></ob:msup></ob:math>, <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>t</rb:mi><rb:mo stretchy="false">→</rb:mo><rb:mi>u</rb:mi><rb:msup><rb:mo>ℓ</rb:mo><rb:mo>+</rb:mo></rb:msup><rb:msup><rb:mo>ℓ</rb:mo><rb:mo>−</rb:mo></rb:msup></rb:math>, etc., correlated according to the relations obtained in this paper.