Drell-Yan production in universal theories beyond dimension-six SMEFT

We study Drell-Yan production in universal theories consistently including effects beyond dimension six in the Standard Model effective field theory (SMEFT). Within universal SMEFT and with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>P</c:mi></c:math> conservation we find that 11 dimension-eight operators contribute in addition to the six contributing at dimension six. We first work in an operator basis in which operators with higher derivatives of the bosonic fields have been rotated by equations of motion in favor of combinations of operators involving SM fermion currents. We derive the general form of the amplitudes consistently in the expansion to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="script">O</e:mi><e:mo stretchy="false">(</e:mo><e:msup><e:mi mathvariant="normal">Λ</e:mi><e:mrow><e:mo>−</e:mo><e:mn>4</e:mn></e:mrow></e:msup><e:mo stretchy="false">)</e:mo></e:math> and identify eight combinations of the 17 Wilson coefficients which are physically distinguishable by studying the invariant mass distribution of the lepton pairs produced. We then introduce an extension of the parametrization of universal effects in terms of oblique parameters obtained by linearly expanding the self-energies of the electroweak gauge bosons to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">O</k:mi><k:mo stretchy="false">(</k:mo><k:msup><k:mi>q</k:mi><k:mn>6</k:mn></k:msup><k:mo stretchy="false">)</k:mo></k:math>. It contains 11 oblique parameters of which only eight are generated within SMEFT at dimension eight: <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mover accent="true"><p:mi>S</p:mi><p:mo stretchy="false">^</p:mo></p:mover></p:math>, <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mover accent="true"><t:mi>T</t:mi><t:mo stretchy="false">^</t:mo></t:mover></t:math>, <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>W</x:mi></x:math>, <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>Y</z:mi></z:math>, <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mover accent="true"><bb:mi>U</bb:mi><bb:mo stretchy="false">^</bb:mo></bb:mover></bb:math>, <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>X</fb:mi></fb:math>, plus two additional which we label <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msup><hb:mi>W</hb:mi><hb:mo>′</hb:mo></hb:msup></hb:math> and <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msup><jb:mi>Y</jb:mi><jb:mo>′</jb:mo></jb:msup></jb:math> and show how they match at linear order with the eight identified combinations of operator coefficients. We then perform a combined analysis of a variety of LHC data on the neutral- and charged-current Drell-Yan processes with the aim of constraining the eight combinations. We compare and combine the LHC bounds with those from electroweak precision <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mi>W</lb:mi></lb:math> and <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>Z</nb:mi></nb:math> pole observables which can only provide constraints in four directions of the eight-parameter space. We present the results in terms of limits on the eight effective Wilson coefficients as well as on the eight oblique parameters. In each case, we study the dependence of the derived constraints on the order of the expansion considered.