Study of Lorentz invariance violation in polarized top quark decay

Abstract Different processes have yet studied the effect of Lorentz symmetry violation and different limits have determined for the Lorentz violation (LV) coefficients. Top-quark physics offers a rich variety of options for seeking Lorentz-invariant physics beyond the standard model (SM). In this work, we study the effect of Lorentz-violating terms on the partonic decay rates of polarized top quark. The polar and azimuthal correlations between the planes formed by the vectors $$(\vec {p}_l,\,\vec {p}_{X_b})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>l</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msub> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(\vec {p}_l,\, \vec {P}_t)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mover> <mml:mi>p</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>l</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msub> <mml:mover> <mml:mi>P</mml:mi> <mml:mo>→</mml:mo> </mml:mover> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> in the semileptonic rest frame decay of a polarized top quark belongs to a class of polarization observables involving the top quark so that the azimuthal correlation vanishes at the Born term level in the SM. We will show that the LV effect leads to different results for the partonic decay rates, specifically the azimuthal correlation contribution deviates from the corresponding SM value. These spin-momentum correlations between the top quark spin and its decay product momenta will allow to search for the non-SM effects. We also determine an upper bound on the LV coefficients within the SME framework as $$c_L^{XZ}\le 23.6\times 10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>XZ</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>≤</mml:mo> <mml:mn>23.6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and $$c_L^{XX}\le 2.65\times 10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi>XX</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>≤</mml:mo> <mml:mn>2.65</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> which are compatible with the bounds on LV from the CMS Collaboration, where the LV is introduced as an extension of the SM with an effective field theory predicting the modulation of $$t\bar{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> cross section with sidereal time.