Measuring the low-energy weak mixing angle with supernova neutrinos

Abstract The weak mixing angle $$\theta _W$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>W</mml:mi> </mml:msub> </mml:math> is a fundamental parameter in the electroweak theory with a value running according to the energy scale, and its precision measurement in the low-energy regime is still ongoing. We propose a method to measure the low-energy $$\sin {^2\theta _W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>sin</mml:mo> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>2</mml:mn> </mml:mmultiscripts> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>W</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> by taking advantage of Argo, a future ton-scale liquid argon dark matter detector, and the neutrino flux from a nearby core-collapse supernova (CCSN). We evaluate the expected precision of this measurement through the coherent elastic neutrino-nucleus scattering (CE $$\nu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ν</mml:mi> </mml:math> NS) channel. We show that Argo is potentially capable of achieving a few percent determination of $$\sin {^2\theta _W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>sin</mml:mo> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>2</mml:mn> </mml:mmultiscripts> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>W</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , at the momentum transfer of $$q \sim 20{\,\text {MeV}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>20</mml:mn> <mml:mrow> <mml:mspace/> <mml:mtext>MeV</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> , in the observation of a CCSN within $$\sim 3{\,\text {kpc}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>3</mml:mn> <mml:mrow> <mml:mspace/> <mml:mtext>kpc</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> from the Earth. Such a measurement is valuable for both the precision test of the electroweak theory and searching for new physics beyond the standard model in the neutrino sector.