We investigate the origin of the unusually large electroweak (EW) radiative effects observed in the extraction of the spin-density matrix and related observables at colliders, focusing on leptonic Z-boson decays. We compute the Z-boson decay spin-density matrix at next-to-leading order (NLO) and find that, while its analytic structure remains essentially unchanged with respect to leading order, the EW corrections induce a sizeable $\textit{−}$35% shift in the spin-analysing power parameter $\textit{η}$ . This effect alone accounts for the striking size of the corrections. For boosted Z bosons, we further show that the treatment of photon radiation in lepton-dressing algorithms significantly affects the extraction of spin-density-matrix coefficients at NLO and must be carefully controlled. To address these challenges, we propose a quantum tomography procedure that is applicable to any final state with one or more on-shell Z bosons that is robust under higher-order corrections. We illustrate its validity and limitations in pp → ZZ → 4$\textit{ℓ}$ and in heavy ($\textit{M}$ > 2$\textit{M}$ ) Higgs boson decay H → ZZ → 4$\textit{ℓ}$.

Italy

Morgan Gratta

Federica Fabbri

Switzerland

Michele Grossi

Belgium

Fabio Maltoni

Davide Pagani

Giovanni Pelliccioli

Alessandro Vicini

Z-boson quantum tomography at next-to-leading order

We report on the complete computation of the mixed QCD-electroweak corrections to the neutral-current Drell-Yan process. Our calculation holds in the entire range of dilepton invariant masses. We present phenomenological results for several kinematical distributions in the case of bare muons both in the resonant region and for high invariant masses. We also consider the forward-backward asymmetry, which is a key observable to measure the weak mixing angle. We finally extend our calculation to dressed leptons and compare our results in the massless limit to those available in the literature.

Tommaso Armadillo

Roberto Bonciani

Luca Buonocore

Simone Devoto

Massimiliano Grazzini

Stefan Kallweit

India

Narayan Rana

Mixed QCD-EW corrections to the neutral-current Drell-Yan process

Motivated by the growing interest in accessing the spin structure of multi-boson processes and in measuring quantum entanglement at high energies, we study polarisation and spin-correlation coefficients in di-boson systems. We show that higher-order corrections of QCD and electroweak type, off-shell modeling, and realistic effects such as fiducial selections and neutrino reconstruction are unavoidable to properly determine such coefficients, and consequently to provide a sound interpretation of observables sensitive to quantum entanglement and Bell-inequality violation. Our findings are based on a detailed phenomenological analysis of boson pairs at the LHC, either in inclusive electroweak production or coming from Higgs-boson decays.

CERN

Germany

From angular coefficients to quantum observables: a phenomenological appraisal in di-boson systems

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the W-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the W-boson mass within their radius of convergence in a negligible amount of time.

Two-loop mixed QCD-EW corrections to charged current Drell-Yan

We introduce an observable relevant for the determination of the W-boson mass  $$m_W$$  <math> <msub> <mi>m</mi> <mi>W</mi> </msub> </math>   at hadron colliders. This observable is defined as an asymmetry around the jacobian peak of the charged-lepton transverse-momentum distribution in the charged-current Drell–Yan process. We discuss the observable’s theoretical prediction, presenting results at different orders in QCD, and showing its perturbative stability. Its definition as a single scalar number and its linear sensitivity to  $$m_W$$  <math> <msub> <mi>m</mi> <mi>W</mi> </msub> </math>   allow a clean extraction of the latter and a straightforward discussion of the associated theoretical systematics: a perturbative QCD uncertainty of  $${{{\mathcal {O}}}}(\pm 5)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <mo>±</mo> <mn>5</mn> <mo>)</mo> </mrow> </math>   MeV on  $$m_W$$  <math> <msub> <mi>m</mi> <mi>W</mi> </msub> </math>   can be established by means of this observable, relying solely on charged-current Drell–Yan information. Owing to its relatively inclusive nature, the observable displays desirable properties also from the experimental viewpoint, especially for the unfolding of detector effects. We show that a measurement of this observable can lead to a competitive experimental error on  $$m_W$$  <math> <msub> <mi>m</mi> <mi>W</mi> </msub> </math>   at the LHC.

Luca Rottoli

Paolo Torrielli

Determination of the W-boson mass at hadron colliders

Measurements of neutral current Drell-Yan production at large invariant dilepton masses can be used to test the energy scale dependence (running) of the electroweak mixing angle. In this work, we make use of a novel implementation of the full next-to-leading order electroweak radiative corrections to the Drell-Yan process using the <math><mover><mrow><mrow><mi>MS</mi></mrow></mrow><mo>‾</mo></mover></math> renormalization scheme for the electroweak mixing angle. The potential of future analyses using proton-proton collisions at <math><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13.6</mn><mspace width="0.25em"></mspace><mtext>TeV</mtext></math> in the Run 3 and High-Luminosity phases of the LHC is explored. In this way, the Standard Model predictions for the <math><mover><mrow><mrow><mi>MS</mi></mrow></mrow><mo>‾</mo></mover></math> running at TeV scales can be probed.

Simone Amoroso

Mauro Chiesa

Clara Lavinia Del Pio

Katerina Lipka

Fulvio Piccinini

Federico Vazzoler

Probing the weak mixing angle at high energies at the LHC and HL-LHC

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, as supplementary material, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.

Two-loop mixed QCD-EW corrections to neutral current Drell-Yan

The analytical expressions of the mixed QCD-EW corrections to on-shell Z boson inclusive production cross section at hadron colliders are presented, together with computational details. The results are given in terms of polylogarithmic functions and elliptic integrals. The impact on the prediction of the Z boson production total cross section is discussed, comparing different proton parton density sets.

United Kingdom

Federico Buccioni

On-shell Z boson production at hadron colliders through 𝒪(αα  s )

We report on the first complete computation of the mixed QCD-electroweak (EW) corrections to the neutral-current Drell-Yan process. Superseding previously applied approximations, our calculation provides the first result at this order that is valid in the entire range of dilepton invariant masses. The two-loop virtual contribution is computed by using semianalytical techniques, overcoming the technical problems in the evaluation of the relevant master integrals. The cancellation of soft and collinear singularities is achieved by a formulation of the <math><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></math> subtraction formalism valid in the presence of charged massive particles in the final state. We present numerical results for the fiducial cross section and selected kinematical distributions. At large values of the lepton <math><msub><mi>p</mi><mi>T</mi></msub></math> the mixed QCD-EW corrections are negative and increase in size, to about <math><mo>−</mo><mn>15</mn><mo>%</mo></math> with respect to the next-to-leading-order QCD result at <math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>=</mo><mn>500</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Up to dilepton invariant masses of 1 TeV the computed corrections amount to about <math><mo>−</mo><mn>1.5</mn><mo>%</mo></math> with respect to the next-to-leading-order QCD result.

Francesco Tramontano

Mixed Strong-Electroweak Corrections to the Drell-Yan Process

We discuss the determination of electroweak parameters from hadron collider observables, focusing on the <math><mi>W</mi></math>-boson mass measurement. We revise the procedures adopted in the literature to include in the experimental analysis the uncertainty due to our imperfect knowledge of the proton structure. We show how the treatment of the proton parton density functions’ (PDFs’) uncertainty as a source of systematic error leads to the automatic inclusion in the fit of the bin-bin correlation of the kinematic distributions with respect to PDF variations. In the case of the determination of <math><msub><mi>M</mi><mi>W</mi></msub></math> from the charged lepton transverse momentum distribution, we observe that the inclusion of this correlation factor yields a strong reduction of the PDF uncertainty, given a sufficiently good control over all the other error sources. This improvement depends on a systematic accounting of the features of the QCD-based PDF model, and it is achieved by relying only on the information available in current PDF sets. While a realistic quantitative estimate requires taking into account the details of the experimental systematics, we argue that, in perspective, the proton PDF uncertainty will not be a bottleneck for precision measurements.

Emanuele Bagnaschi

Parton Density Uncertainties and the Determination of Electroweak Parameters at Hadron Colliders