A precise evaluation of the electroweak contribution to the anomalous magnetic moment of the muon requires control over all aspects of the standard model, ranging from Higgs physics, over multiloop computations for bosonic and (heavy-)fermion diagrams, to nonperturbative effects in the presence of light quarks. Currently, the dominant uncertainties arise from such hadronic effects in the vector–vector–axial-vector three-point function, an improved understanding of which has recently emerged in the context of hadronic light-by-light scattering. Profiting from these developments as well as new perturbative and nonperturbative input for the charm contribution, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>EW</mi></mrow></msubsup><mo>=</mo><mn>154.4</mn><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>.

Switzerland

Martin Hoferichter

Austria

Jan Lüdtke

Luca Naterop

Massimiliano Procura

Peter Stoffer

Improved Evaluation of the Electroweak Contribution to Muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>

In Refs. <cross-refs refid='br0010 br0020' id='crs0080'>[1,2]</cross-refs> we provided a complete dispersive evaluation of the hadronic light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon. While the evaluation strategy was developed for the kinematic situation determined by the muon mass, a similar approach also applies to the HLbL corrections to the anomalous magnetic moments of the electron and <italic>&#964;</italic> lepton, shifting the sensitivity in the loop integrals to smaller and larger momenta, respectively. In this Letter, we propagate the corresponding uncertainties of the various contributions, obtaining <math altimg='si1.svg'><msubsup><mrow><mi>a</mi></mrow><mrow><mi>e</mi></mrow><mrow><mtext>HLbL</mtext></mrow></msubsup><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>3.51</mn><mo stretchy='false'>(</mo><mn>23</mn><mo stretchy='false'>)</mo><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>14</mn></mrow></msup></math> and <math altimg='si2.svg'><msubsup><mrow><mi>a</mi></mrow><mrow><mi>&#964;</mi></mrow><mrow><mtext>HLbL</mtext></mrow></msubsup><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>3.77</mn><mo stretchy='false'>(</mo><mn>29</mn><mo stretchy='false'>)</mo><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>8</mn></mrow></msup></math>.

Maximilian Zillinger

Hadronic light-by-light scattering in the anomalous magnetic moments of electron and <italic>&#964;</italic>

We present analytical expressions for the transverse momentum dependent (unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, the analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and nonsinglet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from the combined fit to precision data on the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. Comparison with the numerical results obtained by other groups is presented, and the phenomenological application to the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-jet production at the LHC is given.

JINR

A.V. Kotikov

Russia

A.V. Lipatov

Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach

Next to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math> pole, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> intermediate states give rise to the leading singularities of the hadronic light-by-light tensor, resulting in sizable contributions to the anomalous magnetic moment of the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>. The strength of the poles is determined by the respective transition form factors (TFFs) to two (virtual) photons. We present a calculation of these TFFs that implements a number of low- and high-energy constraints, including the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><mi>γ</mi><mi>γ</mi></math> decay widths, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mi>γ</mi></mrow></math> spectra, chiral symmetry for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo stretchy="false">(</mo><mo>′</mo><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><mn>2</mn><mo stretchy="false">(</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> amplitudes, vector-meson couplings, and asymptotic limits. Crucially, we investigate the role of the leading left-hand singularity generated by the exchange of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>2</mn></msub></math> tensor meson, yielding, for the first time, an estimate of the associated factorization-breaking corrections. Our final results, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>η</mi><mtext> </mtext><mrow><mi>pole</mi></mrow></mrow></msubsup><mo>=</mo><mn>14.7</mn><mo stretchy="false">(</mo><mn>9</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup><mtext> </mtext><mrow><mi>pole</mi></mrow></mrow></msubsup><mo>=</mo><mn>13.5</mn><mo stretchy="false">(</mo><mn>7</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>, conclude a dedicated effort to evaluate the pseudoscalar-pole contributions to hadronic light-by-light scattering using dispersion relations, amounting to a combined <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mtext>PS poles</mtext></mrow></msubsup><mo>=</mo><msubsup><mrow><mn>91.2</mn></mrow><mrow><mo>−</mo><mn>2.4</mn></mrow><mrow><mo>+</mo><mn>2.9</mn></mrow></msubsup><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>.

Simon Holz

Germany

Bai-Long Hoid

Bastian Kubis

Precision Evaluation of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math>- and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math>-Pole Contributions to Hadronic Light-by-Light Scattering in the Anomalous Magnetic Moment of the Muon

The pseudoscalar-pole contributions to hadronic light-by-light scattering are determined by the respective transition form factors (TFFs) into two virtual photons. These TFFs constitute complicated functions of the photon virtualities that, in turn, can be reconstructed in a dispersive approach from their discontinuities. In this work, we present such an analysis for the $\textit{η}$ TFFs, implementing a number of constraints from both experiment and theory: normalizations from the $\textit{η}$ → $\textit{γγ}$ decay widths, unitarity constraints from the $\textit{η}$ → $\textit{π}$ $\textit{π}$ $\textit{γ}$ spectra, chiral symmetry for the $\textit{η}$ → 2($\textit{π}$ $\textit{π}$ ) amplitudes, vector-meson couplings, singly-virtual data from $\textit{e}$ $\textit{e}$ → $\textit{e}$ $\textit{e}$ $\textit{η}$ , and the asymptotic behavior predicted by the light-cone expansion. In particular, we account for the leading left-hand-cut singularity by including effects from the $\textit{a}$ resonance, necessitating the solution of an inhomogeneous Muskhelishvili-Omnès problem via a carefully chosen path deformation. The resulting TFFs allow us to evaluate the $\textit{η}$ -pole contributions to the anomalous magnetic moment of the muon, $$ {a}_{\mu}^{\upeta -\textrm{pole}} $$ = 14$\textit{.}$7(9)×10 and $$ {a}_{\mu}^{\upeta^{\prime }-\textrm{pole}} $$ = 13$\textit{.}$5(7)×10 , completing a dedicated program for the lowest-lying pseudoscalar intermediate states in a dispersive approach to hadronic light-by-light scattering, $$ {a}_{\mu}^{\textrm{PS}-\textrm{poles}} $$ = $$ {91.2}_{-2.4}^{+2.9} $$ × 10 .

Dispersion relation for hadronic light-by-light scattering: $\textit{η}$ and $\textit{η}$

A correction to this paper has been published: https://doi.org/10.1007/JHEP08(2022)295

Gilberto Colangelo

Joachim Monnard

Spain

Jacobo Elvira

Erratum to: Radiative corrections to the forward-backward asymmetry in

Romania

Victor E. Ambrus

France

Maxim N. Chernodub

Corrigendum to “Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism” [Physics Letters B 855 (2024) 138757/PLB 138795]

In this work, we present an evaluation of subleading effects in the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Using a recently derived optimized basis, we first study the matching of axial-vector contributions to short-distance constraints at the level of the scalar basis functions, finding that also the tails of the pseudoscalar poles and tensor mesons play a role. We then develop a matching strategy that allows for a combined evaluation of axial-vector and short-distance constraints, supplemented by an estimate of tensor-meson contributions based on simplified assumptions for their transition form factors. Uncertainties are primarily propagated from the axial-vector transition form factors and the variation of the matching scale, but we also consider estimates of the low-energy effect of hadronic states not explicitly included. In total, we obtain $$ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{subleading}} $$ = 33 2(7 2) × 10 , which in combination with previously evaluated contributions in the dispersive approach leads to $$ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{total}} $$ = 101 9(7 9) × 10

Dispersion relation for hadronic light-by-light scattering: subleading contributions

Hadronic light-by-light (HLbL) scattering defines one of the critical contributions in the Standard Model prediction of the anomalous magnetic moment of the muon. In this Letter, we present a complete evaluation using a dispersive formalism, in which the HLbL tensor is reconstructed from its discontinuities, expressed in terms of simpler hadronic matrix elements that can be extracted from experiment. Profiting from recent developments in the determination of axial-vector transition form factors, short-distance constraints for the HLbL tensor, and the vector–vector–axial-vector correlator, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mi>HLbL</mi></msubsup><mo>=</mo><mn>101.9</mn><mo stretchy="false">(</mo><mn>7.9</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup></math>, which meets the precision requirements set by the final result of the Fermilab experiment.

Complete Dispersive Evaluation of the Hadronic Light-by-Light Contribution to Muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>

The accuracy of <math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>u</mi><mi>d</mi></mrow></msub></mrow></math> determinations from superallowed <math><mi>β</mi></math> decays critically hinges on control over radiative corrections. Recently, substantial progress has been made on the single-nucleon, universal corrections, while nucleus-dependent effects, typically parametrized by a quantity <math><msub><mi>δ</mi><mi>NS</mi></msub></math>, are much less well constrained. Here, we lay out a program to evaluate this correction from effective field theory (EFT), highlighting the dominant terms as predicted by the EFT power counting. Moreover, we compare the results to a dispersive representation of <math><msub><mi>δ</mi><mi>NS</mi></msub></math> and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way toward ab initio calculations of <math><msub><mi>δ</mi><mi>NS</mi></msub></math> and thereby addresses the dominant uncertainty in <math><msub><mi>V</mi><mrow><mi>u</mi><mi>d</mi></mrow></msub></math>.

United States

Vincenzo Cirigliano

Wouter Dekens

Netherlands

Jordy de Vries

Stefano Gandolfi

Emanuele Mereghetti

Radiative Corrections to Superallowed <math><mi>β</mi></math> Decays in Effective Field Theory