Electroweak Radiative Corrections with an Effective Lagrangian: Four-Fermion Processes
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We determine the four Fermi effective theory of neutrino interactions within the Standard Model including one-loop electroweak radiative corrections, in combination with the measured muon lifetime and precision electroweak data. Including two-loop matching and three-loop running corrections, we determine lepton coefficients accounting for all large logarithms through relative order $\cal{O}(\alpha \alpha_s)$ and quark coefficients accounting for all large logarithms through ${\cal{O}}(\alpha)$. We present four-fermion coefficients valid in $n_f=3$ and $n_f=4$ flavor quark theories, as well as in the extreme low-energy limit. We relate the coefficients in this limit to neutrino charge radii governing matter effects via forward neutrino scattering on charged particles.
The current status of electroweak radiative corrections to the muon anomalous magnetic moment is discussed. Asymptotic expansions for some important electroweak two-loop top quark triangle diagrams are illustrated and extended to higher order. Results are compared with the more general integral representation solution for generic fermion triangle loops coupled to pseudoscalar and scalar bosons of arbitrary mass. Furthermore, excellent agreement is found for a broader than expected range of mass parameters.
We introduce a useful framework for high-precision studies of the neutron beta decay by merging the current algebra description and the fixed-order effective field theory calculation of the electroweak radiative corrections to the neutron axial form factor. We discuss the advantages of this hybrid method and show that it only requires a minimal amount of lattice QCD inputs to achieve a 10 –4 theory accuracy for the Standard Model prediction of the neutron lifetime and the axial-to-vector coupling ratio λ, both important to the search for physics beyond the Standard Model.
We present the analysis and comparison of predictions of the main codes for electroweak radiative corrections for the Drell-Yan process in the high lepton pair invariant mass region.
We review the status of the Standard Model theory of neutron beta decay. Particular emphasis is put on the recent developments in the electroweak radiative corrections. Given that some existing approaches give slightly different results, we thoroughly review the origin of discrepancies, and provide our recommended value for the radiative correction to the neutron and nuclear decay rates. The use of dispersion relation, lattice Quantum Chromodynamics, and an effective field theory framework allows for high-precision theory calculations at the level of 10 –4 , turning neutron beta decay into a powerful tool to search for new physics, complementary to high-energy collider experiments. We offer an outlook to the future improvements.
Now that the Higgs boson has been discovered, the question is: why is it so light when its mass is expected to blow up to the highest mass scale of the particles to which it couples? Supersymmetry tames these quadratic divergences, yet there is as yet no sign of superparticles at LHC. Sparticle mass limits and the Higgs mass suggest sparticles which reside in the multi-TeV range if at all. This situation heightens the Little Hierarchy or SUSY naturalness question: why the mass gap between weak scale and sparticle mass scale? In the past several years, our group has been highly focused on understanding the naturalness question (H. Baer). During this period, we have made some major clarifications in naturalness, showing how conventional measures overestimate fine-tuning and showing that ``natural SUSY'' requires light higgsino states-- with mass the closer to the 100 GeV scale the better. Such an inverted electroweakino spectrum leads to new, distinctive signatures at LHC (e.g. same-sign diboson production) while the ILC is expected to be a higgsino factory. We have found a deep connection between naturalness and the Peccei-Quinn scale. Dark matter is expected to occur as a higgsino-like WIMP plus axion admixture and detection of both is ultimately expected. Additional objectives of our research program are making more precise predictions for the production and decay rates of new particles, developing techniques and computer codes to discover these particles and to measure their properties, and searching for new phenomena and new interactions at present and future colliders. In addition, we will investigate direct and indirect searches for supersymmetric dark matter: both WIMPs and axions. % To carry out these studies, we will calculate production rates for SUSY particles, other new particles in various extensions to the Standard Model and physics backgrounds, as well as evaluate QCD and electroweak radiative corrections. Since the cross sections of most signals are expected to be small relative to those of the backgrounds, we plan on developing analysis techniques suitable for extracting small signals. In this project, we propose continuing along these productive investigation lines so as to facilitate discoveries which can be made at LHC, ILC and at various dark matter detectors. These projects facilitate the DoE goals at the Energy and Cosmic Frontiers.
Radiative corrections are essential for an accurate determination of V ud from superallowed β decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for V ud . In this work, we provide a detailed account of the electroweak corrections to superallowed β decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. Here, we present a first numerical evaluation of the dominant corrections in light nuclei based on quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parametrize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in V ud , as illustrated in detail for the 14 O → 14 N transition.
We study the Abelian Higgs model with multiple scalar fields, but without mass terms. Solving the model nonperturbatively order-by-order in the number of scalar fields, we find that radiative corrections generate masses for the scalar and gauge boson, without spontaneous symmetry breaking. The mass scales are set by the Λ -parameter of the electroweak running coupling, thereby naturally avoiding the hierarchy problem. No part of our calculation employs a weak-coupling expansion, and we find that the perturbative vacuum is metastable, and hence must decay to the stable nonperturbative vacuum of the theory, which we identify. Although the field content of our Lagrangian is standard, our results predict the existence of two heavy scalar resonances in addition to the Higgs. We believe that these predicted resonances will ultimately allow experimentalists to discriminate between our method and standard solutions of the Higgs model. Published by the American Physical Society 2024
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We propose a novel dispersive treatment of the so-called inner radiative correction to the neutron and nuclear β decay. We show that it requires knowledge of the parity-violating structure function $F$$^{(0)}_{3}$ that arises from the interference of the axial vector charged current and the isoscalar part of the electromagnetic current. By isospin symmetry, we relate this structure function to the charged current inelastic scattering of neutrinos and antineutrinos. Applying this new data-driven analysis we obtain a new, more precise evaluation for the universal radiative correction $Δ$$^{V,new}_{R}$ = 0.02467(22) that supersedes the previous estimate by Marciano and Sirlin, $Δ$$^{V}_{R}$ = 0.02361(38). The substantial shift in the central value of $Δ$$^{V}_{R}$ reflects in a respective shift of Vud and a considerable tension in the unitarity constraint on the first row of the Cabibbo-Kobayashi-Maskawa matrix which is used as one of the most stringent constraints on new physics contributions in the charged current sector. We also point out that dispersion relations offer a unifying tool for treating hadronic and nuclear corrections within the same framework. We explore the potential of the dispersion relations for addressing the nuclear structure corrections absorbed in the Ft values, a crucial ingredient alongside $Δ$$^{V}_{R}$ in extracting Vud from superallowed nuclear decays. In particular, we estimate the quenching of the free neutron Born contribution in the nuclear environment, corresponding to a quasielastic single-nucleon knockout, and find a significantly stronger quenching effect as compared to currently used estimates based on the quenching of spin operators in nuclear transitions. Furthermore, this observation suggests that the currently used theoretical uncertainties of Ft values might be underestimated and require a renewed scrutiny, while emphasizing the importance of new, more precise measurements of the free neutron decay where nuclear corrections are absent.
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In this work, we compute the electromagnetic corrections to neutron β decay using a low-energy hadronic effective field theory. We identify new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the β-ν angular correlations and the β asymmetry. We comment on implications of our results for the comparison of the experimentally measured nucleon axial charge with first-principles computations using lattice QCD and on the potential of β decay experiments to constrain beyond-the-standard-model interactions.
Details of the two-loop analysis of long-distance QED radiative corrections to neutron beta decay are presented. Explicit expressions are given for hard, jet, and soft functions appearing in the factorization formula that describes the limit of small electron mass and large electron energy. Numerical enhancements from the infrared region are resummed using renormalization group methods. Power corrections, cancellation of singularities in the small-mass expansion, renormalization scheme dependence, and bound-state effects are also discussed. These results provide the most precise determination of long-distance radiative corrections to neutron beta decay and impact the determination of |𝑉 𝑢𝑑 | from the measured neutron lifetime and thus set a target for uncertainty reductions in the experimental and short-distance inputs.
Interactions of charged leptons with nuclei and the naive tree-level kinematics of these processes are affected by radiation of photons induced by the QED nuclear medium. We evaluate cross section modifications at leading orders of the number of correlated interactions inside the nucleus, known as the opacity expansion. We derive results for soft and collinear types of the bremsstrahlung at the first three orders in opacity and generalize them to higher orders. We present the leading in opacity energy spectra of soft and collinear photons and radiative energy loss inside the nucleus for experiments with lepton kinematics in the GeV energy range. At leading power of the Glauber soft-collinear effective field theory, the soft radiation is further resummed to all orders both in opacity and in the electromagnetic coupling constant. We find that the soft and collinear medium-induced radiation is vacuumlike, and additional corrections are power suppressed. Despite the negligible modification to the induced photon spectra, the nuclear medium-induced radiation sizably affects the broadening of charged leptons in the direction orthogonal to their propagation. Published by the American Physical Society 2024
The accuracy of V u d determinations from superallowed β 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 δ NS , 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 δ NS and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way toward calculations of δ NS and thereby addresses the dominant uncertainty in V u d . Published by the American Physical Society 2024