Explore the vast range of titles available.

Casher and Susskind [Casher A, Susskind L (1974) Phys Rev 9:436–460] have noted that in the light-front description, spontaneous chiral symmetry breaking is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon condensates in quantum chromodynamics (QCD) are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the Anti de Sitter/conformal field theory correspondence, and the Bethe—Salpeter—Dyson—Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of \"in-hadron\" condensates by Roberts and coworkers [Maris P, Roberts CD, Tandy PC (1998) Phys Lett B 420:267–273], using the Bethe—Salpeter—Dyson—Schwinger formalism for QCD-bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, because all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.

C N Yang, one of the greatest physicists of the 20th Century, was awarded the Nobel Prize in 1957, jointly with T D Lee, for their investigation of the relationship (parity symmetry) between left- and right-handed states, leading to a discovery that astounded the world of physics — the nonconservation of parity by elementary particles and their reactions. With R L Mills, he created the concept of non-abelian gauge theories, the foundation of the modern description of elementary particles and forces. Professor Yang has worked on a wide range of subjects in physics, but his abiding interests have been symmetry principles, particle physics, and statistical mechanics.In 1999, a symposium was held at the State University of New York at Stony Brook to mark the retirement of C N Yang as Einstein Professor and Director of the Institute for Theoretical Physics, and to celebrate his many achievements. A noteworthy selection of the papers presented at the symposium appears in this invaluable volume in honor of Professor Yang.

We present a model for dark matter with extra spatial dimensions in which Standard-Model (SM) fermions have localized wave functions. The underlying gauge group is \\(G_ SM U(1)_z\\), and the dark matter particle is a SM-singlet Dirac fermion, \\(\\), which is charged under the \\( U(1)_z\\) gauge symmetry. We show that the conventional wisdom that the mass of a Dirac fermion is naturally at the ultraviolet cutoff scale does not hold in this model. We further demonstrate that this model yields a dark matter relic abundance in agreement with observation and discuss constraints from direct and indirect searches for dark matter. The dark matter particle interacts weakly with matter and has negligibly small self-interactions. Very good fits to data from cosmological observations and experimental dark matter searches are obtained with \\(m_\\) in the multi-TeV range. A discussion is given of observational signatures and experimental tests of the model.

This biennial Review summarizes much of Particle Physics. Using data from previous editions, plus 1600 new measurements from 550 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http: //pdg. lbl. gov.

Using a low-energy effective field theory approach, we study some properties of models with large extra dimensions, in which quarks and leptons have localized wave functions in the extra dimensions. We consider models with two types of gauge groups: (i) the Standard-Model gauge group, and (ii) the left-right symmetric (LRS) gauge group. Our main focus is on the lepton sector of models with \\(n=2\\) extra dimensions, in particular, neutrino masses and mixing. We analyze the requisite conditions that the models must satisfy to be in accord with data and present a solution for lepton wave functions in the extra dimensions that fulfills these conditions. As part of our work, we also present a new solution for quark wave function centers. Issues with flavor-changing neutral current effects are assessed. Finally, we remark on baryogenesis and dark matter in these models.

A detailed discussion is given of the analysis of recent data to obtain improved upper bounds on the couplings \\(|U_{e4}|^2\\) and \\(|U_{\\mu 4}|^2\\) for a mainly sterile neutrino mass eigenstate \\(\\nu_4\\). Using the excellent agreement among \\({\\cal F}t\\) values for superallowed nuclear beta decay, an improved upper limit is derived for emission of a \\(\\nu_4\\). The agreement of the ratios of branching ratios \\(R^{(\\pi)}_{e/\\mu}=BR(\\pi^+ \\to e^+ \\nu_e)/BR(\\pi^+ \\to \\mu^+ \\nu_\\mu)\\), \\(R^{(K)}_{e/\\mu}\\), \\(R^{(D_s)}_{e/\\tau}\\), \\(R^{(D_s)}_{\\mu/\\tau}\\), and \\(R^{(D)}_{e/\\tau}\\), and the branching ratios \\(BR(B^+\\rightarrow e^+\\nu_e)\\) and \\(BR(B^+\\rightarrow \\mu^+\\nu_\\mu)\\) decays with predictions of the Standard Model, is utilized to derive new constraints on \\(\\nu_4\\) emission covering the \\(\\nu_4\\) mass range from MeV to GeV. We also discuss constraints from peak search experiments probing for emission of a \\(\\nu_4\\) via lepton mixing, as well as constraints from pion beta decay, CKM unitarity, \\(\\mu\\) decay, leptonic \\(\\tau\\) decay, and other experimental inputs.

Improved upper bounds are presented on the coupling \\(|U_{e4}|^2\\) of an electron to a sterile neutrino \\(\\nu_4\\) from analyses of data on nuclear and particle decays, including superallowed nuclear beta decays, the ratios \\(R^{(\\pi)}_{e/\\mu}=BR(\\pi^+ \\to e^+ \\nu_e)/BR(\\pi^+ \\to \\mu^+ \\nu_\\mu)\\), \\(R^{(K)}_{e/\\mu}\\), \\(R^{(D_s)}_{e/\\tau}\\), and \\(B^+_{e 2}\\) decay, covering the mass range from MeV to GeV.

We consider an asymptotically free vectorial gauge theory, with gauge group \\(G\\) and \\(N_f\\) fermions in a representation \\(R\\) of \\(G\\), having an infrared (IR) zero in the beta function at \\(\\alpha_{IR}\\). We present general formulas for scheme-independent series expansions of quantities, evaluated at \\(\\alpha_{IR}\\), as powers of an \\(N_f\\)-dependent expansion parameter, \\(\\Delta_f\\). First, we apply these to calculate the derivative \\(d\\beta/d\\alpha\\) evaluated at \\(\\alpha_{IR}\\), denoted \\(\\beta'_{IR}\\), which is equivalent to the anomalous dimension of the \\({\\rm Tr}(F_{\\mu\\nu}F^{\\mu\\nu})\\) operator, to order \\(\\Delta_f^4\\) for general \\(G\\) and \\(R\\), and to order \\(\\Delta_f^5\\) for \\(G={\\rm SU}(3)\\) and fermions in the fundamental representation. Second, we calculate the scheme-independent expansions of the anomalous dimension of the flavor-nonsinglet and flavor-singlet bilinear fermion antisymmetric Dirac tensor operators up to order \\(\\Delta_f^3\\). The results are compared with rigorous upper bounds on anomalous dimensions of operators in conformally invariant theories. Our other results include an analysis of the limit \\(N_c \\to \\infty\\), \\(N_f \\to \\infty\\) with \\(N_f/N_c\\) fixed, calculation and analysis of Padé approximants, and comparison with conventional higher-loop calculations of \\(\\beta'_{IR}\\) and anomalous dimensions as power series in \\(\\alpha\\).

PIONEER is a rapidly developing effort aimed to perform a pristine test of lepton flavour universality (LFU) and of the unitarity of the first row of the CKM matrix by significantly improving the measurements of rare decays of the charged pion. In Phase I, PIONEER aims to measure the charged-pion branching ratio to electrons vs.\\ muons \\(R_{e/\\mu}\\) to 1 part in \\(10^4\\), improving the current experimental result \\(R_{e/\\mu}\\,\\text{(exp)} =1.2327(23)\\times10^{-4}\\) by a factor of 15. This precision on \\(R_{e/\\mu}\\) will match the theoretical accuracy of the SM prediction allowing for a test of LFU at an unprecedented level, probing non-SM explanations of LFU violation through sensitivity to quantum effects of new particles up to the PeV mass scale. Phase II and III will aim to improve the experimental precision of the branching ratio of pion beta decay, \\(\\pi^+\\to \\pi^0 e^+ \\nu (\\gamma)\\), currently at \\(1.036(6)\\times10^{-8}\\), by a factor of three and six, respectively. The improved measurements will be used to extract \\(V_{ud}\\) in a theoretically pristine manner. The ultimate precision of \\(V_{ud}\\) is expected to reach the 0.05\\,\\% level, allowing for a stringent test of CKM unitarity. The PIONEER experiment will also improve the experimental limits by an order of magnitude or more on a host of exotic decays that probe the effects of heavy neutrinos and dark sector physics. This input to the 2026 update of the European Strategy for Particle Physics Strategy describes the physics motivation and the conceptual design of the PIONEER experiment, and is prepared based on the PIONEER proposal submitted to and approved with high priority by the PSI program advisory committee (PAC). Using intense pion beams, and state-of-the-art instrumentation and computational resources, the PIONEER experiment is aiming to begin data taking by the end of this decade.