This is the third out of five chapters of the final report [1] of the Workshop on Physics at HL-LHC, and perspectives on HE-LHC [2]. It is devoted to the study of the potential, in the search for Beyond the Standard Model (BSM) physics, of the High Luminosity (HL) phase of the LHC, defined as $3~\mathrm{ab}^{-1}$ of data taken at a centre-of-mass energy of $14~\mathrm{TeV}$, and of a possible future upgrade, the High Energy (HE) LHC, defined as $15~\mathrm{ab}^{-1}$ of data at a centre-of-mass energy of $27~\mathrm{TeV}$. We consider a large variety of new physics models, both in a simplified model fashion and in a more model-dependent one. A long list of contributions from the theory and experimental (ATLAS, CMS, LHCb) communities have been collected and merged together to give a complete, wide, and consistent view of future prospects for BSM physics at the considered colliders. On top of the usual standard candles, such as supersymmetric simplified models and resonances, considered for the evaluation of future collider potentials, this report contains results on dark matter and dark sectors, long lived particles, leptoquarks, sterile neutrinos, axion-like particles, heavy scalars, vector-like quarks, and more. Particular attention is placed, especially in the study of the HL-LHC prospects, to the detector upgrades, the assessment of the future systematic uncertainties, and new experimental techniques. The general conclusion is that the HL-LHC, on top of allowing to extend the present LHC mass and coupling reach by $20-50\%$ on most new physics scenarios, will also be able to constrain, and potentially discover, new physics that is presently unconstrained. Moreover, compared to the HL-LHC, the reach in most observables will generally more than double at the HE-LHC, which may represent a good candidate future facility for a final test of TeV-scale new physics.

The PADME apparatus was built at the Frascati National Laboratory of INFN to search for a dark photon ($A'$) produced via the process $e^+ e^- \rightarrow A' \gamma$. The central component of the PADME detector is an electromagnetic calorimeter composed of 616 BGO crystals dedicated to the measurement of the energy and position of the final state photons. The high beam particle multiplicity over a short bunch duration requires reliable identification and measurement of overlapping signals. A regression machine-learning-based algorithm has been developed to disentangle with high efficiency close-in-time events and precisely reconstruct the amplitude of the hits and the time with sub-nanosecond resolution. The performance of the algorithm and the sequence of improvements leading to the achieved results are presented and discussed.

The Amaterasu cosmic ray particle appears to have come from the direction of the local cosmic void. We take this as evidence that it is a magnetic monopole rather than a proton or nucleus. This in turn strongly suggests physics at high energy is described by a quiver gauge theory.

In a previous study, the flavor-changing fermion-graviton interactions have been analyzed in the framework of the standard model, where analytical results for the relevant form factors were obtained at the leading order in the external fermion masses. These interactions arise at one-loop level by the charged electroweak corrections to the fermion-graviton vertex, when the off-diagonal flavor transitions in the corresponding charged weak currents are taken into account. Due to the conservation of the energy-momentum tensor, the corresponding form factors turn out to be finite and gauge invariant when external fermions are on-shell. Here we extend this previous analysis by including the exact dependence on the external fermion masses. Complete analytical results are provided for all the relevant form factors to the flavor-changing fermion-graviton transitions.

We investigate the mapping of conformal correlators and of their anomalies from configuration to momentum space for general dimensions, focusing on the anomalous correlators $TOO$, $TVV$ - involving the energy-momentum tensor $(T)$ with a vector $(V)$ or a scalar operator ($O$) - and the 3-graviton vertex $TTT$. We compute the $TOO$, $TVV$ and $TTT$ one-loop vertex functions in dimensional regularization for free field theories involving conformal scalar, fermion and vector fields. Since there are only one or two independent tensor structures solving all the conformal Ward identities for the $TOO$ or $TVV$ vertex functions respectively, and three independent tensor structures for the $TTT$ vertex, and the coefficients of these tensors are known for free fields, it is possible to identify the corresponding tensors in momentum space from the computation of the correlators for free fields. This works in general $d$ dimensions for $TOO$ and $TVV$ correlators, but only in 4 dimensions for $TTT$, since vector fields are conformal only in $d=4$. In this way the general solution of the Ward identities including anomalous ones for these correlators in (Euclidean) position space, found by Osborn and Petkou is mapped to the ordinary diagrammatic one in momentum space. We give simplified expressions of all these correlators in configuration space which are explicitly Fourier integrable and provide a diagrammatic interpretation of all the contact terms arising when two or more of the points coincide. We discuss how the anomalies arise in each approach [...]

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.

The ATLAS Forward Proton (AFP) detector is intended to measure protons scattered at small angles from the ATLAS interaction point. To this end, a combination of 3D Silicon pixel tracking modules and Quartz-Cherenkov time-of-flight (ToF) detectors is installed 210m away from the interaction point at both sides of ATLAS. Beam tests with an AFP prototype detector combining tracking and timing sub-detectors and a common readout have been performed at the CERN-SPS test-beam facility in November 2014 and September 2015 to complete the system integration and to study the detector performance. The successful tracking-timing integration was demonstrated. Good tracker hit efficiencies above 99.9% at a sensor tilt of 14{\deg}, as foreseen for AFP, were observed. Spatial resolutions in the short pixel direction with 50 {\mu}m pitch of 5.5 +/- 0.5 {\mu}m per pixel plane and of 2.8 +/- 0.5 {\mu}m for the full four-plane tracker at 14{\deg} were found, largely surpassing the AFP requirement of 10 {\mu}m. The timing detector showed also good hit efficiencies above 99%, and a full-system time resolution of 35 +/- 6 ps was found for the ToF prototype detector with two Quartz bars in-line (half the final AFP size) without dedicated optimisation, fulfilling the requirements for initial low-luminosity AFP runs.

The Gamow-Teller (GT) matrix element contributing to tritium $\beta$ decay is calculated with trinucleon wave functions obtained from hyperspherical-harmonics solutions of the Schrödinger equation with the chiral two- and three-nucleon interactions including $\Delta$ intermediate states that have recently been constructed in configuration space. Predictions up to N3LO in the chiral expansion of the axial current (with $\Delta$'s) overestimate the empirical value by 1--4 \%. By exploiting the relation between the low-energy constant (LEC) in the contact three-nucleon interaction and two-body axial current, we provide new determinations of the LECs $c_D$ and $c_E$ that characterize this interaction by fitting the trinucleon binding energy and tritium GT matrix element. Some of the implications that the resulting models of three-nucleon interactions have on the spectra of light nuclei and the equation of state of neutron matter are briefly discussed. We also provide a partial analysis, which ignores $\Delta$'s, of the contributions due to loop corrections in the axial current at N4LO. Finally, explicit expressions for the axial current up to N4LO have been derived in configuration space, which other researchers in the field may find useful.

Swampland conjectures (SCs) of string theory require that a constant cosmological constant $\Lambda$ be replaced by a time-dependent scalar-field quintessence with constrained parameters. The constraints limit the duration of the present expansion era because, although the SCs may be fulfilled at the present time, they will be violated at a finite time in the future allowing only an order-one number of e-foldings. In contrast, cyclic cosmology requires $\sim94$ e-foldings of the present universe before turnaround from expansion to contraction. This presents a dilemma to the original SCs. One possibility is that one of the SCs, the range conjecture, be significantly weakened. A second possibility, difficult to believe, is that cyclic cosmology vastly overestimates the number of e-foldings. A third possibility, which is the least disfavoured, is that string theory is not the correct theory of quantum gravity.

The present work deals with the e+ e- pair production in the d(p,e+e-)3He and d(n,e+ e-)3H processes, in order to evidentiate possible effects due to the exchange of a hypothetical low-mass boson, the so-called X17. These processes are studied for energies of the incident beams in the range 18-30 MeV, in order to have a sufficient energy to produce such a boson, whose mass is estimated to be around 17 MeV. We first analyze them as a purely electromagnetic processes, in the context of a state-of-the-art approach to nuclear strong-interaction dynamics and nuclear electromagnetic currents, derived from chiral effective field theory chiEFT. Next, we examine how the exchange of a hypothetical low-mass boson would impact the cross sections for such processes. We consider several possibilities, that this boson is either a scalar, pseudoscalar, vector, or axial particle. The main aim of the study is to exploit the specular structure of the 3He and 3H nuclei to investigate the isospin dependency of the X17-nucleon interaction, as the alleged "proto-phobicity".

The interaction of QCD and electroweak sector with gravity is characterized by the generation of a massless pole in a specific form factor present in the 1-loop effective action. We briefly illustrate how to single out this behaviour in perturbation theory, by taking as an example the $TJJ$ vertex, with $T$ denoting the energy momentum tensor of the Standard Model. The breaking of scale invariance, due to the trace anomaly, is then related to the appearance of a local degree of freedom in the effective action, which is of dilaton type.

Soft theorems can be recast as Ward identities of asymptotic symmetries. We review such relation for the leading and subleading soft graviton theorems in arbitrary even dimensions. While soft theorems are trivially generalized to dimensions higher than four, the charges of asymptotic symmetries are plagued by divergences requiring a renormalization. We argue that the renormalized charges of these symmetries can be determined by rewriting soft theorems as Ward identities. In order to show that the charges of such identities generate asymptotic symmetries, we propose a suitable commutation relation among certain components of the metric fields

We discuss a model of the universe where dark energy is replaced by electrically-charged extremely-massive dark matter. The cosmological constant has a value of the same order as the mean matter density, consistent with observations, and is obtained classically without fine-tuning.

Stress-energy correlation functions in a general Conformal Field Theory (CFT) in four dimensions are described in a fully covariant approach, as metric variations of the quantum effective action in an arbitrary curved space background field. All Conservation, Trace and Conformal Ward Identities (CWIs), including contact terms, are completely fixed in this covariant approach. The Trace and CWIs are anomalous. Their anomalous contributions may be computed unambiguously by metric variation of the exact 1PI quantum effective action determined by the conformal anomaly of $\left\langle T^{\mu\nu}\right\rangle$ in $d = 4$ curved space. This action implies the existence of massless propagator poles in three and higher point correlators of $T^{\mu\nu}$ . The metric variations of the anomaly effective action in its local form in terms of a scalar conformalon field are carried out explicitly for the case of the correlator of three CFT stress-energy tensors, and the result is shown to coincide with the algebraic reconstruction of $\left\langle TTT\right\rangle$ from its transverse, tracefree parts, determined independently by the solution of the CWIs in d dimensional flat space in the momentum representation. This demonstrates that the specific analytic structure and massless poles predicted by the general curved space anomaly effective action are in fact a necessary feature of the exact solution of the anomalous CWIs in any $d = 4$ CFT.

To describe the dark side of the Universe, we adopt a novel approach where dark energy is explained as an electrically charged majority of dark matter. Dark energy, as such, does not exist. The Friedmann equation at the present time coincides with that in a conventional approach, although the cosmological "constant" in the Electromagnetic Accelerating Universe (EAU) Model shares a time dependence with the matter component. Its equation of state is $\omega \equiv P/\rho \equiv -1$ within observational accuracy.

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider.

${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei represent essential elements for life on Earth. The study of their formation plays a key role in understanding heavy element nucleosynthesis and stellar evolution. In this paper we present the study of ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei as systems composed of $\alpha$-particle clusters using the short-range effective field theory approach. The fundamental and excited states of the studied nuclei are calculated within an ab-initio approach, using the Hyperspherical Harmonics method. Thanks to the two-body potential and fine-tuning of the three-body force, we have found the ${}^{12}{\rm C}$ system nicely reproduced by theory. However, for the ${}^{16}{\rm O}$ case, it is necessary to include a 4-body force in order to achieve agreement with the experimental data.

After a Preface written by the Editors, there follow twelve papers submitted by theoretical physicists from Asia, Europe and the USA.

We examine the structure of off-shell effective actions arising from chiral and gravitational anomalies, focusing on the $JJJ_A$ (axial-vector/vector/vector) and $J_A TT$ (axial-vector/stress-energy tensors) correlators, relevant in the analysis of anomaly-driven interactions in perturbation theory. Our approach relies on conformal field theory in momentum space, extended to chiral anomalies. The analysis centers on the presence of both particle poles and anomaly poles within these interactions, characterizing their behavior both in the conformal and non conformal limits. Through explicit computations, we show that universal sum rules in the longitudinal sector regulate these interactions for all kinematic conditions, extending previous analysis, and we discuss the resulting spectral flow, an area law of the absorptive part of the anomaly form factors as one moves away from or returns to the conformal point. These features are absent in the local effective action of anomaly interactions, commonly used in the description of axion-like particles. The spectral densities in both cases are shown to be self-similar. Our results further show that anomaly poles correspond to true particle poles only in the conformal limit, when the interaction describes a massless S-matrix process supported on a null-surface. Under these conditions, they can be effectively described by two kinetically mixed pseudoscalar fields propagating on the light-cone. These studies find application in polarized deeply inelastic scattering, axion-like dark matter and analogue systems such as topological materials.

The Amaterasu (named for a sun goddess in Japanese mythology) cosmic ray particle announced in November 2023 is extraordinary. Its direction points back to the Local Void which contains no galaxies or known source. It is possible to show that the direction could not have been bent significantly by magnetic fields within the Milky Way. This collection of facts constitutes a paradox. In the present paper, we offer a resolution within the Electromagnetic Accelerating Universe (EAU) model in which a central r\^ole is played by charged Primordial Extremely Massive Black Holes (PEMBHs) whose Coulomb interactions underly accelerating expansion. Because structure formation of PEMBHs is electromagnetic while that for galaxies is gravitational, it is reasonable to expect PEMBHs inside the Local Void. We provide an example where the cosmic ray primary is an antiproton and present it as supportiing evidence for the EAU model.