I will summarize the discussions at the recent plenary workshop at KEK and give an update of recent lattice calculations.

We explore the prospects of very heavy millicharged particles as candidates for some or all of dark matter (DM). Constraints on their properties like charge, dipole moment and mass are obtained by translating the current limits set by state-of-the-art nuclear recoil experiments like XENONnT and LZ. We contrast the extracted limits with those coming from astrophysical considerations, such as the decoupling of DM from regular matter during the recombination epoch and the suitability of the dynamical environments in the galactic halo for these heavy and charged beyond the Standard Model particles to remain lodged-in and available for future detections. 

Thanks! 

The parton distribution functions (PDFs) are crucial to the understanding of the internal structure of hadrons, and their precise determination is necessary for searches of BSM physics in collider experiments. Directly accessing PDFs in Lattice QCD calculations is impossible due to the Euclidean space-time geometry. The moments of PDFs are defined in terms of local operators that can be computed in Lattice QCD, but suffer from power divergent mixing beyond a certain order due to the hypercubic symmetry of the lattice. Recently, a method was proposed [1] to use gradient flow in order to circumvent this mixing and access moments of PDFs of any order. In this talk, I will summarize this method, and present preliminary results on moments of the unpolarized isovector PDF of the pion using four stabilized Wilson fermion ensembles generated by the OpenLat [2] initiative.

[1] A. Shindler 2311.18704

[2] https://openlat1.gitlab.io

 ``Axion Stars: Mass Functions and Constraints''

The QCD axion and axion-like particles, as leading dark matter candidates, can also have interesting implications for dark matter substructures if the Peccei-Quinn symmetry is broken after inflation. In such a scenario, axion perturbations on small scales will lead to the formation of axion miniclusters at matter-radiation equality, and subsequently the formation of axion stars. Such compact objects open new windows for indirect searches for axions. We compute the axion star mass function based on recent axion minicluster studies and Bose star simulations. Applying this mass function, we find post-inflation axion-like particles with masses 1.8×10^−21 eV<ma<3.3×10^−17 eV are constrained by the lack of dynamical heating of stars in ultrafaint dwarfs. We also find that current microlensing surveys are insensitive to QCD axion stars. While we focus on the gravitational detectability of axion stars, our result can be directly applied to other interesting signatures of axion stars, e.g. their decay to photons, that require as input the abundance, mass, and density distribution of axion stars.

We compute tree level scattering amplitudes involving more than one highly excited states in bosonic string theory. We use these amplitudes to understand chaotic and thermal aspects of the excited string states lending support to the Susskind-Horowitz- Polchinski correspondence principle. The unaveraged amplitudes exhibit chaos in the resonance distribution as a function of kinematic parameters, which can be described by random matrix theory. Upon coarse-graining these amplitudes exponentiate, and give certain thermal indications.

The percolation problem describes the statistical properties of a lattice from which a fraction p of the bonds has been removed at random.   There is a critical value p_c such that there is long ranged connectedness for p > p_c and only finite sized clusters for p < p_c.    The percolation problem and its generalization, the percolation conduction problem, have phenomenology similar to "classical" critical phenomena, even though they are not described by thermodynamics.   I'll explain the connections, and go on to show how the resistance from an internal point to the boundary of a square  containing a percolating network at p_c can be explained using ideas from critical phenomena and conformal field theory. 
 

Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof.  We will particularly discuss the use of non-invertible chiral symmetries in BSM model-building. The identification of a non-invertible symmetry in Z' models of L_µ - L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this symmetry is present by virtue of the SM having the same numbers of colors and generations.

In this talk I will consider asymptotically free gauge theories with gauge group $SU(N_c)$ and $N_f$ quarks with mass $m_q <<\Lambda_{QCD}$ that undergo chiral symmetry breaking and confinement. I will described a proposal for a bootstrap method to compute the S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy physics. For the important case of $N_c=3$, $N_f=2$, a numerical implementation of the method gives the phase shifts of the $S0$, $P1$ and $S2$ waves in good agreement with experimental results. The method incorporates gauge theory information ($N_c$, $N_f$, $m_q$, $\Lambda_{QCD}$) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules. This requires, in addition, the values of the quark and gluon condensates. At low energy we impose constraints from chiral symmetry breaking which additionally require knowing the pion mass $m_\pi$.

Nonrelativistic bound states lie at the core of quantum physics,

permeating the fabric of nature across diverse realms, spanning particle

to nuclear physics, and from condensed matter to astrophysics. These

systems are pivotal in addressing contemporary challenges at the forefront

of particle physics. Characterized by distinct energy scales, they serve

as unique probes of complex environments. Historically, their

incorporation into quantum field theory was fraught with difficulty until

the emergence of nonrelativistic effective field theories (NREFTs).



In this talk, we delve into the construction of a potential NREFT

(pNREFT), a framework that directly tackles bound state dynamics

reimagining quantum mechanics from field theory.

Focusing on heavy quarkonia, pNRQCD facilitates systematic definitions and

precise calculations for high-energy collider

observables. At the cutting edge, we investigate nonrelativistic bound

states in intricate environments, like the newly discovered exotics X, Y,

Z  above the strong decay threshold and the behavior in out-of-equilibrium

scenarios, such as quarkonium suppression in a Quark Gluon Plasma or dark

matter interactions in the early universe.



Our ability to achieve precision calculations and control strongly

interacting systems is closely linked to bridging perturbative methods

with nonperturbative tools, notably numerical lattice gauge theories.