In this study, we investigate a scenario based on the effects of the Loop Quantum Gravity (LQG) on the electromagnetic sector of the Standard Model of Fundamental Interactions and Particle Physics (SM). Starting from a post-Maxwellian version of electromagnetism that includes LQG effects, we derive and discuss the influence of LQG parameters on classical quantities such as the components of the stress-tensor. Furthermore, we inspect the propagation of electromagnetic waves and examine the optical properties of the QED vacuum in this scenario. Among these, we contemplate the combined effect of the LQG parameters and a homogeneous background magnetic field on the propagation of electromagnetic waves by considering issues such as group velocities and refractive indices of the QED vacuum, in detail. Finally, with the aid of the previously analyzed LQG-extended photonic dispersion relations, we re-discuss the kinematics of the Compton effect and conclude that an interesting nonlinear profile emerges in the wavelengths of the incoming and deflected photons.

Brazil

P.A.L. Mourão

G.L.L.W. Levy

J.A. Helayël-Neto

Reassessing aspects of LQG-modified dispersion relations of photons * P. A. L. Mourão is support by CAPES. G. L. L. W. L. Levy is support by the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant No. E-26/202.437/2024.

Holographic models that consider classical vector fields in a 5-d background provide effective descriptions for heavy vector meson spectra. This is true both in vacuum and a thermal medium, such as quark gluon plasma. However, the manner in which these phenomenological models work is unclear. In particular, what is the role of the fifth dimension, and what is the relation between the holographic 5-d background and physical (4-d) heavy mesons? Hadrons, in contrast to leptons, are composite particles with some internal structure that depends on the energy at which they are observed. In this study, a static meson is represented by a heavy quark-antiquark pair with an interaction described by a Nambu Goto string existing in the same 5-d background that provides field solutions leading to masses and decay constants of charmonium states. The resulting interaction potential is linear for large distances, with a string tension consistent with the effective Cornell potential. Introducing temperature $\textit{T}$ in the background, it is found for the $J/\psi$ case that there is a deconfining transition at some critical value of $\textit{T}$. The obtained results indicate that the 5-d background effectively represents the internal structure of the (static) charmonium (quasi) states.

Nelson R.F. Braga

Yan F. Ferreira

William S. Cunha

Holography and the internal structure of charmonium * The authors are partially supported by CNPq — Conselho Nacional de Desenvolvimento Científico e Tecnologico, by FAPERJ — Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro and by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior — Brasil (CAPES), Finance Code 001

Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form.

Germany

Leonardo Chimirri

Ireland

Patrick Fritzsch

Japan

Jochen Heitger

United Kingdom

Fabian Joswig

Italy

Marco Panero

Spain

Carlos Pena

David Preti

Non-perturbative renormalisation and improvement of non-singlet tensor currents in N f = 3 QCD

We present our first set of results for charm physics, using the mixed-action setup introduced in a companion paper [1]. Maximally twisted Wilson valence fermions are used on a sea of non-perturbatively O(a)-improved Wilson fermions, made up by CLS  $$N_\mathrm {\scriptstyle f}=2+1$$  <math> <mrow> <msub> <mi>N</mi> <mstyle> <mi>f</mi> </mstyle> </msub> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </math>   ensembles. Our charm-sector observables are free from  $$O(am_c)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <mi>a</mi> <msub> <mi>m</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </math>   discretisation effects, without need of tuning any improvement coefficient, and show continuum-limit scaling properties consistent with leading cutoff effects of  $$O(a^2)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </math>  . We consider a subset of CLS ensembles – including four values of the lattice spacing and pion masses down to 200 MeV – allowing to take the continuum limit and extrapolate to the physical pion mass. A number of techniques are incorporated in the analysis in order to estimate the systematic uncertainties of our results for the charm quark mass and the  $$D_{(s)}$$  <math> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </math>  -meson decay constants. This first study of observables in the charm sector, where the emphasis has been on the control of the methodology, demonstrates the potential of our setup to achieve high-precision results.

Andrea Bussone

Alessandro Conigli

Julien Frison

Gregorio Herdoíza

Alejandro Sáez

Javier Ugarrio

Hadronic physics from a Wilson fermion mixed-action approach: charm quark mass and  $$D_{(s)}$$  <math> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </math>   meson decay constants

We study the scaling of kaon decay amplitudes with the number of colours, $$N_c$$ <math><msub><mi>N</mi><mi>c</mi></msub></math> , in a theory with four degenerate flavours, $$N_f=4$$ <math><mrow><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></mrow></math> . In this scenario, two current-current operators, $$Q^\pm $$ <math><msup><mi>Q</mi><mo>±</mo></msup></math> , mediate $$\Delta S=1$$ <math><mrow><mi>Δ</mi><mi>S</mi><mo>=</mo><mn>1</mn></mrow></math>  transitions, such as the two isospin amplitudes of non-leptonic kaon decays for $$K\rightarrow (\pi \pi )_{I=0,2}$$ <math><mrow><mi>K</mi><mo>→</mo><msub><mrow><mo>(</mo><mi>π</mi><mi>π</mi><mo>)</mo></mrow><mrow><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></math> , $$A_0$$ <math><msub><mi>A</mi><mn>0</mn></msub></math>  and $$A_2$$ <math><msub><mi>A</mi><mn>2</mn></msub></math> . In particular, we concentrate on the simpler $$K\rightarrow \pi $$ <math><mrow><mi>K</mi><mo>→</mo><mi>π</mi></mrow></math>  amplitudes, $$A^\pm $$ <math><msup><mi>A</mi><mo>±</mo></msup></math> , mediated by these two operators. A diagrammatic analysis of the large-$$N_c$$ <math><msub><mi>N</mi><mi>c</mi></msub></math>  scaling of these observables is presented, which demonstrates the anticorrelation of the leading $${{\mathcal {O}}}(1/N_c)$$ <math><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub><mo>)</mo></mrow></math>  and $${{\mathcal {O}}}(N_f/N_c^2)$$ <math><mrow><mi>O</mi><mo>(</mo><msub><mi>N</mi><mi>f</mi></msub><mo>/</mo><msubsup><mi>N</mi><mi>c</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math>  corrections in both amplitudes. Using our new $$N_f=4$$ <math><mrow><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn></mrow></math>  and previous quenched data, we confirm this expectation and show that these corrections are naturally large and may be at the origin of the $$\Delta I=1/2$$ <math><mrow><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>  rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, $$g^\pm $$ <math><msup><mi>g</mi><mo>±</mo></msup></math> , can be determined. A NLO estimate of the $$K \rightarrow (\pi \pi )_{I=0,2}$$ <math><mrow><mi>K</mi><mo>→</mo><msub><mrow><mo>(</mo><mi>π</mi><mi>π</mi><mo>)</mo></mrow><mrow><mi>I</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></math>  isospin amplitudes can then be derived, which is in good agreement with the experimental value.

Andrea Donini

Pilar Hernández

Fernando Romero-López

Dissecting the $$\Delta I=1/2$$ <math><mrow><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>  rule at large $$N_c$$ <math><msub><mi>N</mi><mi>c</mi></msub></math>