We establish a link between the concepts of infrared renormalons, infrared fixed point, and dynamical nonperturbative mass generation of gluons in pure Yang-Mills theories. By utilizing recent results in the resurgent analysis of renormalons through non-linear ordinary differential equations, we develop a new description for the gluon propagator, thereby realizing the Schwinger mechanism. Specifically, this approach leads to a nonperturbative, dynamic mass generation for Yang-Mills gauge bosons in the deep infrared region, a phenomenon closely associated with color confinement. Furthermore, we present arguments about the limit of applicability of the Borel-Ecalle resummation of the renormalons by comparing it with the Kallen-Lehman representation of the gluon propagator.

Italy

Alessio Maiezza

United States

Juan Carlos Vasquez

Gluon mass generation from renormalons and resurgence

Neutrinoless double beta decay is a textbook example of lepton number violation, often claimed to be a probe of neutrino Majorana mass. However, it could be triggered by new physics; after all, neutrino Majorana mass requires physics beyond the Standard Model. If at least one electron were right-handed, it would automatically signify new physics rather than neutrino mass. In case both electrons were left-handed, the situation would become rather complicated, and additional effort would be needed to untangle the source for this process. We offer a comprehensive study of this issue from both the effective operator approach and the possible UV completions, including the Pati-Salam quark-lepton unification. While neutrino exchange is natural and physically preferred, our findings show that new physics can still be responsible for the neutrinoless double beta decay. In particular, the Pati-Salam theory can do the job, consistently with all the phenomenological and unification constraints, as long as the unification scale lies above <math><msup><mn>10</mn><mn>12</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, albeit at the price of fine-tuning of some scalar masses.

Germany

Gia Dvali

Goran Senjanović

Vladimir Tello

Neutrinoless double beta decay: Neutrino mass versus new physics

We argue that Left-Right parity symmetry  $${\mathcal {P}}$$  <math> <mi>P</mi> </math>   can arise as a discrete remnant of a unified gauge symmetry. The high-energy unification necessarily includes the gauging of the Lorentz symmetry, bringing into the game gravitational interactions, and leading to a gravi-GUT scheme. Parity emerges unbroken below the Planck scale, and can be broken spontaneously at lower energies making contact with the Standard Model. This framework motivates the spontaneous origin of parity violation as in Left-Right symmetric theories with  $${\mathcal {P}}$$  <math> <mi>P</mi> </math>  . The possible unifying gauge groups are identified as  $$\mathrm{SO}(1,7)$$  <math> <mrow> <mi>SO</mi> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>7</mn> <mo>)</mo> </mrow> </math>   for gravitational and weak interactions, or  $$\mathrm{SO}(7,7)$$  <math> <mrow> <mi>SO</mi> <mo>(</mo> <mn>7</mn> <mo>,</mo> <mn>7</mn> <mo>)</mo> </mrow> </math>   for a complete unification.

Croatia

Fabrizio Nesti

Parity from gauge symmetry

We study the QCD Adler function in the energy region <math><mo>≈</mo><mn>0.7</mn><mo>−</mo><mn>2.5</mn></math> GeV, in which the non-perturbative effects become dominant. Our analysis is a renormalon-based evaluation using transseries within the resurgence of the Renormalization-Group-Equation and does not require the Operator-Product-Expansion.

Resurgence of the QCD Adler function

Within the minimal left-right (LR) symmetric model we revisit the predictions for the kaon <math><mi>C</mi><mi>P</mi></math> violating observables <math><mi>ϵ</mi></math> and <math><msup><mi>ϵ</mi><mo>′</mo></msup></math> in correlation with the neutron electric dipole moment. We perform a complete study of the cross constraints on the model parameters, phases and the <math><msub><mi>M</mi><msub><mi>W</mi><mi>R</mi></msub></msub></math> scale, considering the two cases of extended parity or charge conjugation as LR discrete symmetries, together with the possible presence of a Peccei-Quinn symmetry. We discuss in particular two scenarios: whether the Standard Model saturates the experimental value of <math><msup><mi>ϵ</mi><mo>′</mo></msup><mo>/</mo><mi>ϵ</mi></math> or whether new physics is needed, still an open issue after the recent lattice results on the QCD penguin matrix elements. Within the first scenario, we find no constraints on the LR scale in the charge-conjugation case while in the parity case we show that <math><msub><mi>M</mi><msub><mi>W</mi><mi>R</mi></msub></msub></math> can be as low as 13 TeV. On the other side, the request that new physics contributes dominantly to <math><msup><mi>ϵ</mi><mo>′</mo></msup></math> implies strong correlations among the model parameters, with an upper bound of <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></msub><mo>&lt;</mo><mn>8</mn><mi>–</mi><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math> depending on <math><mi>tan</mi><mi>β</mi></math> in the case of charge conjugation and a range of <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>R</mi></mrow></msub></mrow></msub><mo>≃</mo><mn>7</mn><mi>–</mi><mn>45</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math> in the parity setup. Both scenarios may be probed directly at future colliders and only indirectly at the LHC.

Stefano Bertolini

Kaon <math><mi>C</mi><mi>P</mi></math> violation and neutron EDM in the minimal left-right symmetric model

We propose a new approach for computing tunneling rates in quantum or thermal field theory with multiple scalar fields. It is based on exact analytical solutions of piecewise linear potentials with many segments that describes any given potential to arbitrary precision. The method is first developed for the single field case in three and four space-time dimensions and demonstrated on examples of classical potentials as well as the calculation of quantum fluctuations. A systematic expansion of the potential beyond the linear order is considered, taking into account higher order corrections, which paves the way for multiple scalar fields. We thereby provide a fast semianalytical tool for evaluating the bounce action for theories with an extended scalar sector.

Slovenia

Victor Guada

Miha Nemevšek

Multifield polygonal bounces

We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the <math><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></math> model where we estimate the non-perturbative β-function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative β-function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety.