A theoretical high energy physics program: Annual progress report for 1989: Task B

In this talk, we consider the interplay of fundamental and matter-induced T-violating effects in neutrino oscillations in matter. We present a simple approximative analytical formula for the T-violating probability asymmetry for three flavor neutrino oscillations in matter with an arbitrary density profile. We also discuss some implications of the obtained results. Since there are no T-violating effects in two flavor neutrino case (in the limit of vanshing $\theta_{13}$ or $\Delta m_{21}^2$, the three flavor neutrino oscillations reduces to the two flavor ones), the T-violating probability asymmetry can, in principle, provide a way to measure $\theta_{13}$ and $\Delta m_{21}^2$.

T-violating effects in neutrino oscillations with three flavors in matter

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.

In this paper, an introduction to the evolution operator method for three flavor neutrino oscillations in matter based on the Cayley–Hamilton formalism is presented as well as some its theoretical and experimental applications.

A modification of perturbation theory, known as the delta expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative expansions. In a generalization of the variationally improved perturbation technique appropriate to renormalizable asymptotically free theories, we show that the large expansion orders of certain physical quantities are similarly improved, and prove the Borel convergence of the corresponding series for $m_{\mathrm {v}} \lessim 0$ , with $m_{\mathrm {v}}$ the new (arbitrary) mass perturbation parameter. We argue that non-ambiguous estimates of quantities relevant to dynamical (chiral) symmetry breaking in QCD are possible in this resummation framework.

Charge symmetry breaking (CSB) effects associated with the $u$ and $d$ quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu--Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed $u$ and $d$ quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiquark governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with a pion mass difference given by $m_{\pi^+}^2 - m_{\pi^0}^2 \propto (m_u - m_d)^2$ as demanded by dynamical chiral symmetry breaking. We find significant CSB effects for realistic current quark mass ratios ($m_u/m_d \sim 0.5$) in the quark flavor-sector electromagnetic form factors of both the pion and kaon. For example, the difference between the $u$ and $d$ quark contributions to the $\pi^+$ electromagnetic form factors is about 8\% at a momentum transfer of $Q^2 \simeq 10\,$GeV$^2$, while the analogous effect for the light quark sector form factors in the $K^+$ and $K^0$ is about twice as large. For the Parton distribution functions, we find CSB effects which are considerably smaller than those found in the electromagnetic form factors.

Dynamical symmetry breaking can happen through a Higgs mechanism but also spontaneously within a strongly-enough coupled theory. We treat a field-theoretical quark model of QCD based on a linear+Coulomb Cornell potential (to account for the longitudinal interaction), together with a transverse interaction (to account for Coulomb-gauge gluons) in BCS approximation. After extracting the well-known BCS ground state on which abundant hadron phenomenology implementing dynamical chiral symmetry breaking has been built, we find two excited replica vacuum like states shown in figure 1. At the BCS level they are classically unstable, but second quantization blocks transitions between them in volumes much larger than a hadron size. Mesons built over the replica vacua have relative masses similar to normal mesons on the ordinary vacuum; we find no negative-mass mode, confirming their stability found earlier with a harmonic oscillator potential.

The effect of coherent forward scattering must be taken into account when considering the oscillations of neutrinos traveling through matter. In particular, for the case of massless neutrinos for which vacuum oscillations cannot occur, oscillations can occur in matter if the neutral current has an off-diagonal piece connecting different neutrino types. Applications discussed are solar neutrinos and a proposed experiment involving transmission of neutrinos through 1000 km of rock.

A new flavor changing electron neutrino interaction with matter would always dominate the nu_e oscillation probability at sufficiently high neutrino energies. Being suppressed by theta_{13}, the energy scale at which the new effect starts to be relevant may be within the reach of realistic experiments, where the peculiar dependence of the signal with energy could give rise to a clear signature in the nu_e --> nu_tau channel. The latter could be observed by means of a coarse large magnetized detector by exploiting tau --> mu decays. We discuss the possibility of identifying or constraining such effects with a high energy neutrino factory. We also comment on the model independent limits on them.

The Jarlskog invariant which controls the size of intrinsic CP violation in neutrino oscillation appearance experiments is modified by Wolfenstein matter effects for neutrinos propagating in matter. In this paper we give the exact factorization of the Jarlskog invariant in matter into the vacuum Jarlskog invariant times two, two-flavor matter resonance factors that control the matter effects for the solar and atmospheric resonances independently. We compare the location of the minima of the factorizing resonance factors with the location of the solar and atmospheric resonances, precisely defined. They are not identical but the fractional differences are both found to be less than 0.1%. In addition, we explain why symmetry polynomials of the square of the mass of the neutrino eigenvalues in matter, such as inverse of the square of the Jarlskog invariant in matter, can be given as polynomials in the matter potential.

Using lattice QCD, we examine several key features associated with dynamical chiral symmetry breaking and quark confinement. Calculations are performed in pure SU(3) gauge theory using the chiral overlap fermion action. Vortex-only and vortex-removed configurations are derived from the the original Monte Carlo gauge fields via a centre vortex identification procedure. The topological charge density, static quark potential, quark mass function and hadron spectrum are compared across the three ensembles. Remarkably, in each instance, the vortex-only degrees of freedom (after some smoothing) are able to encapsulate the pertinent features of the original gauge fields. The removal of centre vortices is consistently associated with a loss of dynamical chiral symmetry breaking. In particular, preliminary results for the vortex-removed meson spectrum hint at the restoration of chiral symmetry at light quark masses.

The fermion propagator is studied in the whole Minkowski space with the help of the Schwinger-Dyson equations. Various integral representations are employed to get solutions for the dynamical breaking of chiral symmetry in different regimes of the coupling constant. In particular, in the case of massive boson, we extend the singularity structure of the fermion propagator to the two real pole Ansatz.

Using realistic quark propagators and meson Bethe-Salpeter amplitudes based on the Dyson-Schwinger equations, we calculate the pion and kaon's valence parton distribution functions (PDF) through the modified impulse approximation. The PDFs we obtained at hadronic scale have the purely valence characteristic and exhibit both dynamical chiral symmetry breaking and SU(3) flavor symmetry breaking effects. A new calculation technique is introduced to determine the valence PDFs with precision. Through NLO DGLAP evolution, our result is compared with pion and kaon valence PDF data at experimental scale. Good agreement is found in the case of pion, while deviation emerges for kaon. We point out this situation can be resolved by incorporating gluon contributions into the mesons if the pion hosts more gluons than kaon nonperturbatively.

There is strong evidence supporting center vortices as underpinning confinement and dynamical chiral symmetry breaking—the two key features of nonperturbative QCD. In our recent paper [1] we find that dynamical mass generation vanishes upon vortex removal in full QCD with a near-physical quark mass. In this work we extend those results and consider the influence of center vortex removal on the overlap Landau-gauge quark propagator at multiple valence quark masses on the same dynamical QCD ensemble, keeping fixed the near-physical sea quark mass. After carefully applying a smoothing process we also find that dynamical mass generation is reproduced on the corresponding vortex-only fields. This vortex-only dynamical mass shows qualitative agreement with the untouched Monte Carlo gauge field results. The results reported herein lend further credence to the important relationship between dynamical fermions and center vortices and the mediation of nonperturbative phenomena in QCD. Published by the American Physical Society 2025

Proper vertex in studies of dynamical chiral symmetry breaking