There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s.

https://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-014-2890-7.pdf

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the light-quark masses, the form factor [Formula: see text], arising in the semileptonic [Formula: see text] transition at zero momentum transfer, as well as the decay constant ratio [Formula: see text] and its consequences for the CKM matrix elements [Formula: see text] and [Formula: see text]. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of [Formula: see text] and [Formula: see text] Chiral Perturbation Theory. We review the determination of the [Formula: see text] parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for [Formula: see text] and [Formula: see text] (also new compared to the previous review), as well as those for D- and B-meson-decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant [Formula: see text].

/pdf/review-of-lattice-results-concerning-low-energy-particle-4ppyuq45zk.pdf

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG).

The mass of the axion, a particle that is central to many dark-matter theories, is calculated via the equation of state of the Universe and the temperature dependence of the so-called topological susceptibility of quantum chromodynamics. Calculations that need to consider the theory of quantum chromodynamics, which describes how the strong interaction holds quarks together, are daunting because of the nonlinearity of the strong force. Despite the numerical difficulties, Szabolcs Borsanyi et al. have managed to perform an accurate calculation of the mass of an axion. These particles are at the heart of many dark-matter theories. Key in this paper is the ability to calculate the equation of state and the so-called topological susceptibility of quantum chromodynamics over a very wide temperature range. With their determination of the axion mass, the authors make important predictions about the evolution of the Universe that will help to test dark-matter theories involving axions in the near future. Unlike the electroweak sector of the standard model of particle physics, quantum chromodynamics (QCD) is surprisingly symmetric under time reversal. As there is no obvious reason for QCD being so symmetric, this phenomenon poses a theoretical problem, often referred to as the strong CP problem. The most attractive solution for this1 requires the existence of a new particle, the axion2,3—a promising dark-matter candidate. Here we determine the axion mass using lattice QCD, assuming that these particles are the dominant component of dark matter. The key quantities of the calculation are the equation of state of the Universe and the temperature dependence of the topological susceptibility of QCD, a quantity that is notoriously difficult to calculate4,5,6,7,8, especially in the most relevant high-temperature region (up to several gigaelectronvolts). But by splitting the vacuum into different sectors and re-defining the fermionic determinants, its controlled calculation becomes feasible. Thus, our twofold prediction helps most cosmological calculations9 to describe the evolution of the early Universe by using the equation of state, and may be decisive for guiding experiments looking for dark-matter axions. In the next couple of years, it should be possible to confirm or rule out post-inflation axions experimentally, depending on whether the axion mass is found to be as predicted here. Alternatively, in a pre-inflation scenario, our calculation determines the universal axionic angle that corresponds to the initial condition of our Universe.

/pdf/calculation-of-the-axion-mass-based-on-high-temperature-52sd6do9oz.pdf

Calculation of the axion mass based on high-temperature lattice quantum chromodynamics

Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared

We perform a study of the effects from maximal Abelian gauge Gribov copies in the context of the dual superconductor scenario of confinement, on the basis of a novel approach for the estimation of systematic uncertainties from incomplete gauge fixing. We present numerical results, in SU(2) lattice gauge theory, using the overrelaxed simulated annealing gauge-fixing algorithm. We find Abelian and non-Abelian string tensions to differ significantly, their ratio being 0.92(4) at {beta}=2.5115. An approximate factorization of the Abelian potential into monopole and photon contributions has been confirmed, the former giving rise to the Abelian string tension. {copyright} {ital 1996 The American Physical Society.}

http://cds.cern.ch/record/299315/files/9603012.pdf

Dual superconductor scenario of confinement: A Systematic study of Gribov copy effects

We study the behavior of the gluon and ghost dressing functions in $SU(3)$ Landau gauge at low momenta available on lattice sizes ${12}^{4}--{32}^{4}$ at $\ensuremath{\beta}=5.8$, $6.0$ and $6.2$. We demonstrate the ghost dressing function to be systematically dependent on the choice of Gribov copies, while the influence on the gluon dressing function is not resolvable. The running coupling given in terms of these functions is found to be decreasing for momenta $ql0.6\text{ }\text{ }\mathrm{GeV}$. We study also effects of the finite volume and of the lattice discretization.

/pdf/towards-the-infrared-limit-in-su-3-landau-gauge-lattice-kvs6k5i3bc.pdf

Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found the Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale mIR

I. L. Bogolubsky a, E.-M. Ilgenfritzb, M. Muller-Preusskerb, and A. Sternbeckc a Joint Institute for Nuclear Research, 141980 Dubna, Russia b Humboldt Universitat zu Berlin, Institut fur Physik, 12489 Berlin, Germany c CSSM, School of Chemistry & Physics, University of Adelaide, SA 5005, Australia E-mail: bogolubs@lxpub04.jinr.ru, ilgenfri@physik.hu-berlin.de, mmp@physik.hu-berlin.de, andre.sternbeck@adelaide.edu.au

/pdf/landau-gauge-gluon-and-ghost-propagators-in-4d-su-3-hyyhbyw7ly.pdf

Michael Müller-Preussker

Papers

Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared

Dual superconductor scenario of confinement: A Systematic study of Gribov copy effects

Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale mIR

Landau-gauge gluon and ghost propagators in 4D SU(3) gluodynamics on large lattice volumes