Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation

We study two aspects of the CFL phase of QCD in the NJL approximation. The first one is the issue of the dependence on \mu of the ultraviolet cutoff in the gap equation, which is solved allowing a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using the high density effective theory we perform an expansion in the parameter (m_s/\mu)^2 after checking that its numerical validity is very good already at first order.Comment: LaTeX file, 6 figure

Ginzburg-Landau approach to the three flavor LOFF phase of QCD

We explore, using a Ginzburg-Landau expansion of the free energy, the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using the NJL four-fermion coupling to mimic gluon interactions. We find that, below the point where the QCD homogeneous superconductive phases should give way to the normal phase, Cooper condensation of the pairs u-s and d-u is possible, but in the form of the inhomogeneous LOFF pairing.Comment: 8 pages, 4 figures. Eq. (20) corrected. As a consequence figures have been modified to show only the solution with parallel total momenta of the us, ud pairs, as the other configurations are suppressed. Main conclusions of the paper are unchange

Effective gluon interactions in the Colour Superconductive Phase of two flavor QCD

The gluon self-energies and dispersion laws in the color superconducting phase of QCD with two massless flavors are calculated using the effective theory near the Fermi surface. These quantities are calculated at zero temperature for all the eight gluons, those of the remaining SU(2) color group and those corresponding to the broken generators. The construction of the effective interaction is completed with the one loop calculation of the three- and four-point gluon interactions.Comment: LaTeX, p 17, 4 figures. Final version to be published in Phys. Lett. B. Several corrections have been done and some point clarifie

Heating (Gapless) Color-Flavor Locked Quark Matter

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass Ms. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number and Delta is the gap in the CFL phase. We find this distinction blurred at nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu, we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do not make any small-Ms approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of Ms that there are no strange quarks present.Comment: 24 pages; 22 figures; typos in labelling of Figs. 7, 20 correcte

Self-consistent parametrization of the two-flavor isotropic color-superconducting ground state

Lack of Lorentz invariance of QCD at finite quark chemical potential in general implies the need of Lorentz non-invariant condensates for the self-consistent description of the color-superconducting ground state. Moreover, the spontaneous breakdown of color SU(3) in this state naturally leads to the existence of SU(3) non-invariant non-superconducting expectation values. We illustrate these observations by analyzing the properties of an effective 2-flavor Nambu-Jona-Lasinio type Lagrangian and discuss the possibility of color-superconducting states with effectively gapless fermionic excitations. It turns out that the effect of condensates so far neglected can yield new interesting phenomena.Comment: 16 pages, 3 figure

Effective Field Theory for the Crystalline Colour Superconductive Phase of QCD

We present an effective field theory for high density, low temperature QCD in the crystalline colour superconductive phase (LOFF phase). This interesting phase of QCD is characterized by a gap parameter with a crystalline pattern, breaking traslational and rotational invariance, and could have astrophysical applications. In the effective theory the fermions have a Majorana mass, which, besides colour, breaks translation and rotation symmetries. Fermions couple to the three phonons arising from the breaking of rotation and translation invariance. Integrating out the fermions leads eventually to an effective lagrangian in terms of the phonon fields only, which satisfies an anisotropic dispersion relation.Comment: Latex, 17 pages, Modifications in the effective goldstone boson descriptio

Livestock Farming Systems in the Northern Tablelands of NSW: An Economic Analysis

The Northern Tablelands region of New South Wales covers an area of approximately 3.12 million hectares including 2.11 million hectares occupied by some 2300 agricultural establishments producing agricultural commodities valued at more than $220 million. Sheep and wool production and cattle production are the dominant agricultural enterprises. In this Report, a whole-farm model of a representative livestock farming system in the Northern Tablelands is developed. Whole-farm economic models of the relevant farming system are a useful first step in understanding the nature of the biological and economic constraints facing producers in their decision making in relation to their choices of inputs and outputs. Such models are also useful in relation to more general concerns such as the expected impacts of investments in new technologies applicable to grazing systems, or of external events such as drought conditions or a depreciation in the exchange rate. A whole farm budget for a representative farm includes a statement of assets and liabilities, based upon estimates of the various capital items including land, livestock and plant and machinery and farm structures. There is also an annual operating budget that includes the cash income and costs associated with each of the farm enterprises as well as the fixed costs incurred for running the farm over the year to derive the farm cash income. Allowances for depreciation and interest costs are deducted from farm cash income to determine farm operating surplus. No family labor allowance is subtracted, so the resulting farm operating surplus represents a return on owner-operated labor, management and farm assets. Pasture costs are not apportioned to the specific animal enterprises and therefore appear as separate negative gross margins. Similarly, supplementary feeding costs and fodder conservation activities are listed as a separate negative gross margin. A representative farm model of the Northern Tablelands livestock farming system was developed based on ABS and ABARE data on the relevant industries, from simulations with a linear programming model, and from discussions with local graziers and extension officers. The farm comprises 920 ha of which about half is native pasture and about half is introduced pasture. This farm runs a flock of 1,108 first-cross ewes, a flock of 1,732 Merino wethers and a 127 cow herd producing 18 month old steers suitable for the heavy feeder steer market. Using average prices and costs over an extended period of time, the annual operating budget for the farm shows a total gross margin of$86,191 and total overhead costs for the year of $24,720. This results in a farm cash income of$61,471 and a farm operating surplus of $37,471 after depreciation and interest costs. The statement of assets and liabilities shows total assets of the farm to be$1,498,060 and liabilities of $100,000 which equates to an equity level of 93.3 per cent. The farm operating surplus achieved on this model farm as a percentage of the owner's equity is 2.7 per cent. This represents a return on operator and family labor, management and equity. Low returns to equity are typical of Australian broadacre agriculture. Other scenarios examined included whole-farm budgets based on 2002 actual market prices and on 2003 expected prices. Given the relatively high prices for sheep relative to cattle in these years, the representative farm would be more profitable running 1,558 first-cross ewes and 3,595 Merino wethers. Such an enterprise mix would achieve a farm total gross margin of$165,736. After overhead costs, depreciation and interest costs there would be a farm operating surplus of $111,818. Based on equity totaling$1,472,870, this operating surplus would represent a business return on operator labor, management and equity of 8.1 per cent. However, while the Northern Tablelands representative farm model would suggest that greater profits could be achieved from changing enterprises as commodity prices change, in practice various biological lags, infrastructure, financial and management constraints prevent regular changes in farm enterprises. In fact, diversification amongst a variety of farm enterprises between various sheep and cattle enterprises as evidenced in the Northern Tablelands is one management response to this commodity price variability. A hypothetical new improved-pasture technology suggested by researchers, involving the selection of pasture varieties with improved winter pasture growth, was examined using the whole-farm model. If the existing 450 ha of improved pasture was replaced by a new variety that gave a 10 per cent increase in winter pasture growth, this would result in a 4.9 per cent increase in farm total gross margin. This corresponds to an increase in farm cash income of 6.9 per cent. These improvements in the profitability of the representative farm would be achieved by increasing the investment in first-cross ewes and in cows producing heavy feeder steers (by 3.5 per cent and 7.8 per cent respectively) and by decreasing the Merino wether enterprise from 1,732 to 1,672 wethers. This indicates that the prime lamb and cow enterprises, under the current assumptions of the model, are better able to utilize the farm resources available given an increase in winter pasture growth. The main conclusions from the analysis are that: Returns to equity are quite low in the Northern Tablelands livestock farming system; variable commodity prices, largely determined in world markets, result in variable levels of profitability of the farming system over time; The optimal farm plan is quite sensitive to small changes in the relative prices of the different outputs produced; In practice farm plans do not change very much as prices change, with most farms maintaining a range of cattle and sheep enterprises; Thus a "representative year" is a more realistic basis for assessing potential changes in farm plans; and new technologies can potentially have large impacts of farm profits and on the mix of resources used and outputs produced.Industrial Organization, Production Economics,

A Northern Tablelands Whole-Farm Linear Program for Economic Evaluation of New Technologies at the Farm-Level

The benefits of evaluating a new technology in a whole-farm context using a linear programming framework are well known. Linear programming allows the joint evaluation of concurrent farm activities, while considering the costs and returns of all enterprises and any resource adjustments imposed by adoption of the technology. This Report provides a rationale for and description of a whole-farm linear programming model that can be used for the economic evaluation of new technologies that are applicable to beef/sheep grazing farms typical of the Northern Tablelands of New South Wales. In this farming system, the whole-farm focus incorporates various aspects of the pasture base, resource constraints and sheep and cattle interactions. An overview of economic tools that are available to assess technologies at the farm level is provided first, listing some of the major benefits and limitations of each of these various techniques. A representative farm for the selected farming system is then developed and a whole-farm linear program based on this representative farm is described in some detail. A series of modelling experiments is undertaken to examine variations of the base model and their impact on the resulting technology evaluation. An example technology, involving the genetic improvement of beef cattle for improved feed efficiency (NFE), is evaluated. The optimal farm plan for a "typical" (single) year is generated, given the objective of maximising farm total gross margin. Three enterprises are selected: 1,108 first-cross ewes, 1,732 Merino wethers and a beef herd of 127 cows producing 18 month old heavy feeder steers (HFS) at 448kg liveweight and excess heifers sold as 9 month old weaners. For this farm plan, the annual operating budget shows a total gross margin for the farm of $86,191. The optimal farm plan for the representative farm is found to be sensitive to relatively small changes in input or output prices and production parameters. Only small improvements in a number of the individual enterprise gross margins would result in them displacing the currently selected enterprises. These results suggest relatively similar profitability levels between these sheep and beef enterprises. This would be anticipated given that all the enterprises described in this report were identified by local experts as being common in the Northern Tablelands. Further, the relatively small differences in enterprise profitability when viewed in a whole farm context also reflect the similar resources that each of the enterprises require, making them readily substitutable. For new technologies that have dynamic attributes, measuring the cashflow over time becomes important. Genetic traits in ruminants that have long biological lags are such technologies. This means that a single-year equilibrium model will be unable to effectively measure the costs of introducing the new technology over time. In the case of the NFE technology in beef cattle, any herd expansion that is possible as a result of the trait is measured by the opportunity cost of heifer sales forgone that are instead retained to increase the breeding herd. These herd dynamics can be represented explicitly within a multi-period version of a whole-farm LP model. The NFE cow enterprise is offered to the model, with the initial sheep enterprises set the same as the base case (1,108 prime lamb producing ewes, 1,732 19-micron Merino wethers). The model again selects 127 HFS producing cows in the first year, but the new optimal farm plan is to invest in the new technology by purchasing NFE-superior bulls in successive years and expanding the cow herd while concurrently decreasing the scale of the Merino wether enterprise. Substitution of Merino wethers for NFE cows occurs up to year 12 after which additional breeding cows are possible from their increasing net feed efficiency alone. There is an increase in cow numbers of 12.6 per cent by year 25, which equates to an improvement in the NPV per breeding cow per year over the base herd of$5.02, using a 5 per cent discount rate. Other experiments reported include adding constraints for fixed costs, family drawings and an overdraft facility; alternate discount rates for the NPV calculations; alternate terminal values for the livestock assets at the end of the simulation period; and a post-optimality risk analysis. This study has highlighted several additional benefits of evaluating a technology in a whole-farm multi-period linear programming framework. First, apart from determining the type and size of the optimal farm enterprise mix and the optimal value of the objective function, whole-farm multi-period linear programming also provides important additional information including shadow costs and prices and constraint slacks, and how they change over time. Shadow costs of activities show how sensitive the optimal farm enterprise mix is to changes in the gross margins of alternate farm activities not included in the current farm plan. The shadow prices for resources indicates how much a farm manager could pay for additional units of a limiting resource, for example, additional labour. Second, in terms of the specific NFE technology examined in this report, it would appear that there may well be regions where such feed efficiencies may be of greater benefit due to particularly large variations in pasture growth patterns throughout the year. The Northern Tablelands with its recognised winter feed deficit may be one such area. This information may be of benefit to researchers in extending the NFE technology to farmers. Third, the deterministic multi-period version of the model highlighted the impact of the inclusion of overhead and capital constraints in the modelling process in determining the potential adoption of a technology by a farm manager. The availability and cost of capital is shown to influence the extent to which the NFE technology may be adopted by an individual farm business. Fourth, from a modelling perspective, the effect of uncertain terminal values and the bearing that they have on measuring the level of adoption of a new technology is an area for further investigation. Finally, the impact of risk was assessed in this study post-optimally by the inclusion of stochastic output prices in the optimal whole farm budgets. This is an area for further research, including the potential of alternate modelling techniques such as MOTAD programming or stochastic dynamic programming. However due to size constraints, such approaches may necessitate trade-offs in terms of the detail of whole-farm models to which they are applied.Research and Development/Tech Change/Emerging Technologies,

Farm-level Economic Evaluation of Net Feed Efficiency in Australia’s Southern Beef Cattle Production System: A Multi-period Linear Programming Approach

Selection of beef cattle for increased net feed efficiency is a current major focus for research. At present the trait seems to be more apparent in Australia’s southern beef production system which is dominated by mixed farming enterprises. Farm-level evaluation of net feed efficiency should take account of the farming system for which it is proposed along with the dynamic nature of genetic selection. Gross margin, linear programming and multi-period linear programming approaches to evaluation of the trait at the farm-level using a representative farm are compared. Implications of the trait for researchers and beef producers are identifiedfarm-level evaluation, genetic traits, linear programming, Farm Management,