Thermal Corrections to $π$-$π$ Scattering Lengths in the Linear Sigma Model
Marcelo Loewe, Cristian Martínez
备注：
8 pages. Keywords: Finite temperature field theory; scattering lengths; linear sigma model. A new reference has been added. Written in RevTex4. The paper is being accepted for publication in Phys. Rev. D. The size of the manuscript was reduced considerably
In this article we explore the thermal evolution of the $π$-$π$ scattering lengths in the frame of the linear sigma model. We compute, using thermofield dynamics, all the one loop diagrams that contribute to $π$-$π$ scattering. We restrict ourselves to temperature correction only in the pion sector, due to the Boltzmann supression for the sigma meson. From this analysis we obtain the thermal behavior of $a_0^0$ and $a_0^2$, s-waves scattering lengths in the isospin channel I=0 and I=2 respectively. It turns out that $a_0^0$ grows whereas $a_0^2$ diminishes as function of temperature. We compare our results with other determinations of the thermal behavior of these magnitudes.
Numerical precision radiative corrections to the Dalitz plot of light and heavy quark unpolarized baryon semileptonic decays. The cases Xi^0 \to Sigma^+ e \barν and Λ_c^+ \to Λe^+ ν
我们提出并讨论了我们以前的精确结果的数值使用非极化自旋二分之一重子半轻子衰变的辐射校正，这是不妥协的固定形状因子在规定的值。我们提出了各种crosscheriches和其他结果的比较，在文献中的这种分析辐射校正。然而，我们的分析是通用的，适用于重夸克允许的重子的所有电荷分配。该过程以过程^+ e \bar v和Λ_c^+ \to Λe^+ v为例。
In this article we consider the magnetic corrections to $π$-$π$ scattering lengths in the frame of the linear sigma model. For this we consider all the one loop corrections in the s, t and u channels, associate to the insertion of a Schwinger propagator for charged pions, working in the region of small values of the magnetic field. Our calculation relies on an appropriate expansion for the propagator. It turns out that the leading scattering length, $l = 0$ in the S-channel, increases for an increasing value of the magnetic field, in the isospin $I = 2$ case whereas the opposite effect is foun…
We analyze the $f_0(500)$ state generated as a pole of $ππ$ scattering within unitarized low-energy effective theories at finite temperature. First, we report on the $σ$ self-energy in the LSM, which is used as a benchmark in order to test the hypotheses carried out. The relation of that thermal pole with the scalar susceptibility is studied within a scalar saturation approach, which yields results complying with lattice data. The robustness and predictability of this method are studied in terms of the low-energy constants involved and the unitarization method. Our analysis highlights the impo…
Estimates of the O(alpha_s^4) corrections to sigma_{tot}(e^+e^- \rightarrow hadrons), Gamma(τ\rightarrow ν_τ +hadrons) and deep inelastic scattering sum rules
In this article, we extend our previous study of the $π$-$π$ scattering lengths under the presence of an external magnetic field, including finite temperature effects. The novelty of this work is precisely the introduction of temperature into the discussion, and its interplay with the magnetic field. As in the previous article, we base our analysis in the linear sigma-model, and our calculations are exact within this context. Although the effects are comparatively small, it is interesting to remark that magnetic field and temperature display opposite effects over the scattering lengths.
In this article, a new perspective for obtaining the magnetic evolution of $π-π$ scattering lengths in the frame of the linear sigma model is presented. When computing the relevant one-loop diagrams that contribute to these parameters, the sum over Landau levels --emerging from the expansion of the Schwinger propagator-- is handled in a novel way that could also be applied to the calculation of other magnetic-type corrections. Essentially, we have obtained an expansion in terms of Hurwitz Zeta functions. It is necessary to regularize our expressions by an appropriate physical subtraction when …
We summarize recent evidence, both from lattice QCD and chiral perturbation theory, that suggests that larger-than-expected excited-state contamination could be the reason for the tension between phenomenological determinations and previous direct lattice-QCD calculations of the pion--nucleon sigma term $σ_{πN}$. In addition, we extend the $χ$PT analysis by calculating the corrections due to including the $Δ(1232)$ resonance as an explicit degree of freedom. This correction is found to be small, thereby corroborating the excited-state effects found in the $Δ$-less calculation and the result fo…
We compute the magnetic field-induced modifications to the boson self-coupling and the boson-fermion coupling, in the static limit, using an effective model of QCD, the linear sigma model with quarks. The former is computed for arbitrary field strengths as well as using the strong field approximation. The latter is obtained in the strong field limit. The arbitrary field result for the boson self-coupling depends on the ultraviolet renormalization scale and this dependence cannot be removed by a simple vacuum subtraction. Using the strong field result as a guide, we find the appropriate choice …
The by now well-established scalar-isoscalar resonance $f_{0}(500)$ (the $σ$ meson) seems potentially relevant in the evaluation of thermodynamic quantities of a hadronic gas, since its mass is low. However, we recall that its contribution to isospin-averaged observables is, to a surprising accuracy, canceled by the repulsion from the pion-pion scalar-isotensor channel. As a result, in practice one should not incorporate $f_0(500)$ in standard hadronic resonance-gas models for studies of isospin averaged quantities. In our analysis we use the formalism of the virial expansion, which allows one…
In this paper, we give formal results of Schwinger pair production correction in thermal systems with external background field by using the evolution operator method of thermo field dynamics, where especially tree level correction of thermal photons is considered with linear response approaches by an effective mass shift. We consider initial systems in two types of vacuums as zero temperature and thermal vacuum, respectively, with correction of thermal photons is or not included. As an example we give results of these corrections to pair production for a constant external background electric …
In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-$σ$ model (PLSM) is analysed for chiral phase-transition, $σ_l$ and $σ_s$ and for deconfinement order-parameters, $ϕ$ and $ϕ^*$ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates ($Δ_{l,s}$). All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modelling of the relaxation time is…
We reconsider gravitational corrections to vacuum decay, confirming and simplifying earlier results and extending them by allowing for a non-minimal coupling of the Higgs to gravity. We find that leading-order gravitational corrections suppress the vacuum decay rate. Furthermore, we compute minor corrections to thermal vacuum decay in the SM by adding one-loop contributions to the Higgs kinetic term, two-loop contributions to the Higgs potential and allowing for time-dependent bounces.
Coupling of `t Hooft's determinant term is investigated in the framework of the three flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field dependent correction to the coupling of the conventional U_A(1) breaking determinant term. It is found that at low temperatures mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid-gas transition.
The linear-sigma model, in which information about confining gluons is included through the Polyakov-loop potential (PLSM), is considered in order to perform a systematic study for various magnetic properties of QCD matter under extreme conditions of high temperatures and densities and finite magnetic field strengths. The introduction of magnetic field to the PLSM Lagrangian requires suitable utilization of Landau quantization, modification in the dispersion relations, and momentum-space dimension-reduction. We observed that increasing the magnetic field leads to filling-up lower Landau levels…
Complete one-loop self-energies of the linear sigma model coupled to quarks at finite temperature and in a magnetic field
Universidad Autónoma Metropolitana-Iztapalapa（墨西哥自治大学伊察帕拉帕分校）；Centro de Investigación y Desarrollo en Ciencias Aeroespaciales (CIDCA), Academia Politécnica Aeronáutica, Fuerza Aérea de Chile（智利空军航空航天科学研究与开发中心（CIDCA）、空军理工学院）；Universidad San Sebastián（圣塞巴斯蒂安大学）
We provide a model-independent argument indicating that for a black hole of entropy N the non-thermal deviations from Hawking radiation, per each emission time, are of order 1/N, as opposed to exp(-N). This fact abolishes the standard a priory basis for the information paradox.
