arXiv subjects
Publications and source records attributed to Paulo F. Bedaque.
We discuss two technical issues related to the gap equation in high-density QCD: i) how to obtain the asymptotic solution with well controlled approximations, and ii) the renormalization of four-quark operators in the high-density effective field theory.
The phase shifts for the higher partial waves (l\ge 1) in the spin quartet and doublet channel of nd scattering at centre-of-mass energies up to 15 MeV are presented at next-to-leading and next-to-next-to-leading order in an effective field theory in which pions are integrated out. As available, the results agree with both phase shift analyses and potential model calculations.
The renormalization group is used to resum leading logarithmic contributions of the form alpha_s^{n+1} beta_0^n log^n (Delta/mu) to the gap equation appropriate for high density QCD. The scale dependence of the strong coupling constant alpha_s increases the gap by a factor of exp(33/16 (pi^2/4 - 1)) ~ 20 in the small coupling limit.
The low-energy effective theories for the two- and three-flavor color-superconductors arising in the high density limit of QCD are discussed. Using an effective field theory to describe quarks near the fermi surface, we compute the masses of the pseudo-Goldstone bosons that dominate the low-momentum dynamics of these systems.
A measurement of parity-violating spin-dependent gamma proton Compton scattering will provide a theoretically clean determination of the parity-violating pion-nucleon coupling constant $h_{πNN}^{(1)}$. We calculate the leading parity-violating amplitude arising from one-loop pion graphs in chiral perturbation theory. An asymmetry of ~5 10^{-8} is estimated for Compton scattering of 100 MeV photons.
The influence of different chemical potential for different flavors on color superconductivity is analyzed. It is found that there is a first order transition as the asymmetry grows. This transition proceeds through the formation of bubbles of low density, flavor asymmetric normal phase inside a high density, superconducting phase with a gap {\it larger} than the one found in the symmetric case. For small fixed asymmetries the system is normal at low densities and superconducting only above some critical density. For larger asymmetries the two massless quarks system stays in the mixed state for arbitrarily high densities.
The real and imaginary part of the quartet S wave phase shift in nd scattering (^4 S_{3/2}) for centre-of-mass momenta of up to 300 MeV (E_cm \approx 70 MeV) is presented in effective field theory, using both perturbative pions and a theory in which pions are integrated out. As available, the calculation agrees with both experimental data and potential model calculations, but extends to a higher, so far untested momentum régime above the deuteron breakup point. A Lagrangean more feasible for numerical computations is derived.
We compute the finite temperature pole mass shifts of the octet and decuplet baryons using heavy baryon chiral perturbation theory and the 1/N_c expansion, where N_c is the number of QCD colors. We consider temperatures of the order of the pion mass m_π, and truncate the chiral and 1/N_c expansions assuming that m_π\sim 1/N_c. There are three scales in the problem: the temperature T, the pion mass m_π, and the octet--decuplet mass difference. Therefore, the result is not simply a power series in T. We find that the nucleon and Δtemperature mass shifts are opposite in sign, and that their mass difference changes by 20% in the temperature range 90 MeV < T < 130 MeV, that is the range where the freeze out in relativistic heavy ion collisions is expected to occur. We argue that our results are insensitive to the neglect of 1/N_c- supressed effects; the main purpose of the 1/N_c expansion in this work is to justify our treatment of the decuplet states.
We consider flavor breaking in the the octet and decuplet baryon masses at second order in large-$N$ chiral perturbation theory, where $N$ is the number of QCD colors. We assume that $1/N \sim 1/N_F \sim m_s / Λ\gg m_{u,d}/Λ, α_{EM}$, where $N_F$ is the number of light quark flavors, and $m_{u,d,s} / Λ$ are the parameters controlling $SU(N_F)$ flavor breaking in chiral perturbation theory. We consistently include non-analytic contributions to the baryon masses at orders $m_q^{3/2}$, $m_q^2 \ln m_q$, and $(m_q \ln m_q) / N$. The $m_q^{3/2}$ corrections are small for the relations that follow from $SU(N_F)$ symmetry alone, but the corrections to the large-$N$ relations are large and have the wrong sign. Chiral power-counting and large-$N$ consistency allow a 2-loop contribution at order $m_q^2 \ln m_q$, and a non-trivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are non-trivial consequences of the $1/N$ expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is $7 \MeV$ for the $\De I = 0$ mass differences and $0.35 \MeV$ for the $\De I \ne 0$ mass differences, consistent with the expectation that the error is of order $1/N^2 \sim 10\%$.
We compare results from $δ$--expansion, in simple theories, with self--consistent calculations as well as calculations involving the principle of minimal sensitivity. We show that the latter methods give relatively more accurate results order by order.
We give an alternate derivation of Weldon's formula for combining products of factors with non identical analytic behavior. While such a formula would appear to be useful in finite temperature calculations, we give an example of a zero temperature calculation, namely, the degenerate electron gas, to justify the result.