arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 145 records · Page 8Linked to original sources

arXiv2001

Solution to the 3-Loop $Φ$-Derivable Approximation for Massless Scalar Thermodynamics

We develop a systematic method for solving the 3-loop $Φ$-derivable approximation to the thermodynamics of the massless $ϕ^4$ field theory. The method involves expanding sum-integrals in powers of $g^2$ and m/T, where g is the coupling constant, m is a variational mass parameter, and T is the temperature. The problem is reduced to one with the single variational parameter m by solving the variational equations order-by-order in $g^2$ and m/T. At the variational point, there are ultraviolet divergences of order $g^6$ that cannot be removed by any renormalization of the coupling constant. We define a finite thermodynamic potential by truncating at $5^{th}$ order in g and m/T. The associated thermodynamic functions seem to be perturbatively stable and insensitive to variations in the renormalization scale.

hep-ph↗

arXiv2001

Solution to the 3-loop $Φ$-derivable Approximation for Scalar Thermodynamics

We solve the 3-loop $Φ$-derivable approximation to the thermodynamics of the massless $ϕ^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.

hep-ph↗

arXiv2001

Three-body recombination into deep bound states in a Bose gas with large scattering length

An effective field theory for the three-body system with large scattering length a is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant αis calculated to first order in the short-distance interactions that allow the recombination. For a < 0, the dimensionless combination m α/(\hbar a^4) is a periodic function of \ln |a| that exhibits resonances at values of a that differ by multiplicative factors of 22.7. This dramatic behavior should be observable near a Feshbach resonance when a becomes large and negative.

cond-mat↗

arXiv2001

Fragmentation Functions for Lepton Pairs

We calculate the fragmentation function for a light quark to decay into a lepton pair to leading order in the QCD coupling constant. In the formal definition of the fragmentation function, a QED phase must be included in the eikonal factor to guarantee QED gauge invariance. We find that the longitudinal polarization fraction is a decreasing function of the factorization scale, in accord with the intuitive expectation that the virtual photon should behave more and more like a real photon as the transverse momomentum of the fragmenting quark increases.

hep-ph↗

arXiv2001

Screened Perturbation Theory to Three Loops

The thermal physics of a massless scalar field with a phi^4 interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast to the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.

hep-ph↗

arXiv2000

Polarization of Upsilon(nS) at the Tevatron

The polarization of inclusive Upsilon(nS) at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. We use a recent determination of the NRQCD matrix elements from fitting the CDF data on bottomonium production from Run IB of the Tevatron. The result for the polarization of Upsilon(1S) integrated over the transverse momentum bin 8 < p_T < 20 GeV is consistent with a recent measurement by the CDF Collaboration. The transverse polarization of Upsilon(1S) is predicted to increase steadily for p_T greater than about 10 GeV. The Upsilon(2S) and Upsilon(3S) are predicted to have significantly larger transverse polarizations than Upsilon(1S).

hep-ph↗

arXiv2000

Nonuniversal Effects in the Homogeneous Bose Gas

Effective field theory predicts that the leading nonuniversal effects in the homogeneous Bose gas arise from the effective range for S-wave scattering and from an effective three-body contact interaction. We calculate the leading nonuniversal contributions to the energy density and condensate fraction and compare the predictions with results from diffusion Monte Carlo calculations by Giorgini, Boronat, and Casulleras. We give a crude determination of the strength of the three-body contact interaction for various model potentials. Accurate determinations could be obtained from diffusion Monte Carlo calculations of the energy density with higher statistics.

cond-mat.stat-mech↗

arXiv2000

NRQCD Analysis of Bottomonium Production at the Tevatron

Recent data from the CDF collaboration on the production of spin-triplet bottomonium states at the Tevatron p \bar p collider are analyzed within the NRQCD factorization formalism. The color-singlet matrix elements are determined from electromagnetic decays and from potential models. The color-octet matrix elements are determined by fitting the CDF data on the cross sections for Upsilon(1S), Upsilon(2S), and Upsilon(3S) at large p_T and the fractions of Upsilon(1S) coming from chi_b(1P) and chi_b(2P). We use the resulting matrix elements to predict the cross sections at the Tevatron for the spin-singlet states eta_b(nS) and h_b(nP). We argue that eta_b(1S) should be observable in Run II through the decay eta_b -> J/psi + J/psi.

hep-ph↗

arXiv2000

Polarization of Prompt J/psi at the Tevatron

The polarization of prompt J/psi at the Fermilab Tevatron is calculated within the nonrelativistic QCD factorization framework. The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum. The angular distribution parameter alpha for leptonic decays of the J/ψis predicted to increase from near 0 at p_T = 5 GeV to about 0.5 at p_T = 20 GeV. The prediction is consistent with measurements by the CDF Collaboration at intermediate values of p_T, but disagrees by about 3 standard deviations at the largest values of p_T measured.

hep-ph↗

arXiv2000

Next-to-leading Order Calculation of the Color-Octet 3S1 Gluon Fragmentation Function for Heavy Quarkonium

The short-distance coefficients for the color-octet 3S1 term in the fragmentation function for a gluon to split into heavy quarkonium states is calculated to order alpha_s^2. The gauge-invariant definition of the fragmentation function by Collins and Soper is employed. Ultraviolet divergences are removed using the MS-bar renormalization procedure. The longitudinal term in the fragmentation function agrees with a previous calculation by Beneke and Rothstein. The next-to-leading order correction to the transverse term disagrees with a previous calculation.

hep-ph↗

arXiv2000

The Massive Thermal Basketball Diagram

The "basketball diagram" is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a phi^4 interaction to three-loop order.

hep-ph↗

arXiv2000

Power-suppressed Thermal Effects from Heavy Particles

In quantum field theory, heavy particles with mass $M$ much greater than the temperature $T$ give not only effects suppressed by the Boltzmann factor $e^{-M/T}$, but also effects suppressed by powers of $T/M$. We show that power-suppressed terms in equilibrium observables arise from effective interactions among light particles due to virtual heavy particles. We study a model introduced by Matsumoto and Yoshimura in which study a model introduced by Matsumoto and Yoshimura in which heavy bosons interact only through a term that allows pair annihilation into light particles. We construct an effective Lagrangian for the light field by integrating out the heavy field, and use it to calculate the leading power-suppressed terms in the energy density. The thermal average of the Hamiltonian density for the heavy field includes a term proportional to $T^6/M^2$, but we show that this term can be eliminated by a field redefinition and therefore cannot have any physical significance.

hep-ph↗

arXiv1999

Hard-thermal-loop Resummation of the Free Energy of a Hot Quark-Gluon Plasma

The quark contribution to the free energy of a hot quark-gluon plasma is calculated to leading order in hard-thermal-loop (HTL) perturbation theory. This method selectively resums higher order corrections associated with plasma effects, such as screening, quasiparticles, and Landau damping. Comparing to the weak-coupling expansion of QCD, the error in the one-loop HTL free energy is of order alpha_s, but the large alpha_s^(3/2) correction from QCD plasma effects is included exactly.

hep-ph↗

arXiv1999

Hard-thermal-loop Resummation of the Thermodynamics of a Hot Gluon Plasma

We calculate the thermodynamic functions of a hot gluon plasma to leading order in hard-thermal-loop (HTL) perturbation theory. Effects associated with screening, gluon quasiparticles, and Landau damping are resummed to all orders. The ultraviolet divergences generated by the HTL propagator corrections can be cancelled by a counterterm that depends on the thermal gluon mass parameter. The HTL thermodynamic functions are compared to those from lattice gauge theory calculations and from quasiparticle models. For reasonable values of the HTL parameters, the deviations from lattice results for T > 2 T_c have the correct sign and roughly the correct magnitude to be accounted for by next-to-leading order corrections in HTL perturbation theory.

hep-ph↗

arXiv1999

Renormalons in Electromagnetic Annihilation Decays of Quarkonium

We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/psi --> e^+e^- and eta_c --> gamma gamma. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-N_f limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the Coulomb singularity in the short-distance coefficients. We verify that the ambiguities in the short-distance coefficients from the first infrared renormalon are canceled by ambiguities in the nonperturbative NRQCD matrix elements that contribute through relative order v^2. Our results are used to estimate the coefficients of higher order radiative corrections in the decay rates for J/psi --> e^+ e^-, eta_c --> gamma gamma, and J/ψ--> gamma gamma gamma.

hep-ph↗

arXiv1999

Semiclassical Corrections to a Static Bose-Einstein Condensate at Zero Temperature

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equations for a general time-independent state of the condensate, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be taken into account by adding a local correction term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the semiclassical corrections can be taken into account by adding local correction terms to the hydrodynamic equations.

cond-mat↗

arXiv1999

Associated Production of Upsilon and Weak Gauge Bosons at the Tevatron

We calculate the rate of production of W+Upsilon and Z+Upsilon at the Tevatron. We find the cross sections at a center-of-mass energy of 1.8 TeV to be roughly 450 pb for W+Upsilon and 150 pb for Z+Upsilon. The dominant production mechanism involves the binding of a color-octet b-bbar pair into a P-wave bottomonium state which subsequently decays into Upsilon. The purely leptonic decay modes of Upsilon, W, and Z provide signatures with small backgrounds. In Run I of the Tevatron, the number of events in the purely leptonic decay channels before allowing for detector acceptances and efficiencies should be about 500 for W+Upsilon and about 60 for Z+Upsilon. We conclude that W+Upsilon events may be observable in the Run I data.

hep-ph↗

arXiv1999

Hard-thermal-loop Resummation of the Free Energy of a Hot Gluon Plasma

We calculate the free energy of a hot gluon plasma to leading order in hard-thermal-loop perturbation theory. Effects associated with screening, gluon quasiparticles, and Landau damping are resummed to all orders. The ultraviolet divergences generated by the hard-thermal-loop propagator corrections can be cancelled by a temperature-independent counterterm. The deviation of the hard-thermal-loop free energy from lattice QCD results for T > 2 T_c has the correct sign and roughly the correct magnitude to be accounted for by next-to-leading order corrections.

hep-ph↗