arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 181 records · Page 10Linked to original sources

arXiv1995

On the Convergence of Perturbative QCD at High Temperature

The free energy for QCD at high temperature $T$ is calculated to order $g^5$ using effective-field-theory methods to separate the contributions from the momentum scales $T$ and $gT$. The effects of the scale $T$ enter through the coefficients in the effective lagrangian for the 3-dimensional effective theory obtained by dimensional reduction. The perturbation series for these coefficients seem to be well-behaved if the running coupling constant is sufficiently small: $α_s(2 πT) \ll 1$. For the contribution to the free energy from the scale $gT$, the perturbation series is well-behaved only if $α_s(2 πT)$ is an order of magnitude smaller. The implication for applications of perturbative QCD to the quark-gluon plasma are briefly discussed.

hep-ph↗

arXiv1995

Gluon Fragmentation into Spin-Triplet S-Wave Quarkonium

The leading color-singlet contribution to the fragmentation function for a gluon to split into spin-triplet S-wave quarkonium is presented. In the case of charmonium, we find that this color-singlet term is always negligible compared to the leading color-octet contribution.

hep-ph↗

arXiv1995

QCD Radiative Corrections to the Leptonic Decay Rate of the B_c Meson

The QCD radiative corrections to the leptonic decay rate of the $B_c$ meson are calculated using the formalism of nonrelativistic QCD (NRQCD) to separate short-distance and long-distance effects. The $B_c$ decay constant is factored into a sum of NRQCD matrix elements each multiplied by a short-distance coefficient. The short-distance coefficient for the leading matrix element is calculated to order $α_s$ by matching a perturbative calculation in full QCD with the corresponding perturbative calculation in NRQCD. This short-distance correction decreases the leptonic decay rate by approximately $15\%$.

hep-ph↗

arXiv1995

Effective Field Theory Approach to High-Temperature Thermodynamics

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional reduction to the bosonic zero-frequency modes. The parameters of the effective theory can be calculated as perturbation series in the running coupling constant $g^2(T)$. The free energy is separated into the contributions from the momentum scales $T$ and $gT$, respectively. The first term can be written as a perturbation series in $g^2(T)$. If all forces are screened at the scale $gT$, the second term can be calculated as a perturbation series in $g(T)$ beginning at order $g^3$. The parameters of the effective theory satisfy renormalization group equations that can be used to sum up leading logarithms of $T/(gT)$. We apply this method to a massless scalar field with a $Φ^4$ interaction, calculating the free energy to order $g^6 \log g$ and the screening mass to order $g^5 \log g$.

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arXiv1994

Color-Octet Fragmentation and the psi' Surplus at the Tevatron

The production rate of prompt $ψ'$'s at large transverse momentum at the Tevatron is larger than theoretical expectations by about a factor of 30. As a solution to this puzzle, we suggest that the dominant $ψ'$ production mechanism is the fragmentation of a gluon into a $c \bar c$ pair in a pointlike color-octet S-wave state, which subsequently evolves nonperturbatively into a $ψ'$ plus light hadrons. The contribution to the fragmentation function from this process is enhanced by a short-distance factor of $1/α_s^2$ relative to the conventional color-singlet contribution. This may compensate for the suppression by $v^4$, where $v$ is the relative momentum of the charm quark in the $ψ'$. If this is indeed the dominant production mechanism at large $p_T$, then the prompt $ψ'$'s that are observed at the Tevatron should almost always be associated with a jet of light hadrons.

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arXiv1994

Asymptotic Behavior of the Correlator for Polyakov Loops

The asymptotic behavior of the correlator for Polyakov loop operators separated by a large distance $R$ is determined for high temperature QCD. It is dominated by nonperturbative effects related to the exchange of magnetostatic gluons. To analyze the asymptotic behavior, the problem is formulated in terms of the effective field theory of QCD in 3 space dimensions. The Polyakov loop operator is expanded in terms of local gauge-invariant operators constructed out of the magnetostatic gauge field, with coefficients that can be calculated using resummed perturbation theory. The asymptotic behavior of the correlator is $\exp(-MR)/R$, where $M$ is the mass of the lowest-lying glueball in $(2+1)$-dimensional QCD. This result implies that existing lattice calculations of the Polyakov loop correlator at the highest temperatures available do not probe the true asymptotic region in $R$.

hep-ph↗

arXiv1994

Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories

The free energy of a nonabelian gauge theory at high temperature $T$ can be calculated to order $g^5$ using resummed perturbation theory, but the method breaks down at order $g^6$. A new method is developed for calculating the free energy to arbitrarily high accuracy in the high temperature limit. It involves the construction of a sequence of two effective field theories by first integrating out the momentum scale $T$ and then integrating out the momentum scale $g T$. The free energy decomposes into the sum of three terms, corresponding to the momentum scales $T$, $gT$, and $g^2T$. The first term can be calculated as a perturbation series in $g^2(T)$, where $g(T)$ is the running coupling constant. The second term in the free energy can be calculated as a perturbation series in $g(T)$, beginning at order $g^3$. The third term can also be expressed as a series in $g(T)$ beginning at order $g^6$, with coefficients that can be calculated using lattice simulations of 3-dimensional QCD. Leading logarithms of $T/(gT)$ and of $gT/(g^2T)$ can be summed up using renormalization group equations.

hep-ph↗

arXiv1994

Radiative Corrections to Quarkonium Decays: From a Model to a Rigorous Theory

Most previous calculations of the annihilation decay rates of heavy quarkonium were based on factorization assumptions that were unproven and, in some cases, even incorrect. The recent development of a general factorization formula for heavy quarkonium annihilation rates has provided a rigorous theoretical foundation for such calculations. The factorization formula is based on the use of the effective field theory NRQCD to factor the decay rate into short-distance coefficients that can be calculated in perturbation theory and long-distance matrix elements that can be computed using lattice simulations. This approach allows annihilation decay rates to be computed entirely from first principles.

hep-ph↗

arXiv1994

Next-to-leading Order Debye Mass for the Quark-gluon Plasma

The Debye screening mass for a quark-gluon plasma at high temperature is calculated to next-to-leading order in the QCD coupling constant from the correlator of two Polyakov loops. The result agrees with the screening mass defined by the location of the pole in the gluon propagator as calculated by Rebhan. It is logarithmically sensitive to nonperturbative effects associated with the screening of static chromomagnetic fields.

hep-ph↗

arXiv1994

Gluon Fragmentation into P-wave Heavy Quarkonium

The fragmentation functions for gluons to split into P-wave heavy quarkonium states are calculated to leading order in the QCD coupling constant. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wavefunction at the origin and a second parameter related to the probability for a heavy-quark-antiquark pair that is produced in a color-octet S-wave state to form a color-singlet P-wave bound state. The fragmentation probabilities for a high transverse momentum gluon to split into the P-wave charmonium states $χ_{c0}$, $χ_{c1}$, and $χ_{c2}$ are estimated to be $0.4 \times 10^{-4}$, $1.8 \times 10^{-4}$, and $2.4 \times 10^{-4}$, respectively. This fragmentation process may account for a significant fraction of the rate for the inclusive production of $χ_{cJ}$ at large transverse momentum in $p \bar p$ colliders.

hep-ph↗

arXiv1993

Perturbative QCD Fragmentation Functions for $B_c$ and $B_c^*$ Production

The dominant production mechanism for ${\bar b} c$ bound states in high energy processes is the production of a high energy ${\bar b}$ or $c$ quark, followed by its fragmentation into the ${\bar b} c$ state. We calculate the fragmentation functions for the production of the S-wave states $B_c$ and $B_c^*$ to leading order in the QCD coupling constant. The fragmentation probabilities for ${\bar b} \rightarrow B_c$ and ${\bar b} \rightarrow B_c^*$ are approximately $2.2 \times 10^{-4}$ and $3.1 \times 10^{-4}$, while those for $c \rightarrow B_c$ and $c \rightarrow B_c^*$ are smaller by almost two orders of magnitude.

hep-ph↗

arXiv1993

Tau Polarimetry with Inclusive Decays

The spin asymmetry parameter $A_τ$ characterizing the angular distribution of the total hadron momentum in the decay of a polarized tau can be calculated rigorously using perturbative QCD and the operator product expansion. Perturbative QCD corrections to the free quark result $A_τ= 1/3$ can be expressed as a power series in $α_s(M_τ)$ and nonperturbative QCD corrections can be expanded systematically in powers of $1/M_τ^2$. The QCD prediction is $A_τ= 0.41 \pm 0.02$. In the decay of a high energy tau into hadrons, the value of the hadronic energy distribution $dR_τ/dz$ evaluated at the maximum hadronic energy fraction $z = 1$ can also be calculated rigorously from QCD.

hep-ph↗

arXiv1993

Effective Field Theory for Plasmas at all Temperatures and Densities

The solution of the plasmon problem and the subsequent development of an effective field theory approach to ultrarelativistic plasmas are reviewed. The effective lagrangians that summarize collective effects in ultrarelativistic quark-gluon and electron-photon plasmas are presented. A generalization that describes an electromagnetic plasma at all temperatures and densities is proposed.

hep-ph↗

arXiv1993

Gluon Fragmentation into Heavy Quarkonium

The dominant production mechanism for heavy quark-antiquark bound states in very high energy processes is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions $D(z,μ)$ describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into S-wave quarkonium states to leading order in the QCD coupling constant. The leading logarithms of $μ/m_Q$, where $μ$ is the factorization scale and $m_Q$ is the heavy quark mass, are summed up using Altarelli-Parisi evolution equations.

hep-ph↗

arXiv1993

Z^0 Decay into Charmonium via Charm Quark Fragmentation

In decays of the $Z^0$, the dominant mechanism for the direct production of charmonium states is the decay of the $Z^0$ into a charm quark or antiquark followed by its fragmentation into the charmonium state. We calculate the fragmentation functions describing the splitting of charm quarks into S-wave charmonium states to leading order in the QCD coupling constant. Leading logarithms of $M_Z/m_c$ are summed up using Altarelli-Parisi evolution equations. Our analytic result agrees with the complete leading order calculation of the rate for $Z^0 \rightarrow ψc {\bar c}$. We also use our fragmentation functions to calculate the production rate of heavy quarkonium states in $W^\pm$, top quark, and Higgs decays.

hep-ph↗

arXiv1993

Neutrino Energy Loss from the Plasma Process at all Temperatures and Densities

We present a unified approach which is accurate at all temperatures and densities for calculating the energy loss from a stellar plasma due to the plasma process, the decay of photons and plasmons into neutrino pairs. To allow efficient numerical calculations, an analytic approximation to the dispersion equations for photons and plasmons is developed. It is correct to order $α$ in the classical, degenerate, and relativistic limits for all momenta $k$ and is correct at small $k$ for all temperatures and electron densities. Within the same approximations, concise expressions are derived for the transverse, longitudinal, and axial vector components of the neutrino emissivity.

hep-ph↗

arXiv1992

Rigorous QCD Predictions for Decays of P-Wave Quarkonia

We present a new factorization theorem for the decay rates of P-wave states of heavy quarkonia. Infrared logarithms that had appeared in previous perturbative calculations of P-wave decays are absorbed into a quantity that is related to the amplitude for the heavy quark and antiquark to be in a relative color-octet S-wave state. We predict all of the light-hadronic and electromagnetic decays rates of the $χ_c$ and $h_c$ states in terms of two phenomenological parameters.

hep-ph↗

arXiv1992

P-Wave Charmonium Production in B-Meson Decays

We calculate the decay rates of $B$ mesons into P-wave charmonium states using new factorization formulas that are valid to leading order in the relative velocity of the charmed quark and antiquark and to all orders in the running coupling constant of QCD. We express the production rates for all four P states in terms of two nonperturbative parameters, the derivative of the wavefunction at the origin and another parameter related to the probability for a charmed-quark-antiquark pair in a color-octet S-wave state to radiate a soft gluon and form a P-wave bound state. Using existing data on $B$ meson decays into $χ_{c1}$ to estimate the color-octet parameter, we find that the color-octet mechanism may account for a significant fraction of the $χ_{c1}$ production rate and that $B$ mesons should decay into $χ_{c2}$ at a similar rate.

hep-ph↗