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D. K. Sinclair

Publications and source records attributed to D. K. Sinclair.

At least 55 records · Page 3Linked to original sources
arXiv2005

Lattice simulations of Born-Infeld non-linear QED

Born-Infeld non-linear electrodynamics was introduced to render the self energy of a point particle finite. It has recently been revived as a field theory for branes and strings. We quantize this theory on a Euclidean space-time lattice, using Metropolis Monte-Carlo simulations to measure the properties of the quantum field theory. Luscher-Weisz methods are used to measure the electromagnetic fields from a static point charge. The D field from a point charge appears to be identical to that for the normal Maxwell Lagrangian. The E field is enhanced by quantum fluctuations, and shows short distance screening as it does in the classical theory.

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arXiv2005

Spin correlations and velocity-scaling in color-octet NRQCD matrix elements

We compute spin-dependent decay matrix elements for S-wave charmonium and bottomonium in lattice nonrelativistic quantum chromodynamics (NRQCD). Particular emphasis is placed upon the color-octet matrix elements, since the corresponding production matrix elements are expected to appear in the dominant contributions to the production cross sections at large transverse momenta. We use three slightly different versions of the heavy-quark lattice Green's functions in order to minimize the contributions that scale as powers of the ultraviolet cutoff. The lattice matrix elements that we calculate obey the hierarchy that is suggested by the velocity-scaling rules of NRQCD.

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arXiv2005

Finite dt dependence of the Binder cumulants for 3-flavor QCD at finite temperature and isospin density

We simulate 3-flavour lattice QCD at small isospin chemical potential $μ_I$ and finite temperature $T$. At $μ_I=0$ there is a critical mass $m_c$ where the finite-temperature transition changes from first order to a crossover. We measure the $μ_I$ dependence of the transition $β$ ($β_c$) for $m$ close to $m_c$. $β_c$ and hence $T_c$ decrease slowly with increasing $μ_I$. $β_c$ at finite $μ_I$ is in good agreement $β_c$ at finite $μ$ (quark-number chemical potential). We use fourth-order Binder cumulants to determine the nature of this transition and to search for a critical endpoint. We measure the $dt$ dependence of these cumulants and extrapolate to $dt=0$. ($dt$ is the `time' increment used in the hybrid molecular-dynamics simulations.) Preliminary measurements of these Binder cumulants show little $μ_I$ dependence. (Simulations at imaginary $μ$ indicate that the $μ$ dependence of the Binder cumulants is also weak.) This contrasts to the $μ_I$ dependence we observed at fixed $dt$.

hep-lat↗
arXiv2004

Simulating lattice QCD at finite temperature and zero quark mass

We simulate lattice QCD with an irrelevant chiral 4-fermion interaction which allows us to simulate at zero quark mass. This enables us to study the finite-temperature chiral-symmetry-restoring phase transition for 2 massless quark flavours, which is believed to be second order. In particular, it enables us to estimate the critical exponents which characterize the universality class of this transition. Our earlier simulations on $N_t=4$ and $N_t=6$ lattices revealed that finite lattice-spacing artifacts on such coarse lattices affect the nature of the transition. We are now simulating on $N_t=8$ lattices ($12^3 \times 8$, $16^3 \times 8$ and $24^3 \times 8$ lattices) where we expect to expose the continuum behaviour of this transition.

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arXiv2004

The finite temperature transition for 3-flavour lattice QCD at finite isospin density

We simulate 3-flavour lattice QCD with a small chemical potential $μ_I$ for isospin, at temperatures close to the finite temperature transition. Using quark masses just above the critical mass for zero chemical potential, we determine the position of the transition from hadronic matter to a quark-gluon plasma as a function of $μ_I$. We see evidence for a critical endpoint where the transition changes from a crossover to a first-order transition as $μ_I$ is increased. We argue that QCD at finite $μ_I$ and QCD at finite quark-numberchemical potential $μ$ should behave similarly in this region.

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arXiv2004

The finite temperature transition for 2-flavour lattice QCD at finite isospin density

We simulate 2-flavour lattice QCD at finite isospin chemical potential mu_I, for temperatures close to the finite temperature transition from hadronic matter to a quark-gluon plasma. The mu_I dependence of the transition coupling is observed and used to estimate the decrease in the transition temperature with increasing mu_I. These simulations are performed on an 8^3 times 4 lattice at 3 different quark masses. Our estimate of the magnitude of the fluctuations of the phase of the fermion determinant at small quark-number chemical potential mu, suggest that the position of the small mu and small mu_I transitions should be the same for mu_I=2mu, and we argue that the nature of these transitions should be the same. For all mu_I < m_pi the smoothness of these transitions and the values of the Binder cumulant B_4, indicate that these transitions are mere crossovers, and show no sign of the expected critical endpoint. For mu_I > m_pi and a small isospin (I_3) breaking term lambda, we do find evidence of a critical endpoint which would indicate that, for lambda=0, there is a tricritical point on the phase boundary where the pion condensate evaporates, where this phase transition changes from second to first order.

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arXiv2003

Finite Density Lattice Gauge Theories with Positive Fermion Determinants

We perform simulations of (3-colour) QCD with 2 quark flavours at a finite chemical potential $μ_I$ for isospin($I_3$), and of 2-colour QCD at a finite chemical potential $μ$ for quark number. At zero temperature, QCD at finite $μ_I$ has a mean-field phase transition at $μ_I=m_π$ to a superfluid state with a charged pion condensate which spontaneously breaks $I_3$. We study the finite temperature transition as a function of $μ_I$. For $μ_I < m_π$, where this is closely related to the transition at finite $μ$, this appears to be a crossover independent of quark mass, with no sign of the proposed critical endpoint. For $μ_I > m_π$ this becomes a true phase transition where the pion condensate evaporates. For $μ_I$ just above $m_π$ the transition seems to be second order, while for larger $μ_I$ it appears to become first order. At zero temperature, 2-colour QCD also possesses a superfluid state with a diquark condensate. We study its spectrum of Goldstone and pseudo-Goldstone bosons associated with chiral and quark-number symmetry breaking.

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arXiv2003

Lattice QCD at finite isospin density and/or temperature

We simulate two-flavour lattice QCD with at a finite chemical potential $μ_I$ for isospin, and finite temperature. At small $μ_I$, we determine the position of the crossover from hadronic matter to a quark-gluon plasma as a function of $μ_I$. At larger $μ_I$ we observe the phase transition from the superfluid pion-condensed phase to a quark-gluon plasma, noting its change from second order to first order as $μ_I$ is increased. We also simulate two-flavour lattice QCD at zero quark mass, using an action which includes an additional 4-fermion interaction, at temperatures close to the chiral transition on $N_t=8$ lattices.

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arXiv2003

The pseudo-Goldstone spectrum of 2-colour QCD at finite density

We examine the spectrum of 2-colour lattice QCD with 4 continuum flavours at a finite chemical potential ($μ$) for quark-number, on a $12^3 \times 24$ lattice. First we present evidence that the system undergoes a transition to a state with a diquark condensate, which spontaneously breaks quark number at $μ=m_π/2$, and that this transition is mean field in nature. We then examine the 3 states that would be Goldstone bosons at $μ=0$ for zero Dirac and Majorana quark masses. The predictions of chiral effective Lagrangians give a good description of the behaviour of these masses for $μ< m_π/2$. Except for the heaviest of these states, these predictions diverge from our measurements, once $μ$ is significantly greater than $m_π/2$. However, the qualitative behaviour of these masses, indicates that the physics is very similar to that predicted by these effective Lagrangians, and there is some indication that at least part of these discrepancies is due to saturation, a lattice artifact.

hep-lat↗
arXiv2003

The N_t=4 finite temperature phase transition for lattice QCD with a weak chiral 4-fermion interaction

We study the finite temperature phase transition of lattice QCD with an irrelevant chiral 4-fermion interaction and two massless quark flavours, on $8^3 \times 4$ and $12^2 \times 24 \times 4$ lattices. The strength of the 4-fermion interaction was reduced to half the minimum value used in previous simulations, to study how the nature of this phase transition depends on this additional interaction. We find that the transition remains first order as the 4-fermion coupling is reduced. Extending our earlier studies indicates that for sufficiently large 4-fermion coupling, the transition is probably second order.

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arXiv2002

Lattice QCD at finite isospin chemical potential and temperature

We simulate lattice QCD at a finite chemical potential $μ_I$ for isospin ($I_3$) at zero and finite temperatures. At some $μ_I=μ_c$ QCD has a second order transition with mean-field critical exponents to a state where ($I_3$) is broken spontaneously by a charged pion condensate. Heating the system with $μ_I > μ_c$ we find there is some temperature at which this condensate evaporates. This transition appears to be second order and mean-field at lower $μ_I$ values, and first order for $μ_I$ sufficiently large. We are determining the dependence of the finite temperature crossover $T_c$ on $μ_I$ for $μ_I < μ_c$. This is expected to be identical to $T_c$'s dependence on quark-number chemical potential $μ_q$ for small $μ_q$.

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arXiv2002

The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $μ$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $μ$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $μ$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $μ$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.

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arXiv2002

Lattice QCD at finite isospin density at zero and finite temperature

We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical potential, $μ_I$, for the third component of isospin ($I_3$), at both zero and at finite temperature. At zero temperature there is some $μ_I$, $μ_c$ say, above which $I_3$ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict $μ_c=m_π$. This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of $I_3$ symmetry at high temperature for $μ_I > μ_c$. For $μ_I$ sufficiently large, this finite temperature phase transition appears to be first order. As $μ_I$ is decreased it becomes second order connecting continuously with the zero temperature transition.

hep-lat↗
arXiv2002

Quenched lattice QCD at finite isospin density and related theories

We study quenched QCD at finite chemical potential, $μ_I$, for the third component of isospin and quenched two-colour QCD at finite chemical potential, $μ$, for quark number. In contrast to the quenched approximation to QCD at finite quark-number chemical potential, the quenched approximations to these theories behave similarly to the full theories. The reason is that these theories have real positive fermion determinants. In both of these theories there is some critical chemical potential above which the charge coupled to the chemical potential is spontaneously broken. In each case, the transition appears to be second order. We study the scaling properties near the critical point using scaling functions suggested by effective (chiral) Lagrangians and find evidence for scaling with mean-field critical exponents in each case. The subtleties associated with observing the critical scaling of these theories are discussed.

hep-lat↗
arXiv2002

Bottomonium Decay Matrix Elements from Lattice QCD with Two Light Quarks

We calculate the long-distance matrix elements for the decays of the Upsilon (eta_b) and chi_b (h_b) states in lattice QCD with two flavors of light dynamical quarks. We relate the lattice matrix elements to their continuum counterparts through one-loop order in perturbation theory. In the case of the leading S-wave matrix element, we compare our result with a phenomenological value that we extract from the experimental leptonic decay rate by using the theoretical expression for the decay rate, accurate through relative order alpha_s. Whereas estimates of the leading S-wave matrix element from quenched QCD are 40--45% lower than the phenomenological value, the two-flavor estimate of the same matrix element is close to the phenomenological value. Extrapolating to the real world of 2+1 light flavors, we find that this matrix element is approximately 6% higher than the phenomenological value, but that the phenomenological value lies within our error bars. We also compute the color-singlet and color-octet matrix elements for P-wave decays. We find the value of the color-singlet matrix element for 2+1 flavors to be approximately 70% larger than the quenched value and the value of the color-octet matrix element for 2+1 flavors to be approximately 40% larger than the quenched value.

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arXiv2001

Lattice QCD at finite isospin density

We have simulated QCD at a finite chemical potential $μ_I$ for isospin ($I_3$) to probe part of the phase diagram for nuclear matter. Preliminary results suggest that for $μ_I > μ_c$, this theory forms a charged pion condensate which spontaneously breaks $I_3$, and the isospin density is non zero.

hep-lat↗
arXiv2001

Two-colour QCD at non-zero quark-number density

We have simulated two-colour four-flavour QCD at non-zero chemical potential $μ$ for quark number. Simulations were performed on $8^4$ and $12^3 \times 24$ lattices. Clear evidence was seen for the formation of a colourless diquark condensate which breaks quark number spontaneously, for $μ> μ_c \sim m_π/2$. The transition appears to be second order. We have measured the spectrum of scalar and pseudoscalar bosons which shows clear evidence for the expected Goldstone boson. Our results are in qualitative agreement with those from effective Lagrangians for the potential Goldstone excitations of this theory.

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