arXiv subjects

D. K. Sinclair

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

At least 19 recordsLinked to original sources

arXiv2023

Lattice QED in an external magnetic field: Evidence for dynamical chiral symmetry breaking

We simulate QED in a strong constant homogeneous external magnetic field on a euclidean space-time lattice using the Rational Hybrid Monte Carlo method, developed for simulating lattice QCD. Our primary goal is to measure the chiral condensate in the limit when the input electron mass $m$ is zero. We observe a non-zero value, indicating that the external magnetic field catalyzes chiral symmetry breaking as predicted by approximate truncated Schwinger-Dyson methods. Such behaviour is associated with dominance by the lowest Landau level which causes the effective dimensional reduction from $3+1$~dimensions to $1+1$ dimensions for charged particles (electrons and positrons) where the attractive forces of QED can produce chiral symmetry breaking with a dynamical electron mass and associated chiral condensate. Since our lattice simulations use bare (lattice) parameters, while the Schwinger-Dyson analyses work with renormalized quantities, direct numerical comparison will require renormalization of our lattice results.

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arXiv2022

Chiral Symmetry Breaking in QED induced by an External Magnetic Field

We simulate Lattice QED in a constant external magnetic field using the RHMC algorithm. We seek evidence for chiral symmetry breaking predicted by truncated Schwinger-Dyson methods. Since the predicted values of the dynamical electron mass and chiral condensate at the physical fine structure constant are too small to be measured, we simulate at a larger value $α=1/5$. This requires using electron masses as low as $m=0.001$ to extrapolate to $m=0$. At a large magnetic field, the electrons occupy the lowest Landau level which has a small profile in the plane orthogonal to the magnetic field, so that we are able to use a lattice with small extent in these 2 directions. If chiral symmetry is unbroken at $m=0$ the chiral condensate is dominated by large momenta and should be insensitive to the lattice extent in the direction of the magnetic field and the time direction. When chiral symmetry is broken at $m=0$, the chiral condensate should be sensitive to the lattice size in these directions as $m \rightarrow 0$. We search for this behaviour by increasing the lattice extent in these 2 directions. Preliminary simulations show strong dependence of the chiral condensate on the lattice extent in these 2 directions for the smallest masses, and these increased condensates appear to be approaching a non-zero limit as $m \rightarrow 0$.

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arXiv2021

Lattice QED in external electromagnetic fields

We study QED in external electromagnetic fields using methods developed for simulating lattice QCD. Our first project is to simulate QED in a constant (in space and time) external magnetic field on a euclidean space-time lattice using the Rational Hybrid Monte Carlo (RHMC) method. Observables we measure include the condensate $\langle\barψψ\rangle$ and the effective electron action after integrating out the fermion fields. We look for evidence that the combined effect of the magnetic field and the electron-positron attraction from QED produces a non-zero condensate in the limit of zero electron mass, a non-perturbative effect analogous to spontaneous chiral symmetry breaking. Very preliminary evidence is that such a condensate exists, at least for strong external magnetic fields and unphysically large electric charge. In addition, we are storing field configurations to measure the expected distortions and screenings of the coulomb field of a charged particle due to the vacuum polarization asymmetries produced by the magnetic field. We hope also to measure the dynamical contribution to the electron mass produced by the same mechanism that produces a finite condensate in the zero input mass limit.

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arXiv2019

Applying Complex Langevin to Lattice QCD at finite $μ$

We continue our simulations of lattice QCD at finite quark-number chemical potential, $μ$, using the complex-Langevin equation (CLE) with gauge-cooling and adaptive updating. The CLE is used because QCD at finite finite $μ$ has a complex fermion determinant, which prevents use of standard simulation methods. Simulations using the standard lattice action show a transition from hadronic to nuclear matter for $μ< m_π/2$ rather than the expected $μ\approx m_N/3$. This suggests that the CLE is being influenced by the phase-quenched theory, which has a transition at $μ= m_π/2$. We are therefore performing CLE simulations with a new action which includes an irrelevant chiral 4-fermion interaction. This separates the physics at energies of order of the pion mass and smaller from that at energies of the other hadrons. In doing this, it breaks the extended symmetry of the phase-quenched theory over that of the full theory, raising the masses of the extra pion-like excitations consisting of a quark and a conjugate quark, which could otherwise produce such an anomalous transition. Our preliminary CLE simulations using massless quarks, so that $m_π=0$, show no transition at $μ=m_π/2=0$, but do show a transition at an appreciably higher value of $μ$. It remains to be seen if this transition is near to $m_N/3$.

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arXiv2019

Applying Complex Langevin Simulations to Lattice QCD at Finite Density

We study the use of the complex-Langevin equation (CLE) to simulate lattice QCD at a finite chemical potential ($μ$) for quark-number, which has a complex fermion determinant that prevents the use of standard simulation methods based on importance sampling. Recent enhancements to the CLE specific to lattice QCD inhibit runaway solutions which had foiled earlier attempts to use it for such simulations. However, it is not guaranteed to produce correct results. Our goal is to determine under what conditions the CLE yields correct values for the observables of interest. Zero temperature simulations indicate that for moderate couplings, good agreement with expected results is obtained for small $μ$ and for $μ$ large enough to reach saturation, and that this agreement improves as we go to weaker coupling. For intermediate $μ$ values these simulations do not produce the correct physics. We compare our results with those of the phase-quenched approximation. Since there are indications that correct results might be obtained if the CLE trajectories remain close to the $SU(3)$ manifold, we study how the distance from this manifold depends on the quark mass and on the coupling. We find that this distance decreases with decreasing quark mass and as the coupling decreases, i.e. as the simulations approach the continuum limit.

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arXiv2018

Complex Langevin for Lattice QCD

We simulate lattice QCD at finite quark-number chemical potential, $μ$, using the complex-Langevin equation (CLE) with gauge-cooling and adaptive updating to prevent instabilities. The CLE is used because QCD at finite $μ$ has a complex fermion determinant which precludes the use of standard simulation methods based on importance sampling. Since, even when CLE simulations converge, they are not guaranteed to produce correct results except under very stringent conditions, which lattice QCD at finite $μ$ does not obey, we need extensive testing to determine under what conditions it produces reliable results. We performed simulations at $β=6/g^2=5.6$ and $β=5.7$, both at $m=0.025$. For small $μ$ and $μ$ large enough to produce saturation, measured observables appear to be approaching their correct values as the coupling is decreased. However, for intermediate $μ$ values, these simulations predict a transition from hadronic to nuclear matter at a $μ$ which is far too small. Since there is evidence that for CLE simulations to produce correct results the trajectories should remain close to the $SU(3)$ manifold (at least for small $μ$), we explore the parameter space to see where this is true. We find that the distance from this manifold decreases as the coupling decreases and as the quark mass (in lattice units) decreases, i.e. as we approach the continuum limit. This indicates that we need to simulate at smaller couplings and quark masses (requiring larger lattices) to see if these can produce the correct physics.

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arXiv2017

Complex Langevin Simulations of QCD at Finite Density -- Progress Report

We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance sampling fail. Adaptive methods and gauge-cooling are used to prevent runaway solutions. Even then, the CLE is not guaranteed to give correct results. We are therefore performing extensive testing to determine under what, if any, conditions we can achieve reliable results. Our earlier simulations at $β=6/g^2=5.6$, $m=0.025$ on a $12^4$ lattice reproduced the expected phase structure but failed in the details. Our current simulations at $β=5.7$ on a $16^4$ lattice fail in similar ways while showing some improvement. We are therefore moving to even weaker couplings to see if the CLE might produce the correct results in the continuum (weak-coupling) limit, or, if it still fails, whether it might reproduce the results of the phase-quenched theory. We also discuss action (and other dynamics) modifications which might improve the performance of the CLE.

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arXiv2016

Complex Langevin for Lattice QCD at $T=0$ and $μ\ge 0$

QCD at finite quark-/baryon-number density, which describes nuclear matter, has a sign problem which prevents direct application of standard simulation methods based on importance sampling. When such finite density is implemented by the introduction of a quark-number chemical potential $μ$, this manifests itself as a complex fermion determinant. We apply simulations using the Complex Langevin Equation (CLE) which can be applied in such cases. However, this is not guaranteed to give correct results, so that extensive tests are required. In addition, gauge cooling is required to prevent runaway behaviour. We test these methods on 2-flavour lattice QCD at zero temperature on a small ($12^4$) lattice at an intermediate coupling $β=6/g^2=5.6$ and relatively small quark mass $m=0.025$, over a range of $μ$ values from $0$ to saturation. While this appears to show the correct phase structure with a phase transition at $μ\approx m_N/3$ and a saturation density of $3$ at large $μ$, the observables show departures from known values at small $μ$. We are now running on a larger lattice ($16^4$) at weaker coupling $β=5.7$. At $μ=0$ this significantly improves agreement between measured observables and known values, and there is some indication that this continues to small $μ$s. This leads one to hope that the CLE might produce correct results in the weak-coupling -- continuum -- limit.

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arXiv2015

Exploring Complex-Langevin Methods for Finite-Density QCD

QCD at non-zero chemical potential ($μ$) for quark number has a complex fermion determinant and thus standard simulation methods for lattice QCD cannot be applied. We therefore simulate this theory using the Complex-Langevin algorithm with Gauge Cooling in addition to adaptive methods, to prevent runaway behaviour. Simulations are performed at zero temperature on a $12^4$ lattice with 2 quarks which are light enough that $m_N/3$ is significantly larger than $m_π/2$. Preliminary results are qualitatively as expected. The quark-number density is close to zero for $μ< m_N/3$, beyond which it increases, eventually reaching its saturation value of $3$ for $μ$ sufficiently large. The chiral condensate decreases as $μ$ is increased approaching zero at saturation, while the plaquette increases towards its quenched value. We have yet to observe the transition to nuclear matter at $μ\approx m_N/3$, presumably because the runs for $μ$ between $m_N/3$ and saturation have yet to equilibrate.

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arXiv2015

The chiral phase transition for lattice QCD with 2 colour-sextet quarks

QCD with 2 flavours of massless colour-sextet quarks is studied as a possible walking-Technicolor candidate. We simulate the lattice version of this model at finite temperatures near to the chiral-symmetry restoration transition, to determine whether it is indeed a walking theory (QCD-like with a running coupling which evolves slowly over an appreciable range of length scales) or if it has an infrared fixed point, making it a conformal field theory. The lattice spacing at this transition is decreased towards zero by increasing the number $N_t$ of lattice sites in the temporal direction. Our simulations are performed at $N_t=4,6,8,12$, on lattices with spatial extent much larger than the temporal extent. A range of small fermion masses is chosen to make predictions for the chiral (zero mass) limit. We find that the bare lattice coupling does decrease as the lattice spacing is decreased. However, it decreases more slowly than would be predicted by asymptotic freedom. We discuss whether this means that the coupling is approaching a finite value as lattice $N_t$ is increased -- the conformal option, or if the apparent disagreement with the scaling predicted by asymptotic freedom is because the lattice coupling is a poor expansion parameter, and the theory walks. Currently, evidence favours QCD with 2 colour-sextet quarks being a conformal field theory. Other potential sources of disagreement with the walking hypothesis are also discussed. We also report an estimate of the position of the deconfinement transition for $N_t=12$, needed for choosing parameters for zero-temperature simulations.

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arXiv2014

Models of Walking Technicolor on the Lattice

We study QCD with 2 colour-sextet quarks as a walking-Technicolor candidate. As such it provides a description of the Higgs sector of the standard model, in which the Higgs field is replaced by the Goldstone `pions' of this QCD-like theory, and the Higgs itself is the $σ$. Such a theory will need to be extended if it is to also give masses to the quarks and leptons. What we are attempting to determine is whether it is indeed QCD-like and hence walking, or if it has an infrared fixed point making it a conformal field theory. We do this by simulating its lattice version at finite temperature and observing the running of the bare (lattice) coupling at the chiral transition, as the lattice spacing is varied, and comparing this running with that predicted by 2-loop perturbation theory. Our results on lattices with temporal extents ($N_t$) up to 12 indicate that the coupling runs, but not as fast as asymptotic freedom predicts. We discuss our program for studying the zero-temperature phenomenology of this theory.

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arXiv2014

Thermodynamics of lattice QCD with 3 flavours of colour-sextet quarks II: N_t=6 and N_t=8

We have been studying QCD with 2 flavours of colour-sextet quarks as a candidate walking-Technicolor theory using lattice-QCD simulations. The evolution of the coupling constant with lattice spacing is measured at the finite-temperature chiral transition to determine if this theory is asymptotically free and hence QCD-like. The lattice spacing is varied by changing the number of lattice sites, $N_t$, in the Euclidean time direction. QCD with 3 flavours is studied for comparison. Since this theory is expected to be conformal, with an infrared fixed point, the coupling constant at the chiral transition should approach a non-zero value as $N_t$ becomes large. Our earlier simulations on lattices with $N_t=4$ and $N_t=6$ exhibited a significant decrease in coupling at the chiral transition as $N_t$ was increased. We have now extended these simulations to $N_t=8$, and performed additional simulations at $N_t=6$ to measure the coupling constant at the chiral transition more precisely. These indicate that while there is an appreciable decrease in coupling between $N_t=6$ and $N_t=8$, this is much smaller than that between $N_t=4$ and $N_t=6$. Thus we are hopeful that we are approaching the large-$N_t$ limit. However, further simulations at larger $N_t$(s) are needed.

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arXiv2013

Further studies of QCD with sextet quarks

We continue our simulations of QCD with 2 flavours of colour-sextet quarks as a model for walking technicolor. QCD with 3 flavours of colour-sextet quarks is also studied for comparison with the 2-flavour theory. We simulate these theories at finite temperatures T, using lattices with a finite extent $N_t a=1/T$ in the (Euclidean) time direction. The lattice coupling at the chiral-symmetry-restoration transition is measured as a function of $N_t$. If this is indeed a finite-temperature transition, the evolution of this coupling with $N_t$ as $N_t \rightarrow \infty$ and hence the lattice spacing $a \rightarrow 0$ should be described by asymptotic freedom. If so, the theory is QCD-like and walking. If, however, this coupling approaches a constant non-zero value in the large $N_t$ limit, the transition is a bulk transition and the continuum theory is conformal. For the 2-flavour theory, the coupling does show a significant decrease between $N_t=8$ and $N_t=12$, favouring the walking scenario. However, preliminary results are that the change is less than that predicted by asymptotic freedom. For the 3-flavour case, which is expected to be conformal, there is still a significant decrease in the coupling between $N_t=6$ and $N_t=8$, indicating that we are not yet at large enough $N_t$.

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arXiv2013

S wave bottomonium states moving in a quark-gluon plasma from lattice NRQCD

We extend our study of bottomonium spectral functions in the quark-gluon plasma to nonzero momentum. We use lattice QCD simulations with two flavours of light quark on highly anisotropic lattices and treat the bottom quark with nonrelativistic QCD (NRQCD). We focus on S wave (Upsilon and eta_b) channels and consider nonrelativistic velocities, v/c < 0.2. A comparison with predictions from effective field theory is made.

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arXiv2012

Bottomonium from lattice QCD as a probe of the Quark-Gluon Plasma

We study the temperature dependence of bottomonium for temperatures in the range 0.4 Tc < T < 2.1 Tc, using non-relativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for Nf=2 light flavors. We consider the behaviour of the correlators in Euclidean space, we analyze the associated spectral functions and we study the dependence on the momentum. Our results are amenable to a successful comparison with effective field theories. They help build a coherent picture of the behaviour of bottomonium in the plasma, consistent which the current LHC results.

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arXiv2012

QCD with colour-sextet quarks

We study QCD with 2 colour-sextet quarks as a model for walking Technicolor, using lattice gauge theory simulations (RHMC) at finite temperature. Our goal is to determine if the massless theory is QCD-like (confining, with spontaneously-broken chiral symmetry) with a slowly varying coupling (walks) or if it is a conformal field theory. We do this by simulating the theory at finite temperature and observing how the coupling at the chiral-symmetry restoration temperature depends on the temporal extent $N_t$ of the lattice (in lattice units). If the theory is QCD-like, this coupling should approach zero in the large $N_t$ limit in the manner predicted by asymptotic freedom. If it is conformal, this coupling should approach a finite value in this limit, i.e. the transition would be a bulk transition. We discuss new results at $N_t=6,8$ and 12. These preliminary results indicate that the coupling does decrease with increasing $N_t$, but it is unclear if this is consistent with asymptotic freedom.

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arXiv2011

What happens to the Upsilon and eta_b in the quark-gluon plasma? Bottomonium spectral functions from lattice QCD

We study bottomonium spectral functions in the quark-gluon plasma in the Upsilon and eta_b channels, using lattice QCD simulations with two flavours of light quark on highly anisotropic lattices. The bottom quark is treated with nonrelativistic QCD (NRQCD). In the temperature range we consider, 0.42 < T/T_c < 2.09, we find that the ground states survive, whereas the excited states are suppressed as the temperature is increased. The position and width of the ground states are compared to analytical effective field theory (EFT) predictions. Systematic uncertainties of the maximum entropy method (MEM), used to construct the spectral functions, are discussed in some detail.

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arXiv2011

Thermodynamics of lattice QCD with 3 flavours of colour-sextet quarks

We have been studying QCD with 2 flavours of colour-sextet quarks to distinguish whether it is QCD-like or conformal. For comparison we are now studying QCD with 3 flavours of colour-sextet quarks, which is believed to be conformal in the chiral limit. Here we present the results of simulations of lattice QCD with 3 colour-sextet quarks at finite temperatures on lattices of temporal extent $N_t=4$ and 6, with masses small enough to yield access to the chiral limit. As for the 2-flavour case, we find well-separated deconfinement and chiral-symmetry restoration transitions, both of which move to appreciably weaker couplings as $N_t$ is increased from 4 to 6. If this theory is conformal, we would expect there to be a bulk chiral transition at a fixed coupling. For this reason we conclude that for $N_t=4$ and 6, the chiral and hence the deconfinement transitions are in the strong-coupling domain where the theory is essentially quenched. The similarity between the behaviours of the 2 and 3 flavour theories suggested that the $N_t=4$ and 6 transitions for the 2-flavour theory also lie in the strong-coupling domain. The phase structure of both theories is very similar.

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