arXiv subjects

Philippe de Forcrand

Publications and source records attributed to Philippe de Forcrand.

At least 37 records · Page 2Linked to original sources

arXiv2016

Higgs-Yukawa model with higher dimension operators via extended mean field theory

Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We note that the discussion of vacuum stability is completely modified in the presence of a $ϕ^6$ term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass $M_h=125$ GeV. By taking a $ϕ^6$ interaction in the Higgs potential as a proxy for a UV completion of the standard model, the transition becomes stronger and turns first order if the scale of new physics, i.e. the mass of the lightest mediator particle, is around $1.5$ TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.

hep-lat↗

arXiv2016

Mean distribution approach to spin and gauge theories

We formulate self-consistency equations for the distribution of links in spin models and of plaquettes in gauge theories. This improves upon known mean-field, mean-link, and mean-plaquette approximations in such that we self-consistently determine all moments of the considered variable instead of just the first. We give examples in both Abelian and non-Abelian cases.

hep-lat↗

arXiv2015

Lattice simulation of the SU(2) chiral model at zero and non-zero pion density

We propose a flux representation based lattice formulation of the partition function corresponding to the SU(2) principal chiral Lagrangian, including a chemical potential and scalar/pseudo-scalar source terms. Lattice simulations are then used to obtain non-perturbative properties of the theory, in particular its mass spectrum at zero and non-zero pion density. We also sketch a method to efficiently measure general one- and two-point functions during the worm updates.

hep-lat↗

arXiv2015

Effects of higher dimension operators on the Standard Model Higgs sector

We study the effect of higher dimension operators on the electroweak finite temperature phase transition in two sectors of the Standard Model. Firstly, the Higgs-Yukawa sector, consisting of the Higgs doublet and the massive Standard Model fermions, is studied with an approximate method, Extended Mean Field Theory. Secondly, the gauge-Higgs sector, consisting of the Higgs doublet and the gauge fields of the weak interaction, is studied using Monte Carlo simulations. In both cases we find that a cutoff scale of around 1.5 TeV is needed to make the electroweak phase transition first order at the experimental value of the Higgs boson mass, which is a requirement for making electroweak baryogenesis viable.

hep-lat↗

arXiv2015

Topological Susceptibility from Slabs

In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.

hep-lat↗

arXiv2015

Integrating out lattice gauge fields

The sign problem is a major obstacle to our understanding of the phase diagram of QCD at finite baryon density. Several numerical methods have been proposed to tackle this problem, but a full solution to the sign problem is still elusive. Motivated by this problem and by recent advances in diagrammatic Monte Carlo methods, we find a new exact representation of the partition function of pure lattice gauge theory that contains no link variables. This approach can be easily extended to include staggered fermions, and results in a diagrammatic representation of fermionic states as arrangements of monomers, dimers, and fermionic loops saturating the spacetime lattice. Our representations are exact for any value of the lattice coupling, and extend previous representations that are only valid in the strong coupling limit and at $O(β)$. As a concrete example, we construct a monomer-dimer-loop representation of compact lattice QED.

hep-lat↗

arXiv2015

Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order? (extended version)

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [5,9] an artificial harmonic potential was added to the action; in [9] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [12]. With these improved methods, on systems of size up to 64k 4-simplices, we confirm that the phase transition is first order. In addition, we discuss a local criterion to decide whether parts of a triangulation are in the elongated or crumpled state and describe a new correspondence between EDT and the balls in boxes model. The latter gives rise to a modified partition function with an additional, third coupling. Finally, we propose and motivate a class of modified path-integral measures that might remove the metastability of the Markov chain and turn the phase transition into second order.

hep-lat↗

arXiv2015

U(1) lattice gauge theory with a topological action

We investigate the phase diagram of the compact $U(1)$ lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. The topological action offers an algorithmic advantage for the computation of the free energy.

hep-lat↗

arXiv2015

QCD phase diagram from the lattice at strong coupling

The phase diagram of lattice QCD in the strong coupling limit can be measured in the full $μ$-$T$ plane, also in the chiral limit. In particular, the phase diagram in the chiral limit features a tricritical point at some $(μ_c,T_c)$. This point may be related to the critical end point expected in the QCD phase diagram. We discuss the gauge corrections to the phase diagram at strong coupling and compare our findings with various possible scenarios in continuum QCD. We comment on the possibility that the tricritical point at strong coupling is connected to the tricritical point in the continuum, massless QCD.

hep-lat↗

arXiv2015

Gauge-invariant signatures of spontaneous gauge symmetry breaking by the Hosotani mechanism

The Hosotani mechanism claims to achieve gauge-symmetry breaking, for instance $SU(3) \to SU(2)\times U(1)$. To verify this claim, we propose to monitor the stability of a topological defect stable under a gauge subgroup but not under the whole gauge group, like a $U(1)$ flux state or monopole in the case above. We use gauge invariant operators to probe the presence of the topological defect to avoid any ambiguity introduced by gauge fixing. Our method also applies to an ordinary gauge-Higgs system.

hep-lat↗

arXiv2015

Condensation phenomena in two-flavor scalar QED at finite chemical potential

We study condensation in two-flavored, scalar QED with non-degenerate masses at finite chemical potential. The conventional formulation of the theory has a sign problem at finite density which can be solved using an exact reformulation of the theory in terms of dual variables. We perform a Monte Carlo simulation in the dual representation and observe a condensation at a critical chemical potential $μ_c$. After determining the low-energy spectrum of the theory we try to establish a connection between $μ_c$ and the mass of the lightest excitation of the system, which are naively expected to be equal. It turns out, however, that the relation of the critical chemical potential to the mass spectrum in this case is non-trivial: Taking into account the form of the condensate and making some simplifying assumptions we suggest an adequate explanation which is supported by numerical results.

hep-lat↗

arXiv2014

The chiral phase transition in two-flavor QCD from imaginary chemical potential

We investigate the order of the finite temperature chiral symmetry restoration transition for QCD with two massless fermions, by using a novel method, based on simulating imaginary values of the quark chemical potential $μ=iμ_i,μ_i\in\mathbb{R}$. Our method exploits the fact that, for low enough quark mass $m$ and large enough chemical potential $μ_i$, the chiral transition is decidedly first order, then turning into crossover at a critical mass $m_c(μ)$. It is thus possible to determine the critical line in the $m - μ^2$ plane, which can be safely extrapolated to the chiral limit by taking advantage of the known tricritical indices governing its shape. We test this method with standard staggered fermions and the result of our simulations is that $m_c(μ=0)$ is positive, so that the phase transition at zero density is definitely first order in the chiral limit, on our coarse $N_t=4$ lattices with $a\simeq 0.3\,\mathrm{fm}$.

hep-lat↗

arXiv2014

Deformations of infrared-conformal theories in two dimensions

We study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular, we demonstrate how to obtain the correct massless behavior from an infinite tower of finite-size-induced masses and show that it is necessary to first take the cylindrical geometry limit in order to get correct results. In the Sommerfield model we also introduce a mass deformation to measure the mass anomalous dimension, $γ_m$. We find that the explicit scale breaking of the lattice setup induces corrections which must be taken into account in order to reproduce $γ_m$ at the infrared fixed point. These results can be used to improve the methodology in the search for the conformal window in QCD-like theories with many flavors.

hep-lat↗

arXiv2014

Lattice gauge theory without link variables

We obtain a sequence of alternative representations for the partition function of pure SU(N) or U(N) lattice gauge theory with the Wilson plaquette action, using the method of Hubbard-Stratonovich transformations. In particular, we are able to integrate out all the link variables exactly, and recast the partition function of lattice gauge theory as a Gaussian integral over auxiliary fields.

hep-lat↗

arXiv2014

Extended Mean Field study of complex $ϕ^4$-theory at finite density and temperature

We review the Extended Mean Field Theory (EMFT) approximation and apply it to complex, scalar $ϕ^4$-theory on the lattice. We study the critical properties of the Bose condensation driven by a nonzero chemical potential $μ$ at both zero and nonzero temperature and determine the $(T,μ)$ phase diagram. The results are in very good agreement with recent Monte Carlo data for all parameter values considered. EMFT can be formulated directly in the thermodynamic limit which allows us to study lattice spacings for which Monte Carlo studies are not feasible with present techniques. We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the "Silver Blaze" behavior at zero temperature and dimensional reduction at finite temperature.

hep-lat↗

arXiv2014

The lattice QCD phase diagram in and away from the strong coupling limit

We study lattice QCD with four flavors of staggered quarks. In the limit of infinite gauge coupling, "dual" variables can be introduced, which render the finite-density sign problem mild and allow a full determination of the $μ-T$ phase diagram by Monte Carlo simulations, also in the chiral limit. However, the continuum limit coincides with the weak coupling limit. We propose a strong-coupling expansion approach towards the continuum limit. We show first results, including the phase diagram and its chiral critical point, from this expansion truncated to next-to-leading order.

hep-lat↗

arXiv2014

The Phase Diagram of Strong Coupling QCD including Gauge Corrections

The strong coupling limit of lattice QCD with staggered fermions has been studied for decades, both via Monte Carlo and via mean field theory. In this model, the finite density sign problem can be made mild and the full phase diagram can be obtained, even in the chiral limit. It is however desirable to understand the effect of a finite lattice gauge coupling $β$ on the phase diagram in the $μ-T$ plane in order to understand how it evolves into the phase diagram of continuum QCD. Here we discuss how to construct a partition function for non-zero lattice coupling, exact to $\mathcal{O}(β)$, and present corresponding Monte Carlo results, in particular for corrections to the chiral susceptibility and to the phase diagram.

hep-lat↗

arXiv2013

Scale hierarchy in high-temperature QCD

Because of asymptotic freedom, QCD becomes weakly interacting at high temperature: this is the reason for the transition to a deconfined phase in Yang-Mills theory at temperature $T_c$. At high temperature $T \gg T_c$, the smallness of the running coupling $g$ induces a hierachy betwen the "hard", "soft" and "ultrasoft" energy scales $T$, $g T$ and $g^2 T$. This hierarchy allows for a very successful effective treatment where the "hard" and the "soft" modes are successively integrated out. However, it is not clear how high a temperature is necessary to achieve such a scale hierarchy. By numerical simulations, we show that the required temperatures are extremely high. Thus, the quantitative success of the effective theory down to temperatures of a few $T_c$ appears surprising a posteriori.

hep-lat↗