Constructing a neutron star in G2-QCD [HEAP]

The inner structure of neutron stars is still an open question. To make progress and understand the qualitative impact of gauge interactions on the neutron star structure we study neutron stars in a modified version of QCD. In this modification the gauge group of QCD is replaced by the exceptional Lie group G$_2$, which has neutrons and is accessible at finite density in lattice calculations. Using an equation of state constructed from lattice calculations we determine the mass-radius-relation for a neutron star in this theory using the Tolman-Oppenheimer-Volkoff equation. The results exhibit an influence of the non-trivial interactions on the mass-radius relation. However, the masses of the quarks are found to have little influence. We also give density profiles and the phase structure inside the neutron star. If the results carry over to full QCD, much of the internal structure of neutron stars could already be inferred from a precise measurement of the mass-radius relation.

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O. Hajizadeh and A. Maas
Wed, 1 Mar 17

Comments: (19 pages, 9 figures)


Ab initio calculations of the isotopic dependence of nuclear clustering [CL]

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (4He nuclei) within the interior of a larger nucleus. While clustering is important for several well-known examples, little is known about the general nature of clustering in nuclei. In this letter we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the effective number of alpha clusters in any nucleus as well as their shape compared to alpha particles in vacuum. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in 12C, 14C, and 16C. The structural similarities among the carbon isotopes suggest that 14C and 16C have excitations analogous to the well-known Hoyle state resonance in 12C.

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S. Elhatisari, E. Epelbaum, H. Krebs, et. al.
Mon, 20 Feb 17

Comments: 5 + 9 pages (main + supplemental materials), 4 + 6 figures (main + supplemental materials)

Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame [CL]

The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\epsilon + p )$. The continuum values of the potentials are well represented by Pad\’e interpolating formulas, which also connect them well to the Stefan-Boltzmann values in the infinite temperature limit. The pressure, the energy and the entropy densities are compared with results in the literature. The discrepancy among previous computations near $T_c$ is analyzed and resolved thanks to the high precision achieved.

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L. Giusti and M. Pepe
Tue, 6 Dec 16

Comments: 7 pages, 3 figures

The topological susceptibility in finite temperature QCD and axion cosmology [CL]

We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings, corresponding to temporal extent of the lattice, $N_\tau=6,8,10$ and $12$. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below $250$ MeV. While for temperatures above $250$ MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the consequence of our results for cosmology wherein we estimate the bounds on the axion decay constant and the oscillation temperature if indeed the QCD axion is a possible dark matter candidate.

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P. Petreczky, H. Schadler and S. Sharma
Tue, 29 Nov 16

Comments: 19 pages and 7 figures; v2: A new figure, a few references and minor comments added; published version

Baryon number transfer could delay Quark-Hadron transition in cosmology [CEA]

In the early Universe, s.i. matter was a quark-gluon plasma. Both lattice computations and heavy ion collision experiments however tell us that, in the absence of chemical potentials, no plasma survives at $T <\sim 150\, $MeV. The cosmological QH transition, however, seems to have been a crossover; cosmological consequences envisaged when it was believed to be a phase transition no longer hold. In this paper we discuss whether even a crossover transition can leave an imprint that cosmological observations can seek or, viceversa, there are questions cosmology should still ask QCD specialists. In this context, we outline, first of all, that it is still unclear how baryons (not hadrons) could form at the cosmological transition. A critical role should be played by diquark states, whose abundance in the early plasma needs to be accurately evaluated. We estimate that, if the number of quarks belonging to a diquark state, at the eve of the cosmological transition, is $<\sim 1:10^6$, its dynamics could be modified by the process of B-transfer from plasma to hadrons. In turn, by assuming B-transfer to cause just mild perturbations and, in particular, no entropy input, we study the deviations from the tracking regime, in the frame of SCDEW models. We find that, in some cases, residual deviations could propagate down to primeval nucleosynthesis.

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S. Bonometto and R. Mainini
Wed, 19 Oct 16

Comments: 15 pages, 8 figures, submitted to Universe

A G2-QCD neutron star [HEAP]

The determination of the properties of neutron stars from the underlying theory, QCD, is still an unsolved problem. This is mainly due to the difficulty to obtain reliable results for the equation of state for cold, dense QCD. As an alternative route to obtain qualitative insights, we determine the structure of a neutron star for a modified version of QCD: By replacing the gauge group SU(3) with the exceptional Lie group G2, it is possible to perform lattice simulations at finite density, while still retaining neutrons. Here, results of these lattice simulations are used to determine the mass-radius relation of a neutron star for this theory. The results show that phase changes express themselves in this relation. Also, the radius of the most massive neutron stars is found to vary very little, which would make radius determinations much simpler if this would also be true in QCD.

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O. Hajizadeh and A. Maas
Fri, 23 Sep 16

Comments: 7 pages, 4 figures. poster presented at the “XXXIV International Symposium on Lattice Field Theory”, July 2016, Southampton, UK

Lattice QCD for Cosmology [CL]

We present a full result for the equation of state (EoS) in 2+1+1 (up/down, strange and charm quarks are present) flavour lattice QCD. We extend this analysis and give the equation of state in 2+1+1+1 flavour QCD. In order to describe the evolution of the universe from temperatures several hundreds of GeV to several tens of MeV we also include the known effects of the electroweak theory and give the effective degree of freedoms. As another application of lattice QCD we calculate the topological susceptibility (chi) up to the few GeV temperature region. These two results, EoS and chi, can be used to predict the dark matter axion’s mass in the post-inflation scenario and/or give the relationship between the axion’s mass and the universal axionic angle, which acts as a initial condition of our universe.

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S. Borsanyi, Z. Fodor, K. Kampert, et. al.
Wed, 29 Jun 16

Comments: pdflatex, 40 figures; Section on experimental setups added, small corrections

On the compatibility of thermodynamic equilibrium conditions with the non-perturbative lattice propagators [CL]

In this paper it is analyzed the compatibility of the non-perturbative equations of state of quarks and gluons arising from the lattice with some natural requirements for self gravitating objects at equilibrium: the existence of an equation of state (namely, the possibility to define the pressure as a function of the energy density), the absence of superluminal propagation and Le Chatelier’s principle. It is discussed under which conditions it is possible to extract an equation of state (in the above sense) from the non-perturbative propagators arising from the fits of the last lattice data. In particular, in the quarks case, there is a small but non vanishing range of temperatures in which it is not possible to define a single-valued functional relation between density and pressure. Interestingly enough, a small change of the parameters appearing in the fit of the lattice quark propagator (of around 10\%) can guarantee the fulfillment of all the three conditions (keeping alive, at the same time, the violation of positivity of the spectral representation which is the expected signal of confinement). As far as gluons are concerned, the analysis shows very similar results. These results can be very relevant in applications. For instance, in astrophysics, Rhoades and Ruffini were able to give an upper bound the maximal possible mass of a neutron star just using the three mentioned conditions. Thus, whether or not the non-perturbative quark and gluon propagators satisfy these conditions can have a strong impact on the estimate of the maximal mass of quark stars.

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F. Canfora, A. Giacomini, P. Pais, et. al.
Wed, 8 Jun 16

Comments: 22 pages, 16 figures

Equation of state of imbalanced cold matter from chiral perturbation theory [CL]

We study the thermodynamic properties of matter at vanishing temperature for non-extreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading order pressure obtained by maximizing the static chiral Lagrangian density we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the chiral perturbation energy density and the Stefan-Boltzmann energy density as well as for the isospin chemical potential at the peak in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For $\mu_I \gtrsim 2 m_\pi$ the leading order chiral perturbation theory breaks down; as an example it underestimates the energy density of the system and leads to a wrong asymptotic behavior.

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S. Carignano, A. Mammarella and M. Mannarelli
Thu, 4 Feb 16

Comments: 6 pages, 4 figures

Gravitational waves from cosmological first order phase transitions [CL]

First order phase transitions in the early Universe generate gravitational waves, which may be observable in future space-based gravitational wave observatiories, e.g. the European eLISA satellite constellation. The gravitational waves provide an unprecedented direct view of the Universe at the time of their creation. We study the generation of the gravitational waves during a first order phase transition using large-scale simulations of a model consisting of relativistic fluid and an order parameter field. We observe that the dominant source of gravitational waves is the sound generated by the transition, resulting in considerably stronger radiation than earlier calculations have indicated.

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M. Hindmarsh, S. Huber, K. Rummukainen, et. al.
Tue, 17 Nov 15

Comments: Presented at the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japan

The Standard Model cross-over on the lattice [CL]

With the physical Higgs mass the Standard Model symmetry restoration phase transition is a smooth cross-over. We study the thermodynamics of the cross-over using numerical lattice Monte Carlo simulations of an effective SU(2) X U(1) gauge + Higgs theory, significantly improving on previously published results. We measure the Higgs field expectation value, thermodynamic quantities like pressure, energy density, speed of sound and heat capacity, and screening masses associated with the Higgs and Z fields. While the cross-over is smooth, it is very well defined with a width of only approximately 5 GeV. We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result $T_c = 159.5 \pm 1.5$ GeV. Outside of the narrow cross-over region the perturbative results agree well with non-perturbative ones.

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M. DOnofrio and K. Rummukainen
Mon, 31 Aug 15

Comments: 10 pages

Latfield2: A c++ library for classical lattice field theory [CL]

latfield2 is a C++ library designed to simplify writing parallel codes for solving partial differen- tial equations, developed for application to classical field theories in particle physics and cosmology. It is a significant rewrite of the latfield framework, moving from a slab domain decomposition to a rod decomposition, where the last two dimension of the lattice are scattered into a two dimensional process grid. Parallelism is implemented using the Message Passing Interface (MPI) standard, and hidden in the basic objects of grid-based simulations: Lattice, Site and Field. It comes with an integrated parallel fast Fourier transform, and I/O server class permitting computation to continue during the writing of large files to disk. latfield2 has been used for production runs on tens of thousands of processor elements, and is expected to be scalable to hundreds of thousands.

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D. David, M. Hindmarsh and N. Bevis
Tue, 25 Aug 15

Comments: 14 pages, 5 figures

Lattice Calculation of the Decay of Primordial Higgs Condensate [CEA]

We study the resonant decay of the primordial Standard Model Higgs condensate after inflation into $SU(2)$ gauge bosons on the lattice. We find that the non-Abelian interactions between the gauge bosons quickly extend the momentum distribution towards high values, efficiently destroying the condensate after the onset of backreaction. For the inflationary scale $H = 10^8$ GeV, we find that 90% of the Higgs condensate has decayed after $n \sim 10$ oscillation cycles. This differs significantly from the Abelian case where, given the same couplings strengths, most of the condensate would persist after the resonance.

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K. Enqvist, S. Nurmi, S. Rusak, et. al.
Wed, 24 Jun 15

Comments: 16 pages, 6 figures

Precision determination of the pion-nucleon $σ$-term from Roy-Steiner equations [CL]

We present a determination of the pion-nucleon ($\pi N$) $\sigma$-term $\sigma_{\pi N}$ based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent precision data from pionic atoms to pin down the threshold $\pi N$ amplitude as well as of constraints from analyticity, unitarity, and crossing symmetry in the form of Roy-Steiner equations to perform the extrapolation to the Cheng-Dashen point in a reliable manner. With isospin-violating corrections included both in the scattering lengths and the LET, we obtain $\sigma_{\pi N}=(59.1\pm 1.9\pm 3.0)$ MeV $=(59.1\pm 3.5)$ MeV, where the first error refers to uncertainties in the $\pi N$ amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.

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M. Hoferichter, J. Elvira, B. Kubis, et. al.
Wed, 17 Jun 15

Comments: 5 pages, 1 figure

Lattice QCD input for axion cosmology [CL]

One intriguing BSM particle is the QCD axion, which could simultaneously provide a solution to the Strong CP problem and account for some, if not all, of the dark matter density in the universe. This particle is a pNGB of the conjectured Peccei-Quinn (PQ) symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry breaking scale, $f_a$, whose value is roughly greater than $10^{9}$ GeV (or, conversely, the axion mass, $m_a$, is roughly less than $10^4\ \mu \text{eV}$). The density of axions in the universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early-universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the QCD free energy with respect to the CP-violating phase, $\theta$. However, this quantity is generically non-perturbative and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small $\theta$ from first-principle lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the universe. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-$\theta$ cumulant of the theta vacua on large volume lattices for SU(3) Yang-Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound $m_a \geq (14.6\pm0.1) \ \mu \text{eV}$ when PQ-breaking occurs after inflation.

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E. Berkowitz, M. Buchoff and E. Rinaldi
Fri, 29 May 15

Comments: 26 pages, 9 figures

Improving cosmic string network simulations [CL]

In real-time lattice simulations of cosmic strings in the Abelian Higgs model, the broken translational invariance introduces lattice artefacts; relativistic strings therefore decelerate and radiate. We introduce two different methods to construct a moving string on the lattice, and study in detail the lattice effects on moving strings. We find that there are two types of lattice artefact: there is an effective maximum speed with which a moving string can be placed on the lattice, and a moving string also slows down, with the deceleration approximately proportional to the exponential of the velocity. To mitigate this, we introduce and study an improved discretisation, based on the tree-level L\”{u}scher-Weisz action, which is found to reduce the deceleration by an order of magnitude, and to increase the string speed limit by an amount equivalent to halving the lattice spacing. The improved algorithm is expected to be very useful for 3D simulations of cosmic strings in the early universe, where one wishes to simulate as large a volume as possible.

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M. Hindmarsh, K. Rummukainen, T. Tenkanen, et. al.
Mon, 9 Jun 14

Comments: 13 pages, 10 figures

QCD and strongly coupled gauge theories: challenges and perspectives [CL]

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

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N. Brambilla, S. Eidelman, P. Foka, et. al.
Wed, 16 Apr 14

The Sphaleron Rate in the Minimal Standard Model [CL]

We use large-scale lattice simulations to compute the rate of baryon number violating processes (the sphaleron rate), the Higgs field expectation value, and the critical temperature in the Standard Model across the electroweak phase transition temperature. While there is no true phase transition between the high-temperature symmetric phase and the low-temperature broken phase, the cross-over is sharply defined at $T_c = (159\pm 1)$\,GeV. The sphaleron rate in the symmetric phase ($T> T_c$) is $\Gamma/T^4 = (18\pm 3)\alpha_W^5$, and in the broken phase in the physically interesting temperature range $130\mbox{\,GeV} < T < T_c$ it can be parametrized as $\log(\Gamma/T^4) = (0.83\pm 0.01)T/{\rm GeV} – (147.7\pm 1.9)$. The freeze-out temperature in the early Universe, where the Hubble rate wins over the baryon number violation rate, is $T_* = (131.7\pm 2.3)$\,GeV. These values, beyond being intrinsic properties of the Standard Model, are relevant for e.g. low-scale leptogenesis scenarios.

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M. DOnofrio, K. Rummukainen and A. Tranberg
Tue, 15 Apr 14

Planning the Future of U.S. Particle Physics (Snowmass 2013): Chapter 1: Summary [CL]

These reports present the results of the 2013 Community Summer Study of the APS Division of Particles and Fields (“Snowmass 2013”) on the future program of particle physics in the U.S. Chapter 1 contains the Executive Summary and the summaries of the reports of the nine working groups.

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Fri, 24 Jan 14

LIFE ON EARTH — AN ACCIDENT? Chiral Symmetry and the Anthropic Principle [CL]

I discuss the fine-tuning of the nuclear forces and in the formation of nuclei in the production of the elements in the Big Bang and in stars.

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Tue, 31 Dec 13

Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects [CL]

We show how to avoid unnecessary and uncontrolled assumptions usually made in the literature about soft SU(3) flavor symmetry breaking in determining the two-flavor nucleon matrix elements relevant for direct detection of WIMPs. Based on SU(2) Chiral Perturbation Theory, we provide expressions for the proton and neutron scalar couplings $f_u^{p,n}$ and $f_d^{p,n}$ with the pion-nucleon sigma-term as the only free parameter, which should be used in the analysis of direct detection experiments. This approach for the first time allows for an accurate assessment of hadronic uncertainties in spin-independent WIMP-nucleon scattering and for a reliable calculation of isospin-violating effects. We find that the traditional determinations of $f_u^p-f_u^n$ and $f_d^p-f_d^n$ are off by a factor of 2.

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Thu, 19 Dec 13