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arXiv2012

On the quark mass dependence of nucleon-nucleon S-wave scattering lengths

In the framework of a Chiral effective theory with dibaryon fields, we calculate the pion mass dependence of the inverse scattering length of the nucleon-nucleon system in the $^3S_1$ channel at order ${(m_π^3 / Λ_χ^2)}\times (m_π^{1/2}m_N^{3/2}/8πf_π^2)^n$ for all $n\ge 0$. We show that certain sets of potentially large higher order contributions vanish. We discuss the difficulties of extending the proof to the $^1S_0$ channel. We apply our results to chiral extrapolations of current lattice data.

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arXiv2012

Variations of nuclear binding with quark masses

We investigate the variation with light quark mass of the mass of the nucleon as well as the masses of the mesons commonly used in a one-boson-exchange model of the nucleon-nucleon force. Care is taken to evaluate the meson mass shifts at the kinematic point relevant to that problem. Using these results, the corresponding changes in the energy of the 1 S0 anti-bound state, the binding energies of the deuteron, triton and selected finite nuclei are evaluated using a one-boson exchange model. The results are discussed in the context of possible corrections to the standard scenario for big bang nucleosynthesis in the case where, as suggested by recent observations of quasar absorption spectra, the quark masses may have changed over the age of the Universe.

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arXiv2011

Has Tc been measured by heavy ion experiments?

We discuss the role of cumulants of net baryon number fluctuations in the analysis of critical behavior in QCD and the study of freeze-out conditions in heavy ion experiments. Through the comparison of the current set of measurements of higher order cumulants of net baryon number fluctuations with lattice QCD calculations and results from hadron resonance gas model we can learn to what extent freeze-out as, determined by such cumulants, occurs close to the QCD transition temperature and thus can probe critical behavior at small values of the baryon chemical potential. Understanding how the relation between freeze-out conditions and the QCD crossover transition is reflected in properties of the experimentally determined cumulants is an important prerequisite to search for the QCD critical point. We point out that even if perfect continuum extrapolated lattice QCD results would be available, it would be inappropriate to use these observables to extract the value of the QCD transition temperature at vanishing baryon chemical potential from experimental data. We furthermore provide indications that a recently performed comparison of lattice QCD results on cumulants with data from heavy ion experiments suffer from systematic as well as statistical uncertainties in the lattice QCD calculations. This makes such comparison of lattice QCD calculations with experimental data at present not useful.

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arXiv2011

On critical scaling at the QCD N_f=2 chiral phase transition

We investigate the critical scaling of the quark propagator of N_f=2 QCD close to the chiral phase transition at finite temperature. We argue that it is mandatory to take into account the back-reaction effects of pions and the sigma onto the quark to observe critical behavior beyond mean field. On condition of self-consistency of the quark Dyson-Schwinger equation we extract the scaling behavior for the quark propagator analytically. Crucial in this respect is the correct pion dispersion relation when the critical temperature is approached from below. Our results are consistent with the known relations for the quark condensate and the pion decay constant from universality. We verify the analytical findings also numerically assuming the critical dispersion relation for the Goldstone bosons.

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arXiv2011

D and D_s meson spectroscopy

Results are presented for the low-lying spectrum of D and D_s mesons calculated in lattice QCD using 2+1 flavor Clover-Wilson configurations made available by the PACS-CS collaboration. For the heavy quark, the Fermilab method is employed. The main focus is S- and P-wave states of charmed and charmed-strange mesons, where previous lattice QCD results have been mostly from quenched calculations. In addition to the ground states, some excited states are extracted. To check the method, calculations of the charmonium spectrum are also carried out. For charmonium, the low-lying spectrum agrees favorably with experiment. For heavy-strange and heavy-light systems substantial differences in comparison to experiment values remain for some states.

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arXiv2011

Slavnov-Taylor constraints for non-trivial backgrounds

We devise an algebraic procedure for the evaluation of Green's functions in SU(N) Yang-Mills theory in the presence of a non-trivial background field. In the ghost-free sector the dependence of the vertex functional on the background is shown to be uniquely determined by the Slavnov-Taylor identities in terms of a certain 1-PI correlator of the covariant derivatives of the ghost and the anti-ghost fields. At non-vanishing background this amplitude is shown to encode the quantum deformations to the tree-level background-quantum splitting. The approach only relies on the functional identities of the model (Slavnov-Taylor identities, $b$-equation, anti-ghost equation) and thus it is valid beyond perturbation theory, and in particular in a lattice implementation of the background field method. As an example of the formalism we analyze the ghost two-point function and the Kugo-Ojima function in an instanton background in SU(2) Yang-Mills theory, quantized in the background Landau gauge.

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arXiv2011

The dynamical origin of the refinement of the Gribov-Zwanziger theory

In recent years, the Gribov-Zwanziger action was refined by taking into account certain dimension 2 condensates. In this fashion, one succeeded in bringing the gluon and the ghost propagator obtained from the GZ model in qualitative and quantitative agreement with the lattice data. In this paper, we shall elaborate further on this aspect. First, we shall show that more dimension 2 condensates can be taken into account than considered so far and, in addition, we shall give firm evidence that these condensates are in fact present by discussing the effective potential. It follows thus that the Gribov-Zwanziger action dynamically transforms itself into the refined version, thereby showing that the continuum nonperturbative Landau gauge fixing, as implemented by the Gribov-Zwanziger approach, is consistent with lattice simulations.

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arXiv2011

The lightest hybrid meson supermultiplet in QCD

We interpret the spectrum of meson states recently obtained in non-perturbative lattice QCD calculations in terms of constituent quark-antiquark bound states and states, called `hybrids', in which the qqbar pair is supplemented by an excitation of the gluonic field. We identify a lightest supermultiplet of hybrid mesons with JPC = (0,1,2)-+, 1-- built from a gluonic excitation of chromomagnetic character coupled to qqbar in an S-wave. The next lightest hybrids are suggested to be quark orbital excitations with the same gluonic excitation, while the next distinct gluonic excitation is significantly heavier. Existing models of gluonic excitations are compared to these findings and possible phenomenological consequences explored.

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arXiv2011

Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory

We study finite-volume effects on the masses of the ground-state octet baryons using covariant baryon chiral perturbation theory (ChPT) up to next-to-leading order by analyzing the latest $n_f=2+1$ lattice Quantum ChromoDynamics (LQCD) results from the NPLQCD collaboration. Contributions of virtual decuplet baryons are taken into account using the "consistent" coupling scheme. We compare our results with those obtained from heavy baryon ChPT and show that, although both approaches can describe well the lattice data, the underlying physics is different: In HBChPT, virtual decuplet baryons play a more important role than they do in covariant ChPT. This is because the virtual octet baryon contributions to finite-volume corrections are larger in covariant ChPT than in HBChPT, while the contributions of intermediate decuplet baryons are smaller, because of relativistic effects. We observe that for the octet baryon masses, at fixed $m_πL$ ($\gg1$) finite-volume corrections decrease as $m_π$ approaches its physical value, provided that the strange quark mass is at or close to its physical value, as in most LQCD setups.

hep-ph↗

arXiv2011

Thermodynamics of lattice QCD with 2 sextet quarks on N_t=8 lattices

We continue our lattice simulations of QCD with 2 flavours of colour-sextet quarks as a model for conformal or walking technicolor. A 2-loop perturbative calculation of the $β$-function which describes the evolution of this theory's running coupling constant predicts that it has a second zero at a finite coupling. This non-trivial zero would be an infrared stable fixed point, in which case the theory with massless quarks would be a conformal field theory. However, if the interaction between quarks and antiquarks becomes strong enough that a chiral condensate forms before this IR fixed point is reached, the theory is QCD-like with spontaneously broken chiral symmetry and confinement. However, the presence of the nearby IR fixed point means that there is a range of couplings for which the running coupling evolves very slowly, i.e. it 'walks'. We are simulating the lattice version of this theory with staggered quarks at finite temperature studying the changes in couplings at the deconfinement and chiral-symmetry restoring transitions as the temporal extent ($N_t$) of the lattice, measured in lattice units, is increased. Our earlier results on lattices with $N_t=4,6$ show both transitions move to weaker couplings as $N_t$ increases consistent with walking behaviour. In this paper we extend these calculations to $N_t=8$. Although both transition again move to weaker couplings the change in the coupling at the chiral transition from $N_t=6$ to $N_t=8$ is appreciably smaller than that from $N_t=4$ to $N_t=6$. This indicates that at $N_t=4,6$ we are seeing strong coupling effects and that we will need results from $N_t > 8$ to determine if the chiral-transition coupling approaches zero as $N_t \rightarrow \infty$, as needed for the theory to walk.

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arXiv2011

Charm quark system at the physical point of 2+1 flavor lattice QCD

We investigate the charm quark system using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3 \times 64$ lattice. The dynamical up-down and strange quark masses are set to the physical values by using the technique of reweighting to shift the quark hopping parameters from the values employed in the configuration generation. At the physical point, the lattice spacing equals $a^{-1}=2.194(10)$ GeV and the spatial extent $L=2.88(1)$ fm. The charm quark mass is determined by the spin-averaged mass of the 1S charmonium state, from which we obtain $m_{\rm charm}^{\msbar}(μ= m_{\rm charm}^{\msbar}) = 1.260(1)(6)(35)$ GeV, where the errors are due to our statistics, scale determination and renormalization factor. An additional systematic error from the heavy quark is of order $α_s^2 f(m_Q a)(a Λ_{QCD})$, which is estimated to be a percent level if the factor $f(m_Q a)$ analytic in $m_Q a$ is of order unity. Our results for the charmed and charmed-strange meson decay constants are $f_D=226(6)(1)(5)$ MeV, $f_{D_s}=257(2)(1)(5)$ MeV, again up to the heavy quark errors of order $α_s^2 f(m_Q a)(a Λ_{QCD})$. Combined with the CLEO values for the leptonic decay widths, these values yield $|V_{cd}| = 0.205(6)(1)(5)(9)$, $|V_{cs}| = 1.00(1)(1)(3)(3)$, where the last error is on account of the experimental uncertainty of the decay widths.

hep-lat↗

arXiv2011

A new determination of α_s from hadronic τ decays

We present a new framework for the extraction of the strong coupling from hadronic τdecays through finite-energy sum rules. Our focus is on the small, but still significant non-perturbative effects that, in principle, affect both the central value and the systematic error. We employ a quantitative model in order to accommodate violations of quark-hadron duality, and enforce a consistent treatment of the higher-dimensional contributions of the Operator Product Expansion to our sum rules. Using 1998 OPAL data for the non-strange isovector vector and axial-vector spectral functions, we find the n_f=3 values α_s(m_τ^2)=0.307+-0.019 in fixed-order perturbation theory, and 0.322+-0.026 in contour-improved perturbation theory. For comparison, the original OPAL analysis of the same data led to the values 0.324+-0.014 (fixed-order) and 0.348+-0.021 (contour-improved).

hep-ph↗

arXiv2011

Improving the Volume Dependence of Two-Body Binding Energies Calculated with Lattice QCD

Volume modifications to the binding of two-body systems in large cubic volumes of extent L depend upon the total momentum and exponentially upon the ratio of L to the size of the boosted system. Recent work by Bour et al determined the momentum dependence of the leading volume modifications to nonrelativistic systems with periodic boundary conditions imposed on the single-particle wavefunctions, enabling them to numerically determine the scattering of such bound states using a low-energy effective field theory and Luscher's finite-volume method. The calculation of bound nuclear systems directly from QCD using Lattice QCD has begun, and it is important to reduce the systematic uncertainty introduced into such calculations by the finite spatial extent of the gauge-field configurations. We extend the work of Bour et al from nonrelativistic quantum mechanics to quantum field theory by generalizing the work of Luscher and of Gottlieb and Rummukainen to boosted two-body bound states. The volume modifications to binding energies can be exponentially reduced from ~ e^{-kappa L}/L to ~ e^{-2 kappa L}/L in nonrelativistic systems (where kappa is the binding momentum of the state) by forming particular combinations of the binding energies determined in the four lowest-lying boosted systems. Relativistic corrections to this combination, and others, that violate the exponential reduction are determined. An analysis of what can be expected from Lattice QCD calculations of the deuteron is performed, the results of which are representative of a generic loosely bound system.

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arXiv2011

Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions

I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, Nogradi and Schroeder. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length xi with the fermion mass m_q, xi proportional to m_q to the power -1/y_m, with y_m ~ 1.35. Shortcomings of the analysis are discussed.

hep-lat↗

arXiv2011

Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory

Wilson chiral perturbation theory (WChPT) is the effective field theory describing the long- distance properties of lattice QCD with Wilson or twisted-mass fermions. We consider here WChPT for the theory with two light flavors of Wilson fermions or a single light twisted-mass fermion. Discretization errors introduce three low energy constants (LECs) into partially quenched WChPT at O(a^2), conventionally called W'_6, W'_7 and W'_8 . The phase structure of the theory at non-zero a depends on the sign of the combination 2W'_6 + W'_8, while the spectrum of the lattice Hermitian Wilson-Dirac operator depends on all three constants. It has been argued, based on the positivity of partition functions of fixed topological charge, and on the convergence of graded group integrals that arise in the epsilon-regime of ChPT, that there is a constraint on the LECs arising from the underlying lattice theory. In particular, for W'_6 = W'_7 = 0, the constraint found is W'_8 \le 0. Here we provide an alternative line of argument, based on mass inequalities for the underlying partially quenched theory. We find that W'_8 \le 0, irrespective of the values of W'_6 and W'_7. Our constraint implies that 2W'_6 > |W'_8| if the phase diagram is to be described by the first-order scenario, as recent simulations suggest is the case for some choices of action.

hep-lat↗

arXiv2012

Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum

The microscopic spectral density of the Hermitian Wilson-Dirac operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac operator can be matched by the predictions from Wilson chiral perturbation theory. We test successfully the finite volume and the mass scaling predicted by Wilson chiral perturbation theory at fixed lattice spacing.

hep-lat↗

arXiv2011

Spontaneous parity and charge-conjugation violations at real isospin and imaginary baryon chemical potentials

The phase structure of two-flavor QCD is investigated at real isospin and imaginary quark chemical potentials by using the Polyakov-loop extended Nambu--Jona-Lasinio model. In the region, parity symmetry is spontaneously broken by the pion superfluidity phase transition, whereas charge-conjugation symmetry is spontaneously violated by the Roberge-Weiss transition. The chiral (deconfinement) crossover at zero isospin and quark chemical potentials is a remnant of the parity (charge-conjugation) violation. The interplay between the parity and charge-conjugation violations are analyzed, and it is investigated how the interplay is related to the correlation between the chiral and deconfinement crossovers at zero isospin and quark chemical potentials.

hep-ph↗

arXiv2011

The nucleon and Delta(1232) form factors at low momentum-transfer and small pion masses

An expansion of the electromagnetic form factors of the nucleon and Delta(1232) in small momentum transfer and pion mass is performed in a manifestly-covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and Delta(1232) electromagnetic form factors, charge radii, and electromagnetic moments in the framework of SU(2) baryon chiral perturbation theory, with nucleon and Delta(1232)-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and electron-scattering process, we extract values for the second derivative of the electric form factor which is a genuine prediction of the p^3 BChPT. The chiral behavior of radii and moments is studied and compared to that obtained in the heavy-baryon framework and lattice QCD. The chiral behavior of Delta(1232)-isobar properties exhibits cusps and singularities at the threshold of Delta->pi N decay, and their physical significance is discussed.

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