Large Quark Mass Research Articles

Hyper-scaling relations in the conformal window from dynamic AdS/QCD

Dynamic AdS/QCD is a holographic model of strongly coupled gauge theories with the dynamics included through the running anomalous dimension of the quark bilinear, $\ensuremath{\gamma}$. We apply it to describe the physics of massive quarks in the conformal window of $\mathrm{SU}({N}_{c})$ gauge theories with ${N}_{f}$ fundamental flavors, assuming the perturbative two-loop running for $\ensuremath{\gamma}$. We show that to find regular, holographic renormalization group flows in the infrared, the decoupling of the quark flavors at the scale of the mass is important, and enact it through suitable boundary conditions when the flavors become on shell. We can then compute the quark condensate and the mesonic spectrum $({M}_{\ensuremath{\rho}},{M}_{\ensuremath{\pi}},{M}_{\ensuremath{\sigma}})$ and decay constants. We compute their scaling dependence on the quark mass for a number of examples. The model matches perturbative expectations for large quark mass and na\"{\i}ve dimensional analysis (including the anomalous dimensions) for small quark mass. The model allows study of the intermediate regime where there is an additional scale from the running of the coupling, and we present results for the deviation of scalings from assuming only the single scale of the mass.

Heavy quarkonium fragmentation functions from a heavy quark pair. I.Swave

A QCD factorization formalism was recently proposed for evaluating heavy quarkonium production at large $p_T$ at collider energies. With systematically calculated short-distance partonic hard parts and evolution kernels of fragmentation functions (FFs), the predictive power of this factorization approach relies on our knowledge of a large number of universal FFs at an input factorization scale $\mu_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively non-relativistic. We evaluate these universal input FFs using non-relativistic QCD (NRQCD) factorization, and express the large number of FFs in terms of a few universal NRQCD long-distance matrix elements (LDMEs) with perturbatively calculated coefficients. We derive complete contributions to the single-parton FFs at both ${\cal O}(\alpha_s)$ and ${\cal O}(\alpha_s^2)$, and the heavy quark pair FFs at ${\cal O}(\alpha_s)$. We present detailed derivation for all contributions involving LDMEs of $S$-wave NRQCD $Q\bar{Q}$-states ($P$-wave contributions in a companion paper). Our results bridge the gap between the QCD factorization formalism and its phenomenological applications.

Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice

We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a \approx$ 0.093, 0.068 and 0.047 fm, and two different physical volumes, $L \approx$ 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark (RHQ) action which can control large discretization errors introduced by large quark mass $m_Q$. The spin-independent central $Q\bar{Q}$ potential for the charmonium system yields the "Coulomb plus linear'' behavior with good scaling and small volume dependence. We explore the quark mass dependence over the wide mass range from the charm to beyond the bottom region, and then demonstrate that the spin-independent central $Q\bar{Q}$ potential in the $m_Q \to \infty$ limit is fairly consistent with the static $Q\bar{Q}$ potential obtained from Wilson loops. The spin-spin potential at finite quark mass provides a repulsive interaction with a finite range, which becomes narrower as the quark mass increases. We also discuss the applicability of the $1/m_Q$ expansion approach for the spin-spin potential.

Complex Langevin dynamics for chiral random matrix theory

We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.

Bootstrap dynamical symmetry breaking with strong Yukawa coupling

The newly discovered 126 GeV boson appears, by all counts, to be the Higgs boson of the Standard Model. Although this seems to exclude the existence of a heavy fourth generation quark doublet Q, for theoretical interest, we document a mechanism of dynamical mass generation via strong Yukawa coupling. The Goldstone boson G (the longitudinal component of the weak boson) couples to Q with Yukawa coupling λ Q . A “bootstrap” gap equation is constructed, where strong λ Q generates large quark mass m Q , thereby breaks electroweak symmetry breaking while self-consistently justifying G as a massless Goldstone particle in the loop. We solve the gap equation numerically and find m Q to be a couple of TeV. Putting in the light Higgs boson raises the strength of λ Q considerably, hence m Q as well, and does not look viable. But the equation allows for a dilaton of scale invariance violation, which has weaker coupling than the Higgs boson, except for gg and γγ modes. Whether a dilaton can be still compatible with current data is relegated to an appendix.

Study ofX(3872)from Effective Field Theory with Pion-Exchange Interaction

We study DD[over ¯]* (D*D[over ¯]) scattering in the framework of unitarized heavy meson chiral perturbation theory with pion exchange and a contact interaction. 3S1-3D1 mixing effects are taken into account. A loosely bound state X(3872), with the pole position being Mpole}=(3871.70-i0.39) MeV, is found. The result is not sensitive to the strength of the contact interaction. Our calculation provides a theoretical confirmation of the existence of the 1++ state X(3872). The light quark mass dependence of the pole position indicates it has a predominately DD[over ¯]* (D*D[over ¯]) molecular nature. When the π mass is larger than 142 MeV, the pole disappears, which makes impossible the lattice simulation of this state at large quark mass.

Mass dependence of the deconfinement and chiral restoration critical temperatures in nonlocal SU(2) Polyakov-Nambu-Jona-Lasinio models

In the framework of nonlocal SU(2) chiral quark models with Polyakov loop, we analyze the dependence of the deconfinement and chiral restoration critical temperatures on the explicit chiral symmetry breaking driven by the current quark mass. Our results are compared with those obtained within the standard local Polyakov-Nambu-Jona-Lasinio model and with lattice QCD calculations. For a wide range of pion masses, it is found that both deconfinement and chiral restoration critical temperatures turn out to be strongly entangled, in contrast with the corresponding results within the Polyakov-Nambu-Jona-Lasinio model. In addition, it is seen that the growth of the critical temperatures with the pion mass above the physical point is basically linear, with a slope parameter that is close to the existing lattice QCD estimates. On the other hand, we find a tendency to favor an early onset of the first order transition expected in the large quark mass limit.

Few-Baryon Interactions from Lattice QCD

We report the recent progress on the determination of three-nucleon forces (3NF) in lattice QCD. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to define the potential in quantum field theory, and extract two-nucleon forces (2NF) and 3NF on equal footing. The enormous computational cost for calculating multi-baryon correlators on the lattice is drastically reduced by developing a novel contraction algorithm (the unified contraction algorithm). Quantum numbers of the three-nucleon (3N) system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel), and we extract 3NF in which three nucleons are aligned linearly with an equal spacing. Lattice QCD simulations are performed using N_f=2 dynamical clover fermion configurations at the lattice spacing of a = 0.156 fm on a 16^3 x 32 lattice with a large quark mass corresponding to m(\pi)= 1.13 GeV. Repulsive 3NF is found at short distance.

Exclusivec→s,dsemileptonic decays of ground-state spin-1/2and spin-3/2doubly heavycbbaryons

We evaluate exclusive semileptonic decays of ground-state spin-1/2 and spin-3/2 doubly heavy $cb$ baryons driven by a $c\to s,d$ transition at the quark level. We check our results for the form factors against heavy quark spin symmetry constraints obtained in the limit of very large heavy quark masses and near zero recoil. Based on those constraints we make model independent, though approximate, predictions for ratios of decay widths.

Exploring Three-Nucleon Forces in Lattice QCD

Three-nucleon forces (3NF) are investigated from two-flavor lattice QCD simulations. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to determine two-nucleon forces (2NF) and 3NF in the same framework. As a first exploratory study, we extract 3NF in which three nucleons are aligned linearly with an equal spacing. This is the simplest geometrical configuration which reduces the huge computational cost of calculating the NBS wave function. Quantum numbers of the three-nucleon system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel). Lattice QCD simulations are performed using N_f=2 dynamical clover fermion configurations at the lattice spacing of a = 0.156 fm on a 16^3 x 32 lattice with a large quark mass corresponding to m_\pi= 1.13 GeV. We find repulsive 3NF at short distance in the triton channel. Several sources of systematic errors are also discussed.

Predicting θ 13 and the neutrino mass scale from quark lepton mass hierarchies

Abstract Flavour symmetries of Froggatt-Nielsen type can naturally reconcile the large quark and charged lepton mass hierarchies and the small quark mixing angles with the observed small neutrino mass hierarchies and their large mixing angles. We point out that such a flavour structure, together with the measured neutrino mass squared differences and mixing angles, strongly constrains yet undetermined parameters of the neutrino sector. Treating unknown $ \mathcal{O} $ (1) parameters as random variables, we obtain surprisingly accurate predictions for the smallest mixing angle, $ {\text{si}}{{\text{n}}^{{2}}}{2}{\theta_{{{13}}}} = 0.0{7}_{{ - 0.05}}^{{ + 0.11}} $ , the smallest neutrino mass, $ {m_{{1}}} = {2}.{2}_{{ - {1}.{4}}}^{{ + 1.7}} \times {1}{0^{{ - {3}}}}{\text{eV}} $ , and one Majorana phase, $ {\alpha_{{{21}}}}/\pi = {1}.0_{{ - 0.2}}^{{ + 0.2}}. $

CHIRAL MAGNETIC EFFECT AND QCD PHASE TRANSITIONS WITH EFFECTIVE MODELS

We study the influence of the chiral phase transition on the chiral magnetic effect. The chiral electric current density along the magnetic field, the electric charge difference between on each side of the reaction plane, and the azimuthal charged-particle correlations as functions of the temperature during the QCD phase transitions are calculated. It is found that with the decrease of the temperature, the chiral electric current density, the electric charge difference, and the azimuthal charged-particle correlations all get a sudden suppression at the critical temperature of the chiral phase transition, because the large quark constituent mass in the chiral symmetry broken phase quite suppresses the axial anomaly and the chiral magnetic effect. We suggest that the azimuthal charged-particle correlations (including the correlators divided by the total multiplicity of produced charged particles which are used in current experiments and another kind of correlators not divided by the total multiplicity) can be employed to identify the occurrence of the QCD phase transitions in RHIC energy scan experiments.

Quark running mass and vacuum energy density in truncated Coulomb gauge QCD for five orders of magnitude of current masses

We study in detail the effect of the finite current quark mass on chiral symmetry breaking, in the framework of truncated Coulomb gauge QCD with a linear confining quark-antiquark potential. In the chiral limit of massless current quarks, the breaking of chiral symmetry is spontaneous. But for a finite current quark mass, some dynamical symmetry breaking continues to add to the explicit breaking caused by the quark mass. Moreover, using as order parameter the mass gap, i. e. the quark mass at vanishing moment or the quark condensate, a finite quark mass transforms the chiral symmetry breaking from a phase transition into a crossover. For the study of the QCD phase diagram it thus is relevant to determine how the current quark mass affects chiral symmetry breaking. Since the current quark masses of the six standard flavours u, d, s, c, b, t span over five orders of magnitude from 1.5 MeV to 171 GeV, we develop an accurate numerical method to study the running quark mass gap and the quark vacuum energy density from very small to very large current quark masses.

Roberge-Weiss endpoint inNf=2QCD

We present the results of extensive simulations regarding the critical behavior at the endpoint of the Roberge-Weiss transition for ${N}_{f}=2$ QCD. We confirm early evidence, presented in Ref. [M. D'Elia and F. Sanfilippo, Phys. Rev. D 80, 111501(R) (2009).], according to which the Roberge-Weiss endpoint is first order in the limit of large or small quark masses, and second order for intermediate masses. A systematic study of the transition strength as a function of the quark mass in the first order regions, permits us to estimate the tricritical values of the quark mass separating the second order region from the first order ones.

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark-meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes.In particular, we find large scaling deviations for physical pion masses and significant finite volume effects for pion masses that are used in current lattice simulations.

Modes with variable mass as an alternative in AdS/QCD models with chiral symmetry breaking

We consider a new possibility of incorporating chiral symmetry breaking in soft wall models with a quadratic dilaton and AdS metric. In particular, we allow the mass of the scalar modes propagating in the bulk to have a dependence on the holographical coordinate. In one of the models that we discuss, it is possible obtain a good meson spectra considering current quark masses, and in the other two models considered, good results can be obtained at the expense of considering rather large quark masses.

Dmesons and charmonium states in asymmetric nuclear matter at finite temperatures

We investigate the in-medium masses of $D$ and $\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$ mesons in the isospin-asymmetric nuclear matter at finite temperatures arising due to the interactions with the nucleons, the scalar-isoscalar meson $\ensuremath{\sigma}$, and the scalar-isovector meson $\ensuremath{\delta}$ within a SU(4) model. However, since the chiral symmetry is explicitly broken for the SU(4) case due to the large charm quark mass, we use the SU(4) symmetry here only to obtain the interactions of the $D$ and $\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$ mesons with the light hadron sector but use the observed values of the heavy hadron masses and empirical values of the decay constants. The in-medium masses of $J/\ensuremath{\psi}$ and the excited charmonium states [$\ensuremath{\psi}(3686)$ and $\ensuremath{\psi}(3770)$] are also calculated in the hot isospin-asymmetric nuclear matter in the present investigation. These mass modifications arise due to the interaction of the charmonium states with the gluon condensates of QCD, simulated by a scalar dilaton field introduced to incorporate the broken scale invariance of QCD within the effective chiral model. The change in the mass of $J/\ensuremath{\psi}$ in the nuclear matter with the density is seen to be rather small, as has been shown in the literature by using various approaches, whereas the masses of the excited states of charmonium [$\ensuremath{\psi}(3686)$ and $\ensuremath{\psi}(3770)$] are seen to have considerable drop at high densities. The present study of the in-medium masses of $D$ ($\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$) mesons as well as of the charmonium states will be of relevance for the observables from the compressed baryonic matter, like the production and collective flow of the $D$ ($\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$) mesons, resulting from the asymmetric heavy-ion collision experiments planned at the future facility of the GSI Facility for Antiproton and Ion Research. The mass modifications of $D$ and $\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$ mesons as well as of the charmonium states in hot nuclear medium can modify the decay of the charmonium states (${\ensuremath{\Psi}}^{\ensuremath{'}},{\ensuremath{\chi}}_{c},J/\ensuremath{\Psi}$) to $D\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$ pairs in the hot dense hadronic matter. The small attractive potentials observed for the $\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$ mesons may lead to formation of the $\mathrm{D\ifmmode \bar{}\else \={}\fi{}}$ mesic nuclei.

Order of the Roberge-Weiss endpoint (finite size transition) in QCD

We consider the endpoint of the Roberge-Weiss (RW) first order transition line present for imaginary baryon chemical potentials. We remark that it coincides with the finite size transition relevant in the context of large $N_c$ QCD and study its order in the theory with two degenerate flavors. The RW endpoint is first order in the limit of large and small quark masses, while it weakens for intermediate masses where it is likely in the Ising 3d universality class. Phenomenological implications and further speculations about the QCD phase diagram are discussed.

Strange and charm quark-pair production in a strong non-Abelian field

We have investigated strange and charm quark-pair production in the early stage of heavy ion collisions. Our kinetic model is based on a Wigner function method for fermion-pair production in strong non-Abelian fields. To describe the overlap of two colliding heavy ions we have applied the time-dependent color field with a pulse-like shape. The calculations have been performed in an SU(2)-color model with finite current quark masses. For strange quark-pair production the obtained results are close to the Schwinger limit, as we expected. For charm quark the large inverse temporal width of the field pulse, instead of the large charm quark mass, determines the efficiency of the quark-pair production. Thus we do not observe the expected suppression of charm quark-pair production connecting to the usual Schwinger formalism, but our calculation results in a relatively large charm quark yield. This effect appears in Abelian models as well, demonstrating that particle-pair production for fast varying non-Abelian gluon field strongly deviates from the Schwinger limit for charm quark. We display our results on number densities for light, strange, charm quark pairs, and different suppression factors as the function of characteristic time of acting chromo-electric field.

Model with strong γ4 T-violation**Supported in part by the U.S. Department of Energy (DE-FG02-92-ER40699)

We extend the T violating model of the paper on ``Hidden symmetry of the CKM and neutrino-mapping matrices'' by assuming its T-violating phases χ↑ and χ↓ to be large and the same, with χ = χ↑ = χ↓. In this case, the model has 9 real parameters: α↑, β↑, ξ↑, η↑ for the ↑-quark sector, α↓, β↓, ξ↓, η↓ for the ↓ sector and a common χ. We examine whether these nine parameters are compatible with ten observables: thesix quark masses and the four real parameters that characterize the CKM matrix (i.e., the Jarlskog invariant \U0001d4a5 and three Eulerian angles). We find that this is possible only if the T violating phase χ is large, between −120° to −135°. In this strong T violating model, the smallness of the Jarlskog invariant \U0001d4a5 ≅ 3×10−5 is mainly accounted for by the large heavy quark masses, with mc/mt < ms/mb ≈ 0.02, as well as the near complete overlap of t and b quark, with (c|b) = −0.04.