Function Of Quark Mass Research Articles

Exploring the 0− bound state with dressed quarks in Minkowski space

The Bethe-Salpeter equation for a pseudoscalar bound-system, with i) a ladder kernel with massive gluons, ii) dynamically-dressed quark mass function and iii) an extended quark-gluon vertex, is solved in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The quark dressing is implemented through a phenomenological ansatz, which was tuned by lattice QCD calculations of the quark running mass. The latter were also used for assigning the range of the gluon mass and the parameter featuring the extended color density. This framework allows to investigate the gluon dynamics that manifest itself in the quark dressing, quark-gluon vertex and the binding, directly in the physical space. We present the first results for low-density pseudoscalar systems in order to elucidate the onset of the interplay between the above mentioned gluonic phenomena, and we discuss both static and dynamical quantities, like valence longitudinal and transverse distributions.

B→K and D→K form factors from fully relativistic lattice QCD

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the $B\to K\ell^+\ell^-$ decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon field configurations generated by the MILC collaboration. These include four flavours of HISQ quarks in the sea, with three ensembles having the light $u/d$ quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy quark mass from the $c$ to the $b$, and so we also obtain new results for the $D\to K$ tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalised fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector $B\to K$ form factors have uncertainties of less than 4% across the entire physical $q^2$ range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons.

Dynamical mass generation in Minkowski space at QCD scale

We undertake the challenging task to reveal the properties of dressed light-quarks in the space- and time-like regions. For that aim, we solved the Dyson-Schwinger equation (DSE) in Minkowski space for the quark propagator in a QCD inspired model, focusing on the realization of dynamical chiral symmetry breaking (DCSB) in the large coupling regime. The DSE is considered in the quenched approximation within the rainbow-ladder truncation with a massive gluon and a Pauli-Villars term, which is used to tune the infrared (IR) physics of the model. The solution of the DSE in Minkowski space is performed by resorting to the integral representation of the quark self-energy and propagator, which leads to a coupled set of closed self-consistent equations for the spectral densities, taking into account finite on-mass-shell renormalization. The parameters of the model are chosen such that the gluon mass scale is consistent with recent lattice QCD (LQCD) calculations, the Pauli-Villars mass is lowered down to about 1 GeV to concentrate strength in the infrared momentum region, and the coupling constant and renormalized mass are tuned to reproduce LQCD results for the quark mass function in the Landau gauge. Future application to study the pion consistently with DCSB within the Bethe-Salpeter framework with self-energies in Minkowski space is also delineated.

Pion model with the Nakanishi integral representation

In the present work, we describe a model for the pion based on an analytic expression for the Bethe-Salpeter (BSA) amplitude, combined with some ingredients from Lattice QCD calculations. The running quark mass function M(p2), used here, reproduces well the results of Lattice QCD calculations. The analytical form of the running quark mass function contains a single time-like pole, which implies in time-like poles of the dressed quark propagator. Such a form allows to build the weight functions, Gi(γ, z), for the Nakanishi integral representation of each scalar function, χi(k, p), appearing in the decomposition of the Bethe-Salpeter amplitude in terms of Dirac operators. Such scalar amplitudes can also be used to obtain the pion valence light-front wave function.

Evaluation of pion-nucleon sigma term in Dyson–Schwinger equations approach of QCD with three-constituent quark approximation

In this paper, we study the pion-nucleon sigma term in Dyson–Schwinger equations approach of QCD with a three-constituent-quark approximation. The constituent quark mass is defined by the quark mass function obtained from the quark gap equation with various quark-gluon vertex and effective interaction models. We investigate the parameter dependence of the numerical results with fixed values of chiral condensate. We found that in all cases the numerical results of the pion-nucleon sigma term decrease with increasing constituent quark mass. Quantitatively, the dependence is insensitive to different interaction models, but is quite different with different quark-gluon vertices. Concerning the experimental results, we give the proper model and parameter range with which the theoretical value of pion-nucleon sigma term is consistent with the experiments.

Two-loop corrections to the QCD propagators within the Curci-Ferrari model

We evaluate all two-point correlation functions of the Curci-Ferrari (CF) model in four dimensions and in the presence of mass-degenerate fundamental quark flavors, as a natural extension of an earlier investigation in the quenched approximation. In principle, the proper account of chiral symmetry breaking ($\ensuremath{\chi}\mathrm{SB}$) and the corresponding dynamical generation of a quark-mass function within the CF model requires one to go beyond perturbation theory [M. Pel\'aez, U. Reinosa, J. Serreau, M. Tissier, and N. Wschebor, Phys. Rev. D 103, 094035 (2021)]. However, it is interesting to assess whether a perturbative description applies to correlation functions that are not directly sensitive to $\ensuremath{\chi}\mathrm{SB}$, such as the gluon, ghost and quark dressing functions. We compare our two-loop results for these form factors to QCD lattice data in the two-flavor case for two different values of the pion mass, one that is relatively far from the chiral limit, and one that is closer to the physical value. Our results confirm that the QCD gluon and ghost dressing functions are well described by a perturbative approach within the CF model, as already observed at one-loop order [M. Pel\'aez, M. Tissier, and N. Wschebor, Phys. Rev. D 90, 065031 (2014)]. Our new main result is that the quark dressing function is also well captured by the perturbative approach, but only starting at two-loop order, as also anticipated [M. Pel\'aez, M. Tissier, and N. Wschebor, Phys. Rev. D 90, 065031 (2014)]. The quark-mass function predicted by the CF model at two-loop order is in good agreement with the data if the quarks are not too light but it shows some clear tension with respect to the two-loop CF dressing functions in the close to physical case, as expected. Interestingly, however, we find that there is much less tension between the nonperturbative quark-mass function, as it can be obtained from lattice simulations or from M. Pel\'aez, U. Reinosa, J. Serreau, M. Tissier, and N. Wschebor, Phys. Rev. D 103, 094035 (2021), and the two-loop CF dressing functions, which confirms the perturbative nature of the latter.

Linking continuum and lattice quark mass functions via an effective charge

The quark mass function is computed both by solving the quark propagator Dyson-Schwinger equation and from lattice simulations implementing overlap and Domain-Wall fermion actions for valence and sea quarks, respectively. The results are confronted and seen to produce a very congruent picture, showing a remarkable agreement for the explored range of current-quark masses. The effective running-interaction is based on a process-independent charge rooted on a particular truncation of the Dyson-Schwinger equations in the gauge sector, establishing thus a link from there to the quark sector and inspiring a correlation between the emergence of gluon and hadron masses.

Screened massive expansion of the quark propagator in the Landau gauge

The infrared behavior of the quark propagator is studied at one loop and in the Landau gauge ($\ensuremath{\xi}=0$) using the screened massive expansion of full QCD and three different resummation schemes for the quark self-energy. The shift of the expansion point of perturbation theory, which defines the screened expansion, together with a nonstandard renormalization of the bare parameters, proves sufficient to describe the dynamical generation of an infrared quark mass also in the chiral limit. Analytically, the scale for such a mass is set by a mass parameter $M$, whose value is fixed by a fit to the lattice data for quenched QCD. The quark mass function $\mathcal{M}({p}^{2})$ is shown to be in very good agreement with the lattice results. The quark $Z$ function, on the other hand, shows the wrong qualitative behavior in all but one of the studied resummation schemes, where its behavior is qualitatively correct, but only at sufficiently high energies.

Spontaneous chiral symmetry breaking in the massive Landau gauge: Realistic running coupling

We investigate the spontaneous breaking of chiral symmetry in QCD by means of a recently proposed approximation scheme in the Landau-gauge Curci-Ferrari model, which combines an expansion in the Yang-Mills coupling and in the inverse number of colors, without expanding in the quark-gluon coupling. The expansion allows for a consistent treatment of ultraviolet tails via renormalization group techniques. At leading order, it leads to the resummation of rainbow diagrams for the quark propagator, with, however, a trivial running of both the gluon mass and the quark-gluon coupling. In a previous work, by using a simple model for a more realistic running of these parameters, we could reproduce the known phenomenology of chiral symmetry breaking, including a satisfactory description of the lattice data for the quark mass function. Here, we get rid of this model-dependence by taking our approximation scheme to next-to-leading order. This allows us to consistently include the realistic running of the parameters and to access the unquenched gluon and ghost propagators to first nontrivial order, which we can compare to available lattice data for an even more stringent test of our approach. In particular, our results for the various two-point functions compare well with lattice data while the parameters of the model are strongly constrained.

Toward accurate form factors for B -to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to\eta_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

Dark matter detection, Standard Model parameters and Intermediate Scale Supersymmetry

The vanishing of the Higgs quartic coupling at a high energy scale may be explained by Intermediate Scale Supersymmetry, where supersymmetry breaks at (109-1012) GeV. The possible range of supersymmetry breaking scales can be narrowed down by precise measurements of the top quark mass and the strong coupling constant. On the other hand, nuclear recoil experiments can probe Higgsino or sneutrino dark matter up to a mass of 1012 GeV. We derive the correlation between the dark matter mass and precision measurements of standard model parameters, including supersymmetric threshold corrections. The dark matter mass is bounded from above as a function of the top quark mass and the strong coupling constant. The top quark mass and the strong coupling constant are bounded from above and below respectively for a given dark matter mass. We also discuss how the observed dark matter abundance can be explained by freeze-out or freeze-in during a matter-dominated era after inflation, with the inflaton condensate being dissipated by thermal effects.

Deconfinement in the presence of a strong magnetic field

We study the impact of a finite magnetic field on the deconfinement phase transition for heavy quarks by computing the fluctuations of the Polyakov loops. It is demonstrated that the explicit Z(3) breaking field increases with the magnetic field, leading to a decrease in the (pseudo) critical temperatures and a shrinking first-order region in the phase diagram. Phenomenological equations that capture the behaviors of the Z(3) breaking field at strong and weak magnetic fields for massive and massless quarks are given. Lastly, we explore the case of dynamical light quarks and demonstrate how an improved constituent quark mass function can enforce the correct magnetic field dependence of the deconfinement temperature in an effective model, as observed in Lattice QCD calculations.

Quark mass function at finite density in real-time formalism

Abstract Chiral symmetry restoration of quarks is investigated at finite density in quantum chromodynamics. The critical chemical potentials at zero temperature, in which the chiral symmetry is restored, are calculated with the Schwinger-Dyson equation in the real-time formalism without the instantaneous exchange approximation. We present some properties of the quark mass functions and the quark propagators.

Quark propagator with two flavors of O(a) -improved Wilson fermions

We compute the Landau gauge quark propagator from lattice QCD with two flavors of dynamical O(a)-improved Wilson fermions. The calculation is carried out with lattice spacings ranging from 0.06 fm to 0.08 fm, with quark masses corresponding to pion masses of 420, 290 and 150 MeV, and for volumes of up to (4.5fm)^4. Our ensembles allow us to evaluate lattice spacing, volume and quark mass effects. We find that the quark wave function which is suppressed in the infrared, is further suppressed as the quark mass is reduced, but the suppression is weakened as the volume is increased. The quark mass function M(p^2) shows only a weak volume dependence. Hypercubic artefacts beyond O(a) are reduced by applying both cylinder cuts and H4 extrapolations. The H4 extrapolation shifts the quark wave function systematically upwards but does not perform well for the mass function.

Quark mass function at finite temperature in real-time formalism

We investigate properties of quark mass functions at finite temperature in quantum chromodynamics calculated by Schwinger-Dyson equation in real-time formalism without the instantaneous exchange approximation, in which one-loop integration is performed in Minkowski space. In our model, an imaginary part of the mass function is directory evaluated.

Search for single production of vector-like quarks decaying to a top quark and a mathrm {W} boson in proton\u2013proton collisions at sqrt{s} = 13 ,text {TeV}

A search is presented for the single production of vector-like quarks in proton–proton collisions at sqrt{s}=13,text {TeV} . The data, corresponding to an integrated luminosity of 35.9,text {fb}^{-1}, were recorded with the CMS experiment at the LHC. The analysis focuses on the vector-like quark decay into a top quark and a mathrm {W} boson, with one muon or electron in the final state. The mass of the vector-like quark candidate is reconstructed from hadronic jets, the lepton, and the missing transverse momentum. Methods for the identification of mathrm {b} quarks and of highly Lorentz boosted hadronically decaying top quarks and mathrm {W} bosons are exploited in this search. No significant deviation from the standard model background expectation is observed. Exclusion limits at 95% confidence level are set on the product of the production cross section and branching fraction as a function of the vector-like quark mass, which range from 0.3 to 0.03,text {pb} for vector-like quark masses of 700 to 2000,text {GeV}. Mass exclusion limits up to 1660,text {GeV} are obtained, depending on the vector-like quark type, coupling, and decay width. These represent the most stringent exclusion limits for the single production of vector-like quarks in this channel.

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space

We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation. This kernel consists of a Lorentz vector effective one-gluon-exchange-type interaction, a vector constant, and a mixed scalar-pseudoscalar covariant linear confining interaction that does not contribute to the mass function. We analyze the gauge dependence of our results, prove the gauge independence of the constituent quark mass and mass gap equation, and identify the Yennie gauge as the appropriate gauge to be used in CST calculations. We compare our results in the spacelike region to lattice QCD data and find good agreement.

Quark Mass Functions and Pion Structure in the Covariant Spectator Theory

The Covariant Spectator Theory is applied to the description of quarks and the pion. The dressed quark mass function is calculated dynamically in Minkowski space and used in the calculation of the pion electromagnetic form factor. The effects of the mass function on the pion form factor and the different quark-pole contributions to the triangle diagram are analyzed.

CT14 intrinsic charm parton distribution functions from CTEQ-TEA global analysis

We investigate the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon, theoretical issues arising in its interpretation, and its potential impact on LHC scattering processes. The “fitted charm” PDF obtained in various QCD analyses contains a process-dependent component that is partly traced to power-suppressed radiative contributions in DIS and is generally different at the LHC. We discuss separation of the universal component of the nonperturbative charm from the rest of the radiative contributions and estimate its magnitude in the CT14 global QCD analysis at the next-to-next-to leading order in the QCD coupling strength, including the latest experimental data from HERA and the Large Hadron Collider. Models for the nonperturbative charm PDF are examined as a function of the charm quark mass and other parameters. The prospects for testing these models in the associated production of a Z boson and a charm jet at the LHC are studied under realistic assumptions, including effects of the final-state parton showering.

Confinement, Chiral Symmetry Breaking and it's Restoration using Dual QCD Formalism

Utilizing the dual QCD model in term of magnetic symmetry structure of non- Abelian gauge theories, the dynamical chiral-symmetry breaking using Schwinger-Dyson equation has been investigated. A close relation among the color confinement and chiralsymmetry breaking has been observed and demonstrated by computing dynamical parameters. The recovery of the chiral symmetry has also been discussed at finite temperature through the variation of quark mass function and quark condensate which gradually decreases with temperature and vanishes suddenly near the critical temperature.