We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the linear sigma model extended by including a Polyakov loop potential, which is fitted to reproduce pure gauge theory thermodynamics, and a coupling between the chiral fields and the Polyakov loop. Thus the resulting models have as relevant degrees of freedom the Polyakov loop and chiral fields. By comparing the extended models with the bare chiral models we can conclude that the addition of the Polyakov loop is necessary in order to obtain both qualitatively and quantitatively correct results at finite temperatures. These results are extended to finite net quark densities, several thermodynamical quantites are investigated in detail and possible applications and consequences for relativistic heavy ion collision phenomenology are discussed.
The values of quark condensate and tensor susceptibility of QCD vacuum are calculated with different number of flavors. It is shown that, the values of tensor susceptibility are obviously dependent on the flavor numbers while the flavor-number dependence of quark condensate is undetermined.
We present an entirely perturbative QCD determination of the critical phase transition flavor number $N^{cr}_{f}$ of QCD. The results obtained are compared with various determinations of $N^{cr}_{f}$ by non-pertrubative methods, including lattice QCD. The wider physics implication of the existence of the Banks-Zaks regime of QCD with only weakly interacting quarks, is discussed briefly.
In analogy to the mixing pattern of the pseudoscalar mesons in QCD we discuss the mixing of massive neutrinos. Unlike the quarks flavor mixing angles the leptonic mixing angles are large, nearly maximal. The three massive neutrinos are nearly degenerate.
We discuss heavy-flavor production at hadron colliders in recent global QCD analyses to determine parton distribution functions (PDFs) in the proton. We discuss heavy-flavor treatments in precision theory predictions at the LHC. In particular, we discuss factorization schemes in presence of heavy flavors in proton-proton collisions, as well as the impact of heavy-flavor production at the LHC on PDFs. We show results of recent updates beyond CT18, the latest global QCD analysis from the CTEQ-TEA group.
In this talk, we give a short review of our recent works on studying the singly heavy baryon, doubly heavy baryon, and triply heavy baryon spectra from QCD sum rules.
Using flavor SU(3) symmetry, we perform a model-independent analysis of charmless $\bar B_{u,d} (\bar B_s) \to PP, ~PV$ decays. All the relevant topological diagrams, including the presumably subleading diagrams, such as the QCD- and EW-penguin exchange diagrams and flavor-singlet weak annihilation ones, are introduced. Indeed, the QCD-penguin exchange diagram turns out to be important in understanding the data for penguin-dominated decay modes. In this work we make efforts to bridge the (model-independent but less quantitative) topological diagram or flavor SU(3) approach and the (quantitativ…
Using the light front wave functions for the nucleons in a quark model in AdS/QCD, we calculate the nucleon electromagnetic form factors. The flavor decompositions of the nucleon form factors are calculated from the GPDs in this model. We show that the nucleon form factors and their flavor decompositions calculated in AdS/QCD are in agreement with experimental data.
We compute in the Ginzburg-Landau approximation the gluon Meissner masses for the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors in the kinematical range where it is energetically favored. We find real Meissner masses and therefore chromomagnetic stability.
In this article, we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in an systematic way, and make reasonable predictions for their masses in the vacuum and in the nuclear matter.
By means of the functional integral method we show that in the case of the quark-antiquark pairing at zero temperature and zero chemical potential (in the vacuum) the singlet pairing is more preferable than that with the color-flavor locking (CFL)
We explore the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using a Ginzburg-Landau expansion of the free energy, and a NJL point-like four-fermion interaction, with the quantum numbers of single-gluon exchange.
Models of strongly interacting theories with a large mass anomalous dimension ($γ_m$) provide an interesting possibility for the dynamical origin of the electroweak symmetry breaking. A laboratory for these models is QCD with many flavors, which may present a non-trivial fixed point associated to a conformal region. Studies based on conformal field theories and on Schwinger-Dyson equations have suggested the existence of bounds on the mass anomalous dimension at the fixed points of these models. In this note we discuss $γ_m$ values of multi-flavor QCD exhibiting a non-trivial fixed point and a…
We derive universal scaling laws for physical observables such as the critical temperature, the chiral condensate, and the pion decay constant as a function of the flavor number near the conformal window of many-flavor QCD in the chiral limit. We argue on general grounds that the associated critical exponents are all interrelated and can be determined from the critical exponent of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point. We illustrate our findings with the aid of nonperturbative functional Renormalization Group (RG) calculations and low-energy QCD models.
We present the first exact analytic result for all partonic channels contributing to the total cross section for the production of a pair of heavy flavors in hadronic collisions in NLO QCD. Our calculation is an essential step in the derivation of the top quark pair production cross section at NNLO in QCD, which is a cornerstone of the precision LHC program. Our results uncover the analytical structures behind observables with heavy flavors at higher orders. They also reveal surprising and non-trivial implications for kinematics close to partonic threshold.
The transition magnetic dipole and electric quadrupole moments of the radiative decays of the sextet heavy flavored spin 3/2 to the heavy spin 1/2 baryons are calculated within the light cone QCD sum rules approach. Using the obtained results, the decay rate for these transitions are also computed and compared with the existing predictions of the other approaches.
A fully back-reaction geometry model of AdS/QCD including the strange quark is described. We find that with the inclusion of the strange quark the impact on the metric is very small and the final predictions are changed only negligibly.
We construct the chiral perturbation theory for two-color QCD with two quark flavors as an effective theory on the SO(6)/SO(5) coset space. This formulation turns out to be particularly useful for extracting the physical content of the theory when finite baryon and isospin chemical potentials are introduced, and Bose--Einstein condensation sets on.
We study in the Ginzburg-Landau approximation, the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors and one plane wave, including terms of order O(1/mu). We show that the LOFF window is slightly enlarged, and actually splits into two different regions, one characterized by u-s and d-u pairings and the other with d-u pairs only.
Heavy flavor production is an important QCD process both in its own right and as a key component of precision global QCD analysis. Apparent disagreements between fixed-flavor scheme calculations of b-production rate with experimental measurements in hadro-, lepto-, and photo-production provide new impetus to a thorough examination of the theory and phenomenology of this process. We review existing methods of calculation, and place them in the context of the general PQCD framework of Collins. A distinction is drawn between scheme dependence and implementation issues related to quark mass effect…
We study the phase structure and condensates of two-flavor QCD at finite isospin chemical potential in the framework of a confining, Dyson-Schwinger equation model. We find that the pion superfluidity phase is favored at high enough isospin chemical potential. A new gauge invariant mixed quark-gluon condensate induced by isospin chemical potential is proposed based on Operator Product Expansion. We investigate the sign and magnitude of this new condensate and show that it's an important condensate in QCD sum rules at finite isospin density.
We revisit confinement/deconfinement transition in holographic QCD to consider the back-reaction of a bulk scalar field. The bulk scalar field is dual to a quark bi-linear operator $\bar qq$, and it encodes explicit and spontaneous chiral symmetry breaking of QCD. To perform the Hawking-Page transition analysis with the back-reaction, we first obtain a deformed AdS black hole solution due to a finite quark mass. Through the Hawking-Page analysis with the back-reacted geometry, we study the flavor number $N_f$ and finite quark mass dependence of the critical temperature of the QCD confinement/d…
The 1/N_c expansion provides a theoretical method for analyzing the spin-flavor symmetry properties of baryons in QCD that is quantitative, systematic and predictive. An exact spin-flavor symmetry exists for large-N_c baryons, whereas for QCD baryons, the spin-flavor symmetry is approximate and is broken by corrections proportional to the symmetry-breaking parameter 1/N_c = 1/3. The 1/N_c expansion predicts a hierarchy of spin and flavor symmetry relations for QCD baryons that is observed in nature. It provides a quantitative understanding of why some SU(3) flavor symmetry relations in the bar…
The structure of an effective light-cone Hamiltonian as recently derived is analyzed with emphasis on its prediction for flavor mixing in physical mesons. In a (perhaps over-simplified) model with one adjustable parameter, the empirical masses of all 25 pseudo-scalar mesons which are possible for 5 flavors are reproduced (almost) quantitatively. These results are coupled with explicit numerical estimates of flavor mixing. In the present approach, the well-known mass degeneracy of the pion triplet is caused by the mass degeneracy of the up and down quark.
Within the framework of Dyson-Schwinger equations (DSEs), we discuss the equation of state (EOS) and quark number densities of 2+1 flavors, that is to say, $u$, $d$, and $s$ quarks. The chemical equilibrium and electric charge neutrality conditions are used to constrain the chemical potential of different quarks. The EOS in the cases of 2 flavors and 2+1 flavors are discussed, and the quark number densities, the pressure, and energy density per baryon are also studied. The results show that there is a critical chemical potential for each flavor of quark, at which the quark number density turns…
Exclusive hadronic B-meson decays into two-body final states consisting of a light pseudoscalar or vector meson along with an eta or eta' meson are of great phenomenological interest. Their theoretical analysis involves decay mechanisms that are unique to flavor-singlet states, such as their coupling to gluons or their ``intrinsic charm'' content. These issues are studied systematically in the context of QCD factorization and the heavy-quark expansion. Theory can account for the experimental data on the B->K^{(*)} eta^{(')} branching fractions, albeit within large uncertainties.
In the normal phase (where no dynamical fermion mass generation occurs) of the D-dimensional quantum electrodynamics with $N_f$ flavors of fermions, we derive an integral equation which should be satisfied by (the inverse of) the wave function renormalization of the fermion in the Landau gauge. For this we use the inverse Landau-Khalatnikov transformation connecting the nonlocal gauge with the Landau gauge. This leads to a similar equation for the running flavor number in the framework of the $1/N_f$ resumed Schwinger-Dyson equation. Solving the equation analytically and numerically, we study …
We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD at finite temperature and density. We consider chiral sector described either using linear sigma model or Nambu-Jona-Lasinio model and study the phase diagram and determine the location of the critical point as a function of the explicit chiral symmetry breaking (i.e. the bare quark mass $m_q$). We also discuss the possible emergence of the quarkyonic phase in this model.
The effect of Polyakov loop on the QCD phase diagram at high density is studied within the Nambu-Jona Lasinio model with Polyakov loop (PNJL model). We point out that the color neutrality is missing in the standard PNJL model at finite density. Moreover, we discuss how the color-flavor locked (CFL) phase is to be distorted by the inclusion of Polyakov loop.
The renormalization constant $Z_J$ of the flavor-singlet axial-vector current with a non-anticommuting $γ_5$ in dimensional regularization is determined to order $α_s^3$ in QCD with massless quarks. In addition, the equality between the $\overline{\mathrm{MS}}$ renormalization constant $Z_{F\tilde{F}}$ associated with the operator $\big[F \tilde{F} \big]_{R}$ and that of $α_s$ is verified explicitly to hold true at 4-loop order.
The $\uparrow\downarrow$-model has produced the physical masses of all flavor-asymmetric mesons like the $π^\pm$ or the $ρ^\pm$. Can the same model also account for the flavor-symmetric mesons like the $π^0$ or the $ρ^0$? -- By adjusting one parameter in a $5\times5$-matrix, the $π$-$η$ degeneracy is lifted and the $η-η'$ splitting falls into the right ball park. The isospin triplets for pions and rhos are caused the mass-degeneracy of the up and down quark.
The couplings and interactions of baryons containing a heavy quark are related by light quark spin-flavor symmetry in the large $N$ limit. The single pion coupling constant which determines all heavy quark baryon-pion couplings is equal to the pion coupling constant for light quark baryons. Light quark symmetry relations amongst the baryon couplings are violated at order $1/N^2$. Heavy quark spin-flavor symmetry is used in conjunction with large $N$ light quark spin-flavor symmetry to determine the couplings of the degenerate doublets of heavy quark baryons.
Recent results for the QCD phase structure at finite temperature and light-quark chemical potential are summarized, where the cases of N_f = 2 + 1 and N_f = 2+1+1 dynamical quark flavors are considered. Order parameters for the chiral and deconfinement transitions are obtained from solutions of a coupled set of truncated Dyson-Schwinger equations for the quark and gluon propagators of Landau gauge QCD. Based on very good agreement with lattice QCD for zero chemical potential the phase diagram in the whole T-μ-plane and the appearance of a putative critical end-point at large chemical potential…
A review of QCD-based theory approaches to study the heavy-flavor and exotic hadrons is given. The focus is on the results from lattice QCD and from lattice QCD complemented by effective field theories. Both approaches are first briefly introduced and applied in few examples. Then the status of various hadrons sectors is presented.
I present a method which can be used to locate the expected critical endpoint of the phase diagram of QCD with two light quark flavors. I illustrate the ideas on a suitable Random Matrix Model and show preliminary results in QCD
I discuss the important role that Lattice QCD plays in testing the Flavor sector of the Standard Model (SM) and in indirect searches of New Physics. I review in particular the Unitarity Triangle Analysis performed by the UTfit collaboration within and beyond the SM, presenting the recent accurate lattice results that enter the analyses. I conclude with a tentative outlook to the further progresses that we can expect in the next years from Flavor Lattice QCD.
The superconductivity in cold dense QCD with three massless flavors is analyzed in the framework of the Schwinger-Dyson equation. The set of two coupled gap equations for the color antitriplet, flavor antitriplet (bar{3},bar{3}) and the color sextet, flavor sextet (6,6) order parameters is derived. It is shown that the antitriplet-antitriplet gives the dominant contribution to the color-flavor locked order parameter, while the sextet-sextet is small but nonzero.
Towards the feasibility study of the electroweak baryogenesis in realistic technicolor scenario, we investigate the phase structure of (2+Nf)-flavor QCD, where the mass of two flavors is fixed to a small value and the others are heavy. For the baryogenesis, an appearance of a first order phase transition at finite temperature is a necessary condition. Using a set of configurations of two-flavor lattice QCD and applying the reweighting method, the effective potential defined by the probability distribution function of the plaquette is calculated in the presence of additional many heavy flavors.…
Recently, there have been reports that the chirally restored phase of QCD is effectively symmetric under $U(N_f) \times U(N_f)$ rather than $SU(N_f)\times SU(N_f)$. We supplement their argument by including the contributions from topologically nontrivial gauge field configurations and discuss how the conclusions are modified. General statements are made concerning the particle spectrum of QCD with light $N_f$ flavors in the high temperature chirally restored phase.
We present lattice studies of the running coupling in 2-flavor QCD. The coupling at zero temperature (T=0) is extracted from Wilson loops while the coupling at finite temperature ($T\neq0$) is determined from Polyakov loop correlation functions.
We derive the effective Lagrangian for the low-energy massive meson excitations of the color-flavor-locking (CFL) phase of QCD with 3 flavors of light quarks. We compute the decay constants, the maximum velocities, and the masses of the mesons at large baryon chemical potential mu. The decay constants are linear in mu. The meson maximum velocities are close to that of sound. The meson masses in the CFL phase are significantly smaller than in the normal QCD vacuum and depend only on bare quark masses. The order of the meson masses is, to some extent, reversed compared to that in the QCD vacuum.…
We review highlights of recent results on the hadron spectrum and flavor physics from lattice QCD. We also discuss recent rapid progress on the muon anomalous magnetic moment.
We evaluate the $πN!N$, $πΣΣ$, $πΛΣ$, $KΛN$ and $K ΣN $ coupling constants and the corresponding monopole masses in lattice QCD with two flavors of dynamical quarks. The parameters representing the SU(3)-flavor symmetry are computed at the point where the three quark flavors are degenerate at the physical $s$-quark mass. In particular, we obtain $α\equiv F/(F+D)=0.395(6)$. The quark-mass dependences of the coupling constants are obtained by changing the $u$- and the $d$-quark masses. We find that the SU(3)-flavor parameters have weak quark-mass dependence and thus the SU(3)-flavor symmetry is …
Understanding flavor physics is one of the most important tasks of particle physics today, which is motivating an extraordinary experimental and theoretical investigational effort. Important progress in this field has already been achieved in the last few years, with Lattice QCD calculations playing an essential role in this effort. I will describe some lattice contributions to the studies of flavor physics by focusing particularly on the determination of the CKM matrix and on the study of CP violation in the Standard Model.
The running of renormalized quark masses is computed in lattice QCD with two flavors of massless O(a) improved Wilson quarks. The regularization and flavor independent factor that relates running quark masses to the renormalization group invariant ones is evaluated in the Schroedinger Functional scheme. Using existing data for the scale r_0 and the pseudoscalar meson masses, we define a reference quark mass in QCD with two degenerate quark flavors. We then compute the renormalization group invariant reference quark mass at three different lattice spacings. Our estimate for the continuum value …
We complete the non-perturbative calculations of the strange quark mass and the Lambda parameter in two flavor QCD by the ALPHA collaboration. The missing lattice scale is determined via the kaon decay constant, for whose chiral extrapolation complementary strategies are compared. We also give a value for the scale r_0 in physical units as well as an improved determination of the renormalization constant Z_A.
We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
We evaluate the strangeness-conserving $N N$, $ΣΣ$, $ΞΞ$, $ΛΣ$ and the strangeness-changing $ΛN$, $ΣN$, $ΛΞ$, $ΣΞ$ axial charges in lattice QCD with two flavors of dynamical quarks and extend our previous work on pseudoscalar-meson-octet-baryon coupling constants so as to include $πΞΞ$, $KΛΞ$ and $KΣΞ$ coupling constants. We find that the axial charges have rather weak quark-mass dependence and the breaking in SU(3)-flavor symmetry is small at each quark-mass point we consider.
The finite temperature transition of QCD with two degenerate light quarks is studied on the lattice with a renormalization group improved gauge action and the Wilson quark action. We have made simulations on an $8^3\times 4$ lattice near the chiral transition point. It is shown that the chiral condensate which is the order parameter of chiral symmetry satisfies remarkably a scaling relation with the exponents of the three dimensional O(4) Heisenberg model. This indicates that the chiral transition in two-flavor QCD is of second order in the continuum limit.
This talk will focus on recent results by the MILC collaboration from simulations of light hadrons in 2+1 flavor lattice QCD. We have achieved high precision results in the pseudoscalar sector, including masses and decay constants, plus quark masses and Gasser-Leutwyler parameters from well controlled chiral perturbation theory fits to our data. We also show spectroscopy results for vector mesons and baryons.
We consider the most general four fermion operators in QCD for two and three massless flavors and study their renormalization in the vicinity of the Fermi surface. We show that, asymptotically, the largest coupling corresponds to scalar diquark condensation. Asymptotically the direct and iterated (molecular) instanton interactions become equal. We provide simple arguments for the form of the operators that diagonalize the evolution equations. Some solutions of the flow equations exhibit instabilities arising out of purely repulsive interactions.
Based on lattice simulations using highly improved staggered quarks for twelve-flavor QCD with several bare fermion masses, we observe a flavor-singlet scalar state lighter than the pion in the correlators of fermionic interpolating operators. The same state is also investigated using correlators of gluonic interpolating operators. Combined with our previous study, that showed twelve-flavor QCD to be consistent with being in the conformal window, we infer that the lightness of the scalar state is due to infrared conformality. This result shed some light on the possibility of a light composite …
I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah-Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point i…
Now that lattice QCD simulations are able to include effects of light sea quarks, the prospects are good for constraining quark flavor phenomenology. This review talk for particle physics experimentalists begins with an introduction intended to describe broadly the steps of lattice Monte Carlo simulations. The remainder of the talk is a brief survey of recent and ongoing calculations relevant for quark flavor physics.
We study the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using N_tau=4 and 6 lattices with Asqtad staggered fermion action. The static free energy was calculated for different values of the quark mass and the entropy contribution at large distances has been extracted. We also calculate the renormalized Polyakov loop following the approach by Kaczmarek et al.
