Formulation Of QCD Research Articles

Dual models of QCD and their implications

Some of the dual formulations of QCD are reviewed and analyzed for their possible implications especially in non-perturbative sector of QCD at zero temperature. Starting from the Nambu-Mandelstam idea and the ’t Hooft Abelian Projection technique, the effective formulations of QCD like the dual GinzburgLandau formulation and magnetic symmetry based dual QCD formulation have been analyzed in which dual magnetic potentials coupled with monopole field act as fundamental variables. The dual dynamics associated with these models is discussed in the quenched approximation and the analysis of symmetry breaking , flux tube configurations, confinement potential and nature of dual QCD vacuum is presented which establishes magnetic symmetry based dual QCD formulation as a more effective topological viable formulation for analysing the non-perturbative aspects of QCD.

Hamiltonian Approach to QCD at Finite Temperature

A novel approach to the Hamiltonian formulation of quantum field theory at finite temperature is presented. The temperature is introduced by compactification of a spatial dimension. The whole finite-temperature theory is encoded in the ground state on the spatial manifold S 1 ( L ) × R 2 where L is the length of the compactified dimension which defines the inverse temperature. The approach is then applied to the Hamiltonian formulation of QCD in Coulomb gauge to study the chiral phase transition at finite temperatures.

Estimates of the Bc wave function from the CDF and LHCb production data

In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of Bc and B*c mesons at the conditions of the CDF andLHCb experiments. We derive first estimations for the Bc wave function from a comparison with the available data.

ϒ(3S) and χb(3P) production and polarization in the NRQCD with kT–factorization

The ϒ(3S) production and polarization at high energies is studied in the framework of kT–factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The transverse momentum dependent (TMD, or unintegrated) gluon densities in a proton were derived from the CiafaloniCatani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the nonperturbative color octet transitions in terms of the mulitpole radiation theory and taking into account feed-down contributions from radiative χb(3P) decays, we extract the corresponding non-perturbative matrix elements for ϒ(3S) and χb(3P) mesons from a combined fit to ϒ(3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies √s = 7 and 13 TeV and central rapidities. Then we apply the extracted values to investigate the polarization parameters λθ, λφ and λθφ, which determine the ϒ(3S) spindensity matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

Dual Meissner Effect and Quark Confinement Potential in SU(3) Dual QCD Formalism

The mechanism of color confinement has been studied in the framework of SU (3) color gauge theory in terms of abelian fields and monopoles extracted by adopting magnetic symmetry. The existence of the mechanism of color confinement corresponds to the dual Meissner effect caused by monopoles. The two length scales, i.e. the penetration depth and coherence length are defined to demonstrate the scaling nature of the QCD vacuum and their ratio defines the Ginzburg-Landau parameter indicating the border of type I and type II dual superconductor. The existence of these two length scales describes the intrinsic shape of the confining flux-tube and is a characteristic of the dual superconductor model of confinement in QCD. As a result, the quark confining potential has been computed and the resulting expression of string tension has been constructed in the infrared sector of SU (3) Dual QCD formulation. Moreover, with the introduction of dynamical quarks the flux tube breaks and leads to the creation of quark anti-quark pairs. Finite temperature quark confining potential and the associated string tension has also been extracted which demonstrates a considerable reduction in the vicinity of critical temperature showing agreement with the recent lattice studies.

First estimates of the Bc wave function from the data on the Bc production cross section

In the framework of perturbative QCD and nonrelativistic bound state formalism, we calculate the production of Bc and Bc⁎ mesons at the conditions of the CDF and LHCb experiments. We derive first estimations for the Bc wave function from a comparison with the available data.

Semileptonic decays of Bc meson to P -wave charmonium states

Inspired by a series of unexpected measurements of semileptonic decays mediated via $b\rightarrow c $ charged current interactions, we explore semileptonic $B_c$ decays to the four lightest $P$-wave charmonium states, $\chi_{c0}, \chi_{c1}, \chi_{c2}, h_c$, by the recently developed improved perturbative QCD formalism, in which the charm quark mass effect is included both in the Sudakov factor and the hard kernels. We first directly evaluate the concerned transition form factors with vector and axial-vector currents in the region of small momentum transfer squared, and then recast them to the full kinematical region by adopting the exponential parametrization. The obtained form factors are used to evaluate the semileptonic decay branching ratios, which can reach the order of $10^{-3}$, letting the corresponding measurement appear feasible. For a better analysis, a comparison of our results with the predictions of other models is provided. We also present the ratios between the tau and light lepton branching ratios and the polarization contributions in the relevant processes, which still need experimental tests in the ongoing and forthcoming experiments. Any significant deviations from the Standard Model results may provide some hints of new physics effects.

Combining QED and QCD transverse-momentum resummation for Z boson production at hadron colliders

We consider the transverse-momentum (qT) distribution of Z bosons produced in hadronic collisions. At small values of qT, we perform the analytic resummation of the logarithmically enhanced QED contributions up to next-to-leading logarithmic accuracy, including the mixed QCD-QED contributions at leading logarithmic accuracy. Resummed results are consistently matched with the next-to-leading fixed-order results (i.e. mathcal{O} (α2)) at small, intermediate and large values of qT. We combine the QED corrections with the known QCD results at next-to-next-to-leading order left(mathcal{O}left({alpha}_S^2right)right) and next-to-next-to-leading logarithmic accuracy. We show numerical results at LHC and Tevatron energies, studying the impact of the QED corrections and providing an estimate of the corresponding perturbative uncertainty. Our analytic results for the combined QED and QCD resummation, obtained through an extension of the qT resummation formalism in QCD, are valid for the production of generic neutral and colourless high-mass systems in hadronic collision.

Nucleon sigma terms from lattice QCD

Nucleon sigma terms are fundamental properties of the nucleons and are important input quantities for direct dark matter detection experiments. Here we present a determination of these sigma terms directly from the underlying theory. We use the lattice formulation of QCD to non-perturbativley calculate the quark mass dependence of the nucleon mass and the Feynman-Hellmann theorem to deduce the sigma terms. We present results for the up, down, and strange sigma terms of the proton and neutron.

Improved perturbative QCD formalism for Bc meson decays

We derive the $k_T$ resummation for doubly heavy-flavored $B_c$ meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the "golden channel" $B_c^+ \to J/\psi \pi^+$. With a reasonable model for the $B_c$ meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the $B_c \to J/\psi$ transition form factor appears to be power suppressed, and the $B_c^+ \to J/\psi \pi^+$ branching ratio is not lower than $10^{-3}$. The above improved perutrbative QCD formalism is applicable to $B_c$ meson decays to other charmonia and charmed mesons.

Branching ratios and CP asymmetries of Brightarrow chi _{c1}K(pi ) decays

We investigate the exclusive nonleptonic decays Brightarrow chi _{c1}K(pi ) in the conventional perturbative QCD (PQCD) formalism. The predictions of branching ratios and CP asymmetries are given in detail. We compare our results with available experimental data as well as predictions of other theoretical studies existing in the literature. It seems that the branching ratios of Brightarrow chi _{c1} K are more consistent with data than the earlier analyses. For the Cabibbo-suppressed B_s decays, the branching ratios can reach the order of 10^{-5}, which would be straight forward for experimental observations. The numerical results show that the direct CP asymmetries of the concerned decays are rather small. The mixing-induced CP asymmetry in the B^0rightarrow chi _{c1}K_S is very close to sin {2beta }, which suggests that this channel offer an alternative method for measuring the Cabbibo–Kobayashi–Maskawa (CKM) angle beta . The obtained results in the present work could be tested by further experiments in the LHCb and forthcoming Belle II.

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.

Relating quark confinement and chiral symmetry breaking in QCD

We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various ‘confinement indicators’, such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue such as , which behaves as a reduction factor for small . Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities, while they are essential for chiral symmetry breaking. These relations indicate that there is no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, and find similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry.

Use of a non-relativistic basis for describing the low energy meson spectrum

We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an a posteriori flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV.

Measurements of charmonium production in p+p, p+Au, and Au+Au collisions at [formula omitted] with the STAR experiment

We present the first results from the STAR MTD of mid-rapidity charmonium measurements via the di-muon decay channel in p+p, p+Au, and Au+Au collisions at sNN=200 GeV at RHIC. The inclusive J/ψ production cross section in p+p collisions can be described by the Non-Relativistic QCD (NRQCD) formalism coupled with the color glass condensate effective theory (CGC) at low transverse momentum (pT) and next-to-leading order NRQCD at high pT. The nuclear modification factor in p+Au collisions for inclusive J/ψ is below unity at low pT and consistent with unity at high pT, which can be described by calculations including both nuclear PDF and nuclear absorption effects. The double ratio of inclusive J/ψ and ψ(2S) production rates for 0 <pT < 10 GeV/c at mid-rapidity between p+p and p+Au collisions is measured to be 1.37 ± 0.42 ± 0.19. The nuclear modification factor in Au+Au collisions for inclusive J/ψ shows significant J/ψ suppression at high pT in central collisions and can be qualitatively described by transport models including dissociation and regeneration contributions.

Prompt charmonia production and polarization at the LHC in the NRQCD with kT -factorization. III. J/ψ meson

In the framework of $k_T$-factorization approach, the production and polarization of prompt $J/\psi$ mesons at the LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. Both the direct production mechanism and feed-down contributions from $\chi_c$ and $\psi(2S)$ decays are taken into account. The transverse momentum dependent (or unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on $J/\psi$ transverse momentum distributions and then applied to describe the ATLAS and LHCb data on $J/\psi$ production and polarization at $\sqrt s = 7$, $8$ and $13$ TeV. We perform an estimation of polarization parameters $\lambda_\theta$, $\lambda_\phi$ and $\lambda_{\theta \phi}$ which determine $J/\psi$ spin density matrix and demonstrate that treating the soft gluon emission as a series of explicit color-electric dipole transitions within NRQCD leads to unpolarized $J/\psi$ production at high transverse momenta, that is in qualitative agreement with the LHC data.

Instantaneous Dynamics of QCD

We start from the observation that, in the confining phase of QCD, the instantaneous color-Coulomb potential in Coulomb gauge is confining. This suggests that, in the confining phase, the dynamics, as expressed in the set of Schwinger-Dyson equations, may be dominated by the purely instantaneous terms. We develop a calculational scheme that expresses the instantaneous dynamics in the local formulation of QCD that includes a cut-off at the Gribov horizon.

Some Developments in Gribov’s Approach to QCD

We review several developments in the formulation of QCD provided by the GZ action. These include the GZ-action at finite temperature, the relation of the horizon condition and the Kugo-Ojima confinement criterion, the relation of the horizon condition and the dual-Meisssner effect, the alternative derivation of the GZ action provided by the Maggiore-Schaden shift, and the spontaneous breaking of BRST symmetry. We conclude with a proposal for the definition of physical states in the presence of BRST breaking.

The {β}-expansion formalism in perturbative QCD and its extension

We discuss the $\{ \beta \}$-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ $R$-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the $\{ \beta \}$-expansion. We illustrate this feature considering the nonsinglet Adler function $D^\text{NS}$ in the third order of perturbation. We propose a generalization of the $\{ \beta \}$-expansion for the renormalization group covariant quantities -- the $\{ \beta,\gamma \}$-expansion.

Induced QCD I: theory

We explore an alternative discretization of continuum SU(N_c) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N_b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N_b can be as small as N_c. In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U(N_c) to SU(N_c), (ii) derive refined bounds on N_b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.