The non-local vacuum condensates of QCD describe the distributions of quarks and gluons in the non-perturbative QCD vacuum. Physically, this means that vacuum quarks and gluons have nonzero mean-squared momentum, called virtuality. In this paper we study the quark virtuality which is given by the ratio of the local quark-gluon mixed vacuum condensate to the quark local vacuum condensate. The two vacuum condensates are obtained by solving Dyson-Schwinger Equations of a fully dressed quark propagator with an effective gluon propagator. Using our calculated condensates, we obtain the virtuality of quarks in the QCD vacuum state. Our numerical predictions differ from the other theoretical model calculations such as QCD sum rules, Lattice QCD and instanton models.
We use next-to-leading-order in perturbation theory to investigate the effects of a finite isospin density on the thermodynamics of cold strongly interacting matter. Our results include nonzero quark masses and are compared to lattice data.
In this paper we rewrite the neutrino mixing angles and mass squared differences in matter given, in our original paper, in a notation that is more conventional for the reader. Replacing the usual neutrino mixing angles and mass squared differences in the expressions for the vacuum oscillation probabilities with these matter mixing angles and mass squared differences gives an excellent approximation to the oscillation probabilities in matter. Comparisons for T2K, NOvA, T2HKK and DUNE are also given for neutrinos and anti-neutrinos, disappearance and appearance channels, normal ordering and inv…
We study the polarized Bjorken sum rule at low momentum transfer squared Q2<3GeV2 in the twist-two approximation and to the next-to-next-to-leading order accuracy.
We extend a previous investigation of the QCD phase diagram with heavy quarks in the context of background field methods by including the two-loop corrections to the background field effective potential. The nonperturbative dynamics in the pure-gauge sector is modeled by a phenomenological gluon mass term in the Landau-DeWitt gauge-fixed action, which results in an improved perturbative expansion. We investigate the phase diagram at nonzero temperature and (real or imaginary) chemical potential. Two-loop corrections yield an improved agreement with lattice data as compared to the leading-order…
We investigate the phase diagram of QCD with heavy quarks at finite temperature and chemical potential in the context of background field methods. In particular, we use a massive extension of the Landau-DeWitt gauge which is motivated by previous studies of the deconfinement phase transition in pure Yang-Mills theories. We show that a simple one-loop calculation is able to capture the richness of the phase diagram in the heavy quark region, both at real and imaginary chemical potential. Moreover, dimensionless ratios of quantities directly measurable in numerical simulations are in good agreem…
We study models in which reheating happens only through non-perturbative processes. The energy transferred can be exponentially suppressed unless the inflaton is coupled to a particle with a parametrically small mass. Additionally, in some models a light scalar with a negative mass squared parameter leads to much more efficient reheating than one with a positive mass squared of the same magnitude. If a theory contains many sectors similar to the Standard Model coupled to the inflaton via their Higgses, such dynamics can realise the Nnaturalness solution to the hierarchy problem. A sector conta…
We calculate the effective potential of the 2SC/g2SC phases including vector condensates ($<gA_z^6>$ and $<gA_z^8>$) and study the gluonic phase and the single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell state at nonzero temperature. Our analysis is performed within the framework of the gauged Nambu--Jona-Lasinio model. We compute potential curvatures with respect to the vector condensates and investigate the temperature dependence of the Meissner masses squared of gluons of color 4--7 and 8 in the neutral 2SC/g2SC phases. The phase diagram is presented in the plane of temperature and coupling…
We use results for the structure functions $F_L$ for a gluon target having nonzero transverse momentum square at order $α_s$, obtained in our previous paper, to compare with recent H1 experimental data for $F_L$ at fixwd W values and with collinear GRV predictions at LO and NLO approximation.
We calculate the one-loop squared contributions to the next-to-next-to-leading order ${\cal O}(α^2α_s^2)$ radiative QCD corrections for the production of heavy quark pairs in the collisions of unpolarized on--shell photons. In particular, we present analytical results for the squared matrix elements that correspond to the product of the one--loop amplitudes. All results of the perturbative calculation are given in the dimensional regularization scheme. These results represent the Abelian part of the corresponding gluon--induced next-to-next-to-leading order cross section for heavy quark pair h…
In perturbative thermal calculations, introducing nonzero quark masses causes considerable complications. In this article we describe an approximation scheme valid for sufficiently light masses which significantly simplifies the relevant calculations with only a small loss in accuracy. We apply the scheme to Quantum Chromodynamics, with two massless and one massive flavor, obtaining analytic results which are in excellent agreement with numerical non-approximated results. Our results are accurate to $O(g^5)$ in the strong coupling parameter $g$, as long as either the chemical potential $μ$ of …
The strange quark mass is determined from a QCD Finite Energy Sum Rule (FESR) optimized to reduce considerably the systematic uncertainties arising from the hadronic resonance sector, as well as from the poor convergence of the pseudoscalar correlator in perturbative QCD. The former is achieved by introducing a suitable integration kernel in the Cauchy integral in the complex squared energy plane. The latter is obtained by optimizing the perturbative expansion to accelerate its convergence. The result for the strange quark mass in the $\bar{MS}$ scheme at a scale of 2 GeV is m_s(2 GeV) = (94 \…
The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections 1/Q^{2n}, a nonperturbative generalization A(Q^2) of the perturbative QCD running coupling a(Q^2)=alpha_s(Q^2)/pi. Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as A(Q^2)~Q^2 when the squared momenta Q^2 go to zero (Q^2<<1 GeV^2). In this work we construct such a QCD coupling A(Q^2) which fulfills also various other physically motiv…
It is shown, that the possibility of a freezing of QCD running coupling constant at zero in the approach with "forced analyticity" can not be in accord with Schwinger-Dyson equation for gluon propagator. We propose to add to the analytic expression the well-known infrared singular term $1/q^2$ as well as pole term corresponding to "excited gluon". With this example we formulate the principle of minimality of nonperturbative contributions in perturbative (ultraviolet) region, which allows us to fix ambiguities in introduction of nonperturbative terms and maintain the finiteness of the gluon con…
Using a program of perturbative resummation I compute the damping rates for fields at nonzero spatial momentum to leading order in weak coupling in hot $QCD$. Sum rules for spectral densities are used to simplify the calculations. For massless fields the damping rate has an apparent logarithmic divergence in the infrared limit, which is cut off by the screening of static magnetic fields (``magnetic mass''). This demonstrates how at high temperature even perturbative quantities are sensitive to nonperturbative phenomenon.
The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.
The proton structure function in the diffraction region of small Bjorken-$x$ and $10 {\rm GeV}^2 \le Q^2 \le 100 {\rm GeV}^2$ behaves as $F_2 (x, Q^2) = F_2 (W^2) = f_0 \cdot (W^2)^{C_2}$, where $x = Q^2 / W^2$. The exponent $C_2$ of the $γ^* p$ center-of-mass energy squared, $W^2$, is predicted from evolution of the flavor-singlet quark distribution, $C_2 = 0.29$, and the only free parameter, the normalization $f_0 = 0.063$, is fitted. The evolution of the gluon density multiplied by $α_s (Q^2)$ is dentical to the evolution of the flavor-singlet quark density. This simple picture is at varian…
The elastic scattering of gqq, gqqbar and gqbarqbar and the thermalization of quark-gluon matter are studied. According to Feynman diagrams at the tree level, squared amplitudes for the elastic gqq scattering and the elastic gqqbar scattering are derived in perturbative QCD. Transport equations including the squared amplitudes for the elastic gqq, gqqbar and gqbarqbar scattering are established. Corresponding to anisotropic gluon and quark distributions created in central Au-Au collisions at RHIC, solutions of the transport equations show that thermalization time of quark matter can be shorten…
We study properties of a gluon plasma above the critical temperature $T_c$ in a generalized quasi-particle approach with a Lorentz spectral function. The model parameters are determined by a fit of the entropy $s$ to lattice QCD data. The effective degrees of freedom are found to be rather heavy and of a sizeable width. With the spectral width being closely related to the interaction rate, we find a large effective cross section, which is comparable to the typical distance squared of the quasiparticles. This suggests that the system should be viewed as a liquid as also indicated by an estimate…
The leading perturbative contributions into the two-point gauge-invariant correlator $Tr<gF(x)U(x,0)U(0,y)F(y)U(y,0)U(0,x)>$ are calculated at the one-loop order. It is shown, that nonlocal condensate is nonzero at this order. The relation with the renormalization properties of Wilson loops is discussed.
We calculate the perturbative parts of the structure functions $F_2^c$ and $F_L^c$ for a gluon target having nonzero transverse momentum squared at order $α_s$. The results of the double convolution (with respect to the Bjorken variable $x_B$ and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with HERA experimental data for $F_2^c$. The contribution from $F_L^c$ structure function ranges (10-30)% of that of $F_2^c$ at the kinematical range of HERA experiments.
We present the perturbative parts of the structure functions F_2^c and F_L^c for a gluon target having nonzero transverse momentum squared at order α_s. The results of the double convolution (with respect to the Bjorken variable x and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with HERA experimental data for F_2^c. The contribution from F_L^c structure function ranges 10\div30% of that of F_2^c at the HERA kinematical range.
Reanalysis of exclusive charmonium production at the $B$ factories
College of Physics and Optoelectronic Engineering, Chongqing Normal University（重庆师范大学物理与光电工程学院）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences, Chinese Academy of Sciences（中国科学院大学）
We study the quark helicity distributions at large x in perturbative QCD, taking into account contributions from the valence Fock states of the nucleon which have nonzero orbital angular momentum. These states are necessary to have a nonzero anomalous magnetic moment. We find that the quark orbital angular momentum contributes a large logarithm to the negative helicity quark distributions in addition to its power behavior, scaling as (1-x)^5\log^2(1-x) in the limit of x\to 1. Our analysis shows that the ratio of the polarized over unpolarized down quark distributions, Δd/d, will still approach…
We apply perturbative QCD to investigate the near threshold heavy quarkonium photoproduction at large momentum transfer. From an explicit calculation, we show that the conventional power counting method will be modified and the three quark Fock state with nonzero orbital angular momentum dominates the near threshold production. It carries a power behavior of $1/(-t)^5$ for the differential cross section. We further comment on the impact of our results on the interpretation of the experiment measurement in terms of the gluonic gravitational form factors of the proton.
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex pla…
We present precise predictions for four-lepton plus jets production at the LHC obtained within the fully automated Sherpa+OpenLoops framework. Off-shell intermediate vector bosons and related interferences are consistently included using the complex-mass scheme. Four-lepton plus 0- and 1-jet final states are described at NLO accuracy, and the precision of the simulation is further increased by squared quark-loop NNLO contributions in the gg -> 4l, gg -> 4l+g, gq -> 4l+q, and qq -> 4l+g channels. These NLO and NNLO contributions are matched to the Sherpa parton shower, and the 0- and 1-jet fina…
Perturbative and non-perturbative aspects of differential cross-sections close to a kinematic threshold are studied applying ``dressed gluon exponentiation'' (DGE). The factorization property of soft and collinear gluon radiation is demonstrated using the light-cone axial gauge: it is shown that the singular part of the squared matrix element for the emission of an off-shell gluon off a nearly on-shell quark is universal. We derive a generalized splitting function that describes the emission probability and show how Sudakov logs emerge from the phase-space boundary where the gluon transverse m…
In the paper, we study the properties of the top-quark $\overline{\rm MS}$ running mass computed from its on-shell mass by using both the four-loop $\overline{\rm MS}$-on-shell relation and the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct magnitude of the strong running coupling of the perturbative series, its prediction avoids the conventional renormalization scale ambiguity, and thus a more precise pQCD prediction can be achieved. After applying the PMC to the four-loop $\overline{\rm MS}$-on-shell relati…
We present a new determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cb}|$ by using the three-loop perturbative QCD corrections for the $B\to D^{\ast}$ semi-leptonic decay. The decay width of $B\to D^{\ast}$ semi-leptonic decay can be factorized as perturbatively calculable short-distance part and the non-perturbative but universal long-distance part. We adopt the principle of maximum conformality (PMC) single-scale setting approach to deal with the perturbative series so as to achieve a precise fixed-order prediction for the short-distance parameter $η_{A}$. By applying the…
Inspired by the recent measurement of the ratio of $B_c$ branching fractions to $J/ψπ^+$ and $J/ψμ^+ν_μ$ final states at the LHCb detector, we study the semileptonic decays of $B_c$ meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions $B_c\rightarrow P,V$, where $P$ and $V$ denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizin…
To investigate the non-perturbative, electric sector of a deconfined gauge theory at nonzero temperature, we consider a SU(2) matrix model. We compute beta-functions to one loop order for the simplest extension of the O(4) nonlinear sigma model, which involves three coupling constants. Computing in the ultraviolet limit in 2 + epsilon dimensions, we find that at least one coupling is not asymptotically free.
We present the perturbative parts of the structure functions F_2^c and F_L^c for a gluon target having nonzero transverse momentum squared at order α_s. The results of the double convolution (with respect to the Bjorken variable x and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with HERA experimental data for F_2^c and F_L at low x values and with predictions of other approaches. The contribution from F_L^c structure function ranges 10\div30% of that of F_2^c at the HERA kinematical range.
We present results for the structure function F_L for a gluon target having nonzero transverse momentum square at order α_s. The results of double convolution (with respect to Bjorken variable x and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with recent experimental data for F_L at low x values and with predictions of other approaches.
The effective potential approach for composite operators is generalized to non-zero temperature in order to derive the non-perturbative analytical equation of state for pure SU(3) Yang-Mills fields valid in the whole temperature range. Adjusting our parametrization of the gluon plasma pressure to the lattice pressure at high temperature for SU(3) Yang-Mills case, we have reproduced well our analytical curves and numbers not only for the pressure but for all other independent thermodynamic quantities as well in the whole temperature range $[0, \infty)$. We explicitly show that the pressure is a…
I reexamine the phenomena of the chromomagnetic gluon condensation in Yang-Mills theory. The extension of the Heisenberg-Euler Lagrangian to the Yang-Mills theory allows to calculate the effective action, the energy-momentum tensor and demonstrate that the energy density curve crosses the zero energy level of the perturbative vacuum state at nonzero angle and continuously enters to the negative energy density region. At the crossing point and further down the effective coupling constant is small and demonstrate that the true vacuum state of the Yang-Mills theory is below the perturbative vacuu…
The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections $1/Q^{2 n}$, a nonperturbative generalization $A(Q^2)$ of the perturbative QCD running coupling $a(Q^2)$ ($\equiv α_s(Q^2)/π$). Recent large volume lattice calculations for these dressing functions strongly indicate that such a generalized coupling goes to zero as $A(Q^2) \sim Q^2$ when the squared momenta $Q^2$ go to zero ($Q^2 \ll 1 \ {\rm GeV}^2$). We construct such a QCD coupling $A(Q^2)$ which fulfills also vari…
The aim of this thesis is to calculate field-theoretically as rigorously as possible the initial state of partonic matter produced in ultrarelativistic heavy-ion collisions at CERN-LHC and BNL-RHIC colliders. The computed minijet initial conditions are then used in the initialization of the relativistic hydrodynamical modeling of these collisions. In the theoretical introduction part the computation of parton production cross section at next-to-leading order (NLO) perturbative QCD (pQCD) is discussed. Furthermore, the full analytical calculation for the squared quark-quark scattering matrix el…
We develop a non-perturbative formalism for scalar metric fluctuations from a 5D extended version of general relativity in vacuum. In this work we concentrate our efforts on calculations valid on large cosmological scales, which are the dominant during the inflationary phase of the universe. The resulting metric in this limit is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution. We calculate the spectrum of these fluctuations with an effective 4D Schwarzschild-de Sitter spacetime on cosmological scales, which is obtained after we make a static fo…
We investigate the behavior of energy momentum tensor correlators in strongly coupled large-N_c Yang-Mills theory at nonzero temperature, working within the Improved Holographic QCD model. In particular, we determine the spectral functions and corresponding imaginary time correlators in the bulk and shear channels, and compare the results to recent perturbative and lattice calculations where available. For the bulk channel imaginary time correlator, for which all three results exist, lattice data is seen to favor the holographic prediction over the perturbative one over a wide range of tempera…
The momemtum dependence of the off-shell $ρ$-$ω$ mixing amplitude is calculated through a two-quark loop diagram, using non-perturbative meson-quark vertex functions for the $ρ$ and $ω$ mesons, as well as non-perturbative quark propagators. Both these quantities are generated self-consistently through an interlinked BSE-cum-SDE approach with a 3D support for the BSE kernel with two basic constants which are pre- checked against a wide cross section of both meson and baryon spectra within a common structural framework for their respective 3D BSE's. With this pre-calibration, the on-shell streng…
We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point co…
The spectroscopic properties of single heavy spin-1/2 $Λ_{Q}$, $Σ_{Q}$, $Ξ^{(\prime)}_{Q}$ and $ Ω_{Q}$ baryons are investigated at finite temperature in the framework of thermal QCD sum rule. We discuss the behavior of the mass and residue of these baryons with respect to temperature taking into account contributions of non-perturbative operators up to dimension eight. We include additional operators coming from the Wilson expansion due to breaking the Lorentz invariance at non-zero temperature. The obtained results show that the mass of these baryons remain stable up to roughly $T=108$ MeV w…
We generalize the state-of-the-art perturbative Equation of State of cold quark matter to nonzero temperatures, needed in the description of neutron star mergers and core collapse processes. The new result is accurate to order g^5 in the gauge coupling, and is based on a novel framework for dealing with the infrared sensitive soft field modes of the theory. The zero Matsubara mode sector is treated using a dimensionally reduced effective theory, while the soft non-zero modes are resummed using the Hard Thermal Loop approximation. This combination of known effective descriptions offers unpreced…
QCD matter at a finite magnetic field and nonzero chemical potential
School of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理与信息技术学院）；School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院）；School of Science, Xi’an Jiaotong University（西安交通大学理学院）
Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest d…
Using the classical recursion relations we compute scattering amplitudes in a spontaneously broken Gauge-Higgs theory into final states involving high multiplicities of massive vector bosons and Higgs bosons. These amplitudes are computed in the kinematic regime where the number of external particles n is >> 1 and their momenta are non-relativistic. Our results generalise the previously known expressions for the amplitudes on the multi-particle thresholds to a more non-trivial kinematic domain. We find that the amplitudes in spontaneously broken gauge theories grow factorially with the numbers…
In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P ρ^\prime(1450), Pρ^{\prime\prime}(1700)\to P ππ$ by employing the perturbative QCD (PQCD) factorization approach, where $P$ is a light pseudoscalar meson $K, π, η$ and $η^{\prime}$. The considered decay modes are studied in the quasi-two-body framework by parameterizing the two-pion distribution amplitude $Φ_{ππ}^{\rm P}$. The $P$-wave time-like form factor $F_π$ in the resonant regions associated with the $ρ^\prime(1450)$ and $ρ^{\prime\prime}(1700)$ i…
We present our study of the renormalization of the chromomagnetic operator,O(CM), which appears in the effective Hamiltonian describing Delta S = 1 transitions in and beyond the Standard Model. We have computed, perturbatively to one-loop, the relevant Green's functions with two (quark-quark) and three (quark-quark-gluon) external fields, at nonzero quark masses, using both the lattice and dimensional regularizations. The perturbative computation on the lattice is carried out using the maximally twisted-mass action for the fermions, while for the gluons we employed the Symanzik improved gauge …
We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff schemes and show explicitly that in certain cases dimensional regularization fails to reproduce the results obtained using cutoff regularization. First we consider a delta-function potential in arbitrary space dimensions. Using cutoff regularization we show that for $d \ge 4$ the renormalized scattering amplitude is trivial. In contrast, dimensional regularizati…
It is well known that Yang-Mills theory in vacuum has a perturbative instability to spontaneously form a large scale magnetic field (the Savvidy mechanism) and that a constant field is unstable so that a possible ground state has to be inhomogenous over the non-perturbative scale Lambda (the Copenhagen vacuum). We argue that this spontaneous instability does not occur at high temperature when the induced field strength gB ~ Lambda^2 is much weaker than the magnetic mass squared (g^2T)^2. At high temperature oscillations of gauge fields acquire a thermal mass M ~ gT and we show that this mass s…
