The present knowledge of the QCD phase diagram based on simulations of lattice QCD is summarised. The main questions are whether there is a critical point in the QCD phase diagram and whether it is related to a chiral phase transition. It is shown that QCD at imaginary chemical potentials has a rich phase structure, which can be determined in a controlled way without sign problem and which severely constrains the phase structure at real chemical potentials.
This an English translation of a review of finite-density lattice QCD. The original version in Japanese appeared in Soryushiron Kenkyu Vol 31 (2020) No. 1.
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized.
Lattice QCD is an important tool for theoretical input for flavor physics. There have been four reviews by the Flavour Lattice Averaging Group (FLAG). This talk will review the current status of the magnitude of eight of the nine CKM matrix elements, borrowing heavily from the most recent FLAG review (co-authored by the speaker). Future prospects for improving the determination of the CKM matrix will be discussed.
This talk gives an overview of how lattice QCD calculations are influencing quark flavor physics. The first part of the talk focuses on the climb to higher precision; the second part surveys views along less-trodden paths.
We summarize our recent results for the (T,mu)-phase diagram of N_f=3 QCD. Finding a strong variation of the critical endpoint mu_c with the quark mass m, we point out that an endpoint within reach of experiment requires fine-tuned quark masses. We further discuss the strategy and first data towards extending our results to the physical N_f=2+1 theory.
For a complete understanding of the QCD phase diagram it is important to connect first-principle thermodynamic calculations to experimental data from the RHIC Beam Energy Scan and the future experimental facilities FAIR, GSI, and NICA, Dubna. This can only be achieved by a realistic modeling of the dynamical evolution of critical fluctuations in heavy-ion collisions at the QCD phase transition. In this note I will summarize the current status of these dynamical models and highlight some of the important issues, which need to be addressed in the future.
We present the current status of $\varepsilon_K$ evaluated directly from the standard model using lattice QCD inputs. The lattice QCD inputs include $\hat{B}_K$, $ξ_0$, $ξ_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$. Recently, FLAG has updated $\hat{B}_K$, exclusive $|V_{cb}|$ has been updated with new lattice data in the $\bar{B}\to D\ell\barν$ decay mode, and RBC-UKQCD has updated $ξ_0$ and $ξ_2$. We find that the standard model evaluation of $\varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) is $3.2σ$ lower than the experimental value, while that with inclusive $|V_{cb}|$ (heavy …
We review the current status of the high order perturbative QCD evaluation of the hadronic decay rates of the Z and Higgs bosons. A systematic classification of the various types of QCD corrections to $O(α_s^2)$ and $O(α_s^3)$ is made and their numerical status is clarified.
We report the current status of $\varepsilon_K$, the indirect CP violation parameter in the neutral kaon system, evaluated using the lattice QCD inputs. We use lattice QCD to fix $\hat{B}_K$, $ξ_0$, $ξ_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$. Since Lattice 2015, FLAG updated $\hat{B}_K$, exclusive $V_{cb}$ has been updated with new lattice data in the $\bar{B}\to D\ellν$ decay channel, and RBC-UKQCD has updated $ξ_0$ and $ξ_2$. Our preliminary results show that the standard model evaluation of $\varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) has $3.2σ$ tension with the experim…
As algorithms and computing power have advanced, lattice QCD has become a precision technique for many QCD observables. However, the calculation of nucleon matrix elements remains an open challenge. I summarize the status of the lattice effort by examining one observable that has come to represent this challenge, average-x: the fraction of the nucleon's momentum carried by its quark constituents. Recent results confirm a long standing tendency to overshoot the experimentally measured value. Understanding this puzzle is essential to not only the lattice calculation of nucleon properties but als…
Significant progress has recently been achieved in the lattice gauge theory calculations required for extracting the fundamental parameters of the standard model from experiment. Recent lattice determinations of such quantities as the kaon $B$ parameter, the mass of the $b$ quark, and the strong coupling constant have produced results and uncertainties as good or better than the best conventional determinations. Many other calculations crucial to extracting the fundamental parameters of the standard model from experimental data are undergoing very active development. I review the status of suc…
We briefly review the status of high precision QCD predictions available for LHC processes, focusing on corrections beyond NLO and ways to make the latter available in a convenient format. As a phenomenological example we discuss the two-loop corrections to Higgs boson pair production in gluon fusion.
We review status of the power corrections in QCD. The topics include shape variables, unconventional 1/Q^2 corrections, tachyonic gluon mass as a fit parameter to the 1/Q^2 corrections. The selection of the material is determined mostly by results presented at the Conference QCD'98 (Montpellier, July 1998). Some background comments are also included.
We provide a brief review of the current status of resummed predictions for QCD final state observables such as event shapes and jet rates in a variety of different hard processes. Particular emphasis is given to more recent developments such as the study of non global observables, development of generalized resummation formulae and resummations for new types of event shape variables.
A brief review on the status of unpolarized parton densities and the determination of the QCD scale $Λ_{\rm QCD}$ from deep-inelastic scattering data is presented.
I have been asked to discuss the status of QCD. It seems to me that there are three main points to be made about the present status of QCD: $\bullet$ QCD is right, and we can do many beautiful things with it. $\bullet$ There are several important concrete problems that lie just beyond the edge of our current understanding. $\bullet$ There are some foundational issues in QCD, and some recent developments, that may point toward entirely new directions. These points will, I believe, emerge quite clearly from the following more detailed discussion. The discussion will be in three parts. I'll first…
We review recent progress in next-to-next-to-leading order (NNLO) perturbative QCD calculations with special emphasis on results ready for phenomenological applications. Important examples are new results on structure functions and jet or Higgs boson production. In addition, we describe new calculational techniques based on twistors and their potential for efficient calculations of multiparticle amplitudes.
I discuss recent developments in the QCD cascade formalism. I focus on the importance of and uncertainties in higher order corrections to the Modified Leading Log approximation for final-state radiation. I also talk about the CCFM and LDC evolution equations for initial-state radiation in DIS.
We present results from the first fully differential next-to-next-to leading order NNLO QCD computation of ZZ production, including off-shell effects, the leptonic decay and non-resonant contributions. We compare theoretical predictions to fiducial cross sections and distributions measured by ATLAS and CMS at 8 TeV and also perform a first comparison with early ATLAS measurements at 13 TeV.
The status of lattice QCD investigations at high temperature is reviewed. After a short introduction into thermal QCD on the lattice we report on the present understanding of the phase diagram and the equation of state, in particular in presence of dynamical quarks. We continue with a discussion of various screening lengths in the plasma phase including results from dimensionally reduced QCD. This is followed by summarizing lattice data on quark number susceptibilities and spectral densities, both of which are of immediate relevance to the interpretation of heavy ion experiments. A major secti…
A summary of the extraction of light quark masses from both QCD sumrules and lattice QCD simulations is presented. The focus is on providing a careful statement of the potential weaknesses in each calculation, and on integrating the work of different collaborations to provide a coherent picture.
I review a few selected topics in Lattice Quantum Chromo Dynamics, focusing more on the recent results. These include i) the equation of state and speed of sound, ii) J/ψsuppression, iii) flavour correlations and iv) the QCD phase diagram in the μ-T plane.
We present results for $\varepsilon_K$, the indirect CP violation parameter, calculated in the Standard Model using inputs from lattice QCD: the kaon bag parameter $\hat{B}_K$, and the CKM matrix element $V_{cb}$ from the axial current form factor for the exclusive decay $\bar{B}\to D^*\ell\barν$ at zero-recoil. In addition, we take the coordinates of the unitarity triangle apex $(\barρ,\barη)$ from the angle-only fit of the UTfit Collaboration and use $V_{us}$ to fix $λ$. In order to estimate the systematic error, we also use Wolfenstein parameters from the CKMfitter and UTfit. We find a $3.3…
Neither the chiral limit nor finite baryon density can be simulated directly in lattice QCD, which severely limits our understanding of the QCD phase diagram. In this review I collect results for the phase structure in an extended parameter space of QCD, with varying numbers of flavours, quark masses, colours, lattice spacings, imaginary and isospin chemical potentials. Such studies help in understanding the underlying symmetries and degrees of freedom, and are beginning to provide a consistent picture constraining the possibilities for the physical phase diagram.
Employing an approach based on the Green functions of Landau-gauge QCD, some selected results from a calculation of meson and baryon properties are presented. A rainbow-ladder truncation to the quark Dyson-Schwinger equation is used to arrive at a unified description of mesons and baryons by solving Bethe-Salpeter and covariant Faddeev equations, respectively.
Studies of hadronic final states are entering a new phase where very precise experimental measurements require better theoretical predictions for a meaningful comparison. Recent results and future developments are briefly reviewed both for the experiments and the theory.
Two parameters that have a strong influence on the finite temperature QCD transition, and play an important role in various physical scenarios are the quark density and the external magnetic field. The effect of these parameters on the thermal properties of QCD is discussed, and an overview of the latest lattice results is given.
We present the Standard Model evaluation of the indirect CP violation parameter $\varepsilon_K$ using inputs determined from lattice QCD together with experiment: $|V_{us}|$, $|V_{cb}|$, $ξ_0$, and $\hat{B}_K$. We use the Wolfenstein parametrization ($|V_{cb}|$, $λ$, $\barρ$, $\barη$) for the CKM matrix elements. For the central value, we take the angle-only fit of the UTfit collaboration, and use $|V_{us}|$ from the $K_{\ell 3}$ and $K_{μ2}$ decays as an independent input to fix $λ$. For the error estimate, we use results of the global unitarity triangle fits from the CKMfitter and UTfit coll…
We review the current status of the theoretical pentaquark search from the direct QCD calculation. The works from the QCD sum rule and the lattice QCD in the literature are carefully examined. The importance of the framework which can distinguish the exotic pentaquark state (if any) from the NK scattering state is emphasized.
I review recent progress in finite temperature lattice calculations, including calculations of Equation of State, fluctuations of conserved charges and spatial correlation functions. I compare lattice results with the predictions of hadron resonance gas model, resummed perturbation theory and 3-dimensional effective field theory. Comparison of the lattice results for certain ratios with the prediction of AdS/CFT correspondence is also discussed.
We summarize our current understanding of the connection between the QCD phase line and the chemical freeze-out curve as deduced from thermal analyses of yields of particles produced in central collisions between relativistic nuclei.
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.
Determining the QCD phase diagram is a pressing task in view of its relevance for nuclear and astro-particle physics programmes. We review the current status of lattice calculations of the phase diagram in the (T,μ_B)-plane for baryon chemical potentials μ_B < 500 MeV. At μ_B=0, simulations of staggered fermion actions predict the quark hadron transition to be a crossover in the continuum limit. As a baryon chemical potential is turned on, there is mounting evidence on coarse lattices for the crossover to weaken, rather than turning into a true phase transition at a critical point, as predicte…
Some consequences of the analyticity of the free energy (pressure) of QCD at finite chemical potential are deduced. These include a method for numerical exploration of the full phase diagram by a novel use of simulations at imaginary chemical potential to extract Yang-Lee zeroes of the grand-canonical partition function. We make use of, and comment on, CPT symmetries, positivity of non-linear susceptibilities and the finiteness of screening lengths. We also comment on the structure of zeroes expected for the usual picture of the phases of QCD, following a discussion of the physics of imaginary…
The current status of global QCD analysis of parton distribution functions of the nucleon is reviewed. Recent progress made in determining various features of the parton structure of the nucleon, as well as outstanding open questions are discussed. These include: the small-$x$ and large-$x$ behavior of the partons, particularly the gluon; the differentiation of $u$ and $d$ quarks; the strangeness sea ($s+\bar{s}$), the strangeness asymmetry ($s-\bar{s}$); and the heavy quark distributions $c$ and $b$. Important issues about assessing the uncertainties of parton distributions and their physical…
We include the full second-order corrections to the static QCD potential in the analysis of the ttbar threshold cross section. Then we examine the difference between the results obtained in the momentum-space approach and in the coordinate-space approach, which was found recently. Contrary to our expectation, the reduction of the difference by the inclusion of the second-order corrections is very small. There still remains a non-negligible deviation, which originates from the difference in the construction of the potentials in the two spaces. We scrutinize this problem. In particular, we estim…
The abundant amount of data to be collected by the ATLAS and CMS collaborations in future runs of the Large Hadron Collider at CERN opens up a new era of precision physics. Some of the most prominent precision observables are related to processes with one or more jets in the final state. In order to fully exploit the potential of the LHC and the HL-LHC, it is imperative to make theoretical predictions at the level of accuracy that matches or even exceeds that of the upcoming measurements. In this talk we present a review of the status of theoretical predictions including NNLO QCD corrections f…
The transition between the hadronic phase and the quark gluon plasma phase at nonzero temperature and quark chemical potentials is studied within the large-Nc expansion of QCD.
We briefly report the modern status of heavy quark sum rules (HQSR) based on stability criteria by emphasizing the recent progresses for determining the QCD parameters (alpha_s, m_{c,b} and gluon condensates)where their correlations have been taken into account. The results: alpha_s(M_Z)=0.1181(16)(3), m_c(m_c)=1286(16) MeV, m_b(m_b)=4202(7) MeV,<alpha_s G^2> = (6.49+-0.35)10^-2 GeV^4, < g^3 G^3 >= (8.2+-1.0) GeV^2 <alpha_s G^2> and the ones from recent light quark sum rules are summarized in Table 2. One can notice that the SVZ value of <alpha_s G^2> has been underestimated by a factor 1.6, <…
The session on effective Hamiltonians and chiral dynamics is overviewed, combined with a review on the bound-state problem. The progress during this session allows to remove all dependence on regularization in an effective interaction, thus to renormalize a Hamiltonian for the first time, and to solve front form as if they were instant-form equations, with all the advantages implied.
Calculations of neutrino-nucleus cross sections begin with the neutrino-nucleon interaction, making the latter critically important to flagship neutrino oscillation experiments, despite limited measurements with poor statistics. Alternatively, lattice QCD (LQCD) can be used to determine these interactions from the Standard Model with quantifiable theoretical uncertainties. Recent LQCD results of $g_{\mathrm{A}}$ are in excellent agreement with data, and results for the (quasi-)elastic nucleon form factors with full uncertainty budgets are expected within a few years. We review the status of th…
We explore the phase diagram of two-flavor QCD at imaginary values of baryon and isospin chemical potentials analyzing the thermodynamic potential of QCD analytically and that of the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model numerically. QCD has no pion condensation at imaginary baryon and isospin chemical potentials, and therefore has discrete symmetries that are not present at real baryon and isospin chemical potentials. The PNJL model possesses all the discrete symmetries. The PNJL model can reproduce qualitatively lattice QCD data presented very lately.
I review recent new lattice QCD results on a few selected topics which are relevant to the heavy ion physics community. Special emphasis is put on the QCD phase diagram towards the chiral limit and at nonzero baryon density as well as the fate of quarkonia and heavy quark drag coefficients.
We give a general overview about the approaches to study the phase diagram of QCD. Thereafter, we examine the evolution of a fireball in a chiral fluid dynamic model including nonequilibrium effects.
The aim of this review is to summarize the contemporary understanding of the QCD phase diagram as a function of temperature and baryo-chemical potential. The focus is on recent theoretical developments due to lattice simulations of the phase diagram.
Lattice QCD allows computations of moments of structure functions from first principles. An overview of the present status of the calculations is given. Recent results and future perspectives are discussed.
The phase diagram of lattice QCD in the strong coupling limit can be measured in the full $μ$-$T$ plane, also in the chiral limit. In particular, the phase diagram in the chiral limit features a tricritical point at some $(μ_c,T_c)$. This point may be related to the critical end point expected in the QCD phase diagram. We discuss the gauge corrections to the phase diagram at strong coupling and compare our findings with various possible scenarios in continuum QCD. We comment on the possibility that the tricritical point at strong coupling is connected to the tricritical point in the continuum,…
We review the theoretical status of the B --> pi K decays, focusing on recent developments in the QCD factorization and perturbative QCD approaches as well as on the Standard-Model correlation between the mixing-induced and direct CP asymmetries of the B^0 --> pi^0 K^0 mode.
I show an updated QCD phase diagram with recent developments from chiral effective theories and phenomenological models. Expected signals of a QCD critical point accessible in heavy-ion collisions are also discussed. In particular, non-monotonic behavior of fluctuations associated with conserved charges is focused on.
Current status of theoretical researches on the QCD phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include; quark deconfinement, chiral symmetry restoration, order of the phase transitions, QCD critical point(s), colour superconductivity, various inhomogeneous states and implications from QCD-like theories.
I shall review the present status of Tevatron QCD studies, focusing on the production of jets, vector bosons, photons and heavy quarks. In general there is good agreement between the results of current calculational tools and the experimental data. The major areas of discrepancy arise when the input parton distributions become uncertain (for example, jets at high $E_T$) or when the momentum scales become relatively small (for example, $b$ production at low $p_T$). We can look forward to continued improvement in both calculations and measurements over the next decade. However, fully exploiting …
QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This paper is a colloquium level overview of the framework for understanding how these effects come about.
