Mass QCD Research Articles

Baryonic screening masses in QCD at high temperature

We compute the baryonic screening masses of the nucleon and of its negative parity partner in thermal QCD with Nf=3 massless quarks for a wide range of temperatures, from T∼1 GeV up to ∼160 GeV. The computation is performed by Monte Carlo simulations of lattice QCD with O(a)-improved Wilson fermions by exploiting a recently proposed strategy to study non-perturbatively QCD at very high temperature. Very large spatial extensions are considered in order to have negligible finite volume effects. For each temperature we have simulated 3 or 4 values of the lattice spacing, so as to perform the continuum limit extrapolation with confidence at a few permille accuracy. The degeneracy of the positive and negative parity-state screening masses, expected from Ward identities associated to non-singlet axial transformations, provides further evidence for the restoration of chiral symmetry in the high temperature regime of QCD. In the entire range of temperatures explored, the baryonic masses deviate from the free theory result, 3πT, by 4–8%. The contribution due to the interactions is clearly visible up to the highest temperature considered, and cannot be explained by the expected leading behavior in the QCD coupling constant g over the entire range of temperatures explored.

On the high-energy behavior of massive QCD amplitudes

In this note, we propose a factorization formula for gauge-theory scattering amplitudes up to two loops in the high-energy boosted limit. Our formula extends existing results in the literature by incorporating the contributions from massive loops. We derive the new ingredients in our formula using the method of regions with analytic regulators for the rapidity divergences. We verify our results with various form factors and the scattering amplitudes for top-quark pair production. Our results can be used to obtain approximate expressions for complicated two-loop massive amplitudes from simpler massless ones, and can be used to resum the mass logarithms to all orders in the coupling constant.

Two-loop massive QCD and QED helicity amplitudes for light-by-light scattering

We present the analytic and compact two-loop helicity amplitudes for QCD and QED corrections to the light-by-light scattering process with massive internal fermions. We express the master integrals either in terms of multiple polylogarithms or in terms of iterated integrals with dlog one-forms. We also elaborate on optimising the analytic results for each phase-space region. This makes the numerical evaluation of the scattering amplitudes fast, stable and suitable for phenomenological applications.

Dual simulation of a Polyakov loop model at finite baryon density: Correlations and screening masses

Computations of screening masses in finite-temperature QCD at finite density are plagued by the sign problem and have been performed so far with an imaginary chemical potential. Here, we use a dual formulation of a Polyakov-loop model which allows the determination of screening masses at real baryon chemical potential. This is a second paper in a series devoted to a detailed study of dual Polyakov-loop models at finite density. While the first paper was mainly devoted to establishing the phase diagram of the model, here we compute correlation functions of the Polyakov loops and the second-moment correlation length at non-zero chemical potential. This enables us to evaluate numerically the screening masses from correlations of the real and imaginary parts of the Polyakov loops. We also compute these masses in the mean-field approximation and compare with numerical results. In addition, we provide a quantitative improvement of the general phase diagram presented in the first paper.

High-precision QED initial state corrections for e+e−→ γ∗/Z∗ annihilation

The precise knowledge of the QED initial state corrections is of instrumental importance in studying high-luminosity measurements in [Formula: see text] annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-[Formula: see text] facility, and the planned FCC_ee. Logarithmic corrections of up to [Formula: see text] are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like [Formula: see text] and also the forward–backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of massive on-shell operator matrix elements, can be used for these calculations. We give an introduction to this topic and present both the calculation methods and the numerical corrections having been reached so far.

Scale symmetry breaking, quantum anomalous energy and proton mass decomposition

We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales. We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition. We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks. We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.

REvolver: Automated running and matching of couplings and masses in QCD

In this article we present REvolver, a C++ library for renormalization group evolution and automatic flavor matching of the QCD coupling and quark masses, as well as precise conversion between various quark mass renormalization schemes. The library systematically accounts for the renormalization group evolution of low-scale short-distance masses which depend linearly on the renormalization scale and sums logarithmic terms of high and low scales that are missed by the common logarithmic renormalization scale evolution. The library can also be accessed through Mathematica and Python interfaces and provides renormalization group evolution for complex renormalization scales as well. Program summaryProgram Title:REvolverCPC Library link to program files:https://doi.org/10.17632/m6cjfmzsxb.1Developer's repository link:https://gitlab.com/REvolver-hep/REvolverCode Ocean capsule:https://codeocean.com/capsule/6150064Licensing provisions: GPLv3 or laterProgramming language:C++, Python, Wolfram LanguageNature of problem: The strong coupling and the quark masses are fundamental parameters of QCD that are scheme and renormalization-scale dependent. The choice of scheme depends on the active number of flavors and the range of scales, and is dictated by the requirements to minimize the size of corrections and to sum large logarithmic corrections to all orders. For the strong coupling and the quark masses at high scales, the MS‾ scheme with logarithmic scale dependence is used. For quark masses at low scales, short-distance mass schemes with linear scale-dependence are used. The REvolver library provides conversions for the strong coupling and the most common quark mass schemes, with renormalization scale evolution implemented such that all types of large logarithmic terms are summed to all orders, accounting for flavor threshold effects and state-or-the-art correction terms. The pole mass, which is not a short-distance mass and contains a sizable renormalon ambiguity, is treated as a derived quantity.Solution method: Renormalization group equations are solved for complex-valued scales to machine precision based on fast-converging iterative algorithms and analytic all-order expressions. Matching relations for the strong coupling at flavor thresholds are computed in a way that gives equal results for upward and downward evolution. Core objects allow to define an arbitrary number of physical scenarios for strong coupling values and quark mass spectra, where options for precision and matching scales can be set freely, and values for quark masses in all common schemes including the pole mass can be extracted. All REvolver routines are implemented entirely in C++ and can be accessed through Mathematica and Python interfaces.

Three-body interactions from the finite-volume QCD spectrum

We perform a fit of the finite-volume QCD spectrum of three pions at maximal isospin to constrain the three-body force. We use the unitarity-based relativistic three-particle quantization condition, with the GWUQCD spectrum obtained at 315 MeV and 220 MeV pion mass in two-flavor QCD. For the heavier pion mass we find that the data is consistent with a constant contact term close to zero, whereas for the lighter mass we see a statistically significant energy dependence in tension with the prediction of leading order ChPT. Our results also suggest that with enough three-body energy levels, the two-body amplitude could be constrained.

Determination of the charm quark mass in lattice QCD with 2 + 1 flavours on fine lattices

We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted from Nf = 2 + 1 flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of the O(a) improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbatively O(a) improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to be Mc = 1486(21) MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in the overline{mathrm{MS}} scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory of Mc(Nf = 4) = 1548(23) MeV, where effects associated with the absence of a charmed, sea quark in the non-perturbative evaluation of the QCD path integral are not accounted for. In the overline{mathrm{MS}} scheme, and at finite energy scales conventional in phenomenology, we quote {m}_{mathrm{c}}^{overline{mathrm{MS}}} ( {m}_{mathrm{c}}^{overline{mathrm{MS}}} ; Nf = 4) = 1296(19) MeV and {m}_{mathrm{c}}^{overline{mathrm{MS}}} (3 GeV; Nf = 4) = 1007(16) MeV for the renormalised charm quark mass.

Loop-level double-copy for massive quantum particles

We find that scattering amplitudes in massive scalar QCD can manifest the duality between color and kinematics at loop-level. Specifically we construct the one-loop integrands for four-point scattering between two distinct massive scalars, and the five-point process encoding the first correction to massive scalar scattering with gluonic radiation. We find that factorization and the color-kinematics duality are sufficient principles to entirely bootstrap these calculations, allowing us to construct all contributions ultimately from the three-point tree-level amplitudes which are themselves entirely constrained by symmetry. Double-copy construction immediately provides the associated predictions for massive scalars scattering in the so called N=0 supergravity theory.

Axial UA(1) Anomaly: A New Mechanism to Generate Massless Bosons

Prior to the establishment of QCD as the correct theory describing hadronic physics, it was realized that the essential ingredients of the hadronic world at low energies are chiral symmetry and its spontaneous breaking. Spontaneous symmetry breaking is a non-perturbative phenomenon, and, thanks to massive QCD simulations on the lattice, we have at present a good understanding of the vacuum realization of the non-abelian chiral symmetry as a function of the physical temperature. As far as the UA(1) anomaly is concerned, and especially in the high temperature phase, the current situation is however far from satisfactory. The first part of this article is devoted to reviewing the present status of lattice calculations, in the high temperature phase of QCD, of quantities directly related to the UA(1) axial anomaly. In the second part, some recently suggested interesting physical implications of the UA(1) anomaly in systems where the non-abelian axial symmetry is fulfilled in the vacuum are analyzed. More precisely it is argued that, if the UA(1) symmetry remains effectively broken, the topological properties of the theory can be the basis of a mechanism, other than Goldstone’s theorem, to generate a rich spectrum of massless bosons at the chiral limit.

Mass of a short-range correlated nucleon * *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030301) and the National Science Foundation China (11305007)

Nucleon properties and structure should be modified by short-range correlations (SRC) among nucleons. By analyzing SRC ratio data, we extract the mass of a nucleon in an SRC pair and the expected number of pn-SRC pairs in deuterium, under the assumption that the SRC nucleon mass is universal for different nuclei. The nucleon mass of a two-nucleon SRC pair is = 852 ± 18 MeV, and the number of pn-SRC pairs in deuterium is =0.021 ± 0.005. The mass deficit of the strongly overlapping nucleon can be explained by the trace anomaly contribution to the mass in QCD or alternatively by the vacuum energy in the MIT bag model.

Double copy of massive scalar QCD

We construct the gravitational theory emerging from the double-copy of massive scalar quantum chromodynamics in general dimensions. The resulting two-form-dilaton-gravity theory couples to flavored massive scalars gravitationally and via the dilaton. It displays scalar self-interaction terms of arbitrary even order in the fields but quadratic in derivatives. We work out the emerging Lagrangian explicitly up to the sixth order in scalar fields and propose an all order form.

On pion and kaon decay constants and their chiral SU(3) extrapolations

We consider the dependence of the pion and kaon decay constants on the up, down and strange quark masses in QCD with strict isospin symmetry. The role of dynamical vector meson degrees of freedom is scrutinized in terms of an effective chiral Lagrangian for vector mesons. Applying a set of low-energy parameters as determined previously from QCD lattice data on the masses of the light vector mesons from PACS-CS, QCDSF-UKQCD and HSC we compute its implications on the pion and kaon decay constants for QCD lattice ensembles of HPQCD, CLS and ETMC. It is shown that with Gasser-Leutwyler L4 and L5 parameters fixed to the empirical decay constants an accurate reproduction of their values at unphysical quark masses as computed by HPQCD, CLS and ETMC is achieved. Results for the masses of the light vector meson, the ω−ϕ mixing angles and the quark mass ratios for the ensembles used by HPQCD, CLS and ETMC are discussed.

Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography

QCD is not supersymmetrical in the traditional sense – the QCD Lagrangian is based on quark and gluonic fields – not squarks or gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The pion eigenstate has zero mass for mq = 0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key tool is the remarkable dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale ӄ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. Although conformal symmetry is strongly broken by the heavy quark mass, the basic underlying supersymmetric mechanism, which transforms mesons to baryons (and baryons to tetraquarks), still holds and gives remarkable mass degeneracy across the entire spectrum of light, heavy-light and double-heavy hadrons. One also predicts the form of the nonperturbative QCD running coupling: αs(Q2) ∝ e−Q2/4ӄ2, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.

Supersymmetric and Conformal Features of Hadron Physics

The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion q q ¯ eigenstate has zero mass for m q = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α s ( Q 2 ) ∝ e − Q 2 / 4 κ 2 , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS 5 space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

On the chiral expansion of vector meson masses

We study the chiral expansion of meson masses and decay constants using a chiral Lagrangian that was constructed previously based on the hadrogenesis conjecture. The one-loop self energies of the Goldstone bosons and vector mesons are evaluated. It is illustrated that a renormalizeable effective field theory arises once specific conditions on the low-energy constants are imposed. For the case where the hadrogenesis mass gap scale Lambda_{HG} is substantially larger than the chiral symmetry breaking scale Lambda_chi a partial summation scheme is required. All terms proportional to (M/\Lambda_\chi)^n can be summed by a suitable renormalization, where M is the chiral and large-N_c limit of the vector meson masses in QCD. The size of loop effects from vector meson degrees of freedom is illustrated for physical quarks masses. Naturally sized effects are observed that have significant impact on the chiral structure of low-energy QCD with three light flavours.

QCD domain walls, Chern-Simons theories and holography

Massive QCD at θ = π breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are supported by the string theory construction.

A simple worldsheet black hole

We study worldsheet theory of confining strings in two-dimensional massive adjoint QCD. Similarly to confining strings in higher dimensions this theory exhibits a non-trivial S-matrix surviving even in the strict planar limit. In the process of two-particle scattering a zigzag is formed on the worldsheet. It leads to an interesting non-locality and exhibits some properties of a quantum black hole. Ordinarily, identical quantum particles do not carry identity. On the worldsheet they acquire off-shell identity due to strings attached. Identity implies complementarity. We discuss similarities and differences of the worldsheet scattering with the Toverline{T} deformation. We also propose a promising candidate for a supersymmetric model with integrable confining strings.

Hadron Spectroscopy and Dynamics from Light-Front Holography and Superconformal Algebra

QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields, not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD and its Pauli matrix representation. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks in the same 4-plet representation with a universal Regge slope. The pion $q \bar q$ eigenstate has zero mass for $m_q=0.$ The superconformal relations also can be extended to heavy-light quark mesons and baryons. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key observation is the remarkable dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $\kappa$ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling, and the mass parameter underlying the form of the nonperturbative QCD running coupling: $\alpha_s(Q^2) \propto \exp{-{Q^2/4 \kappa^2}}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. The mass scale $\kappa$ underlying hadron masses can be connected to the parameter $\Lambda_{\overline {MS}}$ in the QCD running coupling by matching its predicted nonperturbative form to the perturbative QCD regime. One also obtains predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.