Physical Masses Research Articles

Finite-Volume Spectrum of π^{+}π^{+} and π^{+}π^{+}π^{+} Systems.

The abinitio understanding of hadronic three-body systems above threshold, such as exotic resonances or the baryon spectrum, requires the mapping of the finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the infinite volume. We present the first application of such a formalism to a physical system in form of three interacting positively charged pions. The results for the ground state energies agree with the available lattice QCD results by the NPLQCD collaboration at unphysical pion masses. Extrapolations to physical pion masses are performed using input from effective field theory. The excited energy spectrum is predicted. This demonstrates the feasibility to determine three-body amplitudes above threshold from lattice QCD, including resonance properties of axial mesons, exotics, and excited baryons.

The SU(8) GUT with composite quarks and leptons

We consider the L-R symmetric composite model for quarks and leptons where constituent preons possessing some local SU(N)MF metaflavor symmetry are bound by the chiral SO(n)L×SO(n)R gauge metacolor forces. The strengthening of the 't Hooft's anomaly matching condition, when the massless fermion composites are required to complete a single representation of the SU(N)MF rather than some set of its representations, allows to fix the number of basic metaflavors N. Particularly, just eight left-handed and eight right-handed preons and their composites preserving the global chiral symmetry SU(8)L×SU(8)R are turned out to underlie the physical world at small distances that uniquely identifies the local metaflavor symmetry SU(8)MF as its effective unified symmetry. We next show that the spontaneous L-R symmetry violation caused by the simultaneously emerged composite scalars reduces this initially vectorlike SU(8)MF theory down to the conventional SU(5) GUT with an extra local family symmetry SU(3)F and three standard families of quarks and leptons. Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra SU(5)×SU(3)F multiplets of heavy composite fermions may help with a model verification. Generally, they may be located at scales from O(100) TeV up to the Planck mass scale depending on an interplay between the compositeness scale and scale of the family symmetry SU(3)F. Some of them through a natural see-saw mechanism provide the physical neutrino masses which, in contrast to conventional picture, appear to follow an inverted family hierarchy. Others mix with ordinary quark-lepton families in a way that there may arise a marked violation of unitarity in the CKM matrix for leptons.

Electromagnetic currents for dressed hadrons

We propose an extension of the minimal-substitution prescription for coupling the electromagnetic field to hadronic systems with internal structure. The resulting rules of extended substitution necessarily distinguish between couplings to scalar and Dirac particles. Moreover, they allow for the incorporation of electromagnetic form factors for virtual photons in an effective phenomenological framework. Applied to pions and nucleons, assumed to be fully dressed to all orders, the resulting dressed currents are shown to be locally gauge invariant. Moreover, half-on-shell expressions of (hadron propagator)$\times$(electromagnetic current) needed in all descriptions of physical processes will lose \textit{all} information about hadronic dressing for real photons. The Ball-Chiu ansatz for the spin-1/2 current is seen to suffer from an incomplete coupling procedure where some essential aspects of the Dirac particle are effectively treated as those of a scalar particle. Applied to real Compton scattering on pions and nucleons, we find that \emph{all} dressing information cancels exactly when external hadrons are on shell, leaving only gauge-invariant bare Born-type contributions with physical masses. Hence, nontrivial descriptions necessarily require contact-type two-photon processes obtained by hadrons looping around two photon insertion points.

ΩNN and ΩΩN states

The lattice QCD analysis of the HAL QCD Collaboration has recently derived $\Omega N$ and $\Omega\Omega$ interacting potentials with nearly physical quark masses ($m_\pi \simeq $ 146 MeV and $m_K \simeq $ 525 MeV). They found an attractive interaction in the $\Omega N$ $^5S_2$ channel which supports a bound state with a central binding energy of 1.54 MeV. The $\Omega \Omega$ $^1S_0$ channel shows an overall attraction with a bound state with a central binding energy of 1.6 MeV. In this paper we looked closely at the $\Omega NN$ and $\Omega\Omega N$ three-body systems making use of the latest HAL QCD Collaboration $\Omega N$ and $\Omega\Omega$ interactions. Our results show that the $\Omega d$ system in the state with maximal spin $(I)J^P=(0)5/2^+$ is bound with a binding energy of about 20 MeV. The $(I)J^P=(1)3/2^+$ $\Omega nn$ state presents a resonance decaying to $\Lambda \Xi n$ and $\Sigma \Xi n$, with a separation energy of $\sim$ 1 MeV. The $(I)J^P=(1/2)1/2^+$ $\Omega \Omega N$ state also exhibits a resonance decaying to $\Lambda \Xi \Omega$ and $\Sigma \Xi \Omega$, with a separation energy of $\sim$ 4.6 MeV. We have calculated the contribution of the Coulomb potential to differentiate among the different charged states.

Light-Neutrino Exchange and Long-Distance Contributions to 0ν2β Decays: An Exploratory Study on ππ→ee.

We present an exploratory lattice QCD calculation of the neutrinoless double beta decay ππ→ee. Under the mechanism of light-neutrino exchange, the decay amplitude involves significant long-distance contributions. The calculation reported here, with pion masses m_{π}=420 and 140MeV, demonstrates that the decay amplitude can be computed from first principles using lattice methods. At unphysical and physical pion masses, we obtain that amplitudes are 24% and 9% smaller than the predication from leading order chiral perturbation theory. Our findings provide the lattice QCD inputs and constraints for effective field theory. A follow-on calculation with fully controlled systematic errors will be possible with adequate computational resources.

Towards a precise determination of the scattering amplitudes of the charmed and light-flavor pseudoscalar mesons

We study the scattering of the light-flavor pseudoscalar mesons (pi , K, eta ) off the ground-state charmed mesons (D,D_s) within chiral effective field theory. The recent lattice simulation results on various scattering lengths and the finite-volume spectra both in the moving and center-of-mass frames, most of which are obtained at unphysical meson masses, are used to constrain the free parameters in our theory. Explicit formulas to include the S- and P-wave mixing to determine the finite-volume energy levels are provided. After a successful reproduction of the lattice data, we perform a chiral extrapolation to predict the quantities with physical meson masses, including phase shifts, inelasticities, resonance pole positions and the corresponding residues from the scattering of the light pseudoscalar and charmed mesons.

Two Higgs doublets and a complex singlet: disentangling the decay topologies and associated phenomenology

We present a systematic study of an extension of the Standard Model (SM) with two Higgs doublets and one complex singlet (2HDM+S). In order to gain analytical understanding of the parameter space, we re-parameterize the 27 parameters in the Lagrangian by quantities more closely related to physical observables: physical masses, mixing angles, trilinear and quadratic couplings, and vacuum expectation values. Embedding the 125 GeV SM-like Higgs boson observed at the LHC places stringent constraints on the parameter space. In particular, the mixing of the SM-like interaction state with the remaining states is severely constrained, requiring approximate alignment without decoupling in the region of parameter space where the additional Higgs bosons are light enough to be accessible at the LHC. In contrast to 2HDM models, large branching ratios of the heavy Higgs bosons into two lighter Higgs bosons or a light Higgs and a Z boson, so-called Higgs cascade decays, are ubiquitous in the 2HDM+S. Using currently available limits, future projections, and our own collider simulations, we show that combining different final states arising from Higgs cascades would allow to probe most of the interesting region of parameter space with Higgs boson masses up to 1 TeV at the LHC with L = 3000 fb−1 of data.

Higher-order hadronic-vacuum-polarization contribution to the muon g−2 from lattice QCD

We introduce a new method for calculating the ${\rm O}(\alpha^3)$ hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment from ${ab-initio}$ lattice QCD. We first derive expressions suitable for computing the higher-order contributions either from the renormalized vacuum polarization function $\hat\Pi(q^2)$, or directly from the lattice vector-current correlator in Euclidean space. We then demonstrate the approach using previously-published results for the Taylor coefficients of $\hat\Pi(q^2)$ that were obtained on four-flavor QCD gauge-field configurations with physical light-quark masses. We obtain $10^{10} a_\mu^{\rm HVP,HO} = -9.3(1.3)$, in agreement with, but with a larger uncertainty than, determinations from $e^+e^- \to {\rm hadrons}$ data plus dispersion relations.

Renormalization of the multi-Higgs-doublet Standard Model and one-loop lepton mass corrections

Motivated by models for neutrino masses and lepton mixing, we consider the renormalization of the lepton sector of a general multi-Higgs-doublet Standard Model with an arbitrary number of right-handed neutrino singlets. We propose to make the theory finite by overline{mathrm{MS}} renormalization of the parameters of the unbroken theory. However, using a general Rξ gauge, in the explicit one-loop computations of one-point and two-point functions it becomes clear that — in addition — a renormalization of the vacuum expectation values (VEVs) is necessary. Moreover, in order to ensure vanishing one-point functions of the physical scalar mass eigenfields, finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, are required. As a consequence of our renormalization scheme, physical masses are functions of the renormalized parameters and VEVs and thus derived quantities. Applying our scheme to one-loop corrections of lepton masses, we perform a thorough discussion of finiteness and ξ-independence. In the latter context, the tadpole contributions figure prominently.

Topology in full QCD at high temperature: a multicanonical approach

We investigate the topological properties of Nf = 2 + 1 QCD with physical quark masses, at temperatures around 500 MeV. With the aim of obtaining a reliable sampling of topological modes in a regime where the fluctuations of the topological charge Q are very rare, we adopt a multicanonical approach, adding a bias potential to the action which enhances the probability of suppressed topological sectors. This method permits to gain up to three orders magnitude in computational power in the explored temperature regime. Results at different lattice spacings and physical spatial volumes reveal no significant finite size effects and the presence, instead, of large finite cut-off effects, with the topological susceptibility which decreases by 3-4 orders of magnitude while moving from a ≃ 0.06 fm towards the continuum limit. The continuum extrapolation is in agreeement with previous lattice determinations with smaller uncertainties but obtained based on ansatzes justified by several theoretical assumptions. The parameter b2, related to the fourth order coefficient in the Taylor expansion of the free energy density f (θ), has instead a smooth continuum extrapolation which is in agreement with the dilute instanton gas approximation (DIGA); moreover, a direct measurement of the relative weights of the different topological sectors gives an even stronger support to the validity of DIGA.

Higher order fluctuations and correlations of conserved charges from lattice QCD

We calculate several diagonal and non-diagonal fluctuations of conserved charges in a system of 2+1+1 quark flavors with physical masses, on a lattice with size 483 × 12. Higher order fluctuations at μB = 0 are obtained as derivatives of the lower order ones, simulated at imaginary chemical potential. From these correlations and fluctuations we construct ratios of net-baryon number cumulants as functions of temperature and chemical potential, which satisfy the experimental conditions of strangeness neutrality and proton/baryon ratio. Our results qualitatively explain the behavior of the measured cumulant ratios by the STAR collaboration.

Lattice quantum chromodynamics and baryon-baryon interactions

After briefly reviewing the theoretical concepts and numerical methods in lattice QCD, recent simulation results of the hadron masses and hadron interactions with nearly physical quark masses are presented. Special emphasis is placed on the baryon-baryon interactions on the basis of the HAL QCD method where the integro-differential equation for the equal-time Nambu–Bethe–Salpeter amplitude plays a key role to bridge a gap between the multi-baryon correlation and the scattering observable such as the phase shift.

Curvature of the pseudocritical line in QCD: Taylor expansion matches analytic continuation

We determine the curvature of the pseudo-critical line of $N_f = 2 + 1$ QCD with physical quark masses via Taylor expansion in the quark chemical potentials. We adopt a discretization based on stout improved staggered fermions and the tree level Symanzik gauge action; the location of the pseudocritical temperature is based on chiral symmetry restoration. Simulations are performed on lattices with different temporal extent ($N_t = 6, 8, 10$), leading to a continuum extrapolated curvature $\kappa = 0.0145(25)$, which is in very good agreement with the continuum extrapolation obtained via analytic continuation and the same discretization, $\kappa = 0.0135(20)$. This result eliminates the possible tension emerging when comparing analytic continuation with earlier results obtained via Taylor expansion.

QCD phase diagram in a magnetic background for different values of the pion mass

We investigate the behavior of the pseudocritical temperature of ${N}_{f}=2+1$ QCD as a function of a static magnetic background field for different values of the pion mass, going up to ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}660\text{ }\text{ }\mathrm{MeV}$. The study is performed by lattice QCD simulations, adopting a stout staggered discretization of the theory on lattices with ${N}_{t}=6$ slices in the Euclidean temporal direction; for each value of the pion mass the temperature is changed moving along a line of constant physics. We find that the decrease of ${T}_{c}$ as a function of $B$, which is observed for physical quark masses, persists in the whole explored mass range, even if the relative variation of ${T}_{c}$ appears to be a decreasing function of ${m}_{\ensuremath{\pi}}$, approaching zero in the quenched limit. The location of ${T}_{c}$ is based on the renormalized quark condensate and its susceptibility; determinations based on the Polyakov loop lead to compatible results. On the contrary, inverse magnetic catalysis, i.e., the decrease of the quark condensate as a function of $B$ in some temperature range around ${T}_{c}$, is not observed when the pion mass is high enough. That supports the idea that inverse magnetic catalysis might be a secondary phenomenon, while the modifications induced by the magnetic background on the gauge field distribution and on the confining properties of the medium could play a primary role in the whole range of pion masses.

Framework for the chiral extrapolation of the charmed baryon ground-state masses

We consider the chiral Lagrangian for charmed baryon fields with $J^P =\frac{1}{2}^+$ or $J^P =\frac{3}{2}^+$ quantum numbers. A chiral expansion framework for the baryon ground state masses is worked out to N$^3$LO as to compute their dependence on the up, down and strange quark masses for finite box QCD lattice simulations. It is formulated in terms of on-shell meson and baryon masses. The convergence of such a scheme is illustrated with physical masses as taken from the PDG. The counter terms relevant at N$^3$LO are correlated systematically by large-$N_c$ sum rules to leading and subleading order in a manner that keeps the renormalization scale invariance of the approach.

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.

Effects of a strong magnetic field on the QCD flux tube

In this work we investigate the effect of an external magnetic field B on the shape of flux tubes in QCD by means of lattice simulations, performed with N_f=2+1 flavors of stout improved dynamical staggered quarks with physical masses. After having discussed some difficulties in the practical definition of the flux tube at B=0, we show that these ambiguities do not affect the determination of the flux tube modifications induced by the magnetic field. Different results are obtained depending on the relative orientations of the flux tube and of the magnetic field: they confirm that the magnetic field acts as transverse confinement catalyser and longitudinal confinement inhibitor; moreover, the flux tube itself loses its axial symmetry when it is not directed along the magnetic background.

Nonhydrodynamic quasinormal modes and equilibration of a baryon dense holographic QGP with a critical point

We compute the homogeneous limit of non-hydrodynamic quasinormal modes (QNM's) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD) holographic model for the Quark-Gluon Plasma (QGP) that is able to: i) {\it quantitatively} describe state-of-the-art lattice results for the QCD equation of state and higher order baryon susceptibilities with $2+1$ flavors and physical quark masses up to highest values of the baryon chemical potential currently reached in lattice simulations; ii) describe the nearly perfect fluidity of the strongly coupled QGP produced in ultrarelativistic heavy ion collisions; iii) give a very good description of the bulk viscosity extracted via some recent Bayesian analyzes of hydrodynamical descriptions of heavy ion experimental data. This EMD model has been recently used to predict the location of the QCD critical point in the QCD phase diagram, which was found to be within the reach of upcoming low energy heavy ion collisions. The lowest quasinormal modes of the $SO(3)$ rotationally invariant quintuplet, triplet, and singlet channels evaluated in the present work provide upper bounds for characteristic equilibration times describing how fast the dense medium returns to thermal equilibrium after being subjected to small disturbances. We find that the equilibration times in the different channels come closer to each other at high temperatures, although being well separated at the critical point. Moreover, in most cases, these equilibration times decrease with increasing baryon chemical potential while keeping temperature fixed.

Determination of quark masses from nf=4 lattice QCD and the RI-SMOM intermediate scheme

We determine the charm and strange quark masses in the $\overline{\text{MS}}$ scheme, using $n_f=2+1+1$ lattice QCD calculations with highly improved staggered quarks (HISQ) and the RI-SMOM intermediate scheme to connect the bare lattice quark masses to continuum renormalisation schemes. Our study covers analysis of systematic uncertainties from this method, including nonperturbative artefacts and the impact of the non-zero physical sea quark masses. We find $m_c^{\overline{\text{MS}}}(3 \text{GeV}) = 0.9896(61)$ GeV and $m_s^{\overline{\text{MS}}}(3 \text{GeV}) = 0.08536(85)$ GeV, where the uncertainties are dominated by the tuning of the bare lattice quark masses. These results are consistent with, and of similar accuracy to, those using the current-current correlator approach coupled to high-order continuum QCD perturbation theory, implemented in the same quark formalism and on the same gauge field configurations. This provides a strong test of the consistency of methods for determining the quark masses to high precision from lattice QCD. We also give updated lattice QCD world averages for $c$ and $s$ quark masses.

Glueball spectrum from Nf = 2 lattice QCD study on anisotropic lattices**The numerical calculations were carried out on Tianhe-1A at the National Supercomputer Center (NSCC) in Tianjin and the GPU cluster at Hunan Normal University. This work is supported in part by the National Science Foundation of China (NSFC) (11575196, 11575197, 11335001, 11405053, 11405178, 11275169). Y. C., Z. L. and

The lowest-lying glueballs are investigated in lattice QCD using Nf = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ ∼ 938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at mπ ∼ 938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of εijk TrBiDjBk, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1 GeV) and compatible with the expected masses of the flavor singlet meson. This indicates that the operator εijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.