Chromodynamics Research Articles

Split of the pseudocritical temperatures of chiral and confinement-deconfinement transitions by a temperature gradient

Searching of the critical endpoint (CEP) of the phase transition of quantum chromodynamics (QCD) matter in experiments is of great interest. The temperature in the fireball at a collider is location dependent, however, most theoretical studies address the scenario of uniform temperature. In this work, the effect of temperature gradients is investigated using lattice QCD approach. We find that the temperature gradient catalyzes chiral symmetry breaking, meanwhile the temperature gradient increases the Polyakov loop in the confined phase but suppresses the Polyakov loop in the deconfined phase. Furthermore, the temperature gradient decreases the pseudocritical temperature of chiral transition but increases the pseudocritical temperature of the confine-deconfine transition. It is also found that the temperature gradient can drive the system away from the singularity, implying that the CEP in the T−μ plane may move in the direction of the first-order phase transition in the phase diagram due to the temperature gradient. Published by the American Physical Society 2024

P -adic reconstruction of rational functions in multiloop amplitudes

Numerical reconstruction techniques are widely employed in the calculation of multiloop scattering amplitudes. In recent years, it has been observed that the rational functions in multiloop calculations greatly simplify under partial fractioning. In this article, we present a technique to reconstruct rational functions directly in partial-fractioned form, by evaluating the functions at special integer points chosen for their properties under a p-adic metric. As an application, we apply this technique to reconstruct the largest rational function in the integration-by-parts reduction of one of the rank-5 integrals appearing in two-loop five-point full-color massless amplitude calculations in quantum chromodynamics. The number of required numerical probes (per prime field) is found to be around 25 times smaller than in conventional techniques, and the obtained result is 130 times smaller. The reconstructed result displays signs of additional structure that could be used to further reduce its size and the number of required probes. Published by the American Physical Society 2024

Two-loop electroweak corrections to the Higgs boson rare decay process H→Zγ

Recently, the ATLAS and CMS collaborations jointly announced the first evidence of the rare Higgs boson decay channel H→Zγ, with a ratio of 2.2±0.7 times the leading order standard model (SM) prediction. In order to face this challenge, it is urgent to produce an even more accurate calculation within the SM. To this end, we calculate in this paper the next-to-leading order (NLO) electroweak (EW) corrections to the H→Zγ process, in which the NLO quantum chromodynamics (QCD) corrections were found tiny. Our calculation finds that the inclusion of NLO EW corrections greatly enhances the prediction reliability. To tame the theoretical uncertainty, we adopt five different renormalization schemes. Combining our result with previous NLO QCD corrections and the signal-background interference, we conclude that the excess in H→Zγ cannot be explained within the SM. In fact, the incompatibility between the SM prediction and the LHC measurement of the concerned process is exacerbated upon considering the higher order EW corrections, which implies that something beyond the SM could be involved. Published by the American Physical Society 2024

Measurement of the branching fraction of Ds+→ℓ+νℓ via e+e−→Ds*+Ds*−

Based on 10.64 fb−1 of e+e− collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic Ds+ decays using the e+e−→Ds*+Ds*− process. The branching fractions of Ds+→ℓ+νℓ(ℓ=μ,τ) are measured to be BDs+→μ+νμ=(0.547±0.026stat±0.016syst)% and BDs+→τ+ντ=(5.60±0.16stat±0.20syst)%, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element |Vcs| is determined to be fDs+|Vcs|=(246.5±5.9stat±3.6syst±0.5input)μν and fDs+|Vcs|=(252.7±3.6stat±4.5syst±0.6input)τν MeV, respectively. Taking the value of |Vcs| from a global fit in the Standard Model, we obtain fDs+=(253.2±6.0stat±3.7syst±0.6input)μν and fDs+=(259.6±3.7stat±4.6syst±0.6input)τν MeV, respectively. Conversely, taking the value for fDs+ from the latest lattice quantum chromodynamics calculation, we obtain |Vcs|=(0.986±0.023stat±0.014syst±0.003input)μν and |Vcs|=(1.011±0.014stat±0.018syst±0.003input)τν, respectively. Published by the American Physical Society 2024

Nonuniversality of heavy quark hadronization in elementary high-energy collisions

It has been traditionally hypothesized that the heavy quark (charm c and bottom b) fragmentation is universal across different collision systems, based on the notion that hadronization as a soft process should occur at the characteristic nonperturbative quantum chromodynamics (QCD) scale, ΛQCD. However, this universality hypothesis has recently been challenged by the observation that the c- and b-baryon production relative to their meson counterparts in minimum bias proton-proton (pp) collisions at the CERN Large Hadron Collider (LHC) energies is significantly enhanced as compared to the electron-positron (e+e−) collisions. The conception of nonuniversality is unambiguously reinforced by the latest measurement of the charged-particle multiplicity dependence of the b-baryon–to–meson yield ratio, Λb/B, by the LHCb experiment in s=13TeVpp collisions at the LHC, evolving continuously from the saturation value in minimum bias pp collisions toward the small value in e+e− collisions as the system size gradually reduces. We address the multiplicity dependence of b-baryon production in the canonical statistical hadronization model with input b-hadron spectrum augmented with many hitherto unobserved states from quark model predictions. We demonstrate that the decreasing trend of the Λb/B toward low multiplicities can be quantitatively understood from the canonical suppression on the yield of Λb, as caused by the requirement of strict conservation of baryon number in sufficiently small systems. We have therefore proposed a plausible scenario for understanding the origin of the nonuniversality of heavy quark fragmentation in elementary collisions. Published by the American Physical Society 2024

Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions

We present the analytic total cross section of top quark pair production in electron-positron annihilation at next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD). By utilizing the optical theorem, the NNLO corrections are related to the imaginary parts of three-loop self-energy Feynman diagrams, of which the master integrals are calculated with canonical differential equations. The analytic results for the NNLO corrections are expressed in terms of multiple polylogarithms as well as elliptic functions. We discuss the asymptotic expansions near the threshold and in the high energy limit in detail. Numerical results are provided for the total cross section of top quark pair production at future lepton colliders.

The strong coupling constant: state of the art and the decade ahead

Abstract Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant α S . The current O ( 1 % ) uncertainty of the QCD coupling evaluated at the reference Z boson mass, α S ( m Z 2 ) = 0.1179 ± 0.0009 , is one of the limiting factors to more precisely describe multiple processes at current and future colliders. A reduction of this uncertainty is thus a prerequisite to perform precision tests of the Standard Model as well as searches for new physics. This report provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling. The current α S ( m Z 2 ) world average is derived from a combination of seven categories of observables: (i) lattice QCD, (ii) hadronic τ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) e+e−, (vi) e–p, and (vii) p–p collisions, and (viii) quarkonia decays and masses. We review the current status of each of these seven α S ( m Z 2 ) extraction methods, discuss novel α S determinations, and examine the averaging method used to obtain the world-average value. Each of the methods discussed provides a ‘wish list’ of experimental and theoretical developments required in order to achieve the goal of a per-mille precision on α S ( m Z 2 ) within the next decade.

Spin asymmetries for C -even quarkonium production as a probe of gluon distributions

Within the framework of transverse momentum dependent factorization in combination with nonrelativistic quantum chromodynamics (QCD), we study charmonium and bottomonium production in hadronic collisions. We focus on quarkonium states with even charge conjugation, for which the color-singlet production mechanism is expected to be also dominant in the small transverse momentum region, qT2≪4Mc,b2. It is shown that the distributions of linearly polarized gluons inside unpolarized, longitudinally, and transversely polarized protons contribute to the cross sections for scalar and pseudoscalar quarkonia in a very distinctive, parity-dependent way, whereas their effects on higher angular momentum states are strongly suppressed. We derive analytical expressions for single and double spin asymmetries, which would allow for the direct extraction of the gluon transverse momentum dependent distributions, mirroring the phenomenological studies of the Drell-Yan processes aimed at the extraction of their quark counterparts. By adopting Gaussian models for the gluon transverse momentum dependent distributions, which fulfill without saturating everywhere their positivity bounds, we provide numerical predictions for the transverse single-spin asymmetries. These observables could be measured at LHCSpin, the fixed target experiment planned at the LHC. Published by the American Physical Society 2024

SU(2) principal chiral model with tensor renormalization group on a cubic lattice

We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean SU(2) principal chiral field model with the triad tensor renormalization group and the anisotropic tensor renormalization group methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step closer to studying finite-density quantum chromodynamics in four dimensions using tensor network methods. Published by the American Physical Society 2024

Using analytic models to describe effective PDFs

Parton distribution functions play a pivotal role in hadron collider phenomenology. They are nonperturbative quantities extracted from fits to available data, and their scale dependence is dictated by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations. In this article, we discuss machine-assisted strategies to efficiently compute parton distribution functions (PDFs) explicitly incorporating the scale dependence. Analytical approximations to the PDFs as functions of x and Q2, including up to next-to-leading-order effects in quantum chromodynamics, are obtained. The methodology is tested by reproducing the 2.0 set and implementing the analytical expressions in benchmarking codes. It is found that the computational time cost of evaluating the distributions is reduced by ∼50%, while the precision of the simulations stays well under control. Published by the American Physical Society 2024

Efficient computation of Fourier–Bessel transforms for transverse-momentum dependent parton distributions and other functions

We present a method for the numerical computation of Fourier–Bessel transforms on a finite or infinite interval. The function to be transformed needs to be evaluated on a grid of points that is independent of the argument of the Bessel function. We demonstrate the accuracy of the algorithm for a wide range of functions, including those that appear in the context of transverse-momentum dependent parton distributions in Quantum Chromodynamics.

Search for new physics in high-mass diphoton events from proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\ extrm{s}} $$\\end{document} = 13 TeV

Results are presented from a search for new physics in high-mass diphoton events from proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV. The data set was collected in 2016–2018 with the CMS detector at the LHC and corresponds to an integrated luminosity of 138 fb−1. Events with a diphoton invariant mass greater than 500 GeV are considered. Two different techniques are used to predict the standard model backgrounds: parametric fits to the smoothly-falling background and a first-principles calculation of the standard model diphoton spectrum at next-to-next-to-leading order in perturbative quantum chromodynamics calculations. The first technique is sensitive to resonant excesses while the second technique can identify broad differences in the invariant mass shape. The data are used to constrain the production of heavy Higgs bosons, Randall-Sundrum gravitons, the large extra dimensions model of Arkani-Hamed, Dimopoulos, and Dvali (ADD), and the continuum clockwork mechanism. No statistically significant excess is observed. The present results are the strongest limits to date on ADD extra dimensions and RS gravitons with a coupling parameter greater than 0.1.

Medium induced mixing, spatial modulations, and critical modes in QCD

The mixing between the chiral condensate and the density in hot and dense quantum chromodynamics (QCD) matter is familiar. We show that the mixing relevant for the ground state is considerably more extensive, and in particular also involves gluonic degrees of freedom. As a result, the Hessian of the QCD effective action is non-Hermitian, but retains a symmetry under combined charge and complex conjugation. This can lead to complex-conjugate pairs of eigenvalues of this Hessian, signaling regimes with spatially modulated correlations. Furthermore, based on the analytic structure of the quark determinant at a chiral critical point, we demonstrate that the corresponding massless critical mode is composed of the chiral condensate, the density and the Polyakov loops. Due to an avoided crossing, the critical mode turns out to be disconnected from the chiral condensate in vacuum. We present general arguments for all these features and illustrate them through explicit model calculations. Published by the American Physical Society 2024

Quark core-gluon model for heavy hybrid baryons

Besides the ordinary hadrons, quantum chromodynamics (QCD) allows the existence of states in which excitations of the gluonic field can play the role of valence particles, either alone in a glueball, or coupled to quarks in a hybrid. So, hybrid baryons, made of three quarks and a gluon, can exist. Till now, there is no experimental evidence for such exotic hadrons but experimental efforts are being made to search for them at CEBAF Large Acceptance Spectrometer. In this work, a hybrid baryon is considered as a two-body system composed of a color octet three-quark core and a gluon, interacting via a QCD-inspired interaction. A semirelativistic potential model is built in which the dominant interaction is a potential simulating the flux tube confinement, and the Casimir scaling is assumed to link interactions between triplet and octet color sources. This picture is similar to the quark-diquark description for baryons. It is chosen in order to take properly into account the helicity of the gluon. Only cccg and bbbg states are considered because the strong mass asymmetry between the quark core and the gluon is expected to favor the formation of the core. As the results for heavy hybrid baryons seem relevant, we consider this paper as a proof of concept which can be extended for the study of light hybrid baryons. Published by the American Physical Society 2024

Improved measurement of the branching fraction of hc → γη′/η and search for hc→ γπ0

The processes hc→ γP (P = η′, η, π0) are studied with a sample of (27.12 ± 0.14) × 108ψ(3686) events collected by the BESIII detector at the BEPCII collider. The decay hc→ γη is observed for the first time with the significance of 9.0 σ, and the branching fraction is determined to be (3.77 ± 0.55 ± 0.13 ± 0.26) × 10−4, while B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{B} $$\\end{document} (hc→ γη′) is measured to be (1.40 ± 0.11 ± 0.04 ± 0.10) × 10−3, where the first uncertainties are statistical, the second systematic, and the third from the branching fraction of ψ(3686) → π0hc. The combination of these results allows for a precise determination of Rhc=Bhc→γηBhc→γη′,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_{h_c}=\\frac{\\mathcal{B}\\left({h}_c\ o {\\pi}^0\\gamma \\eta \\right)}{\\mathcal{B}\\left({h}_c\ o {\\pi}^0\\gamma {\\eta}^{\\prime}\\right)}, $$\\end{document} which is calculated to be (27.0 ± 4.4 ± 1.0)%. The results are valuable for gaining a deeper understanding of η − η′ mixing, and its manifestation within quantum chromodynamics. No significant signal is found for the decay hc → γπ0, and an upper limit is placed on its branching fraction of B\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{B} $$\\end{document}(hc → γπ0) < 5.0 × 10−5, at the 90% confidence level.

Study of B(s) meson decays to D0*(2300) , Ds0*(2317) , Ds1(2460) and Ds1(2536) within the covariant light-front approach

In this work, we investigate the form factors of the transitions B(s)→D0*(2300),Ds0*(2317), Ds1(2460), and Ds1(2536) in the covariant light-front quark model (CLFQM), where these final states are considered as P-wave excited charmed mesons. In order to obtain the form factors for the physical transition processes, we extend these form factors from the spacelike region to the timelike region. The q2-dependence for each transition form factor is also plotted. Then, combined with those form factors, the branching ratios of the two-body nonleptonic decays B(s)→D(s)0*(2300,2317)M, Ds1(2460,2536)M with M being a light pseudoscalar (vector) meson or a charmed meson are calculated by considering the quantum chromodynamics (QCD) radiative corrections to the hadronic matrix elements within the QCD factorization approach. Most of our predictions are comparable to the results given by other theoretical approaches and the present available data. Published by the American Physical Society 2024

Chiral properties of the nucleon interpolating current and θ -dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents j1 and j2, only two linear combinations j1±j2 transform covariantly under the anomalous U(1)A symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the quantum chromodynamics (QCD) parameter θ, and the θ-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments (dn,p) induced by θ, and the nucleon magnetic moments (μn,p), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, dn,p/μn,p, are numerically consistent, and reflect the required physical dependence on θ. Published by the American Physical Society 2024

Measurement of multijet azimuthal correlations and determination of the strong coupling in proton-proton collisions at s=13TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=13\\,\ ext {Te}\\hspace{-.08em}\ ext {V} $$\\end{document}

A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_{\ extrm{T}}$$\\end{document}. This observable is measured in multijet events over the range of pT=360\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_{\ extrm{T}} = 360$$\\end{document}–3170GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3170\\,\ ext {Ge}\\hspace{-.08em}\ ext {V} $$\\end{document} based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ ext {Te}\\hspace{-.08em}\ ext {V}$$\\end{document}, corresponding to an integrated luminosity of 134fb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ ext {fb}^{-1}$$\\end{document}. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is αS(mZ)=0.1177±0.0013(exp)-0.0073+0.0116(theo)=0.1177-0.0074+0.0117\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _\ extrm{S} (m_{{\ extrm{Z}}}) =0.1177 \\pm 0.0013\\, \ ext {(exp)} _{-0.0073}^{+0.0116} \\,\ ext {(theo)} = 0.1177_{-0.0074}^{+0.0117}$$\\end{document}, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of αS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _\ extrm{S}$$\\end{document} in the TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\,\ ext {Te}\\hspace{-.08em}\ ext {V}$$\\end{document} region shows no deviation from the expected NLO pQCD behaviour.

Cosmological dynamics of string theory axion strings

The quantum chromodynamics (QCD) axion may solve the strong CP problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global U(1)PQ Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals. Published by the American Physical Society 2024

Doubly-charged Tcc++ states in the dynamical diquark model

One of the celebrated tools in explaining the hydrogen atom is Born-Oppenheimer approximation. The resemblance of QQq¯q¯ tetraquarks to hydrogen atom within quantum chromodynamics implies usage of Born-Oppenheimer approximation for these multiquark states. In this work, we use dynamical diquark model to calculate mass spectra and sizes of doubly charmed and charged tetraquark states denoted as Tcc++. Our results for mass spectra indicate some bound-state candidates with respect to corresponding two-meson thresholds. Calculation of expectation values of ⟨r2⟩ reflects that doubly charmed and charged tetraquark states are compact. Published by the American Physical Society 2024