Quark Separation Research Articles

Doubly heavy dibaryons as seen by string theory

We propose the stringy description of the system consisting of two heavy and four light quarks in the case of two light flavors of equal mass. As an application, we consider the three low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis shows that the ground state potential is described in terms of both hadroquarkonia and hadronic molecules. A connected string configuration makes the dominant contribution to the potential of an excited state at small separations, and for separations larger than 0.1 fm, it exhibits the diquark-diquark-diquark structure [Qq][Qq][qq]. For better understanding the quark organization inside the system, we introduce several critical separations related to the processes of string reconnection, breaking and junction annihilation. We also discuss the simplest string configurations including the five-string junctions and their implications for the system, in particular the emergence of composite quark objects different from diquarks and the process of junction fusion. Published by the American Physical Society 2024

Nonperturbative Collins-Soper kernel from chiral quarks with physical masses

We present a lattice QCD calculation of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, up to transverse separations of about 1 fm. This unitary lattice calculation is conducted, for the first time, employing the chiral-symmetry-preserving domain wall fermion discretization and physical values of light and strange quark masses. The CS kernel is extracted from the ratios of pion quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. Also for the first time, we utilize the recently proposed Coulomb-gauge-fixed quasi-TMDWF correlator without a Wilson line. We observe significantly slower signal decay with increasing quark separations compared to the established gauge-invariant method with a staple-shaped Wilson line. This enables us to determine the CS kernel at large nonperturbative transverse separations and find its near-linear dependence on the latter. Our result is consistent with the recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees with various recent phenomenological parametrizations of experimental data.

QQqqq¯ quark system, compact pentaquark, and gauge/string duality

For the case of two light flavors we propose the stringy description of the system consisting of two heavy and three light quarks, with the aim of exploring the quark organization inside the system and its low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis reveals several critical separations related to the processes of string reconnection, breaking and junction annihilation. We find that a compact pentaquark configuration makes the dominant contribution to the potential of the first excited state at small separations, and for separations larger than $0.1\,\text{fm}$, the antiquark-diquark-diquark structure emerges. Moreover, it turns out that the length scale of string junction annihilation is the same as that for the $QQ\bar q\bar q$ system. We also discuss the relation to the potential of the $QQq$ system and some relations among the masses of hadrons in the heavy quark limit.

QQq¯q¯ potential in string models

We propose a string theory construction for the system of two heavy quarks and two light antiquarks. The potential of the system is a function of separation between the quarks. We define a critical separation distance below which the system can be thought of mainly as a compact tetraquark. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. Our estimate of the screening length is in the range of lattice QCD. We also make a comparison with the potential of the $QQq$ system. The potentials look very similar at small quark separations but at larger separations they differ. The reason for this is that the flattening of the potentials happens at two well-separated scales as follows from the two different mechanisms: string breaking by light quarks for $QQq$ and string junction annihilation for $QQ\overline{q}\overline{q}$. Moreover, a similar construction can also be applied to the $\overline{Q}\overline{Q}qq$ system.

Excitations of elementary fermions in gauge Higgs theories

Static quark-antiquark states in QCD, at finite quark separation, have a spectrum of metastable states corresponding to string-like excitations of the gauge field. In this article I suggest that there may also exist an excitation spectrum of heavy fermions in some gauge Higgs theories deep in the Higgs phase. In this situation there are no color electric flux tubes connecting quarks with antiquarks. There may, nonetheless, exist stable excitations of the bosonic fields surrounding an isolated fermion, below the particle production threshold. I present numerical evidence indicating the existence of such excitations in an SU(3) gauge Higgs theory, with the scalar field in the fundamental representation of the gauge group.

Screening without screening: Baryon energy at high baryon density

We compute the Coulomb interaction energy of dense sets of static quarks in a compact volume (much smaller than the lattice volume) containing one quark per lattice site. The quark color charges are combined into either a set of three-quark nucleon states, or into a non-factorizable "one big hadron" state. In both cases we find that the energy per quark is roughly constant as the volume of quarks increases. A surprise is that if we construct the nucleon states from sets of three quarks chosen at random in the volume, then the energy per quark remains roughly constant, even as the average distance between quarks in a nucleon state grows as the volume increases. This energy dependence of a nucleon in a dense medium is at odds with the behavior of an isolated nucleon as quark separation increases, and for static quarks it is not easily explicable in terms of some version of Debye screening.

Correlation of Heavy and Light Flavors in Simulations

The ALICE experiment at the Large Hadron Collider (LHC) ring is designed to study the strongly interacting matter at extreme energy densities created in high-energy heavy-ion collisions. In this paper we investigate correlations of heavy and light flavors in simulations at LHC energies at mid-rapidity, with the primary purpose of proposing experimental applications of these methods. Our studies have shown that investigating the correlation images can aid the experimental separation of heavy quarks and help understanding the physics that create them. The shape of the correlation peaks can be used to separate the electrons stemming from b quarks. This could be a method of identification that, combined with identification in silicon vertex detectors, may provide much better sample purity for examining the secondary vertex shift. Based on a correlation picture it is also possible to distinguish between prompt and late contributions to D meson yields.

Determination of ΛMS¯(nf=2) and analytic parametrization of the static quark-antiquark potential

While lattice QCD allows for reliable results at small momentum transfers (large quark separations), perturbative QCD is restricted to large momentum transfers (small quark separations). The latter is determined up to a reference momentum scale $\Lambda$, which is to be provided from outside, e.g. from experiment or lattice QCD simulations. In this article, we extract $\Lambda_{\overline{\textrm{MS}}}$ for QCD with $n_f=2$ dynamical quark flavors by matching the perturbative static quark-antiquark potential in momentum space to lattice results in the intermediate momentum regime, where both approaches are expected to be applicable. In a second step, we combine the lattice and the perturbative results to provide a complete analytic parameterization of the static quark-antiquark potential in position space up to the string breaking scale. As an exemplary phenomenological application of our all-distances potential we compute the bottomonium spectrum in the static limit.

F4 , E6 and G2 exceptional gauge groups in the vacuum domain structure model

Using vacuum domain structure model, trivial static potentials in various representations of $F_4$, $E_6$ and $G_2$ exceptional groups are calculated by means of the unit center element. Due to the absence of the non-trivial center elements, the potential of every representation is screened at far distances. However, the linear part is observed at intermediate quark separations which is investigated by the decomposition of the exceptional group to its maximal subgroups. Comparing the group factor of the super-group with the corresponding one obtained from the non-trivial center elements of $SU(3)$ subgroup, shows that $SU(3)$ is not the direct cause of temporary confinement in any of the exceptional groups. However, the trivial potential obtained from the group decomposition to the $SU(3)$ subgroup is the same as the potential of the super-group itself. In addition, any regular or singular decomposition to the $SU(2)$ subgroup which produces the Cartan generator with the same elements as $h_1$, in any exceptional group, leads to the linear intermediate potential of the exceptional gauge groups. The other $SU(2)$ decompositions with the Cartan generator different from $h_1$, are still able to describe the linear potential if the number of $SU(2)$ non-trivial center element which emerge in the decompositions is the same. As a result, it is the center vortices quantized in terms of non-trivial center element of the $SU(2)$ subgroup which give rise to the intermediate confinement in the static potentials.

Quarkonium in a thermal BIon

In the present article, the authors intend to propose a new theory that potentially allows the propagation of the formation and the evolution of quarkonium in a thermal BIon. When quarks are close to each other, quarkonium behaves like a scalar and, by their getting away, it transitions to a fermionic system. To analyze this particular behaviour, a new outlook approach needs to be adopted as the concurrent view is found deficient to analyse the aforesaid behaviour. Therefore, the authors, post-deliberation, accept that the fermions and fermionic systems are related. We need to accept a theory in which the origin of fermions and bosons is the same. However, in M-theory, these particles are independent and for this reason, we use a new broader theory based on Lie-N algebra and we call it broad Lie-N algebra (BLNA) theory. Thus, in a way, BLNAis M-theory with 11 dimensions. In this model, two types of energies with opposite signs emerge from nothing such that the sum over them becomes zero. They produce two types of branes with opposite quantum numbers and bosonic fields, which interact with each other and get compact. By compacting branes, the quarks and anti-quarks are produced on branes and exchange the graviton and the gravitino. These particles produce two types of wormholes, which act opposite to each other. They preclude the closing or diverging of the branes and also occurrence of confinement. This confined potential that emerges from these wormholes depends on the separation distance between quarks and anti-quarks and also on the temperature of the system and it is reduced to the predicted potential in experiments and QCD. Also, total entropy of this system grows with increasing temperature and produces a repulsive force, which leads to the separation of quarks and anti-quarks and also to the emergence of deconfinement.

Stiff self-interacting strings at high temperature QCD

We investigate the implications of Nambu-Goto (NG), Lüscher Weisz (LW) and Polyakov-Kleinert (PK) effective string actions for the Casimir energy and the width of the quantum delocalization of the string in 4-dim pure SU(3) Yang-Mills lattice gauge theory. At a temperature closer to the critical point T/Tc=0.9, we found that the next to leading-order (NLO) contributions from the expansion of the NG string in addition to the boundary terms in LW action to decrease the deviations from the lattice data in the intermediate distance scales for both the quark-antiquark QQ̅ potential and broadening of the color tube compared to the free string approximation. We conjecture possible stiffness of the QCD string through studying the effects of extrinsic curvature term in PK action and find a good fitting behavior for the lattice Monte-Carlo data at both long and intermediate quark separations regions.

Trivial center element and Coulombic potential of the thick center vortex model

The thick center vortex potentials in the SU(3) gauge group have been calculated by means of the modified inter-quark potential which consists of two terms. One term is the result of the area law fall-off for the large Wilson loop which leads to the linear potentials. The second term represents vacuum fluctuations leading to the perimeter law fall-off believed to contain the trivial center element. We introduce a new Gaussian flux limited to vary in a finite region of space which causes the corresponding group factor to have only some small deviations from the trivial center element. So, this flux increases the role of the trivial center element and W0 is enhanced in the induced potential of the model at small quark separations. Using both trivial and non-trivial center elements in the potential between static color sources, results in the correct 3-ality dependence at large quark separations and a very good agreement with Casimir scaling at short and intermediate distances. In fact, the ratios of the potential of each representation to that of the fundamental one have been improved — in comparison with the previous work on the short distance potentials, remarkably. So, one might use the thick center vortex model to describe the inter-quark potential of every regime.

Y-stringlike behavior of a static baryon at finite temperature

We look into the signatures of the effective Y-bosonic strings in the gluonic profile due to a system of three static quarks on the lattice. The color field is calculated in pure SU(3) Yang-Mills lattice gauge theory at finite temperature with Polyakov loop operators. The analysis of the action density unveils a filled-$\mathrm{\ensuremath{\Delta}}$ distribution. However, we found that these $\mathrm{\ensuremath{\Delta}}$-shaped action density profiles are structured from three Y-shaped Gaussian-like flux tubes. The geometry of the Y-shaped Gaussian flux tubes changes according to the quark configuration and temperature. The lattice data for the mean-square width of the gluonic action density have been compared to the corresponding width calculated based on the string model at finite temperature. We assume Y-string configuration with minimal length. The growth pattern of the action density of the gluonic field fits to junction fluctuations of the Y-baryonic string model for large quark separation at the considered temperatures.

Gluonic profile of the static baryon at finite temperature

The gluon flux distribution of a static three quark system has been revealed at finite temperature in the pure SU(3) Yang-Mills theory. An action density operator is correlated with three Polyakov loops representing the baryonic state at a temperatures near the end of the QCD plateau, T/T_c = 0.8, and another just before the deconfinement point, T/T_c = 0.9. The flux distributions at short distance separations between the quarks display an action-density profile consistent with a filled Delta shape iso-surface. However the Delta-shaped action iso-surface distributions are found to persist even at large inter-quark separations for both temperatures. The action density distribution in the quark plane exhibits a nonuniform pattern for all quark separations considered. This result contrasts the well-known Y-shaped uniform action density gluonic-flux profile obtained using the Wilson-loop as a quark source operator at zero temperature. We systematically measure and compare the main aspects of the profile of the flux distribution at the two considered temperature scales for three sets of isosceles triangle quark configurations. The radii, amplitudes and rate of change of the width of the flux distribution are found to reverse their behavior as the temperature increase from the end of the QCD plateau region towards the deconfinement point. Remarkably, we find the mean square width of the flux distribution shrinks and localizes for quark separations larger than 1.0 fm at T/T_c = 0.8 which results in an identifiable Y-shaped radius profile. Near the deconfinement point, the action-density delocalizes and the width broadens linearly at large quark separations.

Modification of Gaussian mixture models for data classification in high energy physics

In high energy physics, we deal with demanding task of signal separation from background. The Model Based Clustering method involves the estimation of distribution mixture parameters via the Expectation-Maximization algorithm in the training phase and application of Bayes' rule in the testing phase. Modifications of the algorithm such as weighting, missing data processing, and overtraining avoidance will be discussed. Due to the strong dependence of the algorithm on initialization, genetic optimization techniques such as mutation, elitism, parasitism, and the rank selection of individuals will be mentioned. Data pre-processing plays a significant role for the subsequent combination of final discriminants in order to improve signal separation efficiency. Moreover, the results of the top quark separation from the Tevatron collider will be compared with those of standard multivariate techniques in high energy physics. Results from this study has been used in the measurement of the inclusive top pair production cross section employing DØ Tevatron full Runll data (9.7 fb−1).

Nucleon excited state wave functions from lattice QCD

We apply the eigenvectors from a variational analysis to successfully extract the three-quark color-singlet wave functions of even-parity excited states of the nucleon. We explore the first four states in the spectrum excited by the standard nucleon interpolating field. We find that the states exhibit a structure qualitatively consistent with a constituent quark model, where the ground, first, second, and third excited states have 0, 1, 2, and 3 nodes in the radial wave function of the $d$ quark about two $u$ quarks at the origin. Moreover, the radial amplitude of the probability distribution is similar to that predicted by constituent quark models. We present a detailed examination of the quark-mass dependence of the probability distributions for these states, searching for a nontrivial role for the multiparticle components mixed in the finite-volume QCD eigenstates. Finally we examine the dependence of the $d$-quark probability distribution on the positions of the two $u$ quarks. The results are fascinating, with the underlying $S$-wave orbitals governing the distributions even at rather large $u$-quark separations.

Leptonic and digamma decay properties ofS-wave quarkonia states

Based on Martin like potential, the S-wave masses of quarkonia have been reviewed. Resultant wave functions at zero inter quark separation are employed to compute the hyperfine splitting of the nS states and the leptonic and digamma decay widths of $n{^3S_1}$ and $n{^1S_0}$ states of quarkonia respectively. Analysis on the level differences of S-wave excited states of quantum mechanical bound systems show a systematic behaviour as n-increases. In view of such systematic behaviour expected for quarkonia, we observe that Y(4263) and X(4630) $1^{--}$ states are closer to the 4S and 6S states while $\psi(4415)$ and Z(4430) are closer to the 5S state of $c\bar{c}$ systems. Similarly we find $\Upsilon (10865)$ is not fit to be the 5S state of $b\bar{b}$ system. while $Y_b (10880)$ observed by Belle or (10996) observed by Babar fit to be the 6S state of bottonia. Our predicted leptonic width, 0.242 keV of $\Upsilon (10579, 4S)$ is in good agreement with the experimental value of 0.272 $\pm$ 0.029 keV. We predict the leptonic widths of the pure 5S and 6S states of upsilon states as 0.191 keV and 0.157 keV respectively. In the case of charmonia, we predict the leptonic widths of the 4S, 5S and 6S states as 0.654 keV, 0.489 keV and 0.387 keV respectively.

Primordial Open-System Thermodynamics and the Origin of a Biophysics Selection Principle

Mesons and baryons, according to their rest mass and half-life, show a tendency for de-confinement and re-confinement of energy, contributing to a continuous surge of enthalpy along the primordial chronology. The strong force opposes to the separation of the constitutive quarks of pions, which by self-multiplication, absorb the energy released by decay and pair-annihilation. The 1% of mass apported by quarks requires an additional 99% of energy from this decay to manifest as gluons-hadrons formation. Processes like oscillation neutron-proton and antineutron-antiproton cycles are capable to capture primordial radiation, and may have prevented a Universe immersed into residual gamma radiation.

Search for local strong parity violation in STAR using multiple observables

Parity-odd domains from QCD are predicted to cause charge separation of quarks across the reaction plane created in non-central relativistic heavy-ion collisions—the chiral magnetic effect. Here, we present several measurements to search for charge separation across the reaction plane at STAR. We use three different observables: a three-point correlator, a multiplicity asymmetry correlator as well as a reaction-plane-dependent balance function. The correlations are studied differentially and are presented for several Au+Au collision energies: 200, 62.4, 39, 11.5 and 7.7 GeV. We will discuss the sensitivities of these latest measurements to possible parity odd signals and parity even backgrounds.

Three-quark confinement potential from the Faddeev equation

In the heavy quark limit of Coulomb gauge QCD and by truncating the Yang-Mills sector to include only dressed two-point functions, an analytic nonperturbative solution to the Faddeev equation for three-quark bound states in the case of equal quark separations is presented. A direct connection between the temporal gluon propagator and the three-quark confinement potential is provided and it is shown that only color singlet qqq (baryon) states are physically allowed.