Motivated by recent theoretical arguments that expanding strings can be regarded as having a temperature that is inversely proportional to the proper time, tau, we investigate the consequences of adding a term proportional to 1/tau to the string tension in the Lund string-hadronization model. The lattice value for the tension, kappa0 ~ 0.18 GeV^2 ~ 0.9 GeV/fm, is then interpreted as the late-time/equilibrium limit. A generic prediction of this type of model is that early string breaks should be associated with higher strangeness (and baryon) fractions and higher fragmentation <pT> values. It should be possible to use archival ee data sets to provide model-independent constraints on this type of scenario, and we propose a few simple key measurements to do so.
I discuss a Monte Carlo algorithm for hadronization in the Lund string fragmentation picture, which conserves energy and momentum exactly as is proposed by the model. An embryo to this Monte Carlo is used to calculate the total decay density of a string. This is found to reach its predicted asymptotic behaviour already at a string energy of about six hadron masses.
Recent developments of the model of quantized helical QCD string are presented, notably the baryon production. An overview of the experimental evidence is discussed as well as possible applications.
Baryon production is studied within the framework of quantized fragmentation of QCD string. Baryons appear in the model in a fairly intuitive way, with help of causally connected string breakups. A simple helical approximation of QCD flux tube with parameters constrained by mass spectrum of light mesons is sufficient to reproduce masses of light baryons.
A string model, advocated by Bowler, provides a physical and intuitive picture of heavy quark fragmentation. When supplemented by an ad hoc factor of (1-z), to suppress fragmentation near z=1, it supplies an excellent fit to the data. We extend Bowler's model by accounting for the further decay of the massive mesonic states produced by the initial string breaking. We find that each subsequent string break and cascade decay beyond the first, introduces a factor of (1-z). Furthermore we find that including a finite mass for the quarks, which pop out of the vacuum and split the string, forces the…
A fragmenting relativistic string is widely used for modelling particle production via quark-gluon strings formed in hadron inelastic interactions of high energies. In this note we focus on motion and fragmentation of relativistic string with non-zero transverse separation of its ends and study this scenario as a possible mechanism bringing anisotropy into the asimuthal angle disribution of produced particles in inelastic interactions of hadrons.
StringSpinner is a plugin for the introduction of the spin effects in the hadronization part of the PYTHIA 8 event generator. The spin effects are generated for pseudoscalar meson production by propagating the quark polarization along the fragmentation chain according to the rules of the quantum mechanical string+${}^3P_0$ model. By using parametrizations for the transversity parton distribution functions, StringSpinner allows to simulate the polarized semi inclusive deep inelastic scattering process on protons and neutrons. The instructions to use StringSpinner and to modify the parametrizati…
The experimentally observed enhancement of number of close boson pairs in e+e- collisions is reproduced by local weighting according to the quantum mechanical prescriptions for production of identical bosons. The space-time picture of the process, inherently present in the Lund fragmentation model, is explicitly used. The model is used to check systematic errors in the W mass measurements due to the Bose-Einstein effect. The possibility of direct implementation of the Bose-Einstein effect into string fragmentation is discussed.
The well-known Monte Carlo simulation packet JETSET is not built in order to describe few-body states (in particular at the few GeV level in e^+e^- annihilation as in BEPC). In this note we will develop the formalism to use the basic Lund Model area law directly for Monte Carlo simulations
An improved version of the ``pop-corn'' model for baryon production in quark and gluon jets is presented. With a reduced number of parameters the model reproduces well both production rates for different baryon species and baryon momentum distributions. Predictions are presented for a set of baryon-antibaryon correlations.
The observed limiting fragmentation of charged particle distributions in heavy ion collisions is difficult to explain as it does not apply to the proton spectrum itself. On the other hand, string percolation provides a mechanism to regenerate fast particles, eventually compensating the rapidity shift (energy loss) of the nucleons. However a delicate energy-momentum compensation is required, and in our framework we see no reason for limiting fragmentation to be exact. A prediction, based on percolation arguments, is given for the charged particle density in the full rapidity interval at LHC ene…
The assumptions in the Lund model suffice to prescribe a unique stochastic process for the fragmentation of a string into a set of hadrons, so long as the string is "flat", ie as long as the state described by the string consists only of a quark and an antiquark stretching a constant force field between them. Emission of gluons causes the string to trace more complicated surfaces in Minkowski space, and some form of generalization of the 1+1 dimensional model is required. One such generalizaiotn has been developed and implemented as a Monte Carlo routine "JETSET" by Torbjörn Sjöstrand, which h…
Quark spin effects in hadronization have been recently included in the PYTHIA 8 event generator for the simulation of the deep inelastic scattering (DIS) process off a polarized nucleon target via the external StringSpinner package. The spin effects can be simulated for the production of pseudoscalar mesons using the string+${}^3P_0$ model of polarized quark fragmentation and parametrizations of the transversity PDFs. We present here a major development of StringSpinner which includes the production of vector mesons in the polarized PYTHIA 8 string fragmentation as well as their polarized deca…
It is shown that that Gaussian fluctuations of the string tension can account for the "thermal" distribution of transverse mass of particles created in decay of a colour string.
It is shown that naive two stage scenario of the soft multiparticle production in hadronic and nuclear collisions at high energy, when at first stage the colour strings are formed and at the second stage these strings, or some other (higher colour) strings formed due to fusion of primary strings, are decaying, emitting observed particles, encounters some difficulties at the attempt to analyse the space-time picture of the process. Simple analysis shows the dominant is the process when the formation and the decay of a string occur in parallel - a string breaks into two parts already at rather s…
Here we revisit the bag phenomenology of the deconfining phase transition to replenish it by introducing systematically the bag surface tension. Comparing the free energy of such bags and that one of the strings confining the static quark-antiquark pair, we express the string tension in terms of the bag surface tension and thermal pressure in order to estimate the bag characteristics using the lattice QCD data. Our analysis of the bag entropy density demonstrates that the surface tension coefficient is amazingly negative at the cross-over (continuous transition). This approach allows us to nat…
The production of vector mesons in the fragmentation process of polarized quarks is studied within the recursive String+${}^3P_0$ model, improving a previous version of the model in which the production of pseudoscalar mesons only was considered. Two types of couplings of the vector meson to quarks are introduced, their coupling constants being the additional free parameters of the model. The angular distribution of the decay products of the polarized vector meson is deduced from the spin density matrix of the meson and the spin information is propagated along the fragmentation chain taking in…
We apply the Area Decay Law (ADL) straightforwardly to simulate a quark string hadronization and compare the results with the explicit analytic calculations. We show that the usual "inclusive" Monte--Carlo simulations do not correspond to the ADL because of two mistakes: not proper simulation of two--dimensional probability density and lack of an important combinatorial factor in a binary tree simulation. We also show how to simulate area decay law "inclusively" avoiding the above--mentioned mistakes.
The observation of heavy-ion-like behaviour in pp collisions at the LHC suggests that more physics mechanisms are at play than traditionally assumed. The introduction e.g. of quark-gluon plasma or colour rope formation can describe several of the observations, but as of yet there is no established paradigm. In this article we study a few possible modifications to the Pythia event generator, which describes a wealth of data but fails for a number of recent observations. Firstly, we present a new model for generating the transverse momentum of hadrons during the string fragmentation process, ins…
We present the main theoretical aspects of the quantum mechanical string+${}^3P_0$ model of polarized quark fragmentation for pseudoscalar and vector meson production. The model is an extension of the Lund string fragmentation model that systematically includes the quark spin degree of freedom assuming the ${}^3P_0$ mechanism of quark pair production at string breaking. The recently achieved introduction of vector mesons accounts for the spin correlations between the latter and the quark of the fragmentation chain. The string+${}^3P_0$ model reproduces transverse spin effects such as the Colli…
The entropy and effective string tension of the moving heavy quark-antiquark pair in the strongly coupled plasmas are calculated by using a deformed an anti-de Sitter/Reissner-Nordstr$\ddot{o}$m black hole metric. A sharp peak of the heavy-quarkonium entropy around the deconfinement transition can be realized in our model, which is consistent with the lattice QCD result. The effective string tension of the heavy quark-antiquark pair is related to the deconfinement phase transition. Thus, we investigate the deconfinement phase transition by analyzing the characteristics of the effective string …
The thick- or fat-center-vortices model has been applied to a calculation of the potentials between static sources of various SU(4) representations. For intermediate distances, a linear potential is obtained. For this region the string tensions agree qualitatively with both flux tube counting and Casimir scaling, even though for some representations it favors flux tube counting more. In addition, our results confirm the existence of two different string tensions for non-zero 4-ality representations at large distances. In this area, zero 4-ality representations are screened. In our computations…
We compute, via numerical simulations, the non-perturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
We show that QCD4 with transverse confinement can be approximately compactified into QCD2 with a transverse quark mass $m_{{}_T}$ that is obtained by solving a set of coupled transverse eigenvalue equations. In the limits of a strong coupling and a large number of flavors, QCD2 further admits Schwinger QED2-type bosonized solutions. We therefore examine phenomenologically the space-time dynamics of produced particles in string fragmentation by studying the Wigner function of produced bosons in Schwinger QED2, which mimics many features of string fragmentation in quantum chromodynamics. We find…
String tension is introduced in perturbative QCD without hindering ultra violet renormalizability . The running gauge coupling constant remains unaltered and the string tension in the high energy limit vanishes asymptotically. Using 1/N techinique the theory can be explicitly analytically computable with cofinement built in . Spontaneous chiral symmetry breakdown along with its Goldstone is exhibited.
We discuss the cosmological evolution of cosmic strings with time-dependent tension. We show that, in the case that the tension changes as a power of time, the cosmic string network obeys the scaling solution: the characteristic scale of the string network grows with the time. But due to the time dependence of the tension, the ratio of the energy density of infinite strings to that of the background universe is {\it not} necessarily constant.
We compute the string tension in massive $QCD_2$. It is shown that the string tension vanishes when the mass of the dynamical quark is zero, with no dependence on the representations of the dynamical or of the external charges. When a small mass ($m\ll e$) is added, a tension appears and we calculate its value as a function of the representations.
We study the properties of the color-Coulomb string tension obtained from the instantaneous part of gluon propagators in Coulomb gauge using quenched SU(3) lattice simulation. In the confinement phase, the dependence of the color-Coulomb string tension on the QCD coupling constant is smaller than that of the Wilson loop string tension. On the other hand, in the deconfinement phase, the color-Coulomb string tension does not vanish even for $T/T_c = 1 \sim 5$, the temperature dependence of which is comparable with the magnetic scaling, dominating the high temperature QCD. Thus, the color-Coulomb…
We show that at large distances from an infinitely long global U(1) string, low energy Goldstone Bosons contribute a spatially dependent term to the energy density which is non-integrable. Specifically, this term diverges with the same form as the classical field theory contribution to the string tension, except with negative sign. This suggests that a careful analysis of the infrared degrees of freedom around the global string ought to yield an effective theory of the solitary string whose tension is finite. There are implications for axion cosmology.
We investigate cosmological evolution and implications of cosmic strings with time-dependent tension. We derive basic equations of time development of the correlation length and the velocity of such strings, based on the one scale model. Then, we find that, in the case where the tension depends on some power of the cosmic time, cosmic strings with time-dependent tension goes into the scaling solution if the power is lower than a critical value. We also discuss cosmic microwave background anisotropy and matter power spectra produced by these strings. The constraints on their tensions from the W…
Global string networks may be relevant in axion production in the early Universe, as well as other cosmological scenarios. Such networks contain a large hierarchy of scales between the string core scale and the Hubble scale, log(f/H) around 70, which influences the network dynamics by giving the strings large tensions T = pi f^2 log(f/H). We present a new numerical approach to simulate such global string networks, capturing the tension without an exponentially large lattice.
We numerically compute the spatial string tension in the deconfined phase of three dimensional QCD in the large N limit. Our results clearly show that the string tension grows linearly with temperature.
Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University（雅盖隆大学理论物理研究所与马克·卡克复杂系统研究中心）；Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文学系核理论中心）
We investigate the properties of global cosmic string networks as a function of the ratio of string tension to Goldstone-field coupling, and as a function of the Hubble damping strength. Our results show unambiguously that the string density is sensitive to this ratio. We also find that existing semi-analytical (one-scale) models must be missing some important aspect of the network dynamics. Our results point the way towards improving such models.
We find the Casimir-like energies for strings and membranes. We show that the related Casimir forces can be interpreted as quantum corrections to the classical tensions of the strings and membranes. We see that these corrections always increase the tensions of the circular string as well as spherical membrane, while for the straight string, rectangular and cylindrical membranes, these Casimir forces may increase or decrease the tensions. So we find that the quantum vacuum can break the (tensional) isotropy of the rectangular and cylindrical membranes. Also obtaining the nonzero-temperature Cas…
We propose to model hadronization of parton showers in QCD jets through a hybrid approach involving quark recombination and string fragmentation. This is achieved by allowing gluons at the end of the perturbative shower evolution to undergo a non-perturbative splitting into quark and antiquark pairs, then applying a Monte-Carlo version of instantaneous quark recombination, and finally subjecting remnant quarks (those which have not found a recombination partner) to Lund string fragmentation. When applied to parton showers from the PYTHIA Monte Carlo event generator, the final hadron spectra fr…
A strongly-coupled sector can feature a supercooled confinement transition in the early universe. We point out that, when fundamental quanta of the strong sector are swept into expanding bubbles of the confined phase, the distance between them is large compared to the confinement scale. We suggest a modelling of the subsequent dynamics and find that the flux linking the fundamental quanta deforms and stretches towards the wall, producing an enhanced number of composite states upon string fragmentation. The composite states are highly boosted in the plasma frame, which leads to additional parti…
It is shown that a Coulomb potential using a running coupling slightly modified from the perturbative form can produce an interquark potential that appears nearly linear over a large distance range. Recent high-statistics SU(2) lattice gauge theory data fit well to this potential without the need for a linear string-tension term. This calls into question the accuracy of string tension measurements which are based on the assumption of a constant coefficient for the Coulomb term. It also opens up the possibility of obtaining an effectively confining potential from gluon exchange alone.
General properties of the light and heavy quark propagators have been investigated in the context of string tension interaction. Confinement, chiral symmetry breaking, spectral properties of the propagator are analytically studied and numerically validated. We show that the propagator is analytic in the infrared region even for massless quarks with a non zero radius of convergence. Emergence of more than one mass scale is exemplified. Massless limit of the quark propagator does exhibit critical behaviour.
The bosonized QCD2+QED2 system for quarks with two flavors contains QCD2 and QED2 bound states, with an isoscalar photon at about 25 MeV and an isovector (I=1,I_3=0) photon at about 44 MeV. Consequently, when a quark and an antiquark at the two ends of a string pulls apart from each other at high energies, hadrons and soft photons will be produced simultaneously in the fragmentation of the string. The production of the QED2 soft photons in association with hadrons may explain the anomalous soft photon data in hadron-hadron collisions and e+e- annihilations at high energies.
We present results of modeling the temperature dependence of the spatial string tension and thermal phase transition in a five-dimensional framework nowadays known as AdS/QCD. For temperatures close to the critical one we find a behaviour remarkably consistent with the lattice results.
Monopole and photon contributions to abelian Wilson loops are calculated using Monte-Carlo simulations of SU(2) QCD in the maximally abelian gauge. The string tension is well reproduced only by monopole contributions, whereas photons alone are responsible for the Coulomb coefficient of the abelian static potential.
The spatial string tension of a SU(N) gauge theory without quarks is calculated using gauge/string duality for 1.2T_c<T<3T_c. The result is remarkably consistent with the available lattice data for N=2,3. Some evidence is found that to leading order the large distance physics of a string can be described by a five-dimensional geometry without a need for an internal space.
We present an analytical continuum calculation, starting from first principles, of the vacuum wavefunction and string tension for pure Yang-Mills theories in $(2+1)$ dimensions, extending our previous analysis using gauge-invariant matrix variables. The vacuum wavefunction is consistent with what is expected at both high and low momentum regimes. The value of the string tension is in very good agreement with recent lattice Monte Carlo evaluations.
Within the Quark-Gluon String Model A.B. Kaidalov found a behaviour of quark and diquark fragmentation functions for $z\rightarrow 0$ and $z\rightarrow 1$, and proposed interpolation formulae for the functions in the whole region of $z$. These functions must be a solution of the well-known system of the integral equations. A simplified Monte Carlo estimation of the functions, based on usage of the fragmentation functions at $z\rightarrow 1$ as the kernel functions of the system, does not reproduce Kaidalov's results. An improvement of the Monte Carlo simulations is proposed in this paper. It c…
We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $Λ$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=λ=0.1$) can be achieved in the case of D-term inflation on the brane.
In previous work, we constructed a convolutional neural network used to estimate the location of cosmic strings in simulated cosmic microwave background temperature anisotropy maps. We derived a connection between the estimates of cosmic string locations by this neural network and the posterior probability distribution of the cosmic string tension $Gμ$. Here, we significantly improve the calculation of the posterior distribution of the string tension $Gμ$. We also improve our previous plain convolutional neural network by using residual networks. We apply our new neural network and posterior c…
Heavy quark transport coefficients in a strongly coupled Quark-Gluon Plasma can be evaluated using a gauge/string duality and lattice QCD. Via this duality, one can argue that for low momenta the drag coefficient for heavy quarks is proportional to the spatial string tension. Such a tension is well studied on the lattice that allows one to straightforwardly make non-perturbative estimates of the heavy quark diffusion coefficients near the critical point. The obtained results are consistent with those in the literature.
We consider the evolution of a network of strings in an expanding universe, allowing for the formation of junctions between strings of different tensions. By explicitly including, in the velocity-dependent evolution equations for the network, kinematic constraints associated with the formation of Y-shaped string junctions, we show how they lead to scaling solutions in regimes where they would not otherwise be found, thereby extending the range of parameters which lead to scaling. By incorporating these constraints we are able to study their general behaviour for networks with cosmic superstrin…
In a simple reanalysis of the KKLMMT scenario, we argue that the slow roll condition in the D3-anti-D3-brane inflationary scenario in superstring theory requires no more than a moderate tuning. The cosmic string tension is very sensitive to the conformal coupling: with less fine-tuning, the cosmic string tension (as well as the ratio of tensor to scalar perturbation mode) increases rapidly and can easily saturate the present observational bound. In a multi-throat brane inflationary scenario, this feature substantially improves the chance of detecting and measuring the properties of the cosmic …
