Background Perturbation Theory Research Articles

Particle initialization effects on Lyman-α forest statistics in cosmological SPH simulations

ABSTRACT Confronting measurements of the Lyman-α forest with cosmological hydrodynamical simulations has produced stringent constraints on models of particle dark matter and the thermal and ionization state of the intergalactic medium. We investigate the robustness of such models of the Lyman-α forest, focusing on the effect of particle initial conditions on the Lyman-α forest statistics in cosmological SPH simulations. We study multiple particle initialization algorithms in simulations that are designed to be identical in other respects. In agreement with the literature, we find that the correct linear theory evolution is obtained when a glass-like configuration is used for initial unperturbed gas particle positions alongside a regular grid configuration for dark matter particles and the use of non-identical initial density perturbations for gas and dark matter. However, we report that this introduces a large scale-dependent distortion in the 1D Lyman-α transmission power spectrum at small scales (k > 0.05 s km−1). The effect is close to 50 per cent at k ∼ 0.1 s km−1, and persists at higher resolution. This can severely bias inferences in parameters such as the dark matter particle mass. By considering multiple initial conditions codes and their variations, we also study the impact of a variety of other assumptions and algorithmic choices, such as adaptive softening, background radiation density, particle staggering, and perturbation theory accuracy, on the matter power spectrum, the Lyman-α flux power spectrum, and the Lyman-α flux PDF. This work reveals possible pathways towards more accurate theoretical models of the Lyman-α forest to match the quality of upcoming measurements.

Structure of magnetized strange quark star in perturbative QCD

We have performed the leading order perturbative calculation to obtain the equation of state (EoS) of the strange quark matter (SQM) at zero temperature under the magnetic field B=1018G. The SQM comprises two massless quark flavors (up and down) and one massive quark flavor (strange). Consequently, we have used the obtained EoS to calculate the maximum gravitational mass and the corresponding radius of the magnetized strange quark star (SQS). We have employed two approaches, including the regular perturbation theory (RPT) and the background perturbation theory (BPT). In RPT the infrared (IR) freezing effect of the coupling constant has not been accounted for, while this effect has been included in BPT. We have obtained the value of the maximum gravitational mass to be more than three times the solar mass. The validity of isotropic structure calculations for SQS has also been investigated. Our results show that the threshold magnetic field from which an anisotropic approach begins to be significant lies in the interval 2×1018G<B<3×1018G. Furthermore, we have computed the redshift, compactness and Buchdahl-Bondi bound of the SQS to show that this compact object cannot be a black hole.

The Fundamental Scale of QCD

There are several scales in the QCD as the theory of strong interaction: the vacuum gluonic condensate (as the divergence of the dilatation current), the nucleon mass as the basic mass scale in our universe, which is connected to the string tension $\sigma$, and the perturbative QCD scale $\Lambda_{\rm QCD}$, which defines the scale of the renormalized perturbative expansions. In this paper we connect all these scales to the vacuum condensate, using the field correlator method, where the string tension is expressed in terms of nonlocal field correlators, which are connected to the local condensates, while the perturbative $\Lambda_V$ is connected to $\sigma$ in the framework of the Background Perturbation Theory (BPT). We also demonstrate how the IR singularities and IR renormalons disappear in BPT making the resulting theory internally consistent.

Neutrinoless double beta decay and QCD running at low energy scales

There is a common belief that the main uncertainties in the theoretical analysis of neutrinoless double beta ($0\nu\beta\beta$) decay originate from the nuclear matrix elements. Here, we uncover another previously overlooked source of potentially large uncertainties stemming from non-perturbative QCD effects. Recently perturbative QCD corrections have been calculated for all dimension 6 and 9 effective operators describing $0\nu\beta\beta$-decay and their importance for a reliable treatment of $0\nu\beta\beta$-decay has been demonstrated. However, these perturbative results are valid at energy scales above $\sim 1$ GeV, while the typical $0\nu\beta\beta$-scale is about $\sim 100$ MeV. In view of this fact we examine the possibility of extrapolating the perturbative results towards sub-GeV non-perturbative scales on the basis of the QCD coupling constant "freezing" behavior using Background Perturbation Theory. Our analysis suggests that such an infrared extrapolation does modify the perturbative results for both short-range and long-range mechanisms of $0\nu\beta\beta$-decay in general only moderately. We also discuss that the tensor$\otimes$tensor effective operator can not appear alone in the low-energy limit of any renormalizable high-scale model and then demonstrate that all five linearly independent combinations of the scalar and tensor operators, that can appear in renormalizable models, are infrared stable.

The vector coupling α V((r) and the scales r 0, r 1 in the background perturbation theory

We study the universal static potential V st(r) and the force, which are fully determined by two fundamental parameters: the string tension σ = 0.18 ± 0.02 GeV2 and the QCD constants $$\Lambda _{\overline {MS} } (n_f )$$ , taken from pQCD, while the infrared (IR) regulator M B is taken from the background perturbation theory and expressed via the string tension. The vector couplings α V(r) in the static potential and α F(r) in the static force, as well as the characteristic scales, r 1(n f = 3) and r 0(n f = 3), are calculated and compared to lattice data. The result $$r_0 \Lambda _{\overline {MS} } (n_f = 3) = 0.77 \pm 0.03$$ , which agrees with the lattice data, is obtained for M B = (1.15 ± 0.02) GeV. However, better agreement with the bottomonium spectrum is reached for a smaller $$\Lambda _{\overline {MS} } (n_f = 3) = (325 \pm 15)$$ MeV and the frozen value of α V = 0.57 ± 0.02. The mass splittings $$\bar M(1D) - \bar M(1P)$$ and $$\bar M(2P) - \bar M(1P)$$ are shown to be sensitive to the IR regulator used. The masses M(1 3 D 3) = 10169(2) MeV andM(1 3 D 1) = 10155(3) MeV are predicted.

Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism

Paramagnetism of gluons is shown to play the basic role in establishing main properties of QCD: IR freezing and asymptotic freedom (AF). Starting with Polyakov background field approach the first terms of background perturbation theory are calculated and shown to ensure not only the classical result of AF but also IR freezing. For the latter only the confining property of the background is needed, and the effective mass entering the IR freezing logarithms is calculated in good agreement with phenomenology and lattice data.

Feynman amplitudes with confinement included

Amplitudes for any multipoint Feynman diagram are written taking into account vacuum background confining field. Higher order gluon exchanges are treated within background perturbation theory. For amplitudes with hadrons in initial or final states vertices are shown to be expressed by the corresponding wave function with the renormalized z factors. Examples of two-point functions, three-point functions (form factors), and decay amplitudes are explicitly considered.

Baryons in the field correlator method: Effects of the running strong coupling

The ground and P-wave excited states of nnn, nns, and ssn baryons are studied in the framework of the field correlator method using the running strong coupling constant in the Coulomb-like part of the three-quark potential. The running coupling is calculated up to two loops in the background perturbation theory. The three-quark problem has been solved using the hyperspherical functions method. The masses of the Sand P-wave baryons are presented. Our approach reproduces and improves the previous results for the baryon masses obtained for the freezing value of the coupling constant. The string correction for the confinement potential of the orbitally excited baryons, which is the leading contribution of the proper inertia of the rotating strings, is estimated.

Nonperturbative equation of state of quark–gluon plasma

The paper is devoted to the systematic derivation of nonperturbative thermodynamics of quark–gluon plasma, on the basis of the background perturbation theory. Vacuum background fields enter only in the form of field correlators, which are known from lattice and analytic calculations. In the lowest order in αs the purely nonperturbative sQGP thermodynamics is expressed through single quark and gluon lines (single line approximation) which are interacting nonperturbatively with vacuum fields and with other lines. Nonperturbative EOS is obtained in terms (of the absolute value) of fundamental (adjoint) Polyakov loop Lfund(adj) and spatial string tension σs(T). In the lowest approximation the pressure for quarks (gluons) has a simple factorized form Pq(g)=PSBLfund(adj), where Li describe the action of vacuum colorelectric fields on particle trajectory.

Method of vacuum correlation functions: Results and prospects

Basic results obtained within the QCD method of vacuum correlation functions over the past 20 years in the context of investigations into strong-interaction physics at the Institute of Theoretical and Experimental Physics (ITEP, Moscow) are formulated Emphasis is placed primarily on the prospects of the general theory developed within QCD by employing both nonperturbative and perturbative methods. On the basis of ab initio arguments, it is shown that the lowest two field correlation functions play a dominant role in QCD dynamics. A quantitative theory of confinement and deconfinement, as well as of the spectra of light and heavy quarkonia, glueballs, and hybrids, is given in terms of these two correlation functions. Perturbation theory in a nonperturbative vacuum (background perturbation theory) plays a significant role, not possessing drawbacks of conventional perturbation theory and leading to the infrared freezing of the coupling constant α s.

New nonperturbative approach to the Debye mass in hot QCD

The Debye mass mD is computed nonperturbatively in the deconfined phase of QCD, where chromomagnetic confinement is known to be present. The latter defines mD to be mD=cDσs, where cD≅2.06 and σs=σs(T) is the spatial string tension. The resulting magnitude of mD(T) and temperature dependence are in good agreement with lattice calculations. Background perturbation theory expansion for mD(T) is discussed in comparison to standard perturbative results and recent gauge-invariant definitions.

Dynamics of confined gluons

Propagation of gluons in the confining vacuum is studied in the framework of background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first, the confined gluon evolves in time together with the static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting, the confined gluon is exchanged between quarks and the gluon Green’s function is calculated, giving rise to the Coulomb potential modified at large distances. The resulting screening radius of 0.5 fm presents a problem when confronted with lattice and experimental data. A possible solution of this discrepancy is discussed.

Restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

The $b\bar b$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings $\Delta_1= \Upsilon({\rm 1D})-\chi_b({\rm 1P})$ and other splittings are very sensitive to the QCD constant $\Lambda_V(n_f)$ which occurs in the Vector scheme, and good agreement with the experimental data is obtained for $\Lambda_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the conventional $\Lambda_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV, $\alpha_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: $\alpha_{\rm crit} (2$-loop, $q^2=0)=\alpha_{\rm crit} (2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $\alpha_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with $\Delta_1({\rm exp})$ and $\Delta_2({\rm exp})$ can be reached for the rather large value $\alpha_{\rm static} =0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV.

The Static Force in Background Perturbation Theory

The static force $F_B(r)$ and the strong coupling $\alpha_F(r)$, which defines the gluon-exchange part of $F_B(r)$, are studied in QCD background perturbation theory (BPT). In the region $r\la 0.6 $ fm $\alpha_F(r)$ turns out to be essentially smaller than the coupling $\alpha_B(r)$ in the static potential. For the dimensionless function $\Phi_B(r) = r^2 F_B(r)$ the characteristic values $\Phi_B(r_1) =1.0$ and $\Phi_B(r_0)=1.65$ are shown to be reached at the following $Q\bar Q$ separations: $r_1\sqrt{\sigma} =0.77, r_0\sqrt{\sigma} =1.09$ in quenched approximation and $r_1\sqrt{\sigma}=0.72, r_0\sqrt{\sigma}=1.04$ for $n_f =3$. The numbers obtained appear to be by only 8% smaller than those calculated in lattice QCD while the values of the couplings $\alpha_F(r_1)$ and $\alpha_F(r_0)$ in BPT are by $\sim 30% (n_f =3)$ and $50% (n_f=0)$ larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained.

A short-distance quark-antiquark potential

Leading terms of the static quark-antiquark potential in the background perturbation theory are reviewed, including perturbative, nonperturbative and interference ones. The potential is shown to describe lattice data at short quark-antiquark separations with a good accuracy.

Novel solutions of RG equations for α(s) and β(α) in the large-N c limit

A general solution of RG equations in the framework of background perturbation theory is written in the large-N c limit. A simplified (model) approximation to the general solution is suggested that allows β(α) and α(s) to be written to any loop order. The resulting α B (Q 2) coincides asymptotically at large |Q 2| with standard (free) α s , saturates at small Q 2≥0, and has poles at timelike Q 2 in agreement with analytic properties of physical amplitudes in the large-N c limit.

The Feynman–Schwinger Representation in QCD

The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative background and valence gluon part. For nonperturbative contributions the background perturbation theory is used systematically, yielding two types of expansions, illustrated by direct physical applications. As an application, we discuss the collinear singularities in the Feynman–Schwinger representation formalism. Moreover, the generalization to nonzero temperature is made and expressions for partition functions in perturbation theory and nonperturbative background are explicitly written down.

Freezing of QCD coupling affects the short distance static potential

A striking contradiction between lattice short range static potential (nf=0) and standard perturbative potential, observed by Bali G.S., is investigated in the framework of the background perturbation theory. With the use of the background coupling which contains the only background parameter - mass mB, fixed by fine structure fit in bottomonium, the lattice data are nicely explained without introduction of exotic short range linear potential with large "string tension" approx. 1 GeV squared. A significant difference between the background coupling and standard perturbative coupling is found in the range 0.05 fm < r<0.15 fm, while at larger distances, r > 0.3 fm the background coupling fast approaches the freezing value. Some problems concerning the strong coupling properties at short and long distances are discussed and solutions are suggested.

Mixing of meson, hybrid, and glueball states

An effective QCD Hamiltonian is constructed with the aid of the background perturbation theory and relativistic Feynman-Schwinger path integrals for Green's functions. The resulting spectrum displays mass gaps of about 1 GeV when an additional valence gluon is added to the bound state. The mixing of meson, hybrid, and glueball states is defined in two ways—through generalized Green's functions and through a modified Feynman diagram technique—giving similar answers. Results for mixing matrix elements are numerically not large (around 0.1 GeV) and agree with earlier analytic estimates and lattice simulations.

Perturbative expansions in QCD and analytic properties of α s

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties,and contain in particular IR generated ghost poles and cuts. As an outcome the rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In a limiting case of large Nc, when QCD amplitudes contain only pole singularities, the strong coupling constant alpha_s(Q) is shown to be also meromorfic function of external momenta. Some simple models and examples are given when nonperturbative beta function and alpha_s(Q) can be written explicitly. General form of amplitudes at large Nc is given in the framework of background perturbation theory and its correspondence with standard perturbation theory at large momenta is demonstrated in the example of e^+e^- annihilation. For time-like momenta the background coupling constant differs drastically from the standard one but the background series averaged over energy intervals has the same (AF) asymptotics at large momenta as in the standard perturbation theory.