arXiv subjects
Publications and source records attributed to Maxim V. Polyakov.
Selected topics related to the physics of the energy-momentum tensor (EMT) form factors are discussed. The topics are: 1) Fundamental mechanical properties of particles and gravity 2) Mechanical properties of non-spherical particles 3) Gravitational form factors of Goldstone bosons 4) Nucleon's seismology?
Leading logarithms (LLs) in massless non-renormalizable effective field theories (EFTs) can be computed with the help of non-linear recurrence relations. These recurrence relations follow from the fundamental requirements of unitarity, analyticity and crossing symmetry of scattering amplitudes and generalize the renormalization group technique for the case of non-renormalizable EFTs. We review the existing exact solutions of non-linear recurrence relations relevant for field theoretical applications. We introduce the new class of quantum field theories (quasi-renormalizable field theories) in which the resummation of LLs for $2 \to 2$ scattering amplitudes gives rise to a possibly infinite number of the Landau poles.
Using the instanton picture of the QCD vacuum we compute the nucleon $\bar c^Q(t)$ form factor of the quark part of the energy momentum tensor (EMT). This form factor describes the non-conservation of the quark part of EMT and contributes to the quark pressure distribution inside the nucleon. Also it can be interpreted in terms of forces between quark and gluon subsystems inside the nucleon. We show that this form factor is parametrically small in the instanton packing fraction. Numerically we obtain for the nucleon EMT a small value of $\bar c^Q(0)\simeq 1.4\cdot 10^{-2}$ at the low normalisation point of $\sim 0.4$ GeV$^2$. This smallness implies interesting physics picture - the forces between quark and gluon mechanical subsystems are smaller than the forces inside each subsystem. The forces from side of gluon subsystem squeeze the quark subsystem - they are compression forces. Additionally, the smallness of $\bar c^Q(t)$ might justify Teryaev's equipartition conjecture. We estimate that the contribution of $\bar c^Q (t)$ to the pressure distribution inside the nucleon is in the range of 1 -20 % relative to the contribution of the quark $D$-term.
The physics related to the form factors of the energy momentum tensor spans a wide spectrum of problems, and includes gravitational physics, hard exclusive reactions, hadronic decays of heavy quarkonia, and the physics of exotic hadrons described as hadroquarkonia. It also provides access to the "last global unknown property:" the D-term. We review the physics associated with the form factors of the energy-momentum tensor and the D-term, their interpretations in terms of mechanical properties, their applications, and the current experimental status.
The chromoelectric polarizability of $J/ψ$ is extracted from lattice QCD data on the nucleon-$J/ψ$ potential in the heavy quark limit. The value of $α(1S) = (1.6 \pm 0.8) \,{\rm GeV}^{-3} $ is obtained. We also comment on the possibility of hadrocharmonia.
We perform the flavour $SU(3)$ analysis of the recently discovered $Ω(2012)$ hyperon. We find that well known (four star) $Δ(1700)$ resonance with quantum numbers of $J^P=3/2^-$ is a good candidate for the decuplet partner of $Ω(2012)$ if the branching for the three-body decays of the latter is not too large $\le 70$\%. That implies that the quantum numbers of $Ω(2012)$ are $I(J^P)=0(3/2^-)$. The predictions for the properties of still missing $Σ$ and $Ξ$ decuplet members are made. We also discuss the implications of the ${ \overline{ K} Ξ(1530)}$ molecular picture of $Ω(2012)$. Crucial experimental tests to distinguish various pictures of $Ω(2012)$ are suggested.
The D-term is a fundamental particle property which is defined through the matrix elements of the energy-momentum tensor and as such in principle on equal footing with mass and spin. Yet the experimental information on the D-term of any hadron is very scarce. The D-term of the nucleon can be inferred from studies of hard-exclusive reactions, and its measurement will give valuable insights on the dynamics, structure, and the internal forces inside the nucleon. We review the latest developments and the fascinating applications of the D-term and other energy-momentum tensor (EMT) form factors. We also suggest a definition of the mechanical mean square radius and make a prediction for its size.
We consider hidden charm pentaquarks as hadroquarkonium states in a QCD inspired approach. Pentaquarks arise naturally as bound states of quarkonia excitations and ordinary baryons. The LHCb $P_c(4450)$ pentaquark is interpreted as a $ψ'$-nucleon bound state with spin-parity $J^P=3/2^-$. The partial decay width $Γ(P_c(4450)\to J/ψ+N)\approx 11$ MeV is calculated and turned out to be in agreement with the experimental data for $P_c(4450)$. The $P_c(4450)$ pentaquark is predicted to be a member of one of the two almost degenerate hidden-charm baryon octets with spin-parities $J^{P}=1/2^-,3/2^-$. The masses and decay widths of the octet pentaquarks are calculated. The widths are small and comparable with the width of the $P_c(4450)$ pentaquark, and the masses of the octet pentaquarks satisfy the Gell-Mann-Okubo relation. Interpretation of pentaquarks as loosely bound $Σ_c\bar D^*$ and $Σ_c^*\bar D^*$ deuteronlike states is also considered. We determine quantum numbers of these bound states and calculate their masses in the one-pion exchange scenario. The hadroquarkonium and molecular approaches to exotic hadrons are compared and the relative advantages and drawbacks of each approach are discussed.
In the large $N_c$ limit both heavy and light baryons are described by the universal mean field, which allows us to relate the properties of heavy baryons to light ones. With the only input from the decays of light octet baryons (due to the universality of the chiral mean field), excellent description of strong decays of both charm and bottom sextets is obtained. The parameter-free prediction for the widths of exotic anti-decapentaplet ($\overline{\boldsymbol{15}}$) baryons is also made. The exotic heavy baryons should be anomalously narrow despite of large phase space available. In particular, the widths of $Ω_c(3050)$ and $Ω_c(3119)$, interpreted as members of $\overline{\boldsymbol{15}}$-plet, are very small: 0.48~MeV and 1.12~MeV respectivly. This result is in very good agreement with the measurements of the LHCb Collaboration and provides natural and parameter free explanation of the LHCb observation that $Ω_c(3050)$ and $Ω_c(3119)$ have anomalously small widths among five recently observed states.
We employ the chiral quark-soliton model to describe excited baryons with one heavy quark. Identifying known charmed baryons with multiplets allowed by the model, we argue that apart from regular excitations of the ground state multiplets, some of recently reported by the LHCb collaboration narrow $Ω^{0}_{c}$ states, may correspond to the exotic pentaquarks. This interpretation can be easily verified experimentally, since exotic $Ω^{0}_{c}$ states -- contrary to the regular excitations -- form isospin triplets, rather than singlets.
The probably most fundamental information about a particle is contained in the matrix elements of its energy momentum tensor (EMT) which are accessible from hard-exclusive reactions via generalized parton distribution functions. The spin decomposition of the nucleon and Ji sum rule are one example. Less prominent but equally important information is encoded in the stress tensor, related to the spatial components of the EMT, which shows in detail how the strong forces inside the nucleon balance to form a bound state. This provides not only unique insights on nucleon structure. It also leads to fascinating new applications to hadron spectroscopy which allow us to formulate new interpretations of the charmonium-nucleon pentaquarks discovered by LHCb. Recent progress is reviewed in this short overview article.
We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the $N_c-1$ light quarks that induce the pion mean field, and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of \textit{model-independent} relations and calculate the heavy baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the $Ω_b^*$ baryon is predicted.
We interpret the newly discovered pentaquark $P_c(4450)$ as a bound state of charmonium $ψ(2S)$ and the nucleon. The binding potential is due to charmonium-nucleon interaction that in the heavy quark approximation is proportional to the product of the charmonium chromoelectric polarizability and the nucleon energy-momentum distribution. We use the large $N_c$ expansion to estimate the quarkonium polarizability and calculate the nucleon properties in the framework of the mean-field picture of light baryons. Two almost degenerate states $J^P=(1/2)^-$ and $J^P=(3/2)^-$ are predicted at the position of the $P_c(4450)$ pentaquark. We find that the nucleon-$ψ(2S)$ bound state has a naturally narrow width in the range of tens of MeV. The unitary multiplet partners of the $P_c(4450)$ pentaquark and the generalization to $b \bar b$-nucleon pentaquark bound states are discussed.
The dual parametrization and the Mellin-Barnes integral approach represent two frameworks for handling the double partial wave expansion of generalized parton distributions (GPDs) in the conformal partial waves and in the $t$-channel ${\rm SO}(3)$ partial waves. Within the dual parametrization framework, GPDs are represented as integral convolutions of forward-like functions whose Mellin moments generate the conformal moments of GPDs. The Mellin-Barnes integral approach is based on the analytic continuation of the GPD conformal moments to the complex values of the conformal spin. GPDs are then represented as the Mellin-Barnes-type integrals in the complex conformal spin plane. In this paper we explicitly show the equivalence of these two independently developed GPD representations. Furthermore, we clarify the notions of the $J=0$ fixed pole and the $D$-form factor. We also provide some insight into GPD modeling and map the phenomenologically successful Kumerički-Müller GPD model to the dual parametrization framework by presenting the set of the corresponding forward-like functions. We also build up the reparametrization procedure allowing to recast the double distribution representation of GPDs in the Mellin-Barnes integral framework and present the explicit formula for mapping double distributions into the space of double partial wave amplitudes with complex conformal spin.
We investigate the electromagnetic mass differences of SU(3) baryons, using an "model-independent approach" within a chiral soliton model. The electromagnetic self-energy corrections to the masses of the baryon are expressed as the baryonic two-point correlation function of the electromagnetic currents. Using the fact that the electromagnetic current can be treated as an octet operator, and considering possible irreducible representations of the correlation function, we are able to construct a general collective operator for the electromagnetic self-energies, which consists of three unknown parameters. These parameters are fixed, the empirical data for the electromagnetic mass differences of the baryon octet being employed. We predict those of the baryon decuplet and antidecuplet. In addition, we obtain various mass relations between baryon masses within the corresponding representation with isospin symmetry breaking considered. We also predict the physical mass differences of the baryon decuplet. The results are in good agreement with the exisiting data.
We propose a scenario in which Roper octet can mix with a putative antidecuplet of exotic baryons and predict the properties of its strange members. We show that 1795 MeV < M_Sigma_{\bar{10}} <1830 MeV and 1900 MeV < M_Xi_{\bar{10}}<1970 MeV. We also estimate total widths: 10 MeV < Gamma_Σ_{\bar{10}}< 30 MeV} and Gamma_Ξ_{\bar{10}}\sim 10 MeV and branching ratios for different decay modes.
We establish a link between the dual parametrization of GPDs and a popular parametrization based on the double distribution Ansatz, which is in prevalent use in phenomenological applications. We compute several first forward-like functions that express the double distribution Ansatz for GPDs in the framework of the dual parametrization and show that these forward-like functions make the dominant contribution into the GPD quintessence function. We also argue that the forward-like functions $Q_{2 ν}(x)$ with $ν\ge 1$ contribute to the leading singular small-$x_{Bj}$ behavior of the imaginary part of DVCS amplitude. This makes the small-$x_{Bj}$ behavior of $\im A^{DVCS}$ independent of the asymptotic behavior of PDFs. Assuming analyticity of Mellin moments of GPDs in the Mellin space we are able to fix the value of the $D$-form factor in terms of the GPD quintessence function $N(x,t)$ and the forward-like function $Q_0(x,t)$.
We study recent Deeply Virtual Compton scattering (DVCS) data within a dual parameterization of the Generalized Parton Distributions (GPDs). This parameterization allows to quantify the maximum amount of information, that can be extracted from DVCS data, in a ``quintessence'' function. We present a ``zero step'' model for the latter solely based on the forward quark density, providing a parameter free prediction for the imaginary part of the DVCS amplitude. It is shown that the bulk effect of the $e p \to e p γ$ beam helicity asymmetry can be understood within such a model.