BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Revisiting the Polyakov loop Nambu-Jona-Lasonio model at finite de nsity of baryon charge DTSTART;VALUE=DATE-TIME:20201221T101000Z DTEND;VALUE=DATE-TIME:20201221T103000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-177@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksii Ivanytskyi (Bogolyubov Institute for Theoret ical Physics)\nWe revisit the Polyakov Loop coupled Nambu-Jona-Lasinio mod el that maintains the Polyakov loop dynamics at zero temperature\, which i s the most interesting for astrophysical applications. For this purpose we re-examine potential for the deconfinement order parameter at finite bary onic densities. Secondly\, and the most important\, we explicitly demonstr ate that naive modification of this potential at any temperature is formal ly equivalent to assigning a baryonic charge to gluons. We develop a gener al formulation of the present model which is free of the discussed defect and is normalized to asymptotic of the QCD equation of state given by $\\m athcal{O}(\\alpha_s^2)$ perturbative results. We also demonstrate that inc orporation of the Polyakov loop dynamics to the present model sizably stif fens the quark matter equation of state supporting an existence of heavy c ompact stars with quark cores.\n\nhttps://indico.bitp.kiev.ua/event/7/cont ributions/177/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/177/ END:VEVENT BEGIN:VEVENT SUMMARY:Equation of State at Finite Baryon Density and External Magnetic F ield from Lattice QCD DTSTART;VALUE=DATE-TIME:20201221T091000Z DTEND;VALUE=DATE-TIME:20201221T093000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-171@indico.bitp.kiev.ua DESCRIPTION:Speakers: Natalia Kolomoyets (JINR)\nThe report is devoted to lattice study of QCD equation of state (EoS) at finite baryon chemical po tential and nonzero external magnetic field. The simulations are performed with rooted dynamical staggered $u$\, $d$\, and $s$ quarks at physical qu ark masses. In view of the sign problem\, the study is carried out at imag inary chemical potential. The results are analytically continued to real chemical potential domain. We present our preliminary results for pressure computed for various values of temperature and magnetic field.\n\nhttps:/ /indico.bitp.kiev.ua/event/7/contributions/171/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/171/ END:VEVENT BEGIN:VEVENT SUMMARY:Femtoscopic analysis of relativistic heavy-ion collisions in the h ydrokinetic approach DTSTART;VALUE=DATE-TIME:20201221T103000Z DTEND;VALUE=DATE-TIME:20201221T105000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-167@indico.bitp.kiev.ua DESCRIPTION:Speakers: Musfer Adzhymambetov (Bogolyubov Institute for Theor etical Physics)\nThe theoretical description of the femtoscopy scales in u ltrarelativistic heavy-ion collisions at different energies and for differ ent colliding ion pairs (Au + Au collisions at the top RHIC energy $\\sqrt {s_{NN}}=200$ GeV\, Pb + Pb collisions at the LHC energies $\\sqrt{s_{NN}} =2.76$ and $\\sqrt{s_{NN}}=5.02$ TeV\, the LHC Xe + Xe collisions at $\\sq rt{s_{NN}}=5.44$ TeV) is provided within the integrated HydroKinetic model (iHKM). The comparison of the model simulation results\, obtained for the considered collision types at the similar values of the mean charged part icle multiplicity ⟨$dNch/dη$⟩ shows that the magnitudes of the corres ponding interferometry radii depend not only on ⟨$dNch/dη$⟩ but also on the geometric sizes of the colliding nuclei.\n\nhttps://indico.bitp.kie v.ua/event/7/contributions/167/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Dark Matter Polarization Operator in the Generalized Yukawa Model DTSTART;VALUE=DATE-TIME:20201222T131000Z DTEND;VALUE=DATE-TIME:20201222T133000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-179@indico.bitp.kiev.ua DESCRIPTION:Speakers: Mykyta Dmytriiev ()\nThe dark matter particle candid ates are searched on various modern colliders\, but nothing has been found \, yet. The possible reason for this is considered in this work. In the on -resonance search method of the new particle\, the latter is identified wi th the resonant peak in the cross-section of some scattering process. The resonance position coincides with the mass of the particle\, and its width is defined as peak width on the half of its height. It is assumed in the experimental data treatment that the new resonance is narrow\, namely its width is up to $3\\%$ of its mass. If it is wider\, such state could be mi ssed in the data as a noise. We consider different scenarios in which dark matter candidate acquires bigger width\, and identify the new particle pa rameters at which it happens.\n \nWe conduct our research in the framework of the generalized Yukawa model\, where dark matter is presented as a sca lar field $\\chi$ and a Dirac fermionic field $\\Psi$. The model also cont ains the sector of visible matter particles\, which consists of scalar fie ld $\\phi$ and Dirac fermionic fields $\\psi_1$ and $\\psi_2$. The lagrang ian of the model reads:\n\n$\n \\mathcal{L} = \\frac{1}{2}\\left[\\lef t(\\partial_{\\mu}\\phi\\right)^2 - \\mu^2\\phi^2 + \\left(\\partial_{\\mu }\\chi\\right)^2 - \\Lambda^2\\chi^2\\right] - \\lambda\\phi^4 - \\rho\\ph i^2\\chi^2 - \\xi\\chi^4 + $\n$\n + \\sum\\limits_{a=1\;2}\\bar{\\psi} _a\\left(i\\gamma^{\\mu}\\partial_{\\mu} - m_a - g_{\\phi}\\phi - g_{\\chi }\\chi\\right)\\psi_a + \\bar{\\Psi}\\left(i\\gamma^{\\mu}\\partial_{\\mu} - M - G_{\\chi}\\chi\\right)\\Psi.\n$\n\nWidth of the $\\chi$ particle is defined generally by the imaginary part of its polarization operator $\\P i_{\\chi\\chi}(p^2)$ taken at the point $p^2 = \\Lambda^2$. Here $p^2$ is the squared momentum transferred through the virtual bosonic state. $\\Pi_ {\\chi\\chi}(p^2)$ is found analytically. Hence\, the width $\\rho$ of the $\\chi$ resonance\, as a fraction of mass $\\Lambda$\, reads:\n\n$$\n \\rho = \\frac{\\Im\\Pi_{\\chi\\chi}(\\Lambda^2)}{\\Lambda^2} = \\frac{g_ {\\chi}^2}{8\\pi}\\left[\\left(1 - \\frac{4m_1^2}{\\Lambda^2}\\right)^{\\f rac{3}{2}} + \\left(1 - \\frac{4m_2^2}{\\Lambda^2}\\right)^{\\frac{3}{2}}\ \right] + \\frac{G_{\\chi}^2}{\\Lambda^2}\\left(1 - \\frac{4M^2}{\\Lambda^ 2}\\right)^{\\frac{3}{2}}.\n$$\nThe lagrangian also introduces the mixing of scalar fields\, which occurs on the one-loop level. That is\, two-point Green function $\\left$ becomes non-zero due to the loop correction from the $\\psi_1$ and $\\psi_2$\, which connects $\\phi$ and $\\chi$ lines on the corresponding diagram. The magnitude of such mixing is defined by the corresponding mixing angle $\\theta_{mix}$. We define this angle from the diagonalization of the bosonic mass matrix\, which is given by the effecti ve potential of the scalar fields. Hence\, $\\theta_{mix}$ reads:\n\n$$\n\ \tan{2\\theta_{mix}} = 2g_{\\phi}g_{\\chi}F\\left[\\frac{4\\pi^2}{3}\\left (\\Lambda^2 - \\mu^2\\right) + \\left(g_{\\phi}^2 - g_{\\chi}^2\\right)F - G_{\\chi}^2M^2\\ln\\frac{M^2}{\\kappa^2}\\right]^{-1}\, \n$$\n$$\nF = m_1 ^2\\ln\\frac{m_1^2}{\\kappa^2} + m_2^2\\ln\\frac{m_2^2}{\\kappa^2}\,\n$$\n \nwhere $\\kappa$ is an arbitrary renormalization parameter.\n \nFrom the explicit analytical expression\, we find areas of the model parameters spa ce where $\\rho\\cdot 100\\% > 3\\%$. We find that the limit of $3\\%$ can be exceeded in many cases. In the framework of our model\, the conditions for that are the following. There should be $\\Lambda > \\mu$\, so DM par ticle is heavier than the visible one. Additionally\, interactions in the visible sector should be weaker than that of between the dark and visible particle or between the particles in the dark sector only. That is\, if ei ther $g_{\\chi} \\gg g_{\\phi}$ or $G_{\\chi} \\gg g_{\\phi}$. Finally\, t here exists an upper bound for the mixing angle -- in our model\, it shoul d be $|\\theta_{mix}|\\leq 10^{-5}$. We find that until mixing between vis ible and dark bosons is small and two resonances are located far enough on e from another\, the parameters of visible particle resonance are independ ent of the characteristics of the dark sector. In this case dark resonance is both wide and does not interfere with the resonance of visible $\\phi$ . The presence of the upper limit on $\\theta_{mix}$ is qualitatively impo rtant.\n \nThe self-interaction of the bosonic particles does not affect t heir widths\, being canceled in the renormalization procedure.\n \nThe con sidered Yukawa model gave a possibility for analyzing the role of the mass es and couplings of particles. Other aspects of the problem such as group symmetry of the extended model and\, hence\, the content of the states rem ain behind it. However\, we have obtained the set of conditions which have to be taken into account when searches for the DM particles are carried o ut. In general\, to avoid the problem of wide resonance states we have to apply additionally non-resonant methods to detect these new states of matt er.\n\nhttps://indico.bitp.kiev.ua/event/7/contributions/179/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/179/ END:VEVENT BEGIN:VEVENT SUMMARY:Bose-Einstein condensation phenomenology in systems with repulsive interactions DTSTART;VALUE=DATE-TIME:20201221T093000Z DTEND;VALUE=DATE-TIME:20201221T095000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-173@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleh Savchuk (Frankfurt Institute For Advanced Studi es)\nThe role of repulsive interactions in statistical systems of Bose par ticles is investigated. Three different phenomenological frameworks are co nsidered: a mean field model\, an excluded volume model\, and a model with a medium dependent effective mass. All three models are tuned to yield si milar equations of state\, with only minor deviations from the ideal Bose gas at small chemical potentials. Our analysis indicates\, however\, that these models lead to qualitatively different results for the Bose-Einstein condensation phenomenon. We discuss the different aspects of this phenome non\, namely\, an onset of the Bose-Einstein condensation\, particle numbe r fluctuations\, and a behavior of the Bose condensate. The obtained resul ts can be helpful for interpreting the lattice QCD data at small temperatu re and large isospin chemical potential and the data on multiple pion prod uction in high energy nuclear collisions.\n\nhttps://indico.bitp.kiev.ua/e vent/7/contributions/173/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/173/ END:VEVENT BEGIN:VEVENT SUMMARY:Production of HNL in 3-body decays of mesons. Comparison with PYTH IA approach DTSTART;VALUE=DATE-TIME:20201221T105000Z DTEND;VALUE=DATE-TIME:20201221T111000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-176@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yuliia Borysenkova (Taras Shevchenko National Univer sity of Kyiv)\nThe Standard Model (SM) is a particle physics theory that i s consistent up to very high energy scales and verified in numerous exper iments up to $\\sim 14$ TeV. However\, it fails to explain some phenomena such as massiveness of neutrinos\, dark matter\, dark energy\, baryon as ymmetry of the Universe etc. Therefore SM is incomplete and requires an ex tension. \n\nOne possible approach is by adding new particles to the theor y. There are two possible answers to the question "Why do we not observe p articles of new physics in experiments?" The first answer is the following . The new particles are very heavy and can not be produced in modern ac celerators like LHC. To detect them one has to build more powerful and mor e expensive accelerators. There is another possibility. The particles of n ew physics can be light particles that feebly interact with SM particles. \nThe last case is very interesting for the experimental search of the new physics in the intensity frontier experiments just now. There are differe nt choices of new renormalized interaction Lagrangian of particles of new physics with SM particles. It's called portals. \n\nIn this paper\, we co nsider a heavy neutral lepton (HNL) portal. The phenomenology of GeV-scale HNL was considered in details in [1]. We will compare the analytical resu lts for HNL production in 3-body decays of mesons with PYTHIA approximatio n. \n\nThe simplest way of neutrino modification of the SM involves extens ion of the SM by neutrino singlets with right chirality (in the SM all rig ht-handed fermions are singlets)\, which extremely faintly interact with S M particles. Such neutrinos are called sterile neutrinos or heavy neutral leptons. Renormalized and gauge-invariant interaction of new neutrinos w ith the SM particles is similar to the Yukawa interaction of left-handed q uarks doublets with singlets of the right-handed quarks\, namely:\n\n$$\n\ \mathcal L_{int}=-\\left(F_{\\alpha I}\\bar L_\\alpha \\tilde H\nN_I+h.c.\ \right)\,\n$$\n\nwhere $\\alpha=e\,\\mu\,\\tau$\, index $I$ \nis from 1 t o full number of the sterile neutrinos\, $L_{\\alpha}$ –\ndoublet of le ptons of $\\alpha$-generation\, $N_I$ – right-handed sterile neutrino\,\ n$F_{\\alpha\nI}$ – new matrix of dimensionless Yukawa couplings\, ${\\t ilde H}=i\\sigma_2H^\\star$.\n\nTaking the low energy limit and considerin g sterile neutrino as Majorana particles\, we can write full Lagrangian of the modified neutrino sector of the SM\n\n$$\n\\mathcal{L}_{\\nu\,N}=i \\ bar{\\nu_k} \\not\\partial \\nu_k + i \\bar{N_I} \\not\\partial N_I -\n \ \left( F_{\\alpha I}\\bar{\\nu}_{\\alpha} N_I + \\frac{M_{I}}{2} \\bar{N_I }^c N_I + h.c. \\right)\,\n$$\n\nwhere $M_I$ – Majorana mass terms.\nAs a result of the neutrino states mixture\, the active neutrino states beco me superposition of the mass states of the active and the sterile neutrino s.\nIt means that sterile neutrinos interact with SM particles similarly t o active neutrinos:\n\n$$\n\\mathcal{L}_{int} = -\\biggl(\\frac{g}{2\\sqrt 2} W^+_\\mu\\!\\sum_{I\,\\alpha} \\overline{N^c}_I U_{I\\alpha} \\gamma^ \\mu (1-\\gamma_5) \\ell^-_\\alpha + \\frac{g}{4 \\cos\\theta_W}Z_\\mu\\! \\sum_{I\,\\alpha}\\overline{N^c}_I U_{I\\alpha} \\gamma^\\mu (1-\\gamma_ 5) \\nu_\\alpha + h.c.\\biggr)\,\n$$\n\nwhere $U_{I\\alpha}=F_{I\\alpha}/M _I$ is so called mixing angle.\n\nFor intensity frontier experiment it is very important to built sensitivity region. It is a region in space of p arameters of new particle (mass and coupling)\, when particle can be detec ted in the experiment. To build it one has to solve inequality $N_{HNL}^{r eg}>N_0$\, where $N_0$ is minimal expected number of new particle for succ essful of experiment\, $N_{HNL}^{reg}$ is number of HNL that can be detect ed:\n\n$$\nN_{HNL}^{reg}\\simeq N^{produced}_{HNL} P_{geom} P_{decay}.\n$$ \n\nHere $N_{HNL}^{produced}$ is number of\nthe produced \\textit{HNL}-pa rticles\, $P_{geom}$ is a probability of the produced HNL-particles to mov e towards the detector\, $P_{decay}$ is a probability of the\nproduced HNL -particles to decay in the volume of the vacuum tank\nbefore the detectors .\n\nFor approximate calculations of the sensitivity region\, PYTHIA is of ten used. It is a widely used program for the generation of high-energy ph ysics events.\nPYTHIA is good for generation of 2-body mesons' decay\, but for HNL production it is important to take into account 3-body decay too. \nPYTHIA uses predefined matrix element to generate 3-body semileptonic de cays of $B$ and $D$ mesons correspondingly\n\n$$\n \\overline{|M_{fi}| ^2_B} = (p_h\\\,p_\\nu) (p_{h^\\prime} \\\, p_\\ell)\,\\quad \n \\overl ine{|M_{fi}|^2_D} = (p_h\\\,p_\\ell) (p_{h^\\prime} \\\, p_\\nu).\n$$\n\n It does not contain mesons' form-factors and its matrix elements obviousl y\ndiffers from correct matrix elements for HNL production in 3-body meson s' decay.\nThe goal of the project is to estimate the importance of this u ncertainty for construction of sensitivity region to HNL.\n\nWe considere d in details probability density function for the energy of the HNL-parti cles $pdf(E_N)$\, $P_{geom}$ and $P_{decay}$ and make following conclusio ns.\n\n\n\nComputations of 3-body decay of $\\tau$-lepton with HNL produc tion in Pythia coincide with correct computations.\n\nFor description of r eactions of pseudoscalar meson 3-body decay into another pseudoscalar meso n ($B^- \\rightarrow D^0 +\\ell^- + N$ and $D^- \\rightarrow K^0 +\\ell^- + N$) the matrix elements of type $B$ in Pythia is better to use \n\nFor description of reactions of pseudoscalar meson 3-body decay into another vector meson ($B^- \\rightarrow D^\\star(2007)^0 +\\ell^- + N$ and $D^- \\ rightarrow K^\\star(892)+\\ell^- + N$) the matrix elements of type $D$ in Pythia is better to use.\n\nAmong the considered 3-body reactions\, due to a suitable choice of PYTHIA matrix elements (type of $B$ and $D$)\, one c an get the smallest difference with correct matrix element for reaction $B^- \\rightarrow D^0 +e^- + N$ (difference $\\sim 1\\%$)\, while the larg est unremovable difference is for reaction $D^- \\rightarrow K^\\star(89 2) +e^- + N$ (difference $\\sim 5\\%$).\n\n\n\n[1] Kyrylo Bondarenko\, Alexey Boyarsky\, Dmitry Gorbunov\, and Oleg Ruchayskiy. Phenomenolo gy of GeV-scale Heavy Neutral Leptons. *JHEP*\, 11:032\, 2018.\n\nhttps:// indico.bitp.kiev.ua/event/7/contributions/176/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/176/ END:VEVENT BEGIN:VEVENT SUMMARY:Phenomenology of GeV-scale Chern-Simons boson DTSTART;VALUE=DATE-TIME:20201221T111000Z DTEND;VALUE=DATE-TIME:20201221T113000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-175@indico.bitp.kiev.ua DESCRIPTION:Speakers: Mariia Tsarenkova (Taras Shevchenko National Univers ity of Kyiv)\nThe Standard Model (SM) is a particle physics theory that is consistent up to very high energy scales and verified in numerous experi ments up to $\\sim 14$ TeV. However\, it fails to explain some phenomena such as massiveness of neutrinos\, dark matter\, dark energy\, baryon asy mmetry of the Universe etc. Therefore\, SM is incomplete and requires an e xtension. \n\nOne possible approach is by adding new particles to the theo ry. There are two possible answers to the question "Why do we not observe particles of new physics in experiments?" The first answer is the followin g. The new particles are very heavy and can not be produced in modern a ccelerators like LHC. To detect them one has to build more powerful and mo re expensive accelerators. There is another possibility. The particles of new physics can be light particles that feebly interact with SM particles .\nThe last case is very interesting for the experimental search of the ne w physics just now. There are three possible choices of new renormalized i nteraction Lagrangian of particles of new physics with SM particles. It's called portals. There are scalar portal\, heavy neutral leptons portal\, vector portal. There are other portals of high-dimensional operators such as portal of pseudoscalar particles (axion-like particles)\, or Chern-Simo ns like (parity odd) interaction of electroweak gauge bosons with a new ve ctor field [1].\n\n\nIn this paper\, we consider a Chern-Simons (CS) porta l with new neutral vector particle ($X$) boson. \nThis extension has not yet been studied sufficiently. This interaction was proposed in [2]. It origins from non-trivial anomaly cancellations in theory with new heavy fe rmions. It has gauge-invariant form\n$$\n \\mathcal{L}_1=\\frac{C _Y}{\\Lambda_Y^2}\\cdot X_\\mu (\\mathfrak D_\\nu H)^\\dagger H B_{\\lambd a\\rho} \\cdot\\epsilon^{\\mu\\nu\\lambda\\rho}+h.c.\, \\quad \n\ \mathcal{L}_2=\\frac{C_{SU(2)}}{\\Lambda_{SU(2)}^2}\\cdot X_\\mu (\\mathfr ak D_\\nu H)^\\dagger F_{\\lambda\\rho} H\\cdot\\epsilon^{\\mu\\nu\\lambda \\rho}+h.c. \n$$\n\nIn the low energy limit (unitary gauge) the effective renormalized Lagrangian of three particle interaction CS boson with SM pa rticles is\n$$\n \\mathcal{L}_{CS}=c_z \\epsilon^{\\mu\\nu\\lambda\\rho} X_\\mu Z_\\nu \\partial_\\lambda Z_\\rho +c_\\gamma \\epsilon^{\\mu\\nu\\l ambda\\rho} X_\\mu Z_\\nu \\partial_\\lambda A_\\rho+\\left\\{ c_w \\epsil on^{\\mu\\nu\\lambda\\rho} X_\\mu W_\\nu^- \\partial_\\lambda W_\\rho^+ + h.c.\\right\\}.\n$$\n\nFor the experimental search of the new particle\, i t is very important to theoretically consider channels of production and d ecay of the new particle. We consider the case of experiments on Cern SPS accelerator\, where CS particles can not be produced from the decay of rea l $W$\, $Z$ bosons. In this paper\, we consider the production of CS GeV- scale particles in mesons' decay. \n \nTo do it we get effective Lagrangia n of CS interaction with different quarks due to presented here loop diagr am in the form\n$$\n \\mathcal{L}_{CSd}= \\sum_{m\\neq n}\\Theta_{1W} \\left( C^d_{mn}\\\, \\bar{\\Psi}_{d_n}\\\, \\gamma^{\\mu}\\\,\\hat\n P_L \\\, \\Psi_{d_m} X_{\\mu}+h.c.\\right)%-\\sum_n\\Theta_W^1 g^2 C^d_{nn}\\\, \\bar{\\Psi}_{d_n}\\\, \\gamma^{\\mu}\\\,\\hat P_L \\\, \\Psi_{d_n} X_{\\mu}\,\n$$\nwhere $\\Theta_{1W}$ is real part of $c_w$ c oupling and $C^d_{bs}=1.97\\cdot 10^{-4}$\, $C^d_{bd}=4.43\\cdot 10^{-5}$\ , $C^d_{sd}=1.77\\cdot 10^{-6}$.\nAs it turned out the loop with different quarks does not suffer from divergence problem and we have to take into a ccount only interaction with down quarks\, because coefficients of intera ction with up quarks are sufficiently smaller. \nSo\, we will consider CS particle production in meson's decay only due to decay of heavy down quark in the meson. \n\nInitial lightest mesons containing $b$ and $s$ quarks are $B$-mesons and $K^\\pm$\, $K^0_S$\, $K^0_L$ mesons.\n\nPossible reacti on of $B$-meson decay with $X$-particle production is decay into pseudosca lar mesons ($K$ and $\\pi$ mesons)\, scalar mesons ($K^{0\\star}(700)$\, $K^{0\\star}(1430)$)\, vector mesons ($K^\\star(892)$\, $K^\\star(1410)$\, $K^\\star(1680)$)\, pseudovector mesons ($K_1(1270)$\, $K_1(1400)$) and t ensor final meson states ($K_2(1430)$).\n\nFor the initial kaons states\, the only possible 2-body decay is the process $K \\to \\pi +X$.\nThere are 3 types of the kaons: $K^{\\pm}$\, $K^0_L$\, $K^0_S$. Since $K^0_S$ is th e $CP$-even eigenstate\, the decay $K^0_S\\to \\pi S$ is proportional to t he CKM $CP$-violating phase and is strongly suppressed. Further we assume that the corresponding branching ratio vanishes and consider only reaction s $K^\\pm \\to \\pi^\\pm +X$ and $K^0_L \\to \\pi^0 +X$.\n\nThe amplitude of $h$-meson decay into $h'$-meson and $X$-particle has the form\n\n$$\n M_{h\\rightarrow h'X}=\\Theta_{1W} C^d_{mn} \\\, \\langle h'(p'))|\\ bar d_n\\gamma^{\\mu} \\hat P_L d_m|h(p)\\rangle\\\,\n \\epsilon^{\\sta r\\lambda_X}_{\\mu}.\n$$\n\nThis quantity can be obtained with help of fo rmalism summarised in [3].\n\nIn the following\, we plan to complete consi deration of the production of CS particles by examining direct CS producti on in $p-p$ collisions. Also\, we plan to consider possible channels of CS particles' decay. \n\n\nFigure 1. a) loop diagram of quarks interactions with CS particles\; b) diagram of CS production in meson's decay c) decay of $B$- and $K$-mesons with CS production.\n\n[1] Sergey Alekhin et al. A facility to Search for Hidden Particles at the CERN SPS: the SHiP physics case. *Rept. Prog. Phys.*\, 79(12):124201\, 2016.\n[2] Ignatios Antonia dis\, Alexey Boyarsky\, Sam Espahbodi\, Oleg Ruchayskiy\, and Jame s D.Wells. Anomaly driven signatures of new invisible physics at the Lar ge Hadron Collider. *Nucl. Phys.*\, B824:296–313\, 2010.\n[3] Iryna Bo iarska\, Kyrylo Bondarenko\, Alexey Boyarsky\, Volodymyr Gorkavenko\ , Maksym Ovchynnikov\, and Anastasia Sokolenko. Phenomenology of GeV-scal e scalar portal. *JHEP*\, 11:162\, 2019.\n\nhttps://indico.bitp.kiev.ua/ev ent/7/contributions/175/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/175/ END:VEVENT BEGIN:VEVENT SUMMARY:S-Matrix unitarity and Pomeron shadowing corrections DTSTART;VALUE=DATE-TIME:20201222T133000Z DTEND;VALUE=DATE-TIME:20201222T135000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-178@indico.bitp.kiev.ua DESCRIPTION:Speakers: Georgy Tersimonov (Bogolyubov Institute for Theoreti cal Physics)\nRegge theory is the only valid framework to describe soft sc attering processes where the perturbative QCD is not applicable. In Regge theory\, the particle diffraction is treated as an exchange of some 'objec t' called Pomeron (which in some way generalizes a particle — in particu lar\, it is described by variable complex angular momentum which generaliz es a spin). That approach was found surprisingly useful to phenomenologica lly calculating cross sections.\nIn 1960s\, it was shown that multi-Pomero n shower production reactions $pp \\rightarrow p + X_1 + X_2 + ... + p$\, where showers $(X_i)$ are separated by large rapidity gaps\, are breaking the S-matrix unitarity because corresponding cross-sections $\\sigma_{tot} $ grow with the rapidity ($\\xi$) faster than allowed by unitarity (the u pper bound is $\\sigma_{tot} \\leq \\xi^2$). This issue is known as Finkel stein-Kajantie problem. In 1974\, a possible solution was proposed [1] in multi-channel Eikonal model. It considered the gap survival probability $S ^2$ — the probability to observe the pure process where the gap is not p opulated by secondaries produced in the additional inelastic interaction. In the impact parameter representation the probability is given by $S^{2}( b) = |e^{-\\Omega(b)}|$\, where $b$ is the impact parameter and $\\Omega$ is the proton opacity. In the black disc limit $Re(\\Omega) \\rightarrow \ \infty$\, so $S^2(b) \\rightarrow 0$. So the additional rescatterings sho uld close the rapidity gaps. The work [2] shows that decreasing of the sur vival probability should overcompensate the original cross-sesction growth so\, as a result\, the cross-sections should also vanish with energy: $\\ frac{d\\sigma}{d\\xi_1} \\sim e^{-{\\Delta}\\xi_1} \\rightarrow 0$\, where $\\xi_1$ is the shower width on the rapidity scale. If the result is corr ect then the unitarity is restored. Over the past decades\, it has been co nsidered a cure for the FK problem [3].\nThe work [4] had discovered that such an approach still fails to unitarize the Pomeron contribution to the single diffraction dissociation amplitude due to an error in the calculati ons. The suspicion had arised: is the cure really effective in terms of al l the processes it is purposed for? Recent TOTEM soft scattering data rene wed the interest to these questions.\nIn the work [5] we investigate the s urvival probability method for all the diffractive processes. The main pro cesses are next. The first is single diffraction dissociation where one of the two incoming protons transforms into a shower: $pp \\rightarrow X + p$. The second is double diffraction dissocastion where both protons trans forms: $pp \\rightarrow X_1 + X_2$. The third is central production: $pp \\rightarrow p + X + p$. Integrated cross-sections of all these processes behave similar to each other\, so only the simplest\, the single dissocia tion\, will be considered in this talk. Its cross-section contains a mult iplier $e^{\\Delta(\\xi_1 + 2\\xi_2 - a\\xi)}$\, where $a \\rightarrow 2\\ frac{\\xi}{\\xi + \\xi_1}$ as $\\xi \\rightarrow \\infty.$ Here $\\xi_2$ i s the rapidity gap between the produced shower and the initial proton\; $\ \xi_1 + \\xi_2 = \\xi$ — the overall rapidity difference between interac ting protons. While investigating the high energy asymptotics ($\\xi \\rig htarrow \\infty$)\, the authors of [2] considered $a$ as $2$ and $e^{\\Del ta(\\xi_1 + 2\\xi_2 - a\\xi)}$ simply became $e^{-\\Delta{\\xi_1}}$. Howev er\, if the calculations are done in an explicit way\, one can see that $a = 2(1 -\\frac{\\xi_1}{\\xi} + O(\\frac{\\xi^2_1}{\\xi^2}))$ and so $e^{\\ Delta(\\xi_1 + 2\\xi_2 - a\\xi)} = e^{\\Delta(\\xi_1 + 2\\xi_2 - 2\\xi (1 -\\frac{\\xi_1}{\\xi}))}$ = $e^{+\\Delta{\\xi_1}}$\, thus the fast cross- section growth is in fact maintained.\nThereby the existing survival proba bility methods are unable to keep the cross-section growth within the unit arity bound. We develop a different approach based on the Pomeron and trip le-Pomeron vertex renormalization via Schwinger-Dyson equations. We take t he Pomeron in it's maximal form providing the maximal strong interactions strength allowed by unitarity. The triple-Pomeron vertex is chosen to cont ain zeroes at some transferred momenta and complex angular momenta. The pa rameters of developing model can be chosen in such a way that the unitarit y bounds are not violated.\n\n[1] J. L. Cardy. General Features of the Reg geon Calculus with $\\alpha > 1$. *Nucl. Phys. B*\, 75 (1974)\n[2] E. Gots man\, E.M. Levin\, U. Maor. Diffractive Dissociation and Eikonalization in High Energy $pp$ and $p\\bar{p}$ Collisions\, *Phys. Rev. D*\, 49 (1994)\ n[3] V.A. Khoze\, A.D. Martin\, M.G. Ryskin. Black disc\, maximal Odderon and unitarity. *Phys.Lett. B*\, 780 (2018)\n[4] E. Martynov\, B. Strumins ky. Unitarized model of hadronic diffractive dissociation. *Phys.Rev. D*\, 53 (1996)\n[5] E. Martynov\, G. Tersimonov. Multigap diffraction cr oss sections: Problems in eikonal methods for the Pomeron unitarization. * Phys. Rev. D*\, 101 (2020)\n\nhttps://indico.bitp.kiev.ua/event/7/contribu tions/178/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/178/ END:VEVENT BEGIN:VEVENT SUMMARY:The equation of state of hot dense qcd- matter\, gravitational wav es and collective flows DTSTART;VALUE=DATE-TIME:20201221T080500Z DTEND;VALUE=DATE-TIME:20201221T085000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-212@indico.bitp.kiev.ua DESCRIPTION:Speakers: Horst Stöcker (FIAS Goethe Universitaet Frankfurt G SI)\nhttps://indico.bitp.kiev.ua/event/7/contributions/212/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/212/ END:VEVENT BEGIN:VEVENT SUMMARY:Connecting fluctuation measurements in heavy ion collisions and gr and canonical susceptibilities: global conservation effects DTSTART;VALUE=DATE-TIME:20201221T085000Z DTEND;VALUE=DATE-TIME:20201221T091000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-172@indico.bitp.kiev.ua DESCRIPTION:Speakers: Roman Poberezhnyuk (Bogolyubov Institute for Theoret ical Physics of the National Academy of Sciences of Ukraine)\nWe present t he relation between cumulants of a conserved charge measured in a subvolum e of a thermal system and the corresponding grand-canonical susceptibiliti es\, taking into account exact global conservation of all QCD charges. The derivation is presented for an arbitrary equation of state\, with the ass umption that the subvolume is sufficiently large to be close to the thermo dynamic limit. Our framework – the subensemble acceptance method (SAM) – quantifies the effect of global conservation laws and is an important step toward a direct comparison between cumulants of conserved charges mea sured in central heavy ion collisions and theoretical calculations of gran d-canonical susceptibilities\, such as lattice QCD. We show that the globa l conservation effects cancel out in any ratio of two second order cumulan ts\, in any ratio of two third order cumulants\, as well as in a ratio of strongly intensive measures Σ and ∆ involving any two conserved charges \, making all these quantities particularly suitable for theory-to-experim ent comparisons in heavy-ion collisions. We also show that the same cancel lation occurs in correlators of a conserved charge\, like the electric cha rge\, with any non-conserved quantity such as net proton or net kaon numbe r. The main results of the SAM are illustrated in the framework of the had ron resonance gas model. We also elucidate how net-proton and net-Λ fluct uations are affected by conservation of electric charge and strangeness in addition to baryon number.\n\nhttps://indico.bitp.kiev.ua/event/7/contrib utions/172/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/172/ END:VEVENT BEGIN:VEVENT SUMMARY:Lambda spin polarization in QGP. DTSTART;VALUE=DATE-TIME:20201222T123000Z DTEND;VALUE=DATE-TIME:20201222T125000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-166@indico.bitp.kiev.ua DESCRIPTION:Speakers: Rajeev Singh (Institute of Nuclear Physics Polish Ac ademy of Sciences)\nMeasurements made recently by the STAR collaboration s how that the Lambda hyperons produced in relativistic heavy-ion collisions are subject to global spin polarization with respect to an axis coinciden t with the axis of rotation of the produced matter. Recently formulated fo rmalism of relativistic hydrodynamics with spin\, which is a generalizatio n of the standard hydrodynamics\, is a natural tool for describing the evo lution of such systems. This approach is based on the conservation laws an d the form of the energy-momentum tensor and spin tensor postulated by de Groot\, van Leeuwen\, and van Weert (GLW). Using Bjorken symmetry we show how this formalism may be used to determine observables describing the pol arization of particles measured in the experiment.\n\nhttps://indico.bitp. kiev.ua/event/7/contributions/166/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Dualities in QCD phase diagram DTSTART;VALUE=DATE-TIME:20201222T125000Z DTEND;VALUE=DATE-TIME:20201222T131000Z DTSTAMP;VALUE=DATE-TIME:20260316T195905Z UID:indico-contribution-27-180@indico.bitp.kiev.ua DESCRIPTION:Speakers: Roman Zhokhov (IZMIRAN\, Troitsk\, Moscow\; IHEP\, P rotvino)\nThe talk is devoted to QCD phase diagram studies\, including the region of large baryon density that will be probed at NICA.\nRecently it has been shown that in the large-Nc limit (Nc is the number of colors of q uarks) there exist duality correspondences (symmetries) in the phase portr ait\, which are the symmetries of the thermodynamic potential and the phas e structure itself. The first one is a duality between the chiral symmetry breaking and the charged pion condensation phenomena. And there are two o ther dualities that hold only for chiral symmetry breaking and charged pio n condensation phenomena separately. For example\, we have shown that char ged pion condensation does not feel the difference between chiral and isos pin imbalances of the medium. They were shown to exist in the matter with chiral imbalance that can be produced in compact stars or heavy ion collis ions. One of the key conclusions of these studies is the fact that chiral imbalance generates charged pion condensation in dense baryonic/quark matt er. It was shown that our results in particular cases are consistent with the simulation of lattice QCD\, which is possible in these cases.\nDuality was used to show that there takes place catalysis of chiral symmetry brea king by chiral imbalance.\nIt was also shown that chiral imbalance generat es the phenomenon of charged pion condensation in dense baryonic/quark mat ter even in the case of charge neutral matter\, which is interesting in th e context of the astrophysics of neutron stars.\nIt is known that chiral i mbalance can occur in high energy experiments of the collision of heavy io ns\, due to temperature and sphaleron transitions. Our studies show that d ifferent types of chiral imbalance can occur in the cores of neutron stars or in heavy ion experiments\, where large baryon densities can be reached \, due to another phenomena - the so-called chiral separation and chiral v ortical effects.\nDuality was shown to exist even in case of inhomogeneous condensates. This example shows that the duality is not just entertaining mathematical property but an instrument with very high predictivity power .\nThe unified picture and full phase diagram of isospin imbalanced dense quark matter have been assembled. Acting on this diagram by a dual transfo rmation\, we obtained\, in the framework of an approach with spatially inh omogeneous condensates and without any calculations\, a full phase diagram of chirally asymmetric dense medium.\nContinuing our studies of dualities \, we noted that there are dualities in 2-color QCD that are connected wit h adiitional symmetry of QCD with two colors namely Pauli-Gursey symmetry. \nIt has been also shown that found duality is a more fundamental and can be shown at the level of Lagrangian. It has been shown that duality is a p roperty of real QCD. It is not bounded by large Nc approximation and exist s in the cases of 2 and 3 and infinite number of colours.\n\nReferences:\n Phys.Rev. D95 (2017) no.10\, 105010\nPhys.Rev. D97 (2018) no.5\, 054036\nP hys.Rev. D98 (2018) no.5\, 054030\nEur.Phys.J. C79 (2019) no.2\, 151\nJHEP 1906 (2019) 006\nPhys. Rev. D 100\, 034009 (2019)\nJHEP 06 (2020) 148\nEu r.Phys.J.C 80 (2020) 10\, 995\n\nhttps://indico.bitp.kiev.ua/event/7/contr ibutions/180/ LOCATION:Online meeting URL:https://indico.bitp.kiev.ua/event/7/contributions/180/ END:VEVENT END:VCALENDAR