### Proceedings Series

#### Tensor Glueball in a Top–Down Holographic Approach to QCD

abstract

Properties of the tensor glueball are discussed in the Witten–Sakai–Sugimoto Model, a top–down holographic approach to the non-perturbative region of Quantum Chromodynamics (QCD).

#### The Role of the Kinematical Constraint and Non-linear Effects in the CCFM Equation

abstract

We report on recent study [M. Deak, K. Kutak, J. High Energy Phys. 1505, 068 (2015)] of the role of the kinematical constraint in the CCFM equation and its non-linear extension. We compare numerical results obtained by solving the CCFM equation and argue that kinematical constraint represents an important correction.

#### Ultra-relativistic Light–Heavy Nuclear Collisions and Collectivity

abstract

We briefly review highlights for ultra-relativistic light–heavy collisions ($p$–Pb, $d$–Au, $^3$He–Au, $^{12}$C–Au) which display collective evolution, with the same very characteristic features as in the $A$–$A$ systems.

#### A New Hydrodynamic Model Using an Exact Riemann Solver

abstract

Hydrodynamic modelling of quark–gluon plasma requires sophisticated numerical schemes that have low numerical viscosity and are able to cope with high gradients of energy density that may appear in initial conditions. We propose to use the Godunov method with an exact Riemann solver for ideal hydrodynamic modelling to meet these conditions. We present the results of numerical tests of the method, such as the sound wave propagation and the shock tube problem, which show both high precision of the method and low numerical viscosity.

#### The Latest STAR Results on Quarkonium Production

abstract

We report the latest results of $J/\psi$, $\psi (2S)$ and ${\mit \Upsilon }$ production in the dielectron decay channel at mid-rapidity from the STAR experiment. We present $J/\psi$ cross section measurements in $p+p$ collisions at $\sqrt {s} = 200$ and 500 GeV, as well as the first measurement of the $\psi (2S)$ to $J/\psi$ ratio at $\sqrt {s} = 500$ GeV. We also show $J/\psi$ and ${\mit \Upsilon }$ production in heavy ion collisions: $J/\psi$ nuclear modification factors ($R_{AA}$) in Au+Au collisions at $\sqrt {s_{NN}} =$ 200, 62.4 and 39 GeV and in U+U collisions at $\sqrt {s_{NN}} =$ 193 GeV, ${\mit \Upsilon }$ $R_{AA}$ in $d+$Au, Au+Au and U+U collisions at $\sqrt {s_{NN}} =$ 200, 200 and 193 GeV, respectively. The results are compared to different model calculations.

#### Unquenching the Three-gluon Vertex: A Status Report

abstract

We discuss unquenching of the three-gluon vertex via its Dyson–Schwinger equation. We review the role of Furry’s theorem and present first results for the quark triangle diagrams using non-perturbatively calculated dressing functions for the quark propagator and the quark–gluon vertex.

#### Hydrodynamics of QCD

abstract

I briefly review the use of hydrodynamics to model heavy-ion collisions at ultrarelativistic energies, and what such modelling has taught us about the properties of QCD matter.

#### Chiral Phase Transition Scenarios from the Vector Meson Extended Polyakov Quark Meson Model

abstract

Chiral phase transition is investigated in an SU$(3)_{\rm L} \times {\rm SU}(3)_{\rm R}$ symmetric vector meson extended linear sigma model with additional constituent quarks and Polyakov loops (extended Polyakov quark meson model). The parameterization of the Lagrangian is done at zero temperature in a hybrid approach, where the mesons are treated at tree-level, while the constituent quarks at 1-loop level. The temperature and baryochemical potential dependence of the two assumed scalar condensates are calculated from the hybrid 1-loop level equations of states. The order of the phase transition along the $T=0$ and $\mu _{\rm B}=0$ axes is determined for various parameterization scenarios. We find that for a first order phase transition at $T=0$ as a function of $\mu _{\rm B}$, a light isoscalar particle is needed.

abstract

I discuss photon production from the Glasma. In particular, I outline the consequences of a power law tail in the distributions of quarks and gluons for the photon production rates and for the times scales of evolution within the Glasma.

#### The Anomalous Magnetic Moment of the Muon and Lattice QCD

abstract

The anomalous magnetic moment of the muon, defined as the fractional difference of its gyromagnetic ratio from the naive value of 2, has been measured with an impressive accuracy of 0.54 parts per million in experiment (BNL E821), thus providing one of the most stringent tests of the Standard Model. Intriguingly, the experimentally measured anomaly disagrees by around 3.6 standard deviations with the calculated value from the Standard Model. The current theoretical uncertainty is dominated by that from the calculation of the QCD contribution — lowest order “hadronic vacuum polarization (HVP)” and the “hadronic light-by-light (HLBL)” diagrams. Improvements in the experimental uncertainty by a factor of 4 in the upcoming experiment at Fermilab (E989) are expected and improvements in the theoretical determination would make the discrepancy (if it remains) really compelling in trying to ascertain the possibility of new physics beyond the Standard Model. I will review the current status of the lattice calculation of the HVP and HLBL contributions with a particular emphasis on the recent progress in the HVP using our (HPQCD) new lattice QCD method [B. Chakraborty et al., Phys. Rev. D 89, 114501 (2014)].

#### Universal Hard-loop Actions

abstract

The effective actions of gauge bosons, fermions and scalars, which are obtained within the hard-loop approximation, are shown to have unique forms for a whole class of gauge theories including QED, scalar QED, super QED, pure Yang–Mills, QCD, super Yang–Mills. The universality occurs irrespective of a field content of each theory and of variety of specific interactions. Consequently, the long-wavelength or semiclassical features of plasma systems governed by these theories such as collective excitations are almost identical. An origin of the universality, which holds within the limits of applicability of the hard-loop approach, is discussed.

#### Refined Lattice/Model Investigation of $u d \bar {b} \bar {b}$ Tetraquark Candidates with Heavy Spin Effects Taken into Account

abstract

We investigate four-quark systems consisting of two heavy anti-bottom quarks and two light up/down quarks. We propose to solve a coupled Schrödinger equation for the anti-bottom–anti-bottom separation using potentials computed via lattice QCD in the limit of static anti-bottom quarks. This coupled Schrödinger equation allows to incorporate effects due to the heavy anti-bottom spins. First exploratory numerical tests are discussed.

#### Scalar Meson $f_0(500)$ from the Analysis of Pion Scalar Form Factor and the Correct $S$-wave Iso-scalar $\pi \pi$ Phase Shift Data

abstract

In the recently elaborated fully solvable mathematical problem, to be concerned of a finding of an explicit form of the pion scalar form factor, the inaccurate experimental information on the $S$-wave iso-scalar $\pi \pi$-scattering phase shift in the elastic region is replaced by the data with theoretical errors to be generated by the Garcia-Martin–Kaminski–Pelaéz–Yndurain Roy-like equations and, as a result, the correct values $m_\sigma =(472\pm 10)$ MeV and ${\mit \Gamma }_\sigma =(524\pm 22)$ MeV of the scalar meson $f_0(500)$ parameters are determined.

#### The $\pi \pi$-Scattering Amplitude and the $\sigma$ Pole

abstract

The multichannel amplitudes used in the analysis of the $\pi \pi$-scattering data and in the description of final-state interaction effects in heavy-meson decays predict too broad and heavy $\sigma$ meson ($f_0$(500) resonance) which is in disagreement with results from other, especially recent, analyses. The amplitudes are constructed using a uniformizing variable and proper analytical continuation of the S-matrix elements but the crossing symmetry constraint, important in the $S$-wave, is not included. We modified, therefore, the amplitudes using the dispersion relations with imposed crossing symmetry (GKPY equations). We also examined the multichannel formalism comparing the single- and two-channel analyses of the $\pi \pi$-scattering data. After the modification and in the single-channel analysis, the $\sigma$ pole acquired values within the limits accepted in the Particle Data Tables.

#### Is Space-time Euclidean “Inside” Hadrons?

abstract

Solution of Schwinger–Dyson and Bethe–Salpeter equations for excited mesons in Minkowski space in the ladder-rainbow approximation is presented. The invalidity of Wick rotation, which historically raised the question, does not prevent the existence of solution in the physical Minkowski space. No analytical continuation in complex Euclidean spacetime was needed in the presented model.

#### Simulations at Fixed Topology: Fixed Topology Versus Ordinary Finite Volume Corrections

abstract

Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing, or when using chirally symmetric quarks. In such cases, computed observables differ from their full QCD counterparts by finite volume corrections, which need to be understood on a quantitative level. We extend a known relation from the literature between hadron masses at fixed and at unfixed topology by incorporating, in addition to topological finite volume effects, also ordinary finite volume effects. We present numerical results for SU(2) Yang–Mills theory.

#### Saturation and Geometrical Scaling: from Deep Inelastic $ep$ Scattering to Heavy Ion Collisions

abstract

Saturation of gluon distribution is a consequence of the non-linear evolution equations of QCD. Saturation implies the existence of the so-called saturation momentum which is defined as a gluon density per unit rapidity per transverse area. At large energies, for certain kinematical domains, saturation momentum is the only scale for physical processes. As a consequence, different observables exhibit geometrical scaling (GS). We discuss a number of examples of GS in different reactions.

all authors

G. Aarts, F. Attanasio, Benjamin Jäger, E. Seiler, D. Sexty, I.-O. Stamatescu

#### The Phase Diagram of Heavy Dense QCD with Complex Langevin Simulations

abstract

The sign problem of QCD prevents standard lattice simulations to determine the phase diagram of strong interactions with a finite chemical potential directly. Complex Langevin simulations provide an alternative method to sample path integrals with complex weights. We report on our ongoing project to determine the phase diagram of QCD in the limit of heavy quarks (HDQCD) using Complex Langevin simulations.

#### Heavy Quarks at the LHC

abstract

Ultra-relativistic collisions of heavy ions allow studying strongly interacting matter at extreme energy densities and temperatures. Quantum Chromodynamics predicts that at such conditions normal, hadronic matter turns into a plasma of deconfined quarks and gluons, which are the constituents of atomic nuclei. In cosmology, it is believed that matter in the early universe must have existed in this Quark–Gluon Plasma (QGP) state within the first microseconds after the Big Bang. After the compelling evidence for the existence of the QGP from the previous heavy-ion accelerators SPS and RHIC, the Large Hadron Collider (LHC) at CERN marks the beginning of the exploration of the QGP properties. In this contribution, I will present an overview of the recent heavy-flavour results from the LHC and discuss them in relation to the previous findings.

#### $\pi \eta$ Photoproduction on the Nucleon

abstract

We calculate the amplitude of the $\pi \eta$ photoproduction on the proton and the associated cross sections. The primary objective of the model is to describe the photoproduction of the isovector resonances in the $\pi \eta$ channel which is important in the context of elucidating the nature of the scalar $a_0(980)$ meson. The model can be also applied to description of the photoproduction of tensor isovector resonance $a_2(1320)$.

#### Tetraquarks from the Bethe–Salpeter Equation

abstract

We present a numerical solution of the four-quark Bethe–Salpeter equation for a scalar tetraquark. We find that the four-body equation dynamically generates pseudoscalar poles in the Bethe–Salpeter amplitude. The sensitivity to the pion poles leads to a light isoscalar tetraquark mass $M_\sigma \sim 400$ MeV, which is comparable to that of the $\sigma /f_0(500)$. The masses of its multiplet partners $\kappa$ and $a_0/f_0$ follow a similar pattern, thereby providing support for the tetraquark interpretation of the light scalar nonet.

#### Flow Anisotropies Due to Momentum Deposition From Hard Partons

abstract

In nuclear collisions at the LHC, a large number of hard partons is created in the initial partonic interactions, so that it is reasonable to suppose that they do not thermalise immediately but deposit their energy and momentum later into the evolving hot quark–gluon fluid. We show that this mechanism leads to contribution to flow anisotropies at all orders which are non-negligible and should be taken into account in realistic simulations.

#### Quark Properties from the Hadron Resonance Gas

abstract

We show how the quark free energy can be determined from a string and the Hadron Resonance Gas model with one heavy quark below the de-confinement phase transition. We discuss the interesting problem of identification of degrees of freedom at increasing temperatures, as well as the relevance of string breaking and avoided crossings.

#### Dilepton Production from the Quark–Gluon Plasma Using Leading-order $(3+1)$D Anisotropic Hydrodynamics

abstract

Dilepton production from the quark–gluon plasma (QGP) phase of ultra-relativistic heavy-ion collisions is computed using the leading-order (3+1)-dimensional anisotropic hydrodynamics. It is shown that high-energy dilepton spectrum is sensitive to the initial local-rest-frame momentum-space anisotropy of the QGP. Our findings suggest that it may be possible to constrain the early-time momentum-space anisotropy in relativistic heavy-ion collisions using high-energy dilepton yields.

#### Towards a Consistent Description of In-medium Parton Branching

abstract

Ultra-relativistic heavy-ion collisions are a window of opportunity to study QCD matter under extreme conditions of temperature and density, such as the quark–gluon plasma. Among the several possibilities, the study of jet quenching — generic name given to in-medium energy loss modifications of the parton branching — is a powerful tool to assess the properties of this new state of matter. The description of the parton shower is very well understood in vacuum (controlled reference), and medium-induced modifications of this process can be experimentally accessed through jet measurements. Current experimental data, however, cannot be entirely described with only energy loss phenomena. Transverse momentum broadening and decoherence effects, both theoretically established by now and their interplay, are essential to build a consistent picture of the medium-modifications of the parton branching and to achieve a correct description of the current experimental data. In this write-up, we will present the latest developments that address such unified description.

#### Latest Results on Anisotropy in $p$Pb and PbPb Collisions from CMS

abstract

In this paper, we present some of the heavy-ion results from CMS, restricting to anisotropic particle emission. Consistency between the results obtained using four-, six- and eight-particle correlations as well as the Lee–Yang zero method reveals a multi-particle nature of the long-range correlations observed in $p$Pb collisions. By correlating an identified strange hadron ($K^{0}_{\rm S}$ or ${\mit \Lambda }$/$\bar {\mit \Lambda }$) with a charged particle at large relative pseudorapidity, the magnitude of the elliptic and triangular flow of strange particles from both $p$Pb and PbPb collisions have been extracted. The results for $K^{0}_{\rm S}$ and ${\mit \Lambda }$/$\bar {\mit \Lambda }$ scaled by the number of constituent quarks as a function of transverse kinetic energy per quark are in a mutual agreement (within 10%) for both $v_{2}$ and $v_{3}$ over a wide range of particle transverse kinetic energy and event multiplicities. Due to the initial-state fluctuations, the event-plane angle depends on both, transverse momentum ($p_{\rm T}$) and pseudorapidity ($\eta$), which consequently induce breaking of the factorization of the two-particle azimuthal anisotropy into a product of single-particle anisotropies. For $p_{\rm T}$, the maximal effect of factorization breaking of about 20% is observed in ultra-central PbPb collisions. For $\eta$, the effect is weakest for mid-central PbPb events and gets larger for more central or peripheral PbPb collisions as well as for high multiplicity $p$Pb collisions. The experimental results are consistent with recent hydrodynamic predictions in which the factorization breakdown effect is incorporated. It is found that the effect is mainly sensitive to the initial-state conditions rather than the shear viscosity of the medium.

#### Different Kinds of Light Mesons at Large $N_{\rm c}$

abstract

In this paper, we review the leading $1/N_{\rm c}$ behavior of different configurations of light mesons. Recently, we studied not just the usual configurations with a fixed number of constituents, like $q \bar q$, tetraquark, molecules, gluonia and $\bar qq g$, but also the so-called “polyquark” which is the natural generalization to large $N_{\rm c}$ of the diquark–antidiquark configuration, whose number of constituents grows with $N_{\rm c}$. With the exception of this polyquark, which has an $O(1)$ width in the large-$N_{\rm c}$ limit, all other configurations have a vanishing width at large $N_{\rm c}$.

#### Deconfinement in Dense (Two-color) Matter

abstract

I review our current understanding of the phase diagram of two-color quark matter with emphasis on the comparison of model and lattice results. Reproducing, even qualitatively, the thermodynamic observables measured on the lattice requires augmenting the standard Polyakov loop Nambu–Jona-Lasinio model with two new elements: explicit chiral symmetry breaking in the contact interaction, and renormalization of the Polyakov loop.

#### Latest Developments in Anisotropic Hydrodynamics

abstract

We discuss the leading order of anisotropic hydrodynamics expansion. It has already been shown that in the (0+1)- and (1+1)-dimensional cases it is consistent with the second-order viscous hydrodynamics, and it provides a striking agreement with the exact solutions of the Boltzmann equation. Quite recently, a new set of equations has been proposed for the leading order of anisotropic hydrodynamics, which is consistent with the second-order viscous hydrodynamics in the most general (3+1)-dimensional case, and does not require a next-to-leading treatment for describing pressure anisotropies in the transverse plane.

#### A Short Review of Some Double-parton Scattering Processes

abstract

A few examples of quickly developing field of double-parton scattering are discussed. We present arguments that the production of two pairs of charm quark–antiquark is the golden reaction to study the double-parton scattering effects. We also discuss briefly a mechanism of single-parton scattering and show that it gives much smaller contribution to the $c \bar c c \bar c$ final state. In this context, we also discuss the contribution of perturbative parton-splitting mechanism which should also be added to the conventional DPS mechanism. The presence of the latter, leads to collision energy and other kinematical variables dependence of the so-called $\sigma _{\rm eff}$. We briefly discuss the production of four jets. We concentrate on estimation of the contribution of DPS for jets widely separated in rapidity. Finally, we briefly mention about DPS effects in production of $W^+ W^-$.

#### Probing QCD at HERA

abstract

The most recent measurements from $ep$ collisions at HERA probing and constraining QCD are presented. Final measurements of inclusive deep inelastic scattering (DIS) by H1 and ZEUS collaborations have been combined for neutral and charged current unpolarised $e^{\pm }p$ cross sections at proton beam energies of 920, 820, 575 and 460 GeV. The combined data correspond to a luminosity of about 1 fb$^{-1}$ and span six orders of magnitude in momentum transfer squared, $Q^{2}$, and Bjorken $x$. It has been used as an input to QCD analyses at LO, NLO and NNLO to determine preliminary versions of new sets of parton distribution functions — HERAPDF2.0 (prel.). The structure of the proton is also constrained through measurements of heavy-quark production which are sensitive to the gluon and heavy-quark content of the proton. The HERA data on charm production in DIS have recently been combined and used differentially as a function of $Q^{2}$ to evaluate the charm quark running mass at different scales to one-loop order. The running beauty-quark mass, $m_{b}$, at the scale $m_{b}$, was determined from a QCD fit at next-to-leading order for the first time at HERA data. High-precision inclusive jet, dijet and trijet differential cross sections have been measured in neutral current DIS and used to determine the value of strong coupling constant and running of the coupling in QCD fit.

#### On Dyson–Schwinger Studies of Yang–Mills Theory and the Four-gluon Vertex

abstract

We review the status of calculations of Yang–Mills Green functions from Dyson–Schwinger equations. The role of truncations is discussed and results for the four-gluon vertex are presented.

#### Hadron Spectroscopy with CLAS and CLAS12

abstract

The CLAS detector completed a highly successful data-taking lifetime in 2012. The mass range accessible with the CEBAF 6 GeV electron beam and the large solid angle of the detector made it the premier facility for studying baryon resonances. The analysis of a great number of final states with differing polarization states is underway and will lead to a greater understanding of the existing nucleon resonances. In the meantime, preparation for an upgraded detector, CLAS12, is progressing. With commissioning due to start in 2016 with a 11 GeV electron beam CLAS12 will kinematically favour the study of mesons. In particular, it will look to resolve outstanding questions as to the make-up of mesonic states in terms of hybrid states with gluonic constituents; states of pure glue; or tetraquark/molecular configurations.

#### Center Vortex Versus Abelian Models of the QCD Vacuum

abstract

We present evidence that the center vortex model of confinement is more consistent with lattice results than other currently available models.

#### The Effects of Scalar Mesons in a Skyrme Model

abstract

We study the effects of scalar mesons on skyrmion properties by using a mesonic model including a two- and four-quark scalar mesons as well as the pion, rho and omega mesons in a framework of the hidden local symmetry. We show that the scalar mesons reduce the skyrmion mass and the lighter two-quark state scalar meson is, the lighter soliton mass becomes. In addition, we find the lighter soliton for the more two-quark component of the lighter scalar $f_{500}$. When vector meson mass partially comes from chiral condensate, the smaller chiral invariant vector meson mass is, the larger soliton mass becomes. In addition to the soliton mass, we study the scalar meson effect on the energy and charge radii.

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