The spectrum of Image 1 exhibits exotic features, e.g., an intruder ground state and shape coexistence, normally associated with the breakdown of a shell closure. While previous phenomenological treatments indicated the ground state has substantial contributions from intruder configurations, it is only with advances in computational abilities and improved interactions that this intruder mixing is observed in ab initio no-core shell model (NCSM) predictions. In this work, we extract electromagnetic observables and symmetry decompositions from the NCSM wave functions to demonstrate that the low-lying positive parity spectrum can be explained in terms of mixing of rotational bands with very different intrinsic structure coexisting within the low-lying spectrum. These observed bands exhibit an approximate <math><mrow><mi>SU</mi></mrow><mo>(</mo><mn>3</mn><mo>)</mo></math> symmetry and are qualitatively consistent with Elliott model predictions.

United States

Anna E. McCoy

Mark A. Caprio

Pieter Maris

Patrick J. Fasano

Intruder band mixing in an Description of Be

The calculation of nuclear electromagnetic sum rules by directly solving for numerous eigenstates in a large basis is numerically challenging and has not been performed for <math><mi>A</mi><mo>&gt;</mo><mn>2</mn></math> nuclei. With the significant progress of high performance computing, we show that calculating sum rules using numerous discretized continuum states obtained with the ab initio no-core shell model in the harmonic oscillator basis is achievable numerically. Specifically, we calculate the $^{4}$He electric dipole (E1) polarizability, that is an inverse energy weighted sum rule, employing the Daejeon16 NN interaction. We demonstrate that the calculations are numerically tractable as the dimension of the basis increases and are convergent. Our results for the $^{4}$He electric dipole polarizability are consistent with the most recent experimental data and are compared with those of other theoretical studies employing different techniques and various interactions.

China

Peng Yin

Russia

Andrey M. Shirokov

He Li

Wei Zuo

James P. Vary

Direct Calculation of the He nuclear electric dipole polarizability

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant,  $$\alpha _s(Q^2)$$  <math> <mrow> <msub> <mi>α</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </math>  , that varies with the energy scale  $$Q^2$$  <math> <msup> <mi>Q</mi> <mn>2</mn> </msup> </math>   characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of  $$\alpha _s$$  <math> <msub> <mi>α</mi> <mi>s</mi> </msub> </math>   at low momentum transfers limits perturbative calculations to the high-energy region where  $$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$  <math> <mrow> <msup> <mi>Q</mi> <mn>2</mn> </msup> <mo>≫</mo> <msubsup> <mi>Λ</mi> <mrow> <mtext>QCD</mtext> </mrow> <mn>2</mn> </msubsup> <mo>≃</mo> </mrow> </math>   (250 MeV) $$^2$$  <math> <msup> <mrow></mrow> <mn>2</mn> </msup> </math>  . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large  $$N_c$$  <math> <msub> <mi>N</mi> <mi>c</mi> </msub> </math>  -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected  $$q{{\bar{q}}}$$  <math> <mrow> <mi>q</mi> <mover> <mrow> <mi>q</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson,  $$W^\pm $$  <math> <msup> <mi>W</mi> <mo>±</mo> </msup> </math>   or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

Franz Gross

Germany

Eberhard Klempt

Stanley Brodsky

Andrzej Buras

Volker Burkert

Gudrun Heinrich

Karl Jakobs

Curtis Meyer

Kostas Orginos

Michael Strickland

Johanna Stachel

Giulia Zanderighi

Nora Brambilla

Peter Braun-Munzinger

Daniel Britzger

Simon Capstick

Tom Cohen

Volker Crede

Martha Constantinou

United Kingdom

Christine Davies

Luigi Debbio

Achim Denig

Carleton DeTar

Alexandre Deur

Latvia

Yuri Dokshitzer

Hans Dosch

Jozef Dudek

Monica Dunford

Evgeny Epelbaum

Spain

Miguel Escobedo

Harald Fritzsch

Japan

Kenji Fukushima

Italy

Paolo Gambino

Canada

Sweden

Dag Gillberg

Steven Gottlieb

CERN

Per Grafstrom

Switzerland

Massimiliano Grazzini

Boris Grube

JINR

Alexey Guskov

Toru Iijima

Xiangdong Ji

Frithjof Karsch

Stefan Kluth

John Kogut

Frank Krauss

Shunzo Kumano

Australia

Derek Leinweber

Heinrich Leutwyler

Hai-Bo Li

Yang Li

France

Bogdan Malaescu

Chiara Mariotti

Simone Marzani

Wally Melnitchouk

Johan Messchendorp

Harvey Meyer

Ryan Mitchell

Chandan Mondal

Frank Nerling

Sebastian Neubert

Marco Pappagallo

Saori Pastore

José Peláez

Andrew Puckett

Jianwei Qiu

Klaus Rabbertz

Alberto Ramos

Patrizia Rossi

Azerbaijan

Anar Rustamov

Andreas Schäfer

Stefan Scherer

Matthias Schindler

Steven Schramm

Mikhail Shifman

Edward Shuryak

Torbjörn Sjöstrand

George Sterman

Iain Stewart

Joachim Stroth

Eric Swanson

Costa Rica

Guy Téramond

Ulrike Thoma

Antonio Vairo

Danny Dyk

James Vary

Javier Virto

Marcel Vos

Christian Weiss

Markus Wobisch

Sau Wu

Christopher Young

Feng Yuan

Xingbo Zhao

Xiaorong Zhou

50 Years of quantum chromodynamics

The lightest meson, the pion, features two faces – one is the elementary Goldstone boson of QCD and the other is the structured bound state of quarks and gluons. To accommodate both in a single light-front wave function in the valence space, we obtain a sum rule by analyzing the conserved axial-vector current and the general structures of the wave functions. Using an analytic model motivated by holography, we show this sum rule is consistent with requirements of chiral symmetry breaking in AdS/QCD. Within this model, we find a remarkable feature of the pion, namely that the density is mostly uniform inside its radius; furthermore, we obtain good agreement with the experimental pion form factor at spacelike momenta.

Chiral sum rule on the light front and the 3D image of the pion

We study the semileptonic decay of the <math><msub><mi>B</mi><mi>c</mi></msub><mo>(</mo><msup><mn>0</mn><mo>−</mo></msup><mo>)</mo></math> to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of <math><msub><mi>B</mi><mi>c</mi></msub></math> decaying into <math><msub><mi>η</mi><mi>c</mi></msub></math> or <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the <math><msup><msub><mi>η</mi><mi>c</mi></msub><mo>′</mo></msup></math> and the <math><msup><mi>ψ</mi><mo>′</mo></msup></math>. We observe unphysical frame dependence of the calculated form factors, which is attributed to only including the valence light-front wave functions. Based on the analysis of the current component, we propose a preferred set of frames to calculate these form factors.

Shuo Tang

Shaoyang Jia

Semileptonic decay of <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> to <math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> and <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> on the light front

We study the heavy-light mesons within basis light-front quantization. The resulting mass spectra of D, $$D_s$$ <math><msub><mi>D</mi><mi>s</mi></msub></math> , B, and $$B_s$$ <math><msub><mi>B</mi><mi>s</mi></msub></math>  agree reasonably well with experiments. We also predict states which could be measured in the near future. In the light-front formalism, we calculate the light-front wave functions and additional experimental observables, such as parton distribution functions, distribution amplitudes, and decay constants by means of integrations over light-front wave functions. We also provide ratios of decay constants for selected pseudoscalar meson decays ($$D_s$$ <math><msub><mi>D</mi><mi>s</mi></msub></math>  to D and $$B_s$$ <math><msub><mi>B</mi><mi>s</mi></msub></math>  to B) as they may prove to be theoretically more robust and more reliably determined in experiments. We find that our ratios are systematically smaller than existing experiments and other approaches by 5–18%.

Heavy-light mesons on the light front

We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wave functions of heavy quarkonia are obtained from the Basis Light-Front Quantization approach in a holographic basis. We study the transition form factor with both the traditional “good current” <math><msup><mi>J</mi><mo>+</mo></msup></math> and the transverse current <math><msub><mover><mi>J</mi><mo>→</mo></mover><mo>⊥</mo></msub></math> (in particular, <math><msup><mi>J</mi><mi>R</mi></msup><mo>=</mo><msup><mi>J</mi><mi>x</mi></msup><mo>+</mo><mi>i</mi><msup><mi>J</mi><mi>y</mi></msup></math>). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections (<math><msub><mi>m</mi><mi>j</mi></msub><mo>=</mo><mn>0</mn><mo>,</mo><mo>±</mo><mn>1</mn></math>). We use the <math><msub><mi>m</mi><mi>j</mi></msub><mo>=</mo><mn>0</mn></math> state of the vector meson to obtain the transition form factor, since this procedure employs the dominant spin components of the light-front wave functions and is more robust in practical calculations. While the <math><msub><mi>m</mi><mi>j</mi></msub><mo>=</mo><mo>±</mo><mn>1</mn></math> states are also examined, transition form factors depend on subdominant components of the light-front wave functions and are less robust. Transitions between states below the open-flavor thresholds are computed, including those for excited states. Comparisons are made with the experimental measurements, as well as with lattice QCD and quark model results. In addition, we apply the transverse current to calculate the decay constant of vector mesons where we obtain consistent results using either <math><msub><mi>m</mi><mi>j</mi></msub><mo>=</mo><mn>0</mn></math> or <math><msub><mi>m</mi><mi>j</mi></msub><mo>=</mo><mn>1</mn></math> light-front wave functions. This consistency provides evidence for features of rotational symmetry within the model.

Meijian Li

Radiative transitions between <math><msup><mn>0</mn><mrow><mo>−</mo><mo>+</mo></mrow></msup></math> and <math><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math> heavy quarkonia on the light front

In light-front dynamics, form factors are traditionally computed with the “good current” <math><mrow><msup><mrow><mi>J</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> within the Drell-Yan frame <math><mrow><msup><mrow><mi>q</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mn>0</mn></mrow></math>. Due to truncations imposed in practical calculations, the from factor may acquire frame dependence, which is often neglected. In this work, we explore the form factors in more general frames, preserving the boost covariance. We find the frame dependence of the elastic form factors for mesons is small in basis light-front holography and related models with two-body Fock space truncation. We suggest to use the difference between form factor results from Drell-Yan frame and the “longitudinal frame” as a metric for the violation of the Lorentz symmetry due to Fock space truncation.

Frame dependence of form factors in light-front dynamics

We present a theoretical study of the Maris polarization effect and its application in quasi-free reactions to assess information on the structure of exotic nuclei. In particular, we explore the dependence of the polarization effect on neutron excess and neutron-skin thickness. We discuss the uncertainties in the calculations of triple differential cross sections and of analyzing powers due the choices of various nucleon–nucleon interactions and optical potentials and the limitations of the method. Our study implies that polarization variables in (p, 2p) reactions in inverse kinematics can be an effective probe of single-particle structure of nuclei in radioactive-beam facilities.

 Shubhchintak

C.A. Bertulani

T. Aumann

Maris polarization in neutron-rich nuclei

In this work we compare mass spectra and decay constants obtained from two recent, independent, and fully relativistic approaches to the quarkonium bound-state problem: the Basis Light-Front Quantization approach, where light-front wave functions are naturally formulated; and, the Covariant Spectator Theory (CST), based on a reorganization of the Bethe–Salpeter equation. Even though conceptually different, both solutions are obtained in Minkowski space. Comparisons of decay constants for more than ten states of charmonium and bottomonium show favorable agreement between the two approaches as well as with experiment where available. We also apply the Brodsky–Huang–Lepage prescription to convert the CST amplitudes into functions of light-front variables. This provides an ideal opportunity to investigate the similarities and differences at the level of the wave functions. Several qualitative features are observed in remarkable agreement between the two approaches even for the rarely addressed excited states. Leading-twist distribution amplitudes as well as parton distribution functions of heavy quarkonia are also analyzed.