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We study spatial isovector J = 1 meson correlators in nf = 2 QCD with dynamical domain-wall fermions on 323 × 8 lattices at temperatures T = 220–380 MeV. We observe an approximate degeneracy of all considered correlators with increasing temperature. This approximate degeneracy suggests emergent SU(2)CS and SU(2nf) symmetries at high temperatures, that mix left- and right-handed quarks. Since these symmetries are symmetries of the chromo-electric interaction in QCD we conclude that at 2Tc temperature the elementary objects are quarks with a definite chirality connected by the chromo-electric field.

Above the pseudocritical temperature T_c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined., Comment: 6 pages, 5 figures. A new figure has been added and discussion that clarifies the main point of the paper has been expanded. Accepted by EPJA

Based on a complete set of $J = 0$ and $J=1$ spatial isovector correlation functions calculated with $N_F = 2$ domain wall fermions we identify an intermediate temperature regime of $T \sim 220 - 500$ MeV ($1.2T_c$--$2.8T_c$), where chiral symmetry is restored but the correlators are not yet compatible with a simple free quark behavior. More specifically, in the temperature range $T \sim 220 - 500$ MeV we identify a multiplet structure of spatial correlators that suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmetries, which are not symmetries of the free Dirac action. The symmetry breaking effects in this temperature range are less than 5%. Our results indicate that at these temperatures the chromo-magnetic interaction is suppressed and the elementary degrees of freedom are chirally symmetric quarks bound into color-singlet objects by the chromo-electric component of the gluon field. At temperatures between 500 and 660 MeV the emergent $SU(2)_{CS}$ and $SU(4)$ symmetries disappear and one observes a smooth transition to the regime above $T \sim 1$ GeV where only chiral symmetries survive, which are finally compatible with quasi-free quarks., A new figure and discussion added. Accepted for publication in PRD

Truncating the low-lying modes of the lattice Dirac operator results in an emergence of the chiral-spin symmetry $SU(2)_{CS}$ and its flavor extension $SU(2N_F)$ in hadrons. These are symmetries of the quark - chromo-electric interaction and include chiral symmetries as subgroups. Hence the quark - chromo-magnetic interaction, which breaks both symmetries, is located at least predominantly in the near - zero modes. Using as a tool the expansion of propagators into eigenmodes of the Dirac operator we here analytically study effects of a gap in the eigenmode spectrum on baryon correlators. We find that both $U(1)_A$ and $SU(2)_L \times SU(2)_R$ emerge automatically if there is a gap around zero. Emergence of larger $SU(2)_{CS}$ and $SU(4)$ symmetries requires in addition a microscopical dynamical input about the higher-lying modes and their symmetry structure., Comment: Accepted by PRD

Properties of QCD matter change significantly around the chiral crossover temperature, and the effects on $U(1)_A$ and topological susceptibilities, as well as the meson spectrum have been studied with much care. Baryons and the effect of parity doubling in this temperature range have been analyzed previously by various other groups employing different setups. Here we construct suitable operators to investigate chiral and axial $U(1)_A$ symmetries in the baryon spectrum. Measurements for different volumes and quark-masses are done with two flavors of chirally symmetric domain-wall fermions at temperatures above the critical one. The possibility of emergent $SU(4)$ and $SU(2)_{CS}$ symmetries is discussed., Comment: 7 pages, 4 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China. Updated numerical data in Fig. 1 and Fig. 2

We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: What is needed to understand the physics of resonances in QCD? Where does QCD lead us to expect resonances with exotic quantum numbers? What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with ${\it up}$, ${\it down}$ and ${\it strange}$ quark content were considered. For heavy-light and heavy-heavy meson systems, those with ${\it charm}$ quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here., Comment: 20 pages, 1 figure, report on the EMMI Rapid Reaction Task Force meeting '{\it Resonances in QCD}', which took place at GSI October 12-14, 2015

In situations where the low lying eigenmodes of the Dirac operator are suppressed one observed degeneracies of some meson masses. Based on these results a hidden symmetry was conjectured, which is not a symmetry of the Lagrangian but emerges in the quantization process. We show here how the difference between classes of meson propagators is governed by the low modes and shrinks when they disappear., 9 pages, 3 figures; final version, accepted at Phys.Rev.D

We present a lattice QCD study of the puzzling positive-parity nucleon channel, where the Roper resonance $N^*(1440)$ resides in experiment. The study is based on an ensemble of gauge configurations with $N_f=2+1$ Wilson-clover fermions with a pion mass of $156$ MeV and lattice size $L=2.9$ fm. We use several $qqq$ interpolating fields combined with $N\pi$ and $N\sigma$ two-hadron operators in calculating the energy spectrum in the rest frame. Combining experimental $N\pi$ phase shifts with elastic approximation and the L\"uscher formalism suggests in the spectrum an additional energy level near the Roper mass $m_R=1.43$ GeV for our lattice. We do not observe any such additional energy level, which implies that $N\pi$ elastic scattering alone does not render a low-lying Roper resonance. The current status indicates that the $N^*(1440)$ might arise as dynamically generated resonance from coupling to other channels, most notably the $N\pi\pi$., Comment: updated references

We present results from our recent lattice QCD study of $N\pi$ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance $N^*(1440)$ resides in experiment. Using a variety of hadron operators, that include $qqq$-like, $N\pi$ in $p$-wave and $N\sigma$ in $s$-wave, we systematically extract the excited lattice spectrum in the nucleon channel up to 1.65 GeV. Our lattice results indicate that N$\pi$ scattering in the elastic approximation alone does not describe a low-lying Roper. Coupled channel effects between $N\pi$ and $N\pi\pi$ seem to be crucial to render a low-lying Roper in experiment, reinforcing the notion that this state could be a dynamically generated resonance. After giving a brief motivation for studying the Roper channel and the relevant technical details to this study, we will discuss the results and the conclusions based on our lattice investigation and in comparison with other lattice calculations., Comment: 8 pages, 5 figures, presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with increasing temperature. This approximate degeneracy suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmeries at high temperatures, that mix left- and right-handed quarks., This revised version contains all corrections that will appear in the forthcoming erratum

We present a lattice QCD study of $N\pi$ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance $N^*(1440)$ resides in experiment. The study is based on the PACS-CS ensemble of gauge configurations with $N_f=2+1$ Wilson-clover dynamical fermions, $m_\pi \simeq 156~$MeV and $L\simeq 2.9~$fm. In addition to a number of $qqq$ interpolating fields, we implement operators for $N\pi$ in $p$-wave and $N\sigma$ in $s$-wave. In the center-of-momentum frame we find three eigenstates below 1.65 GeV. They are dominated by $N(0)$, $N(0)\pi(0)\pi(0)$ (mixed with $N(0)\sigma(0)$) and $N(p)\pi(-p)$ with $p\simeq 2\pi/L$, where momenta are given in parentheses. This is the first simulation where the expected multi-hadron states are found in this channel. The experimental $N\pi$ phase-shift would -- in the approximation of purely elastic $N\pi$ scattering -- imply an additional eigenstate near the Roper mass $m_R\simeq 1.43~$GeV for our lattice size. We do not observe any such additional eigenstate, which indicates that $N\pi$ elastic scattering alone does not render a low-lying Roper. Coupling with other channels, most notably with $N\pi\pi$, seems to be important for generating the Roper resonance, reinforcing the notion that this state could be a dynamically generated resonance. Our results are in line with most of previous lattice studies based just on $qqq$ interpolators, that did not find a Roper eigenstate below $1.65~$GeV. The study of the coupled-channel scattering including a three-particle decay $N\pi\pi$ remains a challenge., Comment: 14 pages, 9 figures, version published in Phys. Rev. D plus additional footnote and reference

Operators for simulating the scattering of two particles with spin are constructed. Three methods are shown to give the consistent lattice operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar meson, vector meson and nucleon. The projection method leads to one or several operators $O_{\Gamma,r,n}$ that transform according to a given irreducible representation $\Gamma$ and row r. However, it gives little guidance on which continuum quantum numbers of total J, spin S, orbital momentum L or single-particle helicities $\lambda_{1,2}$ will be related with a given operator. This is remedied with the helicity and partial-wave methods. There first the operators with good continuum quantum numbers $(J,P,\lambda_{1,2})$ or $(J,L,S)$ are constructed and then subduced to the irreps $\Gamma$ of the discrete lattice group. The results indicate which linear combinations $O_{\Gamma,r,n}$ of various n have to be employed in the simulations in order to enhance couplings to the states with desired continuum quantum numbers. The total momentum of two hadrons is restricted to zero since parity P is a good quantum number in this case., Comment: 7 pages, talk presented at the 34th International Symposium on Lattice Field Theory, 24-30 July 2016, Southampton, UK

We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case., 29 pages, updated to match the version published by JHEP. The relation between partial-wave and helicity operators is now provided (Eq. 4.13) and proved (Appendix D). Discussions on the applicability of the constructed operators and higher partial-waves have been extended

Working with a pion mass ${m}_{\ensuremath{\pi}}\ensuremath{\approx}150\text{ }\text{ }\mathrm{MeV}$, we study $\ensuremath{\pi}\ensuremath{\pi}$ and $K\ensuremath{\pi}$ scattering using two flavors of nonperturbatively improved Wilson fermions at a lattice spacing $a\ensuremath{\approx}0.071\text{ }\text{ }\mathrm{fm}$. Employing two lattice volumes with linear spatial extents of ${N}_{s}=48$ and ${N}_{s}=64$ points and moving frames, we extract the phase shifts for $p$-wave $\ensuremath{\pi}\ensuremath{\pi}$ and $K\ensuremath{\pi}$ scattering near the $\ensuremath{\rho}$ and ${K}^{*}$ resonances. Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}$ appears to be remarkably constant as a function of ${m}_{\ensuremath{\pi}}$.

Wir haben (in den Kap. –9) schon mehrmals darauf hingewiesen, dass man mit Hilfe von Differenzialformen vor allem die allgemeinen Aussagen wie zum Beispiel die Integralsatze auf eine sehr fundamentale Art darstellen kann. Hier wollen wir zumindest den Appetit fur diese Betrachtungsweise anregen – das wird naturlich eher eine Vorspeise als ein 5-gangiges Mahl. Aber wir werden tolle Vereinfachungen ableiten, zum Beispiel eine gemeinsame Formulierung fur die schon betrachteten Differenzialoperatoren \(\mathop{\mathrm{grad}}\nolimits\), \(\mathop{\mathrm{div}}\nolimits\) und \(\mathop{\mathrm{rot}}\nolimits\) sowie fur beide Poincare-Lemmas und die Integralsatze! Allerdings mussen wir anfangs etwas Formalismus in Kauf nehmen, bevor wir zum „Eingemachten“ kommen.

Lattice calculations for hadrons are now entering the domain of resonances and scattering, necessitating a better understanding of the observed discrete energy spectrum. This is a reviewing survey about recent lattice QCD results, with some emphasis on spectrum and scattering., Invited talk at the XVI International Conference on Hadron Spectroscopy September 13-18, 2015, Newport News

Tensoren sind Grosen, mit deren Hilfe man Skalare, Vektoren und weitere Grosen analoger Struktur in ein einheitliches Schema zur Beschreibung mathematischer und physikalischer Zusammenhange einordnen kann. Tensoren sind durch ihre Transformationseigenschaften gegenuber orthogonalen Transformationen (wie etwa Drehungen) definiert. Daher ist das Thema fur die Physik sehr wichtig: Was andert sich und was andert sich nicht, wenn man das Bezugssystem dreht?

Wir haben bereits verschiedene Koordinatensysteme im \(\mathbb{R}^{\scriptstyle 3}\) verwendet: $$\begin{array}[]{ll}x_{1},x_{2},x_{3}&\displaystyle\ldots\textrm{kartesische Koordinaten}\;,\\ \rho\;,\varphi\;,x_{3}&\displaystyle\ldots\textrm{Zylinderkoordinaten}\;,\\ r\;,\varphi\;,\vartheta&\displaystyle\ldots\textrm{Kugelkoordinaten}\;.\end{array}$$ (8.1) Man kann sich im Prinzip beliebig viele Koordinatensysteme ausdenken. Es sind nur nicht alle gleich brauchbar. Besonders angenehme Eigenschaften haben die so genannten orthogonalen Koordinatensysteme. Um deren wesentliche Aspekte zu erlautern, schreiben wir die kartesischen Koordinaten x i als Funktionen anderer Koordinaten u i , $$x_{1}=x_{1}(u_{1},u_{2},u_{3})\;,\quad{}x_{2}=x_{2}(u_{1},u_{2},u_{3})\;,\quad{}x_{3}=x_{3}(u_{1},u_{2},u_{3})\;.$$ (8.2) Dieses Gleichungssystem ist nach den u i auflosbar, wenn die Funktional- oder Jacobi-Determinante (siehe auch Abschn. 5.4.1 und Mathematik-Box 9) ungleich null ist, $$\left|\begin{matrix}\displaystyle\frac{\partial x_{1}}{\partial u_{1}}&\displaystyle\frac{\partial x_{2}}{\partial u_{1}}&\displaystyle\frac{\partial x_{3}}{\partial u_{1}}\cr\displaystyle\frac{\partial x_{1}}{\partial u_{2}}&\displaystyle\frac{\partial x_{2}}{\partial u_{2}}&\displaystyle\frac{\partial x_{3}}{\partial u_{2}}\cr\displaystyle\frac{\partial x_{1}}{\partial u_{3}}&\displaystyle\frac{\partial x_{2}}{\partial u_{3}}&\displaystyle\frac{\partial x_{3}}{\partial u_{3}}\end{matrix}\right|={\partial(x_{1},x_{2},x_{3})\over\partial(u_{1},u_{2},u_{3})}\neq 0\;.$$ (8.3) Mit (8.2) kann man Kurvenscharen bilden, indem man jeweils zwei der Koordinaten festhalt und die dritte als variablen Kurvenparameter betrachtet, der den Kurvenverlauf beschreibt, Dadurch entstehen Koordinatenlinien (vgl. Abschn. ), die in diesem Fall durch den Raumpunkt laufen. Wenn sich diese paarweise unter einem rechten Winkel schneiden, spricht man von oder . Wenn zwei davon parallel (in dem Punkt tangential) zueinander sind, so sind zwei Zeilen der Jacobi-Determinante gleich und diese verschwindet. Dann ist die Koordinatentransformation in diesem Punkt nicht umkehrbar!

Ein lineares Gleichungssystem (kurz: LGS) besteht aus einem Satz von Gleichungen, die alle linear in den Unbekannten sind. Wenn es insgesamt n verschiedene Variablen gibt, dann definiert jede dieser Gleichungen eine Ebene im \(\mathbb{R}^{\scriptstyle n}\) (beziehungsweise eine Gerade, wenn es sich um den \(\mathbb{R}^{\scriptstyle 2}\) handelt). Die Menge der Punkte, die alle Gleichungen erfullen, kann leer sein (parallele Ebenen oder Geraden), nur aus einem Punkt bestehen („die Losung“, Punktlosung), oder eine Gerade oder auch eine Ebene im \(\mathbb{R}^{\scriptstyle n}\) sein. Die Struktur der Losungs- oder Schnittmenge hangt von der Zahl und Art der linearen Gleichungen ab. Wir wollen allgemeine, algebraische Methoden besprechen, um diese Losungsmengen zu identifizieren.

From the parton distributions in the infinite momentum frame one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term "spin crisis". Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal $\bar q q$ chiral basis and a unitary transformation from the chiral basis to the (2S+1)LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson we measure in dynamical lattice simulations a ratio of couplings of interpolarors with different chiral structure. For the rho meson we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?, Comment: 7 pp, Presented at Int. School of Nuclear Physics: "From Quarks and Gluons to Hadrons and Nuclei", Erice-Sicily, 16 - 24 September, 2011

Using interpolators with different SU(2)_L \times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho'-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $\qbar\gamma^i{\tau}q$ and $\qbar\sigma^{0i}{\tau}q$ interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ~1 fm. In the ground state rho meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1) + (1,0) and (1/2,1/2)_b chiral representations with the former being the leading contribution. In contrast, in the rho' meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)_b. Using a unitary transformation from the chiral basis to the {2S +1}L_J basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The rho meson is practically a 3S_1 state with no obvious trace of a "spin crisis". The rho' meson has a sizeable contribution of the 3D_1 wave, which implies that the rho' meson cannot be considered as a pure radial excitation of the rho meson., Comment: 10 pp

We analyze canonical fermion determinants, i.e., fermion determinants projected to a fixed quark number q. The canonical determinants are computed using a dimensional reduction formula and are studied for pure SU(3) gauge configurations in a wide range of temperatures. It is demonstrated that the center sectors of the Polyakov loop very strongly manifest themselves in the behavior of the canonical determinants in the deconfined phase, and we discuss physical implications of this finding. Furthermore the distribution of the quark sectors is studied as a function of the temperature., Comments on the physical interpretation added. Final version to appear in Physics Letters B

We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures up to 380 MeV with various quark masses. We measure the correlators of spin-one isovector operators including vector, axial-vector, tensor and axial-tensor. At temperatures above $T_c$ we observe an approximate degeneracy of the correlators in these channels, which is unexpected because some of them are not related under $SU(2)_L \times SU(2)_R$ nor $U(1)_A$ symmetries. The observed approximate degeneracy suggests emergent $SU(2)_{CS}$ (chiral-spin) and $SU(4)$ symmetries at high $T$., Comment: 8 pages, 2 tables, 4 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain. arXiv admin note: substantial text overlap with arXiv:1707.01881

We perform an exploratory lattice QCD simulation of $D \bar D$ scattering, aimed at determining the masses as well as the decay widths of charmonium resonances above open charm threshold. Neglecting coupling to other channels, the resulting phase shift for $D \bar D$ scattering in p-wave yields the well-known vector resonance $\psi(3770)$. For $m_\pi = 156$ MeV, the extracted resonance mass and the decay width agree with experiment within large statistical uncertainty. The scalar charmonium resonances present a puzzle, since only the ground state $\chi_{c0}(1P)$ is well understood, while there is no commonly accepted candidate for its first excitation. We simulate $D \bar D$ scattering in s-wave in order to shed light on this puzzle. The resulting phase shift supports the existence of a yet-unobserved narrow resonance with a mass slightly below 4 GeV. A scenario with this narrow resonance and a pole at $\chi_{c0}(1P)$ agrees with the energy-dependence of our phase shift. Further lattice QCD simulations and experimental efforts are needed to resolve the puzzle of the excited scalar charmonia., Comment: 24 pages, 8 figures, updated to match published version

We perform a lattice study of charmonium-like mesons with ${J}^{\mathrm{PC}}={1}^{++}$ and three quark contents $\overline{c}c\overline{d}u$, $\overline{c}c(\overline{u}u+\overline{d}d)$ and $\overline{c}c\overline{s}s$, where the later two can mix with $\overline{c}c$. This simulation with ${N}_{f}=2$ and ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}266\text{ }\text{ }\mathrm{MeV}$ aims at the possible signatures of four-quark exotic states. We utilize a large basis of $\overline{c}c$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both antitriplet and sextet color representations. A lattice candidate for $X(3872)$ with $I=0$ is observed very close to the experimental state only if both $\overline{c}c$ and $D{\overline{D}}^{*}$ interpolators are included; the candidate is not found if diquark-antidiquark and $D{\overline{D}}^{*}$ are used in the absence of $\overline{c}c$. No candidate for neutral or charged $X(3872)$, or any other exotic candidates are found in the $I=1$ channel. We also do not find signatures of exotic $\overline{c}c\overline{s}s$ candidates below 4.2 GeV, such as $Y(4140)$. Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.

In a dynamical lattice simulation with the overlap Dirac operator and $N_f=2$ mass degenerate quarks we study all possible $J=0$ and $J=1$ correlators upon exclusion of the low lying "quasi-zero" modes from the valence quark propagators. After subtraction of a small amount of such Dirac eigenmodes all disconnected contributions vanish and all possible point-to-point $J=0$ correlators with different quantum numbers become identical, signaling a restoration of the $SU(2)_L \times SU(2)_R \times U(1)_A$. The original ground state of the $\pi$ meson does not survive this truncation, however. In contrast, in the $I=0$ and $I=1$ channels for the $J=1$ correlators the ground states have a very clean exponential decay. All possible chiral multiplets for the $J=1$ mesons become degenerate, indicating a restoration of an $SU(4)$ symmetry of the dynamical QCD-like string., Comment: 10 pages, 13 figures

We perform a lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $\bar cc \bar du$, $\bar cc(\bar uu+\bar dd)$ and $\bar cc \bar ss$, where the later two can mix with $\bar cc$. This simulation with $N_f=2$ and $m_\pi=266$ MeV aims at the possible signatures of four-quark exotic states. We utilize a large basis of $\bar cc$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. A lattice candidate for X(3872) with I=0 is observed very close to the experimental state only if both $\bar cc$ and $D\bar D^*$ interpolators are included; the candidate is not found if diquark-antidiquark and $D\bar D^*$ are used in the absence of $\bar cc$. No candidate for neutral or charged X(3872), or any other exotic candidates are found in the I=1 channel. We also do not find signatures of exotic $\bar cc\bar ss$ candidates below 4.3 GeV, such as Y(4140). Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations., Comment: 11 pages, 6 figures, version to be published in Phys. Rev. D

In recent years the study of two particle systems on the lattice has led to excellent results in the meson sector of the QCD spectrum, however baryon resonances mostly remain unexplored. We present a study of pion-nucleon systems as decay product of baryon resonances in different channels, with special focus on the nucleon spectrum. We evaluate the correlation functions of single and multi particle interpolators. All the Wick contributions are explicitly computed and the consequences of reduced symmetries in moving frames are taken into account. We discuss the theoretical setup together with results for $n_f=2$ mass degenerate light quarks., Contribution to the 32nd International Symposium on Lattice Field Theory (Lattice 2014)

Several charged charmonium-like hadrons called $Z_c$ have been recently discovered by different experiments. In contrast to conventional hadrons these contain at least two valence quarks and antiquarks ($\bar{c}c\bar{d}u$). We perform a lattice QCD simulation of the $I^G(J^{PC})=1^+(1^{+-})$ channel including all relevant two-meson operators under 4.3 GeV: $J/\psi \pi$, $\psi_{2S}\pi$, $\psi_{1D}\pi$, $D \bar{D}^*$, $D^* \bar{D}^*$, $\eta_c \rho$ as well as additional diquark anti-diquark operators. In our $N_f = 2$ simulation with pion mass at 266 MeV we are able to identify all two-meson levels within the energy region of interest. However we find no additional level identifiable as a candidate for $Z_c$., Comment: 7 pages, 3 figures, Contribution to the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, NY, USA; updated references

${D}_{s}$ mesons are studied in three quantum channels (${J}^{P}={0}^{+}$, ${1}^{+}$ and ${2}^{+}$), where experiments have identified the very narrow ${D}_{s0}^{*}(2317)$, ${D}_{s1}(2460)$ and narrow ${D}_{s1}(2536)$, ${D}_{s2}^{*}(2573)$. We explore the effect of nearby $DK$ and ${D}^{*}K$ thresholds on the subthreshold states using lattice QCD. Our simulation is done on two very different ensembles of gauge configurations (2 or $2+1$ dynamical quarks, Pion mass of 266 or 156 MeV, lattice size $1{6}^{3}\ifmmode\times\else\texttimes\fi{}32$ or $3{2}^{3}\ifmmode\times\else\texttimes\fi{}64$). In addition to $\overline{q}q$ operators we also include meson-meson interpolators in the correlation functions. This clarifies the identification of the states above and below the scattering thresholds. The ensemble with ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}156\text{ }\text{ }\mathrm{MeV}$ renders the ${D}_{s1}(2460)$ as a strong interaction bound state 44(10) MeV below ${D}^{*}K$ threshold, which is in agreement with the experiment. The ${D}_{s0}^{*}(2317)$ is found 37(17) MeV below $DK$ threshold, close to the experiment value of 45 MeV. The narrow resonances ${D}_{s1}(2536)$ and ${D}_{s2}^{*}(2573)$ are also found close to the experimental masses.

Recently experimentalists have discovered several charged charmonium-like hadrons $Z_c^+$ with unconventional quark content $\bar cc\bar d u$. We perform a search for $Z_c^+$ with mass below $4.2~$GeV in the channel $I^G(J^{PC})=1^+(1^{+-})$ using lattice QCD. The major challenge is presented by the two-meson states $J/\psi\, \pi$, $\psi_{2S}\pi$, $\psi_{1D}\pi$, $D\bar D^*$, $D^*\bar D^*$, $\eta_c\rho$ that are inevitably present in this channel. The spectrum of eigenstates is extracted using a number of meson-meson and diquark-antidiquark interpolating fields. For our pion mass of 266~MeV we find all the expected two-meson states but no additional candidate for $Z_c^+$ below $4.2~$GeV. Possible reasons for not seeing an additional eigenstate related to $Z_c^+$ are discussed. We also illustrate how a simulation incorporating interpolators with a structure resembling low-lying two-mesons states seems to render a $Z_c^+$ candidate, which is however not robust after further two-meson states around $4.2~$GeV are implemented., Comment: Version published in PRD. Minor changes with respect to v2. Changes with respect to v1: extended basis of interpolating fields; modified conclusions, text and figures; 11 pages, 6 figures

Using the chirally invariant overlap Dirac operator we remove its lowest-lying quasizero modes from the valence quark propagators and study evolution of isovector mesons with J=1. At the truncation level about 50 MeV SU(2)_L \times SU(2)_R and U(1)_A symmetries get restored. However, we observe a degeneracy not only within the chiral and U(1)_A multiplets, but also a degeneracy of all possible chiral multiplets, i.e., the observed quantum levels have a symmetry larger than U(2)_L \times U(2)_R and their energy does not depend on the spin orientation of quarks and their parities. We offer a possible interpretation of these energy levels as the quantum levels of the dynamical QCD string. The structure of the radial J=1 spectrum is compatible with E =(n_r +1)\hbar\omega with \hbar\omega = 900 \pm 70 MeV., Comment: 5 pp. The title has been changed, the paper has been restructured and a few references have been added. To appear in PRD

The light axial-vector resonances $a_1(1260)$ and $b_1(1235)$ are explored in Nf=2 lattice QCD by simulating the corresponding scattering channels $\rho\pi$ and $\omega\pi$. Interpolating fields $\bar{q} q$ and $\rho\pi$ or $\omega\pi$ are used to extract the s-wave phase shifts for the first time. The $\rho$ and $\omega$ are treated as stable and we argue that this is justified in the considered energy range and for our parameters $m_\pi\simeq 266~$MeV and $L\simeq 2~$fm. We neglect other channels that would be open when using physical masses in continuum. Assuming a resonance interpretation a Breit-Wigner fit to the phase shift gives the $a_1(1260)$ resonance mass $m_{a1}^{res}=1.435(53)(^{+0}_{-109})$ GeV compared to $m_{a1}^{exp}=1.230(40)$ GeV. The $a_1$ width $\Gamma_{a1}(s)=g^2 p/s$ is parametrized in terms of the coupling and we obtain $g_{a_1\rho\pi}=1.71(39)$ GeV compared to $g_{a_1\rho\pi}^{exp}=1.35(30)$ GeV derived from $\Gamma_{a1}^{exp}=425(175)$ MeV. In the $b_1$ channel, we find energy levels related to $\pi(0)\omega(0)$ and $b_1(1235)$, and the lowest level is found at $E_1 \gtrsim m_\omega+m_\pi$ but is within uncertainty also compatible with an attractive interaction. Assuming the coupling $g_{b_1\omega\pi}$ extracted from the experimental width we estimate $m_{b_1}^{res}=1.414(36)(^{+0}_{-83})$., Comment: 15 pages, 4 figures, updated to match published version

In previous studies we have shown that hadrons, except for a pion, survive the removal of the lowest lying Dirac eigenmodes from the valence quark propagators. The low-modes are tied to the dynamical breaking of chiral symmetry and we found chiral symmetry to be restored by means of matching masses of chiral partners, like, e.g., the vector and axial vector currents. Here we investigate the influence of removing the lowest part of the Dirac spectrum on the locality of the Dirac operator. Moreover, we analyze the influence of low-mode truncation on the quark momenta and thereupon on the hadron spectrum and, finally, introduce a reweighting scheme to extend the truncation to the sea quark sector., Comment: 7pages, 4 figures. Proceedings of the 31st International Symposium on Lattice Field Theory, July 29 - August 3, 2013, Mainz, Germany

We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and applies to QCD when chiral symmetry is spontaneously broken. Further, we introduce and examine the concept of normal modes in chiral spectra. Using this formalism we study the consequences of a finite Thouless energy for the zeros of the partition function. This leads to the demonstration that certain features of the QCD partition function are universal., Comment: 13 pages

We study the overlap and the fixed point Dirac operators for massive fermions in the two-flavor lattice Schwinger model. The masses of the triplet (pion) and singlet (eta) bound states are determined down to small fermion masses and the mass dependence is compared with various continuum model approximations. Near the chiral limit, at very small fermion masses the fixed point operator has stability problems, which in this study are dominated by finite size effects, 13 pages, 2 figures

We compare the lower edge spectral fluctuations of the staggered lattice Dirac operator for the Schwinger model with the predictions of chiral Random Matrix Theory (chRMT). We verify their range of applicability, checking in particular the role of non-trivial topological sectors and the flavor symmetry of the staggered fermions for finite lattice spacing. Approaching the continuum limit we indeed find clear signals for topological modes in the eigenvalue spectrum. These findings indicate problems in the verification of the chRMT predictions., Comment: Latex2e, 13 pages, 5 figures

We study the 2-flavor lattice Schwinger model with Wilson fermions in the chiral limit. The quark mass is determined using the PCAC definition. We numerically compute the masses of the iso-triplet (pi) and iso-singlet particles (eta) for different quark masses and compare our results with analytical formulas., 10 pages, 2 figures. Revised version, to appear in Phys. Lett. B, references added, typo corrected

We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action -\sum_P [\beta \cos(\Theta_P) + \gamma \cos(2\Theta_P)], both for dynamical fermions and in the quenched approximation. (\Theta_P denotes the plaquette angle.) In simulations with dynamical fermions at various \gamma \le -0.2 on 6^4 lattices we find the energy gap at the phase transition of a size comparable to the pure gauge theory for \gamma \le 0 on the same lattice, diminishing with decreasing \gamma. This suggests a second order transition in the thermodynamic limit of the theory with fermions for \gamma below some finite negative value. Studying the theory on large lattices at \gamma = -0.2 in the quenched approximation by means of the equation of state we find non-Gaussian values of the critical exponents associated with the chiral condensate, \beta \simeq 0.32 and \delta \simeq 1.8, and determine the scaling function. Furthermore, we evaluate the meson spectrum and study the PCAC relation., Comment: 21 pages

The calculation of quark propagators for Ginsparg-Wilson-type Dirac operators is costly and thus limited to a few different sources. We present a new approach for determining spatially optimized operators for lattice spectroscopy of excited hadrons. Jacobi smeared quark sources with different widths are combined to construct hadron operators with different spatial wave functions. We study the Roper state and excited rho and pion mesons., Lattice2004(spectrum), 3 pages, 1 figure, (LaTeX style file espcrc2.sty and AMS style files)

The scalar meson D*(s0)(2317) is found 37(17) MeV below the DK threshold in a lattice simulation of the J(P)=0(+) channel using, for the first time, both DK as well as s¯c interpolating fields. The simulation is done on N(f)=2+1 gauge configurations with m(π) is approximately equal to 156 MeV, and the resulting M(D*(s0))-1/4(M(D(s))+3M(D*(s)))=266(16) MeV is close to the experimental value 241.5(0.8) MeV. The energy level related to the scalar meson is accompanied by additional discrete levels due to DK scattering states. The levels near threshold lead to the negative DK scattering length a(0)=-1.33(20) fm that indicates the presence of a state below threshold.

We extend our study of the $K\pi$ system to moving frames and present an exploratory extraction of the masses and widths for the $K^*$ resonances by simulating $K\pi$ scattering in p-wave with $I=1/2$ on the lattice. Using $K\pi$ systems with non-vanishing total momenta allows the extraction of phase shifts at several values of $K\pi$ relative momenta. A Breit-Wigner fit of the phase renders a $K^*(892)$ resonance mass and $K^*\to K \pi $ coupling compatible with the experimental numbers. We also determine the $K^*(1410)$ mass assuming the experimental $K^*(1410)$ width. We contrast the resonant $I=1/2$ channel with the repulsive non-resonant $I=3/2$ channel, where the phase is found to be negative and small, in agreement with experiment., Comment: 7 page, 2 figures, contrib. to the 31st International Symposium on Lattice Field Theory - LATTICE 2013, July 29 - August 3, 2013

We study the coupled $\ensuremath{\pi}N$ system (negative parity, isospin $\frac{1}{2}$) based on a lattice QCD simulation for ${n}_{f}=2$ mass degenerate light quarks. Both standard 3-quark baryon operators as well as meson-baryon ($4+1$)-quark operators are included. This is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic $s$-wave scattering and can derive values of the phase shift.