Pattern Of Chiral Symmetry Breaking Research Articles

Light asymmetric dark matter on the lattice: SU(2) technicolor with two fundamental flavors

The SU(2) gauge theory with two massless Dirac flavors constitutes the building block of several models of Technicolor. Furthermore it has also been used as a template for the construction of a natural light asymmetric, or mixed type, dark matter candidate. We use explicit lattice simulations to confirm the pattern of chiral symmetry breaking by determining the Goldstone spectrum and therefore show that the dark matter candidate can, de facto, be constituted by a complex Goldstone boson. We also determine the phenomenologically relevant spin-one and spin-zero isovector spectrum and demonstrate that it is well separated from the Goldstone spectrum.

Chiral dynamics with strange quarks in the light of recent lattice simulations

Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/ or the decay constant in the N f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N f = 2 and N f =3 chiral limits. We discuss the consequences for the ratio of decay constants F K /F π and the K ℓ3 form factor at vanishing momentum transfer.

Implications of quarkyonic phase with an alternative pattern of chiral symmetry breaking

We discuss, along with the anomaly matching, a possible phase at finite density where chiral symmetry is spontaneously broken while its centre remains unbroken. The quark number susceptibility exhibits a strong enhancement at the restoration point of the centre symmetry rather than that of the chiral symmetry. This can be interpreted as the quarkyonic transition which was recently proposed in large Nc quantum chromodynamics.

Masses of vector bosons in two-color dense QCD based on the hidden local symmetry

We construct a low energy effective Lagrangian for the two-color QCD including the "vector" bosons (mesons with J^P=1^- and diquark baryons with J^P=1^+) in addition to the pseudo Nambu-Goldstone bosons with a degenerate mass M_\pi (mesons with J^P=0^- and baryons with J^P=0^+) based on the chiral symmetry breaking pattern of SU(2N_f) \to Sp(2N_f) in the framework of the hidden local symmetry. We investigate the dependence of the "vector" boson masses on the baryon number density \mu_B. We show that the \mu_B-dependence signals the phase transition of U(1)_B breaking. We find that it gives information about mixing among "vector" bosons: e.g. the mass difference between \rho and \omega mesons is proportional to the mixing strength between the diquark baryon with J^P=1^+ and the anti-baryon. We discuss the comparison with lattice data for two-color QCD at finite density.

Enhancement of quark number susceptibility with an alternative pattern of chiral symmetry breaking in dense matter

We explore general features of thermodynamic quantities and hadron mass spectra in a possible phase where chiral $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ symmetry is spontaneously broken while its center ${Z}_{2}$ symmetry remains unbroken. In this phase, chiral symmetry breaking is driven by a quartic quark condensate although a bilinear quark condensate vanishes. A Ginzburg-Landau free energy leads to a new tricritical point between the ${Z}_{2}$ broken and unbroken phases. Furthermore, a critical point can appear even in the chiral limit where explicit breaking is turned off, instead of a tricritical point at which restoration of chiral and its center symmetries takes place simultaneously. The net quark number density exhibits an abrupt change near the restoration of the center symmetry rather than that of the chiral symmetry. Hadron masses in possible phases are also studied in a linear sigma model. We show that, in the ${Z}_{2}$ symmetric phase, the $\overline{q}q$-type scalar meson with zero isospin $I=0$ splits from the $\overline{q}q$-type pseudoscalar meson with $I=1$.

Chiral properties of SU(3) sextet fermions

SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamental representations is considered. A priori it is not known what the pattern of chiral symmetry breaking is in a higher dimensional representation although the general expectation is that if two representations are both complex, the breaking pattern will be the same. This expectation is verified for the sextet at N_f = 0 in several exact zero mode sectors. It is shown that if the volume is large enough the same random matrix ensemble describes both the sextet and fundamental Dirac eigenvalues. The number of zero modes for the sextet increases approximately 5-fold relative to the fundamental in accordance with the index theorem for small lattice spacing but zero modes which do not correspond to integer topological charge do exist at larger lattice spacings. The zero mode number dependence of the random matrix model predictions correctly match the simulations in each sector and each representation.

Holographic dual of QCD from black D5 branes

We study the dynamics of probe D7 flavor probe branes in the background of near extremal D5 branes. This model is a holographic dual to a gauge theory with spontaneous breaking of a U(Nf)L × U(Nf)R chiral symmetry. The spectrum of two such D7 embeddings, contains a single massive 4D meson coming from the world volume U(1) gauge field, the pion, and a single massive 4D scalar meson coming from fluctuations of the embedding of the brane. In addition, there are continuum five dimensional states due to the finite height of the effective potential in the radial direction. We investigate baryons in this model, and find that the size is stabilized due to the Chern-Simons term in the D7 world volume action. The model admits a Hagedorn temperature of 1/2πR where R is the radius parameter in the D5 branes metric. We investigate the pattern of chiral symmetry breaking in the deconfined phase as a function of the asymptotic separation of the branes L. We find that for πR/3 < L 1.068R that chiral symmetry is restored, and that chiral symmetry is broken for L outside this window. We further argue that the solutions with L < π/3 are only classically stable, and in fact no D7 embedding exists with these boundary conditions.

An approach towards a constituent quark model on the light cone

We use the vacuum expectation value of a Wegner–Wilson loop representing a fast moving quark–antiquark pair to derive the light cone Hamiltonian for a q q ¯ meson. We solve the corresponding Schrödinger equation for various trial wave functions. The result shows how confinement determines the meson mass and wave function for valence quarks on the light cone. We also parametrize the effect of the spin-dependent splitting for a light meson and charmonium. The correct chiral-symmetry breaking pattern for the pion mass is obtained due to the self-energy of the quark.

Skyrmions in Yang-Mills theories with massless adjoint quarks

Dynamics of $\mathrm{SU}({N}_{c})$ Yang-Mills theories with ${N}_{f}$ adjoint Weyl fermions is quite different from that of $\mathrm{SU}({N}_{c})$ gauge theories with fundamental quarks. The symmetry breaking pattern is $\mathrm{SU}({N}_{f})\ensuremath{\rightarrow}\mathrm{SO}({N}_{f})$. The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. The case of ${N}_{f}=2$ had been considered previously. Here we discuss ${N}_{f}\ensuremath{\ge}3$. We discuss the coupling between the massless Goldstone bosons and massive composite fermions [with mass $\mathrm{O}({N}_{c}^{0})$] from the standpoint of the low-energy chiral sigma model. We derive the Wess-Zumino-Novikov-Witten term and then determine Skyrmion statistics. We also determine their fermion number (mod 2) and observe an abnormal relation between the statistics and the fermion number. This explains the Skyrmion stability. In addition, we consider another microscopic theory---$\mathrm{SO}({N}_{c})$ Yang-Mills with ${N}_{f}$ Weyl fermions in the vectorial representation---which has the same chiral symmetry breaking pattern and the same chiral Lagrangian. We discuss distinctive features of these two scenarios.

ππ and πK scatterings in three-flavour resummed chiral perturbation theory

The (light but not-so-light) strange quark may play a special role in the low-energy dynamics of QCD. The presence of strange quark pairs in the sea may have a significant impact of the pattern of chiral symmetry breaking: in particular large differences can occur between the chiral limits of two and three massless flavours (i.e., whether ms is kept at its physical value or sent to zero). This may induce problems of convergence in three-flavour chiral expansions. To cope with such difficulties, we introduce a new framework, called Resummed Chiral Perturbation Theory. We exploit it to analyse ππ and πK scatterings and match them with dispersive results in a frequentist framework. Constraints on three-flavour chiral order parameters are derived.

Coupling Nonlinear Sigma-Matter to Yang-Mills Fields: Symmetry Breaking Patterns

We extend the traditional formulation of Gauge Field Theory by incorporating the (non-Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinear-sigma-model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling prescription, which resembles the so-called Stueckelberg transformation [1], but for the non-Abelian case. Here we study the case of internal gauge symmetry groups, in particular, unitary groups U(N). We show how to couple standard Yang-Mills Theory to Nonlinear-Sigma Models on cosets of U(N): complex projective, Grassman and flag manifolds. These different couplings lead to distinct (chiral) symmetry breaking patterns and Higgs-less mass-generating mechanisms for Yang-Mills fields.

Generalized Gross-Neveu models and chiral symmetry breaking from string theory

We consider intersecting D-brane models which have two dimensional chiral fermions localized at the intersections. At weak coupling, the interactions of these fermions are described by generalized Gross-Neveu models. At strong coupling, these configurations are described by the dynamics of probe D-branes in a curved background spacetime. We study patterns of dynamical chiral symmetry breaking in these models at weak and strong coupling, and also discuss relationships between these two descriptions.

Chiral symmetry breaking in confining theories and asymptotic limits of operator product expansion

The pattern of spontaneous chiral symmetry breaking (CSB) in confining background fields is analyzed. It is explicitly demonstrated how to get the inverse square root large proper time asymptotic of the operator product expansion which is needed for CSB.

Finite volume effects in a quenched lattice-QCD quark propagator

We investigate finite volume effects in the pattern of chiral symmetry breaking. To this end we employ a formulation of the Schwinger-Dyson equations on a torus which reproduces results from the corresponding lattice simulations of staggered quarks and from the overlap action. Studying the volume dependence of the quark propagator we find quantitative differences with the infinite volume result at small momenta and small quark masses. We estimate the minimal box length $L$ below which chiral perturbation theory cannot be applied to be $L\ensuremath{\simeq}1.6\text{ }\text{ }\mathrm{fm}$. In the infinite volume limit we find a chiral condensate of $|⟨\overline{q}q⟩{|}_{\overline{MS}}^{2\text{ }\text{ }\mathrm{GeV}}=(253\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{MeV}{)}^{3}$, an up/down quark mass of ${m}_{\overline{MS}}^{2\text{ }\text{ }\mathrm{GeV}}=4.1\ifmmode\pm\else\textpm\fi{}0.3\text{ }\text{ }\mathrm{MeV}$ and a pion decay constant which is only 10% smaller than the experimental value.

Exactly solvable model of low energy QCD

Starting from the QCD Hamiltonian, we derive a schematic Hamiltonian for low energy quark dynamics with quarks restricted to the lowest s-level. The resulting eigenvalue problem can be solved analytically. Even though the Hamiltonian exhibits explicit chiral symmetry the severe restriction of the number of degrees of freedom breaks the pattern of chiral symmetry breaking for finite quark masses.

Chiral extrapolations on the lattice with strange sea quarks

The (light but not-so-light) strange quark may play a special role in the low-energy dynamics of QCD. Strange sea-quark pairs may induce significant differences in the pattern of chiral symmetry breaking in the chiral limits of two and three massless flavours, in relation with the violation of the Zweig rule in the scalar sector. This effect could affect chiral extrapolations of unquenched lattice simulations with three dynamical flavours, and it could be detected through the quark-mass dependence of hadron observables [S. Descotes-Genon, hep-ph/0410233].

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order Lambda_QCD, fluctuations of sea s-s bar pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N_f=2 (m_u=m_d=0, m_s physical) and N_f=3 (m_u=m_d=m_s=0). This effect of vacuum fluctuations of s-s bar pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p^4) low-energy constants L_4 and L_6 of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit a numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with a special care. We investigate the impact of the fluctuations of s-s bar pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes (L around 2.5 fm).

Low-energy chiral Lagrangian from the spectral quark model

We analyze the recently proposed Spectral Quark Model in the light of Chiral Perturbation Theory in curved space-time. In particular, we calculate the chiral coefficients $L_1, ..., L_{10}$, as well as the coefficients $L_{11}$, $L_{12}$, and $L_{13}$, appearing when the model is coupled to gravity. The analysis is carried for the SU(3) case. We analyze the pattern of chiral symmetry breaking as well as elaborate on the fulfillment of anomalies. Matching the model results to resonance meson exchange yields the relation between the masses of the scalar, tensor and vector mesons, $M_{f_0}=M_{f_2}=\sqrt{2} M_V= 4 \sqrt{3 /N_c} \pi f_\pi$. Finally, the large-$N_c$ limit suggests the dual relations in the vector and scalar channels, $M_V=M_S= 2 \sqrt{6 /N_c} \pi f_\pi $ and $<r^2 >^{1/2}_S = < r^2 >^{1/2}_V = 2 \sqrt{N_c} / f_\pi = 0.59 {\rm fm} $.

Confinement without a center: the exceptional group G(2)

We discuss theories with the exceptional centerless gauge group G(2), paying attention to confinement and the pattern of chiral symmetry breaking. Exploiting the Higgs mechanism to break the symmetry down to SU(3), we also present how the familiar features of confinement and chiral symmetry breaking of SU(3) gauge theories reemerge. G(2) gauge theories show up as an unusual theoretical framework to study SU(3) gauge theories without the “luxury” of a center.

Patterns of spontaneous chiral symmetry breaking in vectorlike gauge theories

It has been conjectured that spontaneous chiral symmetry breaking in strongly coupled vectorlike gauge theories falls into only three different classes, depending on the gauge group and the representations carried by the fermions. We test this proposal by studying SU(2), SU(3) and SU(4) lattice gauge theories with staggered fermions in different irreducible representations. Staggered fermions away from the continuum limit should, for all complex representations, still belong to the continuum class of spontaneous symmetry breaking. But for all real and pseudo-real representations we show that staggered fermions should belong to incorrect symmetry breaking classes away from the continuum, thus generalizing previous results. As an unambiguous signal for whether chiral symmetry breaks, and which breaking pattern it follows, we look at the smallest Dirac eigenvalue distributions. We find that the patterns of symmetry breaking are precisely those conjectured.