Recently the Lattice Strong Dynamics Collaboration reported a reduction of the electroweak S parameter for SU(3) gauge theory with Nf=6 fermions in the fundamental representation, compared to scaled-up QCD (arXiv:1009.5967). Here I provide additional details of our calculation. I discuss our use of conserved lattice currents; the relation to vector--axial parity doubling; finite-volume effects; and the sensitivity of our results to the number of fermion doublets with chiral electroweak couplings. Results presented here include additional data, and do not affect our previously-published conclusions.
We examine whether the fact that QCD is chirally invariant at short distances necessarily leads to the prediction that hadrons form approximate parity doublets, as has been recently put forward by Glozman and collaborators. We show that this is not the case, and we exhibit some of the pitfalls of trying to link the operator product expansion to the hadron spectrum. We illustrate our arguments within a model for scalar and pseudo-scalar mesons used recently by Shifman to argue for parity doubling. We find that, whatever the experimental situation may be, there is no theoretical basis for parity…
We describe a lattice simulation of the masses and decay constants of the lowest-lying vector and axial resonances, and the electroweak S parameter, in an SU(3) gauge theory with $N_f = 2$ and 6 fermions in the fundamental representation. The spectrum becomes more parity doubled and the S parameter per electroweak doublet decreases when $N_f$ is increased from 2 to 6, motivating study of these trends as $N_f$ is increased further, toward the critical value for transition from confinement to infrared conformality.
It is expected that nucleons and their parity partners become degenerate when chiral symmetry is restored. We investigate this question in the context of the thermal transition from the hadronic phase to the quark-gluon plasma, using lattice QCD simulations with N_f=2+1 flavours. We observe a clear sign of parity doubling in the quark-gluon plasma. Besides, we find that the nucleon ground state is, within the uncertainty, largely independent of the temperature, whereas temperature effects are substantial in the negative-parity (N^*) channel, already in the confined phase.
We investigate the fate of baryons made out of u, d and s quarks in the hadronic gas and the quark-gluon plasma, using nonperturbative lattice simulations, employing the FASTSUM anisotropic Nf=2+1 ensembles. In the confined phase a strong temperature dependence is seen in the masses of the negative-parity groundstates, while the positive-parity groundstate masses are approximately temperature independent, within the error. At high temperature parity doubling emerges. A noticeable effect of the heavier s quark is seen. We give a simple description of the medium-dependent masses for the negative…
We study what happens to the Nucleon, Delta and Omega baryons in the hadronic gas and the quark-gluon plasma, with particular interest in parity doubling and its emergence as the plasma is heated. This is done using simulations of lattice QCD, employing the FASTSUM anisotropic Nf=2+1 ensembles, with four temperatures below and four above the deconfinement transition temperature. Below Tc we find that the positive-parity groundstate masses are largely temperature independent, whereas the negative-parity ones are reduced considerably as the temperature increases. This may be of interest for heav…
We study the mass spectrum of mesons at high temperature in $SU(2)$ gauge theory with two flavors of Dirac fundamental fermions. Numerical simulations are carried out on anisotropic lattices using Wilson fermions, with lattice parameters tuned so that Euclidean symmetry is restored at low energy. We determine the pseudo-critical temperature $T_c$ using renormalized Polyakov loops. We calculate temporal and spatial meson correlation functions across $T_c$, and observe a clear sign of parity doublings above $T_c$ in both vector and scalar channels. The degeneracy between parity partners in the s…
The spectrum of nucleons and their parity partners is studied as a function of temperature spanning the deconfinement transition. We analyse our results using the correlation functions directly, exponential fits in the hadronic phase, and the Maximum Entropy Method. These techniques all indicate that there is degeneracy in the parity partners' channels in the deconfined phase. This is in accordance with the expectation that there is parity doubling and chiral symmetry in the deconfined phase. In the hadronic phase, we also find that the nucleon ground state is largely independent of temperatur…
We investigate the fluctuations and correlations involving baryon number in hot hadronic matter with modified masses of negative-parity baryons, in the context of the hadron resonance gas. Temperature-dependent masses are adopted from the recent lattice QCD results and from a chiral effective model which implements the parity doubling structure with respect to the chiral symmetry. Confronting the baryon number susceptibility, baryon-charge correlation, and baryon-strangeness correlation and their ratios with the lattice QCD data, we show that the strong downward mass shift in hyperons can acci…
We analyse the behaviour of hyperons with strangeness $S=-1$,$-2$,$-3$ in the hadronic and quark gluon plasma phases, with particular interest in parity doubling and its emergence as the temperature grows. This study uses our FASTSUM anisotropic $N_f\!\!=$~2+1 ensembles, with four temperatures below and four above the deconfinement transition temperature, $T_c$. The positive-parity groundstate masses are found to be largely temperature independent below $T_c$, whereas the negative-parity ones decrease considerably as the temperature increases. Close to the transition, the masses are almost deg…
At zero temperature the negative-parity ground states of the nucleon and delta baryons are non-degenerate with the positive-parity partners due to spontaneous breaking of chiral symmetry. However, chiral symmetry is expected to be restored at sufficiently high temperature, in particular when going from the hadronic to the quark-gluon plasma (QGP) phase. This would imply that channels with opposite parity become degenerate. We study the nucleon (spin $1/2$) and $Δ$ (spin $3/2$) baryons in both parity sectors using lattice QCD. The range of temperatures spans both the hadronic and QGP phases. Us…
In this work we analyse positive- and negative-parity channels for the nucleon (spin $1/2$ octet), $Δ$ and $Ω$ baryons (spin $3/2$ decuplet) using lattice QCD. In Nature, at zero temperature, chiral symmetry is spontaneously broken, causing positive- and negative-parity ground states to have different masses. However, chiral symmetry is expected to be restored (for massless quarks) around the crossover temperature, implying that the two opposite parity channels should become degenerate. Here we study what happens in a temperature range which includes both the hadronic and the quark gluon plasm…
The V-A structure of the weak interactions leads to definite amplitude hierarchies in exclusive heavy-to-light decays mediated by $b \to (d,s)γ$ and $b \to (d,s) \ell \bar{\ell}$. However, the extraction of right-handed currents beyond the Standard Model is contaminated by V-A long-distance contributions leaking into right-handed amplitudes. We propose that these quantum-number changing long-distance contributions can be controlled by considering the almost parity-degenerate vector meson final states by exploiting the opposite relative sign of left- versus right-handed amplitudes. For example,…
We formulate new two dimensional fermions breaking $γ_{5}$hermiticity, based on the minimal doubling fermion. We investigate their properties: (I) Symmetries, (II) eigenvalue distributions, and (III)the number of poles. As a simple application of the fermions, the Gross-Neveu model in two dimensions is studied using the fermion. We obtain the parity broken phase diagram called Aoki phase and the chiral broken phase diagram of the model with an imaginary chemical potential.
We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge $\pm Q$ separated by a distance $s$ in a periodic $L^3$ lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking $L\to\infty$ at fixed $s/L$. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expecte…
Baryonic correlation functions provide an ideal tool to study parity doubling and chiral symmetry using lattice simulations. We present a study using $2+1$ flavors of anisotropic Wilson clover fermions on the FASTSUM ensembles and find clear evidence that parity doubling emerges in the quark-gluon plasma. This result is confirmed on the level of spectral functions, which are obtained using a MEM reconstruction. We further highlight the importance of Gaussian smearing in this study.
We study the spectrum of light baryons and hyperons as a function of temperature using lattice gauge theory methods. We find that masses of positive parity states are temperature independent, within errors, in the hadronic phase. The negative parity states decrease in mass as the temperature increases. Above the deconfining temperature, lattice correlators and spectral functions show a degeneracy between parity sectors, i.e. parity doubling. We apply our findings to an in-medium Hadron Resonance Gas model. The techniques used in this study include direct analysis of the hadronic correlation fu…
Novel chirally symmetric fermion actions containing the minimum amount of fermion doubling have been recently proposed in the literature. We study the symmetries and renormalization of these actions and find that in each case, discrete symmetries, such as parity and time-reversal, are explicitly broken. Consequently, when the gauge interactions are included, these theories radiatively generate relevant and marginal operators. Thus the restoration of these symmetries and the approach to the continuum limit require the fine-tuning of several parameters. With some assumptions, we show that this b…
Motivated by recent examples of three-dimensional lattice Hamiltonians with massless Dirac fermions in their (bulk) spectrum, I revisit the problem of fermion doubling on bipartite lattices. The number of components of the Dirac fermion in a time-reversal and parity invariant d-dimensional lattice system is determined by the minimal representation of the Clifford algebra of $d+1$ Hermitian Dirac matrices that allows a construction of the time-reversal operator with the square of unity, and it equals $2^d$ for $d=2,3$. Possible mass-terms for (spinless) Dirac fermions are listed and discussed. …
Singly, doubly and triply charmed baryons are investigated at multiple temperatures using the anisotropic FASTSUM 'Generation 2L' ensembles. We discuss the temperature dependence of these baryons' spectra in both parity channels with a focus on the confining phase. To further qualify the behaviour of these states around the pseudocritical temperature, we investigate the effect of chiral symmetry restoration for light quarks. We find that an estimate of the pseudocritical temperature can still be found from positive and negative-parity charmed baryon correlators, even when parity doubling itsel…
The hadron resonance gas (HRG) is a widely used description of matter under extreme conditions, e.g. in the context of heavy-ion phenomenology. Commonly used implementations of the HRG employ vacuum hadron masses throughout the hadronic phase and hence do not include possible in-medium effects. Here we investigate this issue, using nonperturbative lattice simulations employing the FASTSUM anisotropic Nf=2+1 ensembles. We study the fate of octet and decuplet baryons as the temperature increases, focussing in particular on the positive- and negative-parity groundstates. While the positive-parity…
We propose a novel solution to the Strong CP problem -- to explain why SU(3) strong force has a nearly zero theta angle $\barθ_3 \simeq 0$ for the 4d Standard Model (SM). The new ingredient is Symmetric Mass Generation (SMG): symmetry-preserving mass or energy gap can be generated without breaking any symmetry $G$ and without any quadratic mean-field mass deformation as long as $G$ is all perturbative local and nonperturbative global anomaly-free. In our first model, we propose a disordered non-mean-field SMG gap (instead of the ordered Anderson-Higgs induced mass gap) for the $u$ quark (or ge…
