Heavy Pion Research Articles

Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions

We study the dependence of the electric conductivity on chemical potential in finite-density $SU(2)$ gauge theory with $N_f = 2$ flavours of rooted staggered sea quarks, in combination with Wilson-Dirac and Domain Wall valence quarks. The pion mass is reasonably small with $m_{\pi}/m_{\rho} \approx 0.4$. We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in fermion density. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficient $c(T)$ of the expansion of conductivity $\sigma(T,\mu) = \sigma(T,0) \left(1 + c(T) (\mu/T)^2 + O(\mu^4)\right)$ in powers of $\mu$, which has rather weak temperature dependence and takes its maximal value $c(T) \approx 0.10 \pm 0.07$ around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows towards the diquark condensation phase, and also becomes closer to the free quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that for $SU(2)$ gauge theory the ratio of crossover temperature to pion mass $T_c/m_{\pi} \approx 0.4$ at $\mu=0$ is significantly smaller than in real QCD.

D⁎(2380) dibaryon from lattice QCD

The ΔΔ dibaryon resonance d⁎(2380) with (JP,I)=(3+,0) is studied theoretically on the basis of the 3-flavor lattice QCD simulation with heavy pion masses (mπ=679,841 and 1018 MeV). By using the HAL QCD method, the central Δ-Δ potential in the S37 channel is obtained from the lattice data with the lattice spacing a≃0.121 fm and the lattice size L≃3.87 fm. The resultant potential shows a strong short-range attraction, so that a quasi-bound state corresponding to d⁎(2380) is formed with the binding energy 25-40 MeV below the ΔΔ threshold for the heavy pion masses. The tensor part of the transition potential from ΔΔ to NN is also extracted to investigate the coupling strength between the S-wave ΔΔ system with JP=3+ and the D-wave NN system. Although the transition potential is strong at short distances, the decay width of d⁎(2380) to NN in the D-wave is kinematically suppressed, which justifies our single-channel analysis at the range of the pion mass explored in this study.

Deconfinement transition line with the complex Langevin equation up to μ/T∼5

We study the deconfinement transition line in QCD for quark chemical potentials up to $\mu_q \sim 5 T$ ($\mu_B \sim 15 T$). To circumvent the sign problem we use the complex Langevin equation with gauge cooling. The plaquette gauge action is used with two flavors of naive Wilson fermions at a relatively heavy pion mass of roughly 1.3 GeV. A quadratic dependence describes the transition line well on the whole chemical potential range.

Finite size and cut-off effects on the Roberge-Weiss transition in Nf=2 QCD with staggered fermions

In the absence of a genuine solution to the sign problem, lattice studies at imaginary quark chemical potential are an important tool to constrain the QCD phase diagram. We calculate the values of the tricritical quark masses in the Roberge-Weiss plane, $\mu=\imath\pi T/3$, which separate mass regions with chiral and deconfinement phase transitions from the intermediate region, for QCD with $N_\text{f}=2$ unimproved staggered quarks on $N_\tau=6$ lattices. A quantitative measure for the quality of finite size scaling plots is developed, which significantly reduces the subjective judgement required for fitting. We observe that larger aspect ratios are necessary to unambiguously determine the order of the transition than at $\mu=0$. Comparing with previous results from $N_\tau=4$ we find a $\sim50$% reduction in the light tricritical pion mass. The heavy tricritical pion mass stays roughly the same, but is too heavy to be resolved on $N_\tau=6$ lattices and thus equally afflicted with cut-off effects. Further comparison with other discretizations suggests that current cut-off effects on the light critical masses are likely to be larger than $\sim100$%, implying a drastic shrinking of the chiral first-order region to possibly zero.

Magnetic catalysis and inverse catalysis for heavy pions

We investigate the QCD phase diagram for nonzero background magnetic fields using first-principles lattice simulations. At the physical point (in terms of quark masses), the thermodynamics of this system is controlled by two opposing effects: magnetic catalysis (enhancement of the quark condensate) at low temperature and inverse magnetic catalysis (reduction of the condensate) in the transition region. While the former is known to be robust and independent of the details of the interactions, inverse catalysis arises as a result of a delicate competition, effective only for light quarks. By performing simulations at different quark masses, we determine the pion mass above which inverse catalysis does not take place in the transition region anymore. Even for pions heavier than this limiting value — where the quark condensate undergoes magnetic catalysis — our results are consistent with the notion that the transition temperature is reduced by the magnetic field. These findings will be useful to guide low-energy models and effective theories of QCD.

Galilean covariant effective theory for bound states of heavy mesons

In this work we formulate the Galilei-covariant version of an effective theory containing nonrelativistic heavy mesons and pions as degrees of freedom. This manifestly Galilean covariant framework is based on a five-dimensional space–time that has been used in the description of covariant nonrelativistic physics. In this context, effective Lagrangian is introduced without ambiguities, containing kinetic and interaction terms that are naturally Galilean invariant. The leading-order scattering amplitudes and the properties of possible heavy-meson bound states are calculated and discussed.

Light meson form factors at high Q2 from lattice QCD

Measurements and theoretical calculations of meson form factors are essential for our understanding of internal hadron structure and QCD, the dynamics that bind the quarks in hadrons. The pion electromagnetic form factor has been measured at small space-like momentum transfer |q2| < 0.3 GeV2 by pion scattering from atomic electrons and at values up to 2.5 GeV2 by scattering electrons from the pion cloud around a proton. On the other hand, in the limit of very large (or infinite) Q2 = −q2, perturbation theory is applicable. This leaves a gap in the intermediate Q2 where the form factors are not known. As a part of their 12 GeV upgrade Jefferson Lab will measure pion and kaon form factors in this intermediate region, up to Q2 of 6 GeV2. This is then an ideal opportunity for lattice QCD to make an accurate prediction ahead of the experimental results. Lattice QCD provides a from-first-principles approach to calculate form factors, and the challenge here is to control the statistical and systematic uncertainties as errors grow when going to higher Q2 values. Here we report on a calculation that tests the method using an ηs meson, a ’heavy pion’ made of strange quarks, and also present preliminary results for kaon and pion form factors. We use the nf = 2 + 1 + 1 ensembles made by the MILC collaboration and Highly Improved Staggered Quarks, which allows us to obtain high statistics. The HISQ action is also designed to have small dicretisation errors. Using several light quark masses and lattice spacings allows us to control the chiral and continuum extrapolation and keep systematic errors in check.

Constraints on color-octet companions of a 750 GeV heavy pion from dijet and photon plus jet resonance searches

Color octet bosons are a universal prediction of models in which the 750 GeV diphoton resonance corresponds to a pion of a QCD-like composite sector. We show that the existing searches for dijet and photon plus jet resonances at the LHC constrain single productions of color octet states and can be translated into stringent limits on the 750 GeV diphoton rate. For a minimal 5 + 5bar model, the 750 GeV diphoton signal cross section at the 13 TeV LHC is constrained to be below around 5 fb. Future LHC searches for the photon plus jet resonances can establish evidence of a new color-octet state with 20/fb and validate a pion-like explanation for the 750 GeV resonance.

Di-photon resonance and Dark Matter as heavy pions

We analyse confining gauge theories where the 750 GeV di-photon resonance is a composite techni-pion that undergoes anomalous decays into SM vectors. These scenarios naturally contain accidentally stable techni-pions Dark Matter candidates. The di-photon resonance can acquire a larger width by decaying into Dark Matter through the CP-violating θ-term of the new gauge theory reproducing the cosmological Dark Matter density as a thermal relic.

B→πℓνat zero recoil from lattice QCD with physicalu/dquarks

The exclusive semileptonic decay $B \rightarrow \pi \ell \nu$ is a key process for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ from the comparison of experimental rates as a function of $q^2$ with theoretically determined form factors. The sensitivity of the form factors to the $u/d$ quark mass has meant significant systematic uncertainties in lattice QCD calculations at unphysically heavy pion masses. Here we give the first lattice QCD calculations of this process for u/d quark masses going down to their physical values, calculating the $f_0$ form factor at zero recoil to 3\%. We are able to resolve a long-standing controversy by showing that the soft-pion theorem result $f_0(q^2_{max}) = f_B/f_{\pi}$ does hold as $m_{\pi} \rightarrow 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{\pi}$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{\pi}$. We also give results for other processes such as $B_s \rightarrow K \ell \nu$.

Towards a high-precision calculation for the pion-nucleus scattering lengths

We calculate the leading isospin-conserving few-nucleon contributions to pion scattering off 2H, 3He, and 4He. We demonstrate that the strong contributions to the pion-nucleus scattering lengths can be controlled theoretically to an accuracy of a few percent for isoscalar nuclei and of 10% for isovector nuclei. In particular, we find the π-3He scattering length to be (62 ± 4 ± 7) × 10−3 m −1π where the uncertainties are due to ambiguities in the π-N scattering lengths and few-nucleon effects, respectively. To establish this accuracy we need to identify a suitable power counting for pion-nucleus scattering. For this purpose we study the dependence of the two-nucleon contributions to the scattering length on the binding energy of 2H. Furthermore, we investigate the relative size of the leading two-, three-, and four-nucleon contributions. For the numerical evaluation of the pertinent integrals, a Monte Carlo method suitable for the momentum space is devised. We observe that, so far, no power counting is able to provide a quantitative understanding of the relative strength of N- and (N + 1)]]-nucleon operators. Empirically, we find a relative suppression by a factor of 5 compared to a factor of 50 predicted from dimensional analysis. On the other hand, the relative importance of different contributions within each class of N-nucleon operators can be understood within Weinberg counting. The relevance of our findings for the extraction of the isoscalar π-N scattering length from pionic 2H and 4He is outlined. We also discuss the applicability of heavy pion effective field to the π-2H system.

NUCLEON σ-TERM AND THE CHIRAL LIMIT

The scalar form factor of the nucleon in configuration space as well as its σ-term were evaluated some time ago in the framework of chiral symmetry. We investigate their dependence on the pion mass, aiming at the behavior of the σ-term at the chiral limit. Using the results for light pions, the nucleon mass as a function of the pion mass is evaluated. We also present the results for the scalar form factor for heavy pions.

Testing axial and electromagnetic nucleon form factors in time-like regions in the processesp¯+n→π−+ℓ−+ℓ+andp¯+p→π0+ℓ−+ℓ+,ℓ=e,μ

In the frame of a phenomenological approach based on Compton-like Feynman amplitudes, we study the annihilation channel in antiproton nucleon collisions with production of a single charged or neutral pion and a lepton-antilepton pair. These reactions allow us to access nucleon and axial electromagnetic form factors in the time-like region and offer a unique possibility to study the kinematical region below the two-nucleon threshold. The differential cross section in an experimental setup where the pion is fully detected is given with explicit dependence on the relevant nucleon form factors. The possibility of measuring a heavy charged pion in the annihilation channel is also discussed.

Generalized form factors, generalized parton distributions, and the spin contents of the nucleon

With a special intention of clarifying the underlying spin contents of the nucleon, we investigate the generalized form factors of the nucleon, which are defined as the $n$th $x$ moments of the generalized parton distribution functions, within the framework of the chiral quark soliton model. A particular emphasis is put on the pion mass dependence of final predictions, which we shall compare with the predictions of lattice QCD simulations carried out in the so-called heavy pion region around ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}(700--900)\text{ }\text{ }\mathrm{MeV}$. We find that some observables are very sensitive to the variation of the pion mass. It will be argued that the negligible importance of the quark orbital angular momentum indicated by the LHPC and QCDSF lattice collaborations might be true in the unrealistic heavy pion world, but it is not necessarily the case in our real world close to the chiral limit.

Moments of generalized parton distribution functions and the nucleon spin contents

It is shown that, based only upon empirically and semiempirically known facts together with some reasonable theoretical postulates, we are inevitably led to a novel conclusion that the quark orbital angular momentum carries nearly half of the total nucleon spin at the low energy scale around ${Q}^{2}\ensuremath{\simeq}(600\text{ }\mathrm{MeV}{)}^{2}$. We also perform an explicit model analysis to find that the quark spin fraction $\ensuremath{\Delta}\ensuremath{\Sigma}$ is extremely sensitive to the pion mass, which may resolve the discrepancy between the observation and the prediction of the recent lattice QCD simulation carried out in the heavy pion region.

Role of fluctuations in the linearσmodel with quarks

We study the thermodynamics of the linear sigma model with constituent quarks beyond the mean-field approximation. By integrating out the quark degrees of freedom we derive an effective action for the meson fields which is then linearized around the ground state including field fluctuations. We propose a new method for performing exact averaging of complicated functions over the meson field fluctuations. Both thermal and zero-point fluctuations are considered. The chiral condensate and the effective meson masses are determined self-consistently in a rigorous thermodynamic framework. At zero chemical potential the model predicts a chiral crossover transition which separates two distinct regimes: heavy quarks and light pions at low temperatures, but light quarks and heavy mesons at high temperatures. The crossover becomes a first order phase transition if the vacuum pion mass is reduced from its physical value.

Measurements of $R_{\rm b}$ , $A_{\rm FB}^{\rm b}$ , and $A_{\rm FB}^{\rm c}$ in ${\rm e^+ e^-}$ collisions at 130 – 189 GeV

The cross-section ratio $R_{\mathrm{b}} = \sigma( \rm e^+ e^- \to{\rm b\overline{\rm b}} )/\sigma(\rm e^+ e^-\to{\mathrm q\bar{\mathrm q}} )$ and the bottom and charm forward-backward asymmetries $A_{\mathrm{FB}}^{\mathrm{b}}$ and $A_{\mathrm{FB}}^{\mathrm c}$ are measured using event samples collected by the OPAL detector at centre-of-mass energies between 130 and 189 GeV. Events with bottom quark production are selected with a secondary vertex tag, and a hemisphere charge algorithm is used to extract $A_{\mathrm{FB}}^{\mathrm{b}}$ . In addition, the bottom and charm asymmetries are measured using leptons from semileptonic decays of heavy hadrons and pions from $\mathrm{D}^{*+}\to\rm D^0{\pi^+}$ decays. The results are in agreement with the Standard Model predictions.

Lattice determination of the [formula omitted] coupling

The coupling gB ∗Bπ is related to the form factor at zero momentum of the axial between B ∗ and B states. Moreover it is related to the effective coupling between heavy mesons and pions that appears in the heavy meson chiral Lagrangian. This coupling has been evaluated on the lattice using static heavy quarks and light quark propagators determined by a stochastic inversion of the fermionic bilinear. We found the value g = 0.42(4)(8). Besides its theoretical interest, this quantity has phenomenological implications in B → π + ll decays.

The HADES dilepton spectrometer

HADES is a high acceptance dielectron spectrometer to be built at GSI, Darmstadt, for measuring lepton pairs produced in heavy ion and pion induced reactions and able to run at the highest SIS intensities. We present recent development results for the detector components, which are designed to identify dilepton pairs in a high multiplicity environment, and to reconstruct their invariant mass with 1% resolution.

Study of the annihilation from S states

The results of the spin-parity analysis of annihilations at very low momentum (≈ 50 MeV/c) are reported. To describe the data the production of the ϱ, f2, a2 and a1 mesons and the presence of the ππ interaction in S-wave (the σ term) in the final state are necessary. The best fit solution requires also the presence of a ϱ′ state of mass and width M = 1.282 ± 0.037, Γ = 0.236 ± 0.036 GeV/c2 and of a heavy pion π(1300) of mass and width M = 1.275 ± 0.015, Γ = 0.218 ± 0.100 GeV/c2. The measured fraction of the annihilation cross section into 2π+2π− is (7.61 ± 0.35) · 10−2.