In this work we compute the axion mass and, from this (exploiting a well-known relation), we also derive an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at $T_c$, making use of a chiral effective Lagrangian model which includes the axion, the scalar and pseudoscalar mesons and implements the $U(1)$ axial anomaly of the fundamental theory. We also provide a numerical estimate of the topological susceptibility at $T=0$ (in the physical case of three light quark flavors) and discuss the question of the temperature and quark-mass dependence of the topological susceptibility in the high-temperature regime.
We present the results on topological susceptibility and chiral observables in $N_f=2+1+1$ QCD for temperature range $120<T<600$ MeV. The lattice simulations are performed with Wilson twisted mass fermions at physical pion, strange and charm masses. In high-$T$ region $T\gtrsim 300$ MeV the chiral observables are shown to follow leading order Griffith analyticity, and the topological susceptibility follows a power-law decay as in the instanton dilute gas models. The measured topological susceptibility is used to estimate the mass of QCD axion. The resulting axion mass constraints are in agreem…
We study the topological susceptibility in 2+1 flavor QCD above the chiral crossover transition temperature using Highly Improved Staggered Quark action and several lattice spacings, corresponding to temporal extent of the lattice, $N_τ=6,8,10$ and $12$. We observe very distinct temperature dependences of the topological susceptibility in the ranges above and below $250$ MeV. While for temperatures above $250$ MeV, the dependence is found to be consistent with dilute instanton gas approximation, at lower temperatures the fall-off of topological susceptibility is milder. We discuss the conseque…
A holographic model of QCD axion is presented. It describes a composite axion in the KSVZ class. Having a gravity dual, based on the Witten-Sakai-Sugimoto model, it is calculable in the strongly coupled regime. Its basic properties are derived, including the low energy Lagrangian, from which the axion couplings to nucleons can be derived. Basic features in the deconfined phase are studied as well. In particular, the temperature dependence of the axion mass is extracted from the topological susceptibility. As an aside, the topological susceptibility of strongly coupled ${\cal N}=4$ SYM at finit…
This is the last in a series of papers on the topological susceptibility in the interacting instanton liquid model (IILM). We will derive improved finite temperature interactions to study the thermodynamic limit of grand canonical Monte Carlo simulations in the quenched and unquenched case with light, physical quark masses. In particular, we will be interested in chiral symmetry breaking. The paper culminates by giving, for the first time, a well-motivated temperature-dependent axion mass. Especially, this work finally provides a computation of the axion mass in the low temperature regime, $m^…
Recently an effective Lagrangian for the interactions of photons, Nambu-Goldstone bosons and superfluid phonons in dense quark matter has been derived using anomaly matching arguments. In this paper we illuminate the nature of certain anomalous terms in this Lagrangian by an explicit microscopic calculation. We also generalize the corresponding construction to introduce the axion field. We derive an anomalous axion effective Lagrangian describing the interactions of axions with photons and superfluid phonons in the dense matter background. This effective Lagrangian, among other things, implies…
We present a consistent implementation of weak decays involving an axion or axion-like particle in the context of an effective chiral Lagrangian. We argue that previous treatments of such processes have used an incorrect representation of the flavor-changing quark currents in the chiral theory. As an application, we derive model-independent results for the decays $K^-\toπ^- a$ and $π^-\to e^-\barν_e a$ at leading order in the chiral expansion and for arbitrary axion couplings and mass. In particular, we find that the $K^-\toπ^- a$ branching ratio is almost 40 times larger than previously estim…
We investigate the most interesting decay processes involving axions, photons and the lightest pseudoscalar mesons, making use of a chiral effective Lagrangian model with $L=3$ light quark flavors, which also includes the flavor-singlet pseudoscalar meson and implements the $U(1)$ axial anomaly of the fundamental theory. In particular, we compute the electromagnetic coupling of the axion to photons and we compare our result with the prediction of the Chiral Effective Lagrangian with $L=2$ light quark flavors. Moreover, we study the decay channels $η/η'\rightarrow ππa$ and we estimate the corre…
Using the well-known low-energy effective Lagrangian of QCD --valid for small (non-vanishing) quark masses and a large number of colors-- we study in detail the regions of parameter space where $CP$ is spontaneously broken/unbroken for a vacuum angle $θ= π$. In the $CP$-broken region there are first order phase transitions as one crosses $θ=π$, while on the (hyper)surface separating the two regions, there are second order phase transitions signaled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at th…
This is the first in a series of papers which ultimately aims on improving on the present estimates on the axion mass by modeling the topological non-perturbative QCD dynamics. Axions couple to instantons and their mass is set by the topological susceptibility whose temperature dependence we estimate with the interacting instanton liquid model (IILM). Since accurate finite temperature instanton calculations have problems and do not consider fluctuations in the topological charge, we develop an improved grand canonical version of the IILM to study topological fluctuations in the quark gluon pla…
We recently obtained an estimate of the axion mass based on the hypothesis that axions make up most of the dark matter in the universe. A key ingredient for this calculation was the temperature-dependence of the topological susceptibility of full QCD. Here we summarize the calculation of the susceptibility in a range of temperatures from well below the finite temperature cross-over to around 2 GeV. The two main difficulties of the calculation are the unexpectedly slow convergence of the susceptibility to its continuum limit and the poor sampling of nonzero topological sectors at high temperatu…
The QCD topological observables are essential inputs to obtain theoretical predictions about axion phenomenology, which are of utmost importance for current and future experimental searches for this particle. Among them, we focus on the topological susceptibility, related to the axion mass. We present lattice results for the topological susceptibility in QCD at high temperatures obtained by discretizing this observable via spectral projectors on eigenmodes of the staggered Dirac operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral…
Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale $Λ$ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, caref…
Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of parallel electric and magnetic fields. We review the Schwinger particle production rate, clarify the emergence of the chiral anomaly equation and compute the induced current of charged fermions. We distinguish the contributions from non-perturbative particle production, from the running of the gauge coupling constant and from non-linearities in the effectiv…
We investigate the topological properties of $N_f = 2+1$ QCD with physical quark masses, both at zero and finite temperature. We adopt stout improved staggered fermions and explore a range of lattice spacings $a \sim 0.05 - 0.12$ fm. At zero temperature we estimate both finite size and finite cut-off effects, comparing our continuum extrapolated results for the topological susceptibility $χ$ with predictions from chiral perturbation theory. At finite temperature, we explore a region going from $T_c$ up to around $4\, T_c$, where we provide continuum extrapolated results for the topological sus…
First I will review the QCD theta problem and the Peccei-Quinn solution, with its new particle, the axion. I will review the possibility of the axion as dark matter. If PQ symmetry was restored at some point in the hot early Universe, it should be possible to make a definite prediction for the axion mass if it constitutes the Dark Matter. I will describe progress on one issue needed to make this prediction -- the dynamics of axionic string-wall networks and how they produce axions. Then I will discuss the sensitivity of the calculation to the high temperature QCD topological susceptibility. My…
We evaluate the efficiency of axion production from spatially random initial conditions in the axion field, so a network of axionic strings is present. For the first time, we perform numerical simulations which fully account for the large short-distance contributions to the axionic string tension, and the resulting dense network of high-tension axionic strings. We find nevertheless that the total axion production is somewhat less efficient than in the angle-averaged misalignment case. Combining our results with a recent determination of the hot QCD topological susceptibility (Borsanyi et al 20…
We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected susceptibility, on lattices with spacings as fine as 0.065 fm. For most observables spacing effects are below statistical errors, which enables us to identify lattice results with continuum estimates. Our estimate of the pseudocritical temperature compares favorably with continuum results from staggered and domain wall fermions, confirming…
We derive the axion-nucleon interaction Lagrangian in heavy baryon chiral perturbation theory up to next-to-next-to-leading order. The effective axion-nucleon coupling is calculated to a few percent accuracy.
We investigate the topological properties of unquenched $QCD$ on the basis of numerical results of simulations at fixed topological charge, recently reported by Borsanyi et al.. We demonstrate that their results for the mean value of the chiral condensate at fixed topological charge are inconsistent with the analytical prediction of the large volume expansion around the saddle point, and argue that the most plausible explanation for the failure of the saddle point expansion is a vacuum energy density $θ$-independent at high temperatures, but surprisingly not too high $(T\sim 2T_c)$, a result w…
We compute the effect of the chiral phase transition of QCD on the axion mass and self-coupling; the coupling of the axion to the quarks at finite temperature is described within the Nambu-Jona-Lasinio model. We find that the axion mass decreases with temperature, following the response of the topological susceptibility, in agreement with previous results obtained within chiral perturbation theory at low and intermediate temperatures. As expected, the comparison with lattice data shows that chiral perturbation theory fails to reproduce the topological susceptibility around the chiral critical …
The properties of the QCD axion are strictly related to the dependence of strong interactions on the topological parameter theta. We present a determination of the topological properties of QCD for temperatures up to around 600 MeV, obtained by lattice QCD simulations with 2+1 flavors and physical quark masses. Numerical results for the topological susceptibility, when compared to instanton gas computations, differ both in size and in the temperature dependence. We discuss the implications of such findings for axion phenomenology, also in comparison to similar studies in the literature, and th…
The introduction of non-orthogonal electric and magnetic fields in the QCD vacuum enhances the weight of topological sectors with a nonzero topological charge. For weak fields, there is a linear response for the expectation value of the topological charge. We study this linear response and relate it to the QCD correction to the axion-photon coupling. We also analyse the magnetic field dependence of the topological susceptibility for a range of temperatures around $T_c$. In this work we use lattice simulations with improved staggered quarks at physical masses, including background magnetic and …
We use the chiral Lagrangian to investigate the global properties of the $N$-flavor QCD vacuum as a function of the $θ$ parameter. In the case of exact quark degeneracy we find evidence for first order phase transitions at $θ= π\cdot ({\rm odd~ integer})$. The first order transitions are smoothed by quark mass splittings, although interesting effects remain at realistic quark masses. We emphasize the role of the $η'$ condensate in our analysis. Finally, we discuss the implications of our results on the internal hadronic structure of axion domain walls and axion cosmology.
Building on Weinberg's approach to effective field theory for inflation, we construct an effective Lagrangian for a pseudo scalar (axion) inflaton field with shift symmetry. In this Lagrangian we allow the axion field to couple to non-Abelian gauge fields via a Chern-Simons term. We then analyze a class of inflation models driven by kinetic terms. We find that the observational constraints on the amplitudes of curvature perturbations and non-Gaussianity yield a lower bound for the tensor-to-scalar ratio of $r\gtrsim 5\times 10^{-3}$ from the vacuum fluctuation. The sourced gravitational wave f…
We present results on QCD with four dynamical flavors in the temperature range $0.9 \lesssim T/T_c \lesssim 2$. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic methods. The topological charge distribution is studied by means of its cumulants, which encode relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility measured with the fermionic method exhibits a power-law decay for $T/T_c \gtrsim 2$, with an exponent close to the one predicted by the Dilute Instan…
The Kaplan-Manohar ambiguity in light quark masses allows for a larger uncertainty in the ratio of up to down quark masses than naive estimates from the chiral Lagrangian would indicate. We show that it allows for a relaxation of experimental bounds on the QCD axion, specifically KSVZ axions in the $2-3 μ$eV mass range composing 100% of the galactic dark matter halo can evade the experimental limits placed by the ADMX collaboration.
We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both nonabelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential v…
Axions are one of the most attractive dark matter candidates. The evolution of their number density in the early universe can be determined by calculating the topological susceptibility $χ(T)$ of QCD as a function of the temperature. Lattice QCD provides an ab initio technique to carry out such a calculation. A full result needs two ingredients: physical quark masses and a controlled continuum extrapolation from non-vanishing to zero lattice spacings. We determine $χ(T)$ in the quenched framework (infinitely large quark masses) and extrapolate its values to the continuum limit. The results are…
Ludwig Maximilian University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Technical University of Munich（慕尼黑工业大学）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Institute for Advanced Study, Technische Universität München（慕尼黑工业大学高等研究院）；Munich Data Science Institute, Technische Universität München（慕尼黑工业大学数据科学研究所）；Kyung Hee University（庆熙大学）
If the QCD axion is a significant component of dark matter, and if the universe was once hotter than a few hundred MeV, the axion relic abundance depends on the function $χ(T)$, the temperature-dependent topological susceptibility. Uncertainties in this quantity induce uncertainties in the axion mass as a function of the relic density, or vice versa. At high temperatures, theoretical uncertainties enter through the dilute instanton gas computation, while in the intermediate and strong coupling regime, only lattice QCD can determine $χ(T)$ precisely. We reassess the uncertainty on the instanton…
We compute the topological charge and its susceptibility in finite temperature (2+1)-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson quarks, we perform simulations on a fine lattice with~$a\simeq0.07\,\mathrm{fm}$ at a heavy $u$, $d$ quark mass with $m_π/m_ρ\simeq0.63$ but approximately physical $s$ quark mass with $m_{η_{ss}}/m_ϕ\simeq0.74$. In a temperature range from~$T\simeq174\,\mathrm{MeV}$ ($N_t=16$) to $697\,\mathrm{MeV}$ ($N_t=4$), we study two topics on the topological susceptibility. One is a compa…
Large N gluodynamics was shown to have a set of metastable vacua with the gluonic domain walls interpolating between them. The walls may separate the genuine vacuum from an excited one, or two excited vacua which are unstable at finite N (here N is the number of colors). One may attempt to stabilize them by switching on the axion field. We study how the light quarks and the axion affect the structure of the domain walls. In pure gluodynamics (with the axion field) the axion walls acquire a very hard gluonic core. Thus, we deal with a wall "sandwich" which is stable at finite N. In the case of …
In this work, extending a previous study at zero temperature ($T=0$), we perform a systematic study of the modifications to the QCD vacuum energy density $ε_{vac}$ in the finite-temperature case, above the chiral transition at $T_c$, caused by a nonzero value of the parameter $θ$, using two different effective Lagrangian models which implement the $U(1)$ axial anomaly of the fundamental theory and which are both well defined also above $T_c$. In particular, we derive (and critically compare) the expressions for the topological susceptibility $χ$ and for the second cumulant $c_4$ starting from …
The temperature dependence of the topological susceptibility in QCD, chi_t, essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched a…
Hunan University of Science and Technology（湖南科技大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Universität Bonn（波恩大学）；Forschungszentrum Jülich（于利希研究中心）；Tbilisi State University（第比利斯国立大学）；University of Chinese Academy of Sciences（中国科学院大学）
We perform a systematic study of the modifications to the QCD vacuum energy density $ε_{vac}$ in the zero-temperature case ($T=0$) caused by a small, but non-zero, value of the parameter $θ$, using different effective Lagrangian models which include the flavour-singlet meson field and implement the $U(1)$ axial anomaly of the fundamental theory. In particular, we derive the expressions for the topological susceptibility $χ$ and for the second cumulant $c_4$ starting from the $θ$ dependence of $ε_{vac}(θ)$ in the various models that we have considered. Moreover, we evaluate numerically our resu…
It is shown that the recently proposed preon model which provides a unified origin of the diverse mass scale and an explanation of family replication as well as of inter-family mass-hierarchy, possesses a Peccei-Quinn symmetry whose spontaneous breaking leads to an automatic invisible axion. Existence of the PQ-symmetry is simply a consequence of supersymmetry and requirement of minimality in the field-content and interactions, which propose that the lagrangian should possess only those terms which are dictated by the gauge principle and no others. In addition to the axion, the model also gene…
Modulo the scale of spontaneous breaking of Peccei-Quinn symmetry, the axion mass $m_a(T)$ is given by the QCD topological susceptibility $χ(T)$ at all temperatures $T$. From an approach tying the $U_A(1)$ and chiral symmetry breaking and getting good $T$-dependence of $η$ and $η$ mesons, we get $χ(T)$ for an effective Dyson-Schwinger model of nonperturbative QCD. Comparison with lattice results for $χ(T)$, and thus also for $m_a(T)$, shows good agreement for temperatures ranging from zero up to the double of the chiral restoration temperature $T_c$.
INFN Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INFN Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；Dipartimento di Fisica, Università di Pisa（比萨大学物理系）；Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）
In this paper we calculate the non-perturbative Euler-Heisenberg Lagrangian for massless QED in a strong magnetic field $H$, where the breaking of the chiral symmetry is dynamically catalyzed by the external magnetic field via the formation of an electro-positron condensate. This chiral condensate leads to the generation of dynamical parameters that have to be found as solutions of non-perturbative Schwinger-Dyson equations. Since the electron-positron pairing mechanism leading to the breaking of the chiral symmetry is mainly dominated by the contributions from the infrared region of momenta m…
