Current-current Correlator Research Articles

Pauli-Heisenberg Oscillations in Electron Quantum Transport.

We measure the current fluctuations emitted by a normal-metal-insulator-normal-metal tunnel junction with a very wide bandwidth, from 0.3 to 13GHz, down to very low temperature T=35 mK. This allows us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise (no dc bias, variable temperature) and shot noise (low temperature, variable dc voltage bias). Because of the very wide bandwidth of our measurement, we deduce the current-current correlator in the time domain. We observe the thermal decay of this correlator as well as its oscillations with a period h/eV, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.

Relaxed superconductors

Momentum relaxation can be built into many holographic models without sacrificing homogeneity of the bulk solution. In this paper we study two such models: one in which translational invariance is broken in the dual theory by spatially-dependent sources for massless scalar fields and another that features an additional neutral scalar field. We turn on a charged scalar field in order to explore the condensation of a charged scalar operator in the dual theories. After demonstrating that the relaxed superconductors we construct are thermodynamically relevant, we find that the finite DC electrical conductivity of the normal phase is replaced by a superfluid pole in the broken phase. Moreover, when the normal phase possesses a Drude behaviour at low frequencies, the optical conductivity of the broken phase at low frequencies can be described by a two-fluid model that is a sum of a Drude peak and a superfluid pole, as was found recently for inhomogeneous holographic superconductors. We also study cases in which this low-frequency behavior does not hold. We find that the Drude description is accurate when the retarded current-current correlator has a purely-dissipative pole that is well-separated from the rest of the excitations.

ϒandϒ′leptonic widths,aμb, andmbfrom full lattice QCD

We determine the decay rate to leptons of the ground-state $\Upsilon$ meson and its first radial excitation in lattice QCD for the first time. We use radiatively-improved NRQCD for the $b$ quarks and include $u$, $d$, $s$ and $c$ quarks in the sea with $u/d$ masses down to their physical values. We find $\Gamma(\Upsilon \rightarrow e^+e^-)$ = 1.19(11) keV and $\Gamma(\Upsilon^{\prime} \rightarrow e^+e^-)$ = 0.69(9) keV, both in good agreement with experiment. The decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD given in the Conclusions. We also test time-moments of the vector current-current correlator against values determined from the $b$ quark contribution to $\sigma(e^+e^- \rightarrow \mathrm{hadrons})$ and calculate the $b$-quark piece of the hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $a_{\mu}^b = 0.271(37) \times 10^{-10}$. Finally we determine the $b$-quark mass, obtaining in the $\overline{MS}$ scheme, $\overline{m}_b(\overline{m}_b, n_f=5)$ = 4.196(23) GeV, the most accurate result from lattice QCD to date.

New predictions on the mass of the 1−+ light hybrid meson from QCD sum rules

We calculate the coefficients of the dimension-8 quark and gluon condensates in the current-current correlator of 1−+ light hybrid current $$ g\overline{q}(x){\gamma}_{\nu }i{G}_{\mu \nu }(x)q(x) $$ . With inclusion of these higher-power corrections and updating the input parameters, we re-analyze the mass of the 1−+ light hybrid meson from Monte-Carlo based QCD sum rules. Considering the possible violation of factorization of higher dimensional condensates and variation of 〈g3G3〉, we obtain a conservative mass range 1.72-2.60 GeV, which favors π1(2015) as a better hybrid candidate compared with π1(1600) and π1(1400).

Electric conductivity from the solution of the relativistic Boltzmann equation

We present numerical results of electric conductivity ${\ensuremath{\sigma}}_{\text{el}}$ of a fluid obtained solving the relativistic transport Boltzmann equation in a box with periodic boundary conditions. We compute ${\ensuremath{\sigma}}_{\text{el}}$ using two methods: the definition itself, i.e., applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in relaxation time approximation (RTA) where the relaxation time for ${\ensuremath{\sigma}}_{\text{el}}$ is determined by the transport cross section ${\ensuremath{\sigma}}_{\text{tr}}$, i.e., the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the two-body scatterings: isotropic and anisotropic cross section as well as massless and massive particles. We find that the RTA underestimates considerably ${\ensuremath{\sigma}}_{\text{el}}$; for example, at screening masses ${m}_{D}\ensuremath{\sim}T$, such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasiparticle model tuned to lattice QCD (lQCD) thermodynamics, as well as the case of a perturbative QCD (pQCD) gas with running coupling. Also, for these cases more directly related to the description of the QGP system, we find that the RTA significantly underestimates the ${\ensuremath{\sigma}}_{\text{el}}$ by about 60%--80%.

Strange and charm quark contributions to the anomalous magnetic moment of the muon

We describe a new technique to determine the contribution to the anomalous magnetic moment of the muon coming from the hadronic vacuum polarization using lattice QCD. Our method reconstructs the Adler function, using Pad\'{e} approximants, from its derivatives at $q^2=0$ obtained simply and accurately from time-moments of the vector current-current correlator at zero spatial momentum. We test the method using strange quark correlators on large-volume gluon field configurations that include the effect of up and down (at physical masses), strange and charm quarks in the sea at multiple values of the lattice spacing and multiple volumes and show that 1% accuracy is achievable. For the charm quark contributions we use our previously determined moments with up, down and strange quarks in the sea on very fine lattices. We find the (connected) contribution to the anomalous moment from the strange quark vacuum polarization to be $a_\mu^s = 53.41(59) \times 10^{-10}$, and from charm to be $a_\mu^c = 14.42(39)\times 10^{-10}$. These are in good agreement with flavour-separated results from non-lattice methods, given caveats about the comparison. The extension of our method to the light quark contribution and to that from the quark-line disconnected diagram is straightforward.

A simple holographic model of momentum relaxation

We consider a holographic model consisting of Einstein-Maxwell theory in (d+1) bulk spacetime dimensions with (d-1) massless scalar fields. Momentum relaxation is realised simply through spatially dependent sources for operators dual to the neutral scalars, which can be engineered so that the bulk stress tensor and resulting black brane geometry are homogeneous and isotropic. We analytically calculate the DC conductivity, which is finite. In the d=3 case, both the black hole geometry and shear-mode current-current correlators are those of a sector of massive gravity.

Anomalous transport with overlap fermions

Anomalous correlators of vector and axial currents which enter the Kubo formulae for the chiral magnetic and the chiral separation conductivities are explicitly calculated for free overlap fermions on the lattice. The results are confronted with continuum calculations in the finite-temperature regularization, and a subtle point of such regularization for chiral magnetic conductivity related to the correct counting of the chiral states is highlighted. In agreement with some previous claims in the literature, we find that in a lattice regularization which respects gauge invariance, the chiral magnetic conductivity vanishes. We point out that the relation of anomalous transport coefficients to axial anomaly is nontrivial due to the non-commutativity of their infrared limit and the Taylor expansion in baryon or chiral chemical potential. In particular, we argue that the vector and axial Ward identities fix the asymptotic behavior of anomalous current-current correlators in the limit of large momenta. Basing on the work of Knecht et al. on the perturbative non-renormalization of the transverse part of the correlator of two vector and one axial currents, we demonstrate that the relation of the anomalous vector-vector correlator to axial anomaly holds perturbatively in massless QCD but might be subject to non-perturbative corrections. Finally, we identify kinematical regimes in which the anomalous transport coefficients can be extracted from lattice measurements.

Light quark pseudoscalar densities and anomaly matrix elements forηandη′mesons

Matrix elements of flavor-diagonal light quark pseudoscalar densities and axial anomaly operators between vacuum and $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson states have been determined. This has been done by evaluating current-current correlators of octet-octet and octet-singlet axial currents using QCD sum rules. The numerical values obtained for the matrix elements compare well with those obtained in the current literature.

Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.

Direct determination of the strange and light quark condensates from full lattice QCD

We determine the strange quark condensate from lattice QCD for the first time and compare its value to that of the light quark and chiral condensates. The results come from a direct calculation of the expectation value of the trace of the quark propagator followed by subtraction of the appropriate perturbative contribution, derived here, to convert the non-normal-ordered $m\overline{\ensuremath{\psi}}\ensuremath{\psi}$ to the $\overline{\mathrm{MS}}$ scheme at a fixed scale. This is then a well-defined physical ``nonperturbative'' condensate that can be used in the operator product expansion of current-current correlators. The perturbative subtraction is calculated through $\mathcal{O}({\ensuremath{\alpha}}_{s})$ and estimates of higher order terms are included through fitting results at multiple lattice spacing values. The gluon field configurations used are ``second generation'' ensembles from the MILC collaboration that include $2+1+1$ flavors of sea quarks implemented with the highly improved staggered quark action and including $u/d$ sea quarks down to physical masses. Our results are $⟨\overline{s}s{⟩}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=\ensuremath{-}(290(15)\text{ }\text{ }\mathrm{MeV}{)}^{3}$, $⟨\overline{l}l{⟩}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=\ensuremath{-}(283(2)\text{ }\text{ }\mathrm{MeV}{)}^{3}$, where $l$ is a light quark with mass equal to the average of the $u$ and $d$ quarks. The strange to light quark condensate ratio is 1.08(16). The light quark condensate is significantly larger than the chiral condensate in line with expectations from chiral analyses. We discuss the implications of these results for other calculations.

Physical response functions of strongly coupled massive quantum liquids

We study physical properties of strongly coupled massive quantum liquids from their spectral functions using the AdS/CFT correspondence. The generic model that we consider is dense, heavy fundamental matter coupled to SU(N_c) super Yang-Mills theory at finite temperature above the deconfinement phase transition but below the scale set by the baryon number density. In this setup, we study the current-current correlators of the baryon number density using new techniques that employ a scaling behavior in the dual geometry. Our results, the AC conductivity, the quasi-particle spectrum and the Drude-limit parameters like the relaxation time are simple temperature-independent expressions that depend only on the mass-squared to density ratio and display a crossover between a baryon- and meson-dominated regime. We concentrated on the (2+1)-dimensional defect case, but in principle our results can also be generalized straightforwardly to other cases.

Scattering matrix approach to interacting electron transport

We investigate the modification in mesoscopic electronic transport due to electron-electron interactions making use of scattering states. We demonstrate that for a specific (finite range) interaction kernel, the knowledge of the scattering matrix is sufficient to take interaction effects into account. We calculate perturbatively the corrections to the current and current-current correlator; in agreement with previous work, we find that, in linear response, interaction effects can be accounted for by an effective (renormalized) transmission probability. Beyond linear response, simple renormalization of scattering coefficients is not sufficient to describe the current-current correlator, as additional corrections arise due to irreducible two-particle processes. Furthermore, we find that the correlations between opposite-spin currents induced by interaction are enhanced for an asymmetric scatterer, generating a nonzero result already to lowest order in the interaction.

Hidden-sector current-current correlators in holographic gauge mediation

We discuss gauge mediation in the case where the hidden sector is strongly coupled but, via the gauge-gravity correspondence, admits a weakly-coupled description in terms of a warped higher-dimensional spacetime. In this framework, known as holographic gauge mediation, the visible-sector gauge group is realized in the gravitational description by probe D-branes and the nonsupersymmetric state by normalizable perturbations to the geometry. Using the formalism of general gauge mediation, supersymmetry-breaking soft terms in the visible sector can be related to the two-point functions of the hidden-sector current superfield that couples to the visible-sector gauge group. Such correlation functions cannot be directly calculated in the strongly coupled field theory but can be determined using the gauge-gravity correspondence and holographic renormalization. We explore this procedure by considering a toy geometry where such two-point functions can be explicitly calculated. Unlike previous implementations of holographic gauge mediation where sfermion masses were not calculable directly in a purely holographic framework, such terms are readily obtained via these correlators, while (due to the simplicity of the geometry considered) the visible-sector gauginos remain massless to leading order in the visible-sector coupling.

Structure function of holographic quark-gluon plasma: Sakai-Sugimoto model versus its noncritical version

Motivated by recent studies of deep inelastic scattering (DIS) off the $\mathcal{N}=4$ super-Yang-Mills (SYM) plasma, holographically dual to $AdS_5\times S^5$ black hole, we in this note use the spacelike flavor current to probe the internal structure of one holographic quark-gluon plasma, which is described by the Sakai-Sugimoto model at high temperature phase (i.e., the chiral symmetric phase). The plasma structure function is extracted from the retarded flavor current-current correlator. Our main aim here is to explore the effect of non-conformality on these physical quantities. As usual, our study is under the supergravity approximation and the limit of large color number. Although the Sakai-Sugimoto model is non-conformal, which makes the calculations more involved than the well-studied $\mathcal {N}$=4 SYM case, the result seems to indicate that the non-conformality has little essential effect on the physical picture of the internal structure of holographic plasma, which is consistent with the intuition from the asymptotic freedom of QCD at high energy. While the physical picture underlying our investigation is same as the DIS off the $\mathcal {N}$=4 SYM plasma with(out) flavor, the plasma structure functions are quantitatively different, especially their scaling dependence on the temperature, which can be recognized as model-dependent. As a comparison, we also do the same analysis for the non-critical version of the Sakai-Sugimoto model which is conformal in the sense that it has a constant dilaton vacuum. The result for this non-critical model is much similar to the conformal $\mathcal{N}=4$ SYM plasma. We therefore attribute the above difference to the effect of non-conformality of the Sakai-Sugimoto model.

Electromagnetic signatures of a strongly coupled anisotropic plasma

In heavy-ion collisions, quark-gluon plasma is likely to be produced with sizable initial pressure anisotropy, which may leave an imprint on electromagnetic observables. In order to model a strongly coupled anisotropic plasma, we use the AdS/CFT correspondence to calculate the current-current correlator of a weakly gauged U(1) subgroup of R symmetry in an N=4 super-Yang-Mills plasma with a (temporarily) fixed anisotropy. The dual geometry, obtained previously by Janik and Witaszczyk, contains a naked singularity which however permits purely infalling boundary conditions and therefore the usual definition of a retarded correlator. We obtain numerical results for the cases of wave vector parallel and orthogonal to the direction of anisotropy, and we compare with previous isotropic results. In the (unphysical) limit of vanishing frequency (infinite time) we obtain a vanishing DC conductivity for any amount of anisotropy, but the anisotropic AC conductivities smoothly approach the isotropic case in the limit of high frequencies. We also discuss hard photon production from an anisotropic plasma and compare with existing hard-loop resummed calculations.

CHIRAL PARTNERS IN A CHIRALLY BROKEN WORLD

The isovector–vector and the isovector–axial-vector current are related by a chiral transformation. These currents can be called chiral partners at the fundamental level. In a world where chiral symmetry was not broken, the corresponding current-current correlators would show the same spectral information. In the real world chiral symmetry is spontaneously broken. A prominent peak — the ρ-meson — shows up in the vector spectrum (measured in e+e--collisions and τ-decays). On the other hand, in the axial-vector spectrum a broad bump appears — the a1-meson (also accessible in τ-decays). It is tempting to call ρ and a1 chiral partners at the hadronic level. Strong indications are brought forward that these "chiral partners" do not only differ in mass but even in their nature: The ρ-meson appears dominantly as a quark-antiquark state with small modifications from an attractive pion-pion interaction. The a1-meson, on the other hand, can be understood as a meson-molecule state mainly formed by the attractive interaction between pion and ρ-meson. A key issue here is that the meson-meson interactions are fixed by chiral symmetry breaking. It is demonstrated that one can understand the vector and the axial-vector spectrum very well within this interpretation. It is also shown that the opposite cases, namely ρ as a pion-pion molecule or a1 as a quark-antiquark state lead to less satisfying results. Finally speculations on possible in-medium changes of hadron properties are presented.

High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD

We use lattice QCD simulations, with MILC gluon configurations and HISQ $c$-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the $\overline{\mathrm{MS}}$ mass of the charm quark and of the $\overline{\mathrm{MS}}$ coupling. We find ${m}_{c}(3\text{ }\text{ }\mathrm{GeV})=0.986(10)\text{ }\text{ }\mathrm{GeV}$, or, equivalently, ${m}_{c}({m}_{c})=1.268(9)\text{ }\text{ }\mathrm{GeV}$, both for ${n}_{f}=4$ flavors; and ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}(3\text{ }\text{ }\mathrm{GeV},{n}_{f}=4)=0.251(6)$, or, equivalently, ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}({M}_{Z},{n}_{f}=5)=0.1174(12)$. The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method.

1/Ncand 1/npreasymptotic corrections to current-current correlators

We obtain the corrections in 1/n and in 1/ln n (n is the principal quantum number of the bound state) of the decay constants of scalar and pseudoscalar currents in two and four dimensions in the large Nc. We obtain them from the operator product expansion provided a model for the large n mass spectrum is given. In the two-dimensional case the spectrum is known and the corrections obtained in this paper are model independent. We confirm these results by confronting them with the numerical solution of the 't Hooft model. We also consider a model at finite Nc and obtain the associated decay constants that are consistent with perturbation theory. This example shows that that the inclusion of perturbative corrections, or finite Nc effects, to the OPE does not constrain the slope of the Regge trajectories, which remain a free parameter for each different channel.

Dynamics of Quantum Noise in a Tunnel Junction under ac Excitation

We report the first measurement of the dynamical response of shot noise (measured at frequency omega) of a tunnel junction to an ac excitation at frequency omega0. The experiment is performed in the quantum regime, variant Planck's over 2piomega approximately variant Planck's over 2piomega0>>kBT at very low temperature T=35 mK and high frequency omega0/2pi=6.2 GHz. We observe that the noise responds in phase with the excitation, but not adiabatically. The results are in very good agreement with a prediction based on a new current-current correlator.