QED in Finite Volume and Finite Size Scaling Effect on Electromagnetic Properties of Hadrons

Standard model physics and the digital quantum revolution: thoughts about the interface

Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by Feynman, a concerted effort across many areas of research and development is introducing prototypical digital quantum devices into the computing ecosystem available to domain scientists. Through interactions with these early quantum devices, the abstract vision of exploring classically-intractable quantum systems is evolving toward becoming a tangible reality. Beyond catalyzing these technological advances, entanglement is enabling parallel progress as a diagnostic for quantum correlations and as an organizational tool, both guiding improved understanding of quantum many-body systems and quantum field theories defining and emerging from the standard model. From the perspective of three domain science theorists, this article compilesthoughts about the interfaceon entanglement, complexity, and quantum simulation in an effort to contextualize recent NISQ-era progress with the scientific objectives of nuclear and high-energy physics.

Electromagnetic finite-size effects beyond the point-like approximation

We present a model-independent and relativistic approach to analytically derive electromagnetic finite-size effects beyond the point-like approximation. The key element is the use of electromagnetic Ward identities to constrain vertex functions, and structure-dependence appears via physical form-factors and their derivatives. We apply our general method to study the leading finitesize structure-dependence in the pseudoscalar mass (at order 1/L3) as well as in the leptonic decay amplitudes of pions and kaons (at order 1/L2). Knowledge of the latter is essential for Standard Model precision tests in the flavour physics sector from lattice simulations.

Round table on Standard Model Anomalies

This contribution to “The XVth Quark confinement and the Hadron spectrum conference" covers a description, both theoretical and experimental, of the present status of a set of very different anomalies. The discussion ranges from the long standing b → sℓℓ anomalies, (g − 2) and the new MW anomaly.

Path from Lattice QCD to the Short-Distance Contribution to 0νββ Decay with a Light Majorana Neutrino

Neutrinoless double-β (0νββ) decay of certain atomic isotopes, if observed, will have significant implications for physics of neutrinos and models of physics beyond the standard model. In the simplest scenario, if the mass of the light neutrino of the standard model has a Majorana component, it can mediate the decay. Systematic theoretical studies of the decay rate in this scenario, through effective field theories matched to ab initio nuclear many-body calculations, are needed to draw conclusions about the hierarchy of neutrino masses, and to plan the design of future experiments. However, a recently identified short-distance contribution at leading order in the effective field theory amplitude of the subprocess nn→pp(ee) remains unknown, and only lattice quantum chromodynamics (QCD) can directly and reliably determine the associated low-energy constant. While the numerical computations of the correlation function for this process are underway with lattice QCD, the connection to the physical amplitude, and hence this short-distance contribution, is missing. A complete framework that enables this complex matching is developed in this Letter. The complications arising from the Euclidean and finite-volume nature of the corresponding correlation function are fully resolved, and the value of the formalism is demonstrated through a simple example. The result of this work, therefore, fills the gap between first-principles studies of the nn→pp(ee) amplitude from lattice QCD and those from effective field theory, and can be readily employed in the ongoing lattice-QCD studies of this process.

The anomalous magnetic moment of the muon: status of lattice QCD calculations

In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about 3.5 σ is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years.

Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment from Lattice QCD

We report the first result for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment with all errors systematically controlled. Several ensembles using 2+1 flavors of physical mass Möbius domain-wall fermions, generated by the RBC and UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find a_{μ}^{HLbL}=7.87(3.06)_{stat}(1.77)_{sys}×10^{-10}. Our value is consistent with previous model results and leaves little room for this notoriously difficult hadronic contribution to explain the difference between the standard model and the BNL experiment.

Lattice calculation of the hadronic leading order contribution to the muon g − 2

The persistent discrepancy of about 3.5 standard deviations between the experimental measurement and the Standard Model prediction for the muon anomalous magnetic moment, aµ, is one of the most promising hints for the possible existence of new physics. Here we report on our lattice QCD calculation of the hadronic vacuum polarisation contribution $ a_\mu ^{{\rm{hvp}}} $, based on gauge ensembles with Nf = 2 + 1 flavours of O(a) improved Wilson quarks. We address the conceptual and numerical challenges that one encounters along the way to a sub-percent determination of the hadronic vacuum polarisation contribution. The current status of lattice calculations of $ a_\mu ^{{\rm{hvp}}} $ is presented by performing a detailed comparison with the results from other groups.

Calculation of the Hadronic Vacuum Polarization Contribution to the Muon Anomalous Magnetic Moment

We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is a_{μ}^{HVP LO}=715.4(18.7)×10^{-10}. By supplementing lattice data for very short and long distances with R-ratio data, we significantly improve the precision to a_{μ}^{HVP LO}=692.5(2.7)×10^{-10}. This is the currently most precise determination of a_{μ}^{HVP LO}.

Leading isospin-breaking corrections to meson masses on the lattice

We present a study of the isospin-breaking (IB) corrections to pseudoscalar (PS) meson masses using the gauge configurations produced by the ETM Collaboration with Nf = 2+1+1 dynamical quarks at three lattice spacings varying from 0.089 to 0.062 fm. Our method is based on a combined expansion of the path integral in powers of the small parameters [see formula in PDF] and αem, where [see formula in PDF] is the renormalized quark mass and αem the renormalized fine structure constant. We obtain results for the pion, kaon and Dmeson mass splitting; for the Dashen’s theorem violation parameters ϵγ(MM, 2 GeV), ϵπ0 ϵK0(MS, 2 GeV) for the light quark masses [see formula in PDF] for the flavour symmetry breaking parameters R(MS, 2 GeV) and Q(MS, 2 GeV) and for the strong IB effects on the kaon decay constants.

HVP contributions to the muon (g−2) including QED corrections with twisted-mass fermions

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic (e.m.) corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with Nf = 2+1 + 1 dynamical quarks at three values of the lattice spacing (a ≃ 0.062,0.082,0.089 fm) with pion masses in the range Mπ ≃ 210 - 450 MeV. The strange and charm quark masses are tuned at their physical values. Neglecting discon-nected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: [see formula in PDF] and [see formula in PDF] for the strange and charm contributions, respectively.!

Towards leading isospin breaking effects in mesonic masses with O(a) improved Wilson fermions

We present an exploratory study of leading isospin breaking effects in mesonic masses using O(a) improved Wilson fermions. Isospin symmetry is explicitly broken by distinct masses and electric charges of the up and down quarks. In order to be able to make use of existing isosymmetric QCD gauge ensembles we apply reweighting techniques. The path integral describing QCD+QED is expanded perturbatively in powers of the light quark’ mass deviations and the electromagnetic coupling. We employ QEDL as a finite volume formulation of QED.

Electromagnetic corrections to the hadronic vacuum polarization of the photon within QEDL and QEDM

We compute the leading QED corrections to the hadronic vacuum polarization (HVP) of the photon, relevant for the determination of leptonic anomalous magnetic moments, al. We work in the electroquenched approximation and use dynamical QCD configurations generated by the CLS initiative with two degenerate flavors of nonperturbatively O(a)-improved Wilson fermions. We consider QEDL and QEDM to deal with the finite-volume zero modes. We compare results for the Wilson loops with exact analytical determinations. In addition we make sure that the volumes and photon masses used in QEDM are such that the correct dispersion relation is reproduced by the energy levels extracted from the charged pions two-point functions. Finally we compare results for pion masses and the HVP between QEDL and QEDM. For the vacuum polarization, corrections with respect to the pure QCD case, at fixed pion masses, turn out to be at the percent level.

Isospin Breaking Corrections to the HVP with Domain Wall Fermions

We present results for the QED and strong isospin breaking corrections to the hadronic vacuum polarization using Nf = 2 + 1 Domain Wall fermions. QED is included in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. Results and statistical errors from both methods are directly compared with each other.

Numerical investigation of finite-volume effects for the HVP

It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass

We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at a physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the 48^{3}×96 ensemble generated with a physical pion mass and a 5.5 fm spatial extent by the RBC and UKQCD Collaborations using the chiral, domain wall fermion formulation. We find a_{μ}^{HLbL}=5.35(1.35)×10^{-10}, where the error is statistical only. The finite-volume and finite lattice-spacing errors could be quite large and are the subject of ongoing research. The omitted disconnected graphs, while expected to give a correction of order 10%, also need to be computed.

Isospin splittings in the light-baryon octet from lattice QCD and QED

While electromagnetic and up-down quark mass difference effects on octet baryon masses are very small, they have important consequences. The stability of the hydrogen atom against beta decay is a prominent example. Here, we include these effects by adding them to valence quarks in a lattice QCD calculation based on Nf=2+1 simulations with five lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. This allows us to gain control over all systematic errors, except for the one associated with neglecting electromagnetism in the sea. We compute the octet baryon isomultiplet mass splittings, as well as the individual contributions from electromagnetism and the up-down quark mass difference. Our results for the total splittings are in good agreement with experiment.