Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD

We present lattice-QCD results for the electromagnetic form factors of the proton and neutron including both quark-connected and -disconnected contributions. The parametrization of the $Q^2$-dependence of the form factors is combined with the extrapolation to the physical point. In this way, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain at the physical pion mass and in the continuum and infinite-volume limit $\sqrt{\langle r_E^2 \rangle^p} = 0.820(14)$ fm, $\sqrt{\langle r_M^2 \rangle^p} = 0.8111(89)$ fm, and $\mu_M^p = 2.739(66)$, where the errors include all systematics.Comment: 7 pages, 3 figures; for the accompanying paper, see arXiv:2309.06590 [hep-lat]. arXiv admin note: substantial text overlap with arXiv:2309.0659

Electromagnetic form factors of the nucleon from Nf=2+1N_f = 2 + 1 lattice QCD

There is a long-standing discrepancy between different measurements of the electric and magnetic radii of the proton. Lattice QCD calculations are a well-suited tool for theoretical investigations of the structure of the nucleon from first principles. However, all previous lattice studies of the proton's electromagnetic radii have either neglected quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit. Here, we present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. From simultaneous fits to the $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of the form factors, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain as our final values $\langle r_E^2 \rangle^p = (0.672 \pm 0.014$ (stat)${} \pm 0.018$ (syst)$)$ fm${}^2$, $\langle r_M^2 \rangle^p = (0.658 \pm 0.012$ (stat)${} \pm 0.008$ (syst)$)$ fm${}^2$, and $\mu_M^p = 2.739 \pm 0.063$ (stat)${} \pm 0.018$ (syst). The magnetic moment is in good agreement with the experimental value, as is the one of the neutron. On the one hand, our result for the electric (charge) radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy and the recent $ep$-scattering experiment by PRad. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 $ep$-scattering experiment.Comment: 48 pages, 10 figure

Probing the gluon Transverse Momentum-Dependent distributions inside the proton through quarkonium-pair production at the LHC

Transverse momentum-dependent factorisation is used to describe hadronic collisions while taking into account the intrinsic transverse momentum of partons inside hadrons. This requires Transverse Momentum-Dependent Parton Distribution Functions (TMDPDFs or simply TMDs) which need to be extracted from experimental data. Gluon TMDs in particular remain poorly known. We propose to use quarkonium-pair production to study the two gluon TMDs accessible through unpolarised proton collisions at the Large Hadron Collider (LHC). Quarkonia are bound states of a heavy flavour quark-antiquark pair. J/psi mesons, made of a charm-anticharm pair, are produced in large amounts at the LHC. J/psi pairs originate from gluon fusion in vast majority, which is important to study gluon TMDs. We first use a simple model of Gaussian-based TMDs to compute observables in J/psi-pair production that are sensitive to the TMDs. These are the transverse-momentum spectrum of the pair and azimuthal asymmetries. We see that J/psi-pair production is an ideal process to probe the linearly-polarised gluon TMD through azimuthal asymmetries. We also use the LHCb data on the J/psi-pair transverse momentum to fit the average gluon transverse momentum. We then improve our predictions by including TMD evolution in our calculations. Indeed some contributions to the gluon TMDs can be evaluated perturbatively to improve the fit procedure. We observe that the asymmetries are suppressed but remain sizeable and could be detected at the LHC. We also provide predictions for Upsilon-pair production. We finally discuss the helicity structure of the quarkonium-pair production amplitude which explains how it maximises some azimuthal asymmetries. Moreover, it shows that the amplitude zero for longitudinally polarised pairs predicted at leading order in the collinear regime could be detected for intermediate masses as hard gluon emissions are suppressed in the TMD regime

Spin dependent nucleon structure at intermediate Q²

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1996.Includes bibliographical references (leaves 94-98).by Peter Unrau.Ph.D

Ab initio calculations of nuclei using chiral interactions with realistic saturation properties

Ab initio calculations of nuclei from the valley of stability to the drip lines are a prime challenge in low-energy nuclear theory. The interactions in atomic nuclei, being composed of protons and neutrons, are governed by strong interactions. The fundamental theory of strong interactions is quantum chromodynamics (QCD). Due to the non-perturbative nature of QCD at low energies a direct calculation of nuclear forces from the underlying theory is presently not possible. However, chiral effective field theory (EFT) connects the symmetries of QCD to nuclear forces, enabling a systematic derivation of nuclear interactions, naturally including many-nucleon forces and uncertainty estimates. Chiral EFT interactions are generally softer than phenomenological interactions, but their low- and high-momentum components can still be coupled strongly. Using renormalization group (RG) methods, e.g., the similarity renormalization group, this coupling can be removed by a unitary transformation, resulting in even softer interactions. In addition to advances on nuclear forces and RG methods, several ab initio approaches have been developed in recent years to calculate medium-mass nuclei in a systematically improvable way. We employ some of these advanced many-body approaches in our calculation of nuclei, starting from a set of chiral two- and three-nucleon interactions that, when used in perturbative calculations of symmetric nuclear matter, reproduce empirical saturation properties within theoretical uncertainties. We study ground- and excited-state energies of doubly open-shell nuclei from oxygen to calcium using valence-space interactions derived using many-body perturbation theory. Given the prominent role of the calcium isotopic chain, we perform coupled-cluster calculations to investigate stable and short-lived neutron-rich calcium isotopes. The ab initio calculations reveal that the size of the neutron skin of $^{48}$Ca is much smaller than results from density functional theory. In addition, the very steep increase in charge radii up to $^{52}$Ca measured recently questions the neutron shell closure at $N=32$ and provides an intriguing benchmark for our coupled-cluster calculations. We extend our study to ground states of closed-shell nuclei from $^4$He to $^{78}$Ni using the in-medium similarity renormalization group (IM-SRG). The experimental binding-energy and charge-radius systematics is well described, encouraging the decoupling of valence-space interactions with the IM-SRG to study also open-shell nuclei. The results for ground- and excited-state energies as well as for charge radii of open-shell nuclei achieve a similar level of agreement found in the closed-shell calculations, enabling broad predictions for future experiments up to mass number $\sim80$

Nucleon form factors from Lattice QCD for neutrino oscillation experiments

The investigation of neutrino oscillations is an ongoing world-leading research that aims to understand fundamental neutrino properties. In particular, the observation that neutrinos can oscillate from one flavor to another suggests that these elementary particles have a very small but non-zero mass. However, high precision is required to reconstruct the neutrino energy with Monte Carlo generators and extract parameters such as the CP violating phase δ. The experiments are most frequently built such that the neutrino beams scatter against heavy nuclei targets and these cross sections are non-trivial to parametrize, depending on the energy scale at which the experiment is carried out. Some of the parameters that enter in these cross sections and that represent systematic uncertainties are the so-called nucleon form factors. These functions can be extracted non-perturbatively with lattice simulations by simulating the theory that describes the strong interactions, also known as Quantum ChromoDynamics (QCD). One of the major challenges faced in the lattice QCD determination of the nucleon matrix elements is excited state contamination, particularly nucleon-pion contamination. State-of-the-art analyses take into account this contamination with multistate fits based on Chiral Perturbation Theory, which is an effective field theory where the degrees of freedom are pion and nucleon fields. In this project, we confront the problem directly. Since the primary source of contamination is understood to be related to nucleon-pion states production, we compute this contribution with lattice QCD simulations and consider it for the ground state. The outcome on a single ensemble is promising and confirms the ChPT-inspired approaches. Furthermore, the nucleon-pion term that is computed and taken into account is proportional to the matrix element 〈Nπ| J |N〉, which is phenomenologically interesting by itself as it enters the CC1π and NC1π experimental processes, which occur in the neutrino oscillation experiments and are considered in the event reconstruction. This pilot study represents the first initiative for determining nucleon matrix elements with the variational method with a basis made of nucleon and nucleon-pion operators. We plan to continue this work by including more statistics, extending it to more ensembles, and computing for the first time 〈Nπ| J |N 〉

Workshop on Harmonic Oscillators

Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics

Dietary Intake, Physical Activity, Food Security and Nutritional Status of Newcomer Children in Saskatchewan

Newcomers are usually healthy when they arrive in Canada, but subsequently experience health declines shortly thereafter. It is important to understand the health and nutrition issues of newcomer children, as well as healthcare access issues, as poor dietary and physical activity patterns established early in childhood combined with poor healthcare access can impact the development of chronic disease. This study evaluates the health/nutritional status of newcomer children through a cross-sectional analysis of 300 participants aged 3 to 13 years who have been in Canada for less than 5 years and currently live in Regina or Saskatoon. Questionnaires evaluate socio-demographics, food security, and physical activity. Participants’ diets were assessed through 24 hour recalls. Physical measurements included total body bone mineral content (TBBMC), blood pressure, serum vitamin D, total cholesterol, and glucose. In-depth interviews were also completed with 19 families and 24 service providers to understand lifestyle changes and barriers and supports to healthcare access in the Regina Qu'Appelle and Saskatoon Health Regions. Sixty-two percent of refugees and 43% of immigrants experienced food insecurity. Recent newcomer families and families that included parents with lower education levels were at higher risk for household food insecurity. Older children, those with better educated parents, and those who consumed a poorer quality diet were at higher risk for being overweight/obese. Although immigration status was not a significant risk factor for overweight/obesity, older immigrants (11-13 yrs) were at significantly higher risk of having waist circumference ≥90th percentile (55%) compared to refugees (20%). Significantly more refugees (23%) had stunted growth compared to immigrants (5%). Refugees, and especially refugee children from Asia, appeared to be at greater risk for lower percentile heights. Participants had low intakes of vitamin D (91%) and calcium (80%). Seventy-two percent of refugee and 53% of immigrant children had insufficient serum vitamin D levels. Sixty percent of refugees and 42% of immigrants had high blood cholesterol. Participants were sufficiently active (71.5%); however, a high proportion also engaged in too much sedentary activity (58.4%). Parents indicated interest in having their children involved in sports and activities that are typical in their cultures. Barriers to participation in physical activities included: recreational physical activity being a foreign concept, cultural limits to women’s and girls’ participation, lack of awareness of available activities, transportation difficulties, busy schedules, limited financial resources, safety concerns, and children’s preference for screen time. Overall, the greatest barrier to accessing healthcare services was health system navigation difficulties; understanding how to access care that resulted in service delays. Service providers experienced difficulties with making appointments with newcomers and having good communication to facilitate shared understanding of health issues. Participants mentioned difficulties with accessing appropriate interpretations services. Changes to interim federal health benefits created confusion around eligibility so some healthcare providers were reluctant to provide care. Newcomers frequently spoke about concerns with high drug costs that would be covered by provincial health benefits programs, but they lacked awareness of these programs. Service providers perceived that gender and cultural concerns were a barrier to care. Overall newcomer children are at high risk for inadequate consumption of milk products, which puts them at risk for low intakes of vitamin D and calcium, and subsequently low levels of serum vitamin D. Health concerns for refugee children include food insecurity, poor diet, stunting and high blood cholesterol levels. Older immigrant children are more at risk for overweight, obesity, as indicated by at-risk waist circumferences. The study results also indicate the need to evaluate how the health system can be adjusted to be more responsive to the healthcare needs of newcomer children and their families. Provincially we need to ensure that all newcomers are aware of provincial health benefit programs. Health regions may give consideration to refining services to better meet the needs of newcomers by providing training to increase the cultural competency of staff and embedding the use of available interpretation services into standard work processes