2c:null 2d:["$","title",null,{"children":"Massive Neutrinos | David Kirkby | Observable"}] 32:T40c,viewof params = Inputs.form( // Default values of mass squared differences from Table 14.7 of Neutrino Mixing review in RPP 2023 { m_nu_sum: Inputs.range([0,3*mmax], { value:0.2, step:0.001, format: x => Number(x).toFixed(3) }), dm21sq: Inputs.range([0,10], { value:7.4, step:0.01, format: x => Number(x).toFixed(2) }), absdm32sq: Inputs.range([1,5], { value:2.5, step:0.01, format: x => Number(x).toFixed(2) }), hierarchy: Inputs.radio(["true (normal hierarchy)", "false (inverted hierarchy)"], { value: "true (normal hierarchy)" }), }, { template: (inputs) => html`

${tex`m_1+m_2+m_3`} [eV]${inputs['m_nu_sum']}

${tex`(m_2^2-m_1^2) \times 10^5`} [eV²] (solar) ${inputs['dm21sq']}

${tex`m_2 \le m_3`} ? ${inputs['hierarchy']}

${tex`\left| m_3^2-m_2^2\right| \times 10^3`} [eV²] (atmospheric) ${inputs['absdm32sq']}

` } )33:T4c8,function rhoPlot() { const labels = [ "PHOTONS", "MATTER", "NEUTRINOS" ]; const colors = [ "blue", "orange", "green" ]; const text = labels.map( (label,i) => Plot.text([label], { x: 1e-5, y: 1e-1, dy: 20*i, text: d=>d, fontSize: 16, fill:colors[i], fontWeight: "bold" })); const marks = [ Plot.frame(), Plot.line(basedata, {x:(_,i)=>agrid[i], y:d=>d.Ogamma/d.Om, stroke:"blue", strokeDasharray: dash}), Plot.line(basedata, {x:(_,i)=>agrid[i], y:1, stroke:"orange", strokeDasharray: dash}), Plot.line(basedata, {x:(_,i)=>agrid[i], y:d=>d.Onu/d.Om, stroke:"green", strokeDasharray: dash}), Plot.line(data, {x:(_,i)=>agrid[i], y:d=>d.Ogamma/d.Om, stroke:"blue"}), Plot.line(data, {x:(_,i)=>agrid[i], y:1, stroke:"orange"}), Plot.line(data, {x:(_,i)=>agrid[i], y:d=>d.Onu/d.Om, stroke:"green"}), ].concat(text); const fmt = (d,i) => `1E${Math.round(Math.log10(d))}`; return Plot.plot({ x: { type: "log", grid: true, label: "Scale Factor a", labelAnchor: "center", labelArrow: false, tickFormat: fmt }, y: { type: "log", grid: true, label: "Omega_x(a) / Omega_m(a)", labelAnchor: "center", labelArrow: false, labelOffset: 50 }, marginLeft: 60, marks }); }34:T7ba,function mixingPlot() { const {m1,m2,m3} = masses; const mmax = Math.max(m1,m2,m3); const sorted = [m1,m2,m3].map((m,k) => ({ state:k+1, mass:m })).sort((a,b) => a.mass - b.mass); const barHeight = 30; // pixels const massScaling = (plotHeight - 3 * barHeight) / mmax; const y = sorted.map((d,i) => d.mass * massScaling + i * barHeight); const flavors = ["e", "μ", "τ"]; const fpat = ["horiz", "cross", "right"]; const data = []; neutrinoMixing.forEach((probs, i) => { const edges = [0].concat(cumsum(probs)); probs.forEach((prob, j) => { data.push({ state: i+1, findex: j, flavor: flavors[j], x1: edges[j], x2: edges[j+1], y1: y[i], y2: barHeight + y[i], }); }); }); const fmt6 = d3.format(".6f"); const fmtSI = d3.format(".3s"); return Plot.plot({ x: { domain: [0,1], grid: true }, y: { domain: [0,plotHeight], axis: null }, height: plotHeight, width: width / 2, marginRight: 45, marginLeft: 70, marks: [ patterns, Plot.rect(data.filter(d => d.findex==0), { x1:0, x2:1, y1:"y1", y2:"y2", fill: d=>stateColors[d.state-1] }), Plot.rect(data, { x1:"x1", x2:"x2", y1:"y1", y2:"y2", fill: d => `url(#pattern-hatch-${fpat[d.findex]})`, fillOpacity: 0.25 }), Plot.text(data, { x: d => (d.x1+d.x2)/2, y: d=>(d.y1+d.y2)/2, text: d=>d.flavor, fill: "black", fontSize: 18 }), Plot.text(sorted, { x: 1.0, dx: 4, y: (_,k)=>y[k]+0.5*barHeight, text: d=>`ν${d.state}`, fontSize: 20, textAnchor: "start", fill: d=>stateColors[d.state-1] }), Plot.text(sorted, { x: 0.0, dx: -4, y: (_,k)=>y[k]+0.5*barHeight, text: d=>`${fmtSI(d.mass)}eV`, fontSize: 14, textAnchor: "end", fill: d=>stateColors[d.state-1] }), Plot.ruleY([0], { y:0, stroke: "black", strokeWidth: 2 }), ] }); }35:T31c2,// Based on https://observablehq.com/@tomshanley/cheysson-color-palettes patterns = () => svg` \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r \r `36:[] 30:{"id":"25cb9a0b9f397e8c","slug":"massive-neutrinos","title":"Massive Neutrinos","thumbnail":"98e9b9ed8cbb48c717d4fc9a7a0d14a49fe0677c80369c82a468a9fea595a09d","access_level":"public","create_time":"$D2024-05-30T20:54:52.324Z","update_time":"$D2024-06-06T12:35:01.561Z","view_time":null,"first_public_time":"$D2024-06-04T13:35:25.342Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"82762c8496f321fe","login":"dkirkby","name":"David Kirkby","avatar_url":"https://avatars-next.observableusercontent.com/5b2c32ac920111620eb8369d40c1cd0353430f60391a4e246bc9822ab20f6f2f","tier":"starter_2024"},"version":598,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"b31e222c78b643d7","login":"dkirkby","name":"David Kirkby","avatar_url":"https://avatars-next.observableusercontent.com/5b2c32ac920111620eb8369d40c1cd0353430f60391a4e246bc9822ab20f6f2f","tier":null}],"members":[{"type":"team","id":"82762c8496f321fe","login":"dkirkby","name":"David Kirkby","avatar_url":"https://avatars-next.observableusercontent.com/5b2c32ac920111620eb8369d40c1cd0353430f60391a4e246bc9822ab20f6f2f","tier":"starter_2024","role":"editor"},{"type":"individual","id":"b31e222c78b643d7","login":"dkirkby","name":"David Kirkby","avatar_url":"https://avatars-next.observableusercontent.com/5b2c32ac920111620eb8369d40c1cd0353430f60391a4e246bc9822ab20f6f2f","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"6ee1ec0d30358592","slug":"cosmology","title":"Cosmology","owner":{"id":"82762c8496f321fe","login":"dkirkby","name":"David Kirkby"}},"type":"notebook","body":{"title":"Massive Neutrinos","cells":[{"id":0,"value":"# Massive Neutrinos\n\nThis [DESI paper](https://arxiv.org/abs/2404.03002) combines DESI and CMB data to constrain the sum of the neutrino masses. Some useful references on neutrino properties are this [Snowmass 2013 report](https://arxiv.org/abs/1307.5487) and the [PDG Report on Particle Physics review article](https://pdg.lbl.gov/2023/reviews/rpp2022-rev-neutrino-mixing.pdf).\n\nUse the sliders below to see how neutrino masses affect the homogeneous background cosmology quantities plotted below, compared with Planck15 FlatLambdaCDM (dashed curves), which assumes ${tex`m_1 = m_2 = 0`} and ${tex`m_3 = 0.06`} eV.\n\nFor a similar study of evolving dark energy see [here](https://observablehq.com/@dkirkby/evolving-dark-energy).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":529,"value":"cosmoPlots = html`\n

\n ${rhoPlot()} ${hPlot()} ${aPlot()} ${dPlot()}\n

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":467,"value":"nuPlots = html`\n

\n ${massPlot()} ${mixingPlot()}\n

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":474,"value":"md`---`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":553,"value":"function dPlot() {\n return Plot.plot({\n x: { grid: true, label: \"Redshift z\", labelAnchor: \"center\", labelArrow: false },\n y: { grid: true, label: \"Comoving Distance D(z) [Gpc]\", labelAnchor: \"center\", labelArrow: false },\n marks: [\n Plot.frame(),\n Plot.line(basedata2, { x: \"z\", y: d=>1e-3*d.comoving_distance, stroke: \"black\", strokeDasharray: dash }),\n Plot.line(data2, { x: \"z\", y: d=>1e-3*d.comoving_distance, stroke: \"black\" }),\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":548,"value":"function hPlot() {\n return Plot.plot({\n x: { grid: true, label: \"Redshift z\", labelAnchor: \"center\", labelArrow: false },\n y: { grid: true, label: \"adot = H(z) / (1 + z)\", labelAnchor: \"center\", labelArrow: false },\n marks: [\n Plot.frame(),\n Plot.line(basedata2, { x: \"z\", y: d => d.H / (1 + d.z), stroke: \"black\", strokeDasharray: dash }),\n Plot.line(data2, { x: \"z\", y: d => d.H / (1 + d.z), stroke: \"black\" }),\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":535,"value":"function aPlot() {\n return Plot.plot({\n x: { type: \"linear\", grid: true, label: \"Time Relative to Today t [Gyr]\", labelAnchor: \"center\", labelArrow: false, domain:[-15,5] },\n y: { type: \"linear\", grid: true, label: \"Scale Factor a(t)\", labelAnchor: \"center\", labelArrow: false, domain: [0,2] },\n clip: true,\n marginLeft: 60,\n marks: [\n Plot.frame(),\n Plot.line(basedata, { x: d=>-d.lookback_time, y: (_,i)=>agrid[i], stroke: \"black\", strokeDasharray: dash }),\n Plot.line(data, { x: d=>-d.lookback_time, y: (_,i)=>agrid[i], stroke: \"black\" }),\n Plot.ruleX([0], { stroke: \"red\", strokeDasharray: [2,6], strokeWidth: 2 }),\n Plot.ruleY([1], { stroke: \"red\", strokeDasharray: [2,6], strokeWidth: 2 }),\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":491,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":504,"value":"dash = [3, 3]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":545,"value":"data2 = model.tidyz(zgrid2, \"H,comoving_distance\" );","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":542,"value":"basedata2 = Planck15.tidyz(zgrid2, \"H,comoving_distance\" )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":538,"value":"zgrid2 = linspace(0, 2.5, 100)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":509,"value":"data = model.tidyz(zgrid, \"Ogamma,Om,Onu,lookback_time\" )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":502,"value":"model = {\n const {m1,m2,m3} = masses;\n const m_nu = [m1,m2,m3];\n const {Om0,Ob0,Neff} = Planck15;\n const H0 = Planck15.H(0);\n const Tcmb0 = Planck15.Tgamma(0);\n return new FlatLambdaCDM({H0, Om0, Ob0, Tcmb0, Neff,m_nu});\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":499,"value":"basedata = Planck15.tidyz(zgrid, \"Ogamma,Om,Onu,lookback_time\" );","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":495,"value":"zgrid = agrid.map(a => 1/a - 1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":493,"value":"agrid = geomspace(1e-6, 10, 100).reverse()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":85,"value":"function massPlot() {\n const {m1,m2,m3} = masses;\n const lightest = m1 <= m3 ? \"m1\" : \"m3\";\n return Plot.plot({\n x: { type: \"symlog\", constant: 0.01, label: \"Lightest neutrino mass [eV]\", domain:[0, mmax], labelAnchor: \"center\", labelArrow: false },\n y: { type: \"symlog\", constant: 0.01, label: \"Neutrino masses [eV]\", domain: [0, 3*mmax], labelAnchor: \"center\", labelArrow: false },\n grid: true,\n height: plotHeight,\n width: width / 2,\n marks: [\n Plot.ruleX([m1], { stroke: \"lightgray\", strokeWidth: 3 }),\n Plot.line(massPlotData, {x:lightest, y:\"m1\", stroke: stateColors[0]}),\n Plot.line(massPlotData, {x:lightest, y:\"m2\", stroke: stateColors[1]}),\n Plot.line(massPlotData, {x:lightest, y:\"m3\", stroke: stateColors[2]}),\n Plot.line(massPlotData, {x:lightest, y:\"msum\", stroke: \"black\", strokeDasharray: [3,3]}),\n Plot.dot([m1,m2,m3], { x: m1, y: m=>m, fill: (_,i) => stateColors[i] }),\n Plot.frame(),\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":353,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":557,"value":"stateColors = {\n const scheme = d3.schemeCategory10;\n return scheme.slice(0,3);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":358,"value":"plotHeight = 400 // pixels","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":318,"value":"masses = {\n const {m_nu_sum} = params;\n const m1grid = massPlotData.map(({m1}) => m1);\n const m2grid = massPlotData.map(({m2}) => m2);\n const m3grid = massPlotData.map(({m3}) => m3);\n const msum = massPlotData.map(({msum}) => msum);\n const m1 = interp(m_nu_sum, msum, m1grid, {clipped: true});\n const m2 = interp(m_nu_sum, msum, m2grid, {clipped: true});\n const m3 = interp(m_nu_sum, msum, m3grid, {clipped: true});\n return { m1, m2, m3 };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":68,"value":"massPlotData = {\n const {sqrt} = Math;\n const {m_nu_sum, hierarchy} = params;\n let {dm21sq, absdm32sq} = params;\n dm21sq *= 1e-5;\n absdm32sq *= 1e-3;\n const mmin = [0].concat(geomspace(1e-3, mmax, 999, {dtype: Array}));\n let m1, m2, m3;\n if(hierarchy.startsWith(\"false\")) {\n // Inverted hierarchy: mmin=m3 < m1 < m2\n m3 = mmin;\n m2 = m3.map(m3 => sqrt(absdm32sq + m3**2));\n m1 = m2.map(m2 => sqrt(m2**2 - dm21sq));\n }\n else {\n // Normal hierarchy: mmin=m1 < m2 < m3\n m1 = mmin;\n m2 = m1.map(m1 => sqrt(dm21sq + m1**2));\n m3 = m2.map(m2 => sqrt(absdm32sq + m2**2));\n }\n const msum = m1.map((m1,i) => m1 + m2[i] + m3[i]);\n return tidy({m1,m2,m3,msum});\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":302,"value":"mmax = 1 // maximum mass of lightest neutrino in eV","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":139,"value":"neutrinoMixing = {\n const {sin, cos, PI} = Math;\n const angles = {}, CS = {};\n ({theta12: angles['12'], theta23: angles['23'], theta13: angles['13'], deltaCP: angles['CP']} = neutrinoParams);\n for (const [name, degrees] of Object.entries(angles)) {\n const radians = degrees * PI/180;\n CS['c'+name] = cos(radians);\n CS['s'+name] = sin(radians);\n }\n const { c12, c13, c23, s12, s13, s23, cCP } = CS;\n // Each row k is [ prob(nu_e, nu_k), prob(nu_mu, nu_k), prob(nu_tau, nu_k) ]\n // with probs calculated from the |Uij|**2 of the PNMS matrix.\n return [\n [\n c12**2*c13**2,\n c23**2*s12**2 + 2*c12*c23*cCP*s12*s13*s23 + c12**2*s13**2*s23**2,\n c12**2*c23**2*s13**2 - 2*c12*c23*cCP*s12*s13*s23 + s12**2*s23**2\n ],\n [\n c13**2*s12**2,\n c12**2*c23**2 - 2*c12*c23*cCP*s12*s13*s23 + s12**2*s13**2*s23**2,\n c23**2*s12**2*s13**2 + 2*c12*c23*cCP*s12*s13*s23 + c12**2*s23**2\n ],\n [\n s13**2,\n c13**2*s23**2,\n c13**2*c23**2\n ]\n ];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":134,"value":"neutrinoParams = ({\n // From the first column of Table 14.7 in the neutrino review article in RPP 2022.\n // https://pdg.lbl.gov/2023/reviews/rpp2022-rev-neutrino-mixing.pdf\n // Mixing angles in degrees.\n theta12: 33.41,\n theta23: 49.1,\n theta13: 8.54,\n deltaCP: 197,\n // Mass squared differences in eV**2\n dm21sq: 7.41e-5,\n absdm32sq: 2.437e-3, // sign is unknown: +1 for normal ordering, -1 for inverted ordering\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":5,"value":"import {Planck15,FlatLambdaCDM} from \"@dkirkby/cosmocalc\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":90,"value":"import {linspace,geomspace,cumsum,interp} from \"@dkirkby/jumpy\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":81,"value":"import {tidy} from '@dkirkby/array-utilities'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":479,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W36","stdlib":"1","titling":"auto"}} 31:"$30:body"