{"product_id":"weinberga-weak-mixing-angle","title":"Weinberga – Weak Mixing Angle \/ The Electroweak Dial Physics Sticker","description":"\u003cp\u003eWeinberga, a two-sword dial-mage of The SI Guard, turns the B and W³ blades through about 29° to forge the photon and the Z.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn the electroweak theory (Glashow, Weinberg, Salam), the neutral gauge fields B and W³ mix. Rotating them by the weak mixing angle θ\u003csub\u003eW\u003c\/sub\u003e gives the massless photon and the massive Z boson. The angle also links the couplings: e = g sin θ\u003csub\u003eW\u003c\/sub\u003e.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003esin²θ\u003csub\u003eW\u003c\/sub\u003e ≈ 0.231 (MS-bar at M\u003csub\u003eZ\u003c\/sub\u003e)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eθ\u003csub\u003eW\u003c\/sub\u003e: weak mixing (Weinberg) angle, about 28.7°\u003c\/li\u003e\n\u003cli\u003eMS-bar: modified minimal-subtraction renormalisation scheme\u003c\/li\u003e\n\u003cli\u003eM\u003csub\u003eZ\u003c\/sub\u003e: Z boson mass scale, about 91.19 GeV\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe PDG 2024 values are ŝ²\u003csub\u003eZ\u003c\/sub\u003e = 0.231 29(4) in the MS-bar scheme at M\u003csub\u003eZ\u003c\/sub\u003e, and s²\u003csub\u003eW\u003c\/sub\u003e = 1 − M\u003csub\u003eW\u003c\/sub\u003e²\/M\u003csub\u003eZ\u003c\/sub\u003e² ≈ 0.223 in the on-shell scheme. It is measured, not exact.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e sin²θ\u003csub\u003eW\u003c\/sub\u003e is not one fixed number. Its value depends on the renormalisation scheme and runs with energy scale (it is about 0.238 at low energy in MS-bar). The sticker's “≈ 0.23” matches the MS-bar value at M\u003csub\u003eZ\u003c\/sub\u003e.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eWeinberga crosses her two glowing violet blades. Printed text: \u003cstrong\u003eWEINBERGA\u003c\/strong\u003e with the line \u003cstrong\u003esin²θ ≈ 0.23\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50963655622759,"sku":"18191939001521695872","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50963655655527,"sku":"23762031985977408371","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50963655688295,"sku":"66817764832497318163","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50963655721063,"sku":"15600990512490940533","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/12636766075850833534_1200.jpg?v=1793665225","url":"https:\/\/pixelatedphysics.com\/id\/products\/weinberga-weak-mixing-angle","provider":"Pixelated Physics","version":"1.0","type":"link"}