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The Neutron Mean Life and Big Bang Nucleosynthesis
oleh: Tsung-Han Yeh, Keith A. Olive, Brian D. Fields
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2023-04-01 |
Deskripsi
We explore the effect of neutron lifetime and its uncertainty on standard big bang nucleosynthesis (BBN). BBN describes the cosmic production of the light nuclides, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">H</mi></mrow></semantics></math></inline-formula>, D, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>3</mn></msup><mi mathvariant="normal">H</mi></mrow></semantics></math></inline-formula>+<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>3</mn></msup><mi>He</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>4</mn></msup><mi>He</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>7</mn></msup><mi>Li</mi></mrow></semantics></math></inline-formula>+<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>7</mn></msup><mi>Be</mi></mrow></semantics></math></inline-formula>, in the first minutes of cosmic time. The neutron mean life <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>n</mi></msub></semantics></math></inline-formula> has two roles in modern BBN calculations: (1) it normalizes the matrix element for weak <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>↔</mo><mi>p</mi></mrow></semantics></math></inline-formula> interconversions, and (2) it sets the rate of free neutron decay after the weak interactions freeze-out. We review the history of the interplay between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>n</mi></msub></semantics></math></inline-formula> measurements and BBN, and present a study of the sensitivity of the light element abundances to the modern neutron lifetime measurements. We find that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>n</mi></msub></semantics></math></inline-formula> uncertainties dominate the predicted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>4</mn></msup><mi>He</mi></mrow></semantics></math></inline-formula> error budget, but these theory errors remain smaller than the uncertainties in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>4</mn></msup><mi>He</mi></mrow></semantics></math></inline-formula> observations, even with the dispersion in recent neutron lifetime measurements. For the other light element predictions, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>n</mi></msub></semantics></math></inline-formula> contributes negligibly to their error budget. Turning the problem around, we combine present BBN and cosmic microwave background (CMB) determinations of the cosmic baryon density to <i>predict</i> a “cosmologically preferred” mean life of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mi>n</mi></msub><mrow><mo>(</mo><mrow><mi>BBN</mi><mo>+</mo><mi>CMB</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>870</mn><mo>±</mo><mn>16</mn><mspace width="4pt"></mspace><mi mathvariant="normal">s</mi></mrow></semantics></math></inline-formula>, which is consistent with experimental mean life determinations. We show that if future astronomical and cosmological helium observations can reach an uncertainty of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>obs</mi></msub><mrow><mo>(</mo><msub><mi>Y</mi><mi>p</mi></msub><mo>)</mo></mrow><mo>=</mo><mn>0.001</mn></mrow></semantics></math></inline-formula> in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>4</mn></msup><mi>He</mi></mrow></semantics></math></inline-formula> mass fraction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Y</mi><mi>p</mi></msub></semantics></math></inline-formula>, this could begin to discriminate between the mean life determinations.