The Standard Model Theory of Neutron Beta Decay
Abstract
:1. Introduction
2. Differential Decay Rate
3. Inner Radiative Corrections
4. -Box Diagram in Dispersive Representation
4.1. Model-Independent Determination of
4.2. Dispersive Determinations of
- “Non-asymptotic” pieces (Born, low-energy continuum, resonances) that are different for different channels of and need to be calculated case-by-case;
- “Asymptotic” piece at high energy which is universal for different channels of (up to Clebsch–Gordon factors). This piece can be extracted from experimental data or other measurable structure functions. Within this latter class we also distinguish the “subasymptotic” part which, while being largely universal, contains a significant amount of model dependence.
4.3. Non-Dispersive Determination of
- 1.
- The integral is equal for and .
- 2.
- The term in is required to vanish at large .
- 3.
- .
4.4. Recommended Values for , , ,
- Both tables define the “DIS” entry as everything above GeV; but the non-DR papers adopts GeV instead as the separation scale between the “perturbative” and “non-perturbative” region of their integral. In order to translate the latter, Ref. [108] subtracts from the DIS results in the non-DR papers an estimated value of the “DIS contribution from 1 to 2 GeV” given in Ref. [67]. In this review we do not follow such a prescription, but compute instead the GeV integral directly using the known analytic formula from pQCD.
- The authors of Ref. [108] followed Ref. [67] and include the effect of the running in the box diagram; to do so they need to manually increase the DIS results in Refs. [60,61,87,92,93] by about 4%; on the contrary, in this work we define with a constant and move the running effect into following Ref. [65]. Consequently, our DIS result is lower than that in Ref. [67] by 4%.
- We display the uncertainty of the “Regge” part of the non-DR works, which was omitted in Ref. [108].
5. Lattice QCD
5.1. The -Box Diagram: Semileptonic Pion and Kaon Decays
5.2. Rc To the Nucleon Axial Coupling Constant
6. Effective Field Theory Description of Radiative Corrections
7. Searches for Physics Beyond the Standard Model: Beta Decays vs. LHC
8. Conclusions & Outlook
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Kinematics
1 | Notice: in Ref. [45] corresponds to in this work. |
2 |
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[60,61] | [92] | [67] | [93] | [87] | Our Value | |
---|---|---|---|---|---|---|
Born | 1.06(6) | 1.06(6) | 1.05(4) | 0.99(10) | 1.06(6) | 1.06(6) |
Res. | 0.05(1) | 0.05(1) | 0.04(1) | - | - | 0.05(1) |
Regge | 0.51(8) | 0.56(9) | 0.52(7) | 0.38(3) | 0.53(7) | 0.54(6) |
DIS | 2.17 | 2.16 | 2.20(3) | 2.16 | 2.16 | 2.20(3) |
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Gorchtein, M.; Seng, C.-Y. The Standard Model Theory of Neutron Beta Decay. Universe 2023, 9, 422. https://doi.org/10.3390/universe9090422
Gorchtein M, Seng C-Y. The Standard Model Theory of Neutron Beta Decay. Universe. 2023; 9(9):422. https://doi.org/10.3390/universe9090422
Chicago/Turabian StyleGorchtein, Mikhail, and Chien-Yeah Seng. 2023. "The Standard Model Theory of Neutron Beta Decay" Universe 9, no. 9: 422. https://doi.org/10.3390/universe9090422
APA StyleGorchtein, M., & Seng, C.-Y. (2023). The Standard Model Theory of Neutron Beta Decay. Universe, 9(9), 422. https://doi.org/10.3390/universe9090422