Three-loop electronic vacuum-polarization corrections due to irreducible diagrams are evaluated for two-body muonic ions with nuclear charge numbers . The corrections are of order , where is the fine-structure constant and is the reduced mass. Numerically, the energy corrections are found to be of the same order of magnitude as the largest of the order corrections, and are thus phenomenologically interesting. Our method of calculation eliminates numerical uncertainty encountered in other approaches. Published by the American Physical Society2025 
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                            Observing black hole mergers beyond the pair-instability mass gap with next-generation gravitational wave detectors
                        
                    
    
            Stellar evolution predicts the existence of a mass gap for black hole remnants produced by pair-instability supernova dynamics, whose lower and upper edges are very uncertain. We study the possibility of constraining the location of the upper end of the pair-instability mass gap, which is believed to appear around , using gravitational wave observations of compact binary mergers with next-generation ground-based detectors. While high metallicity may not allow for the formation of first-generation black holes on the “far side” beyond the gap, metal-poor environments containing population III stars could lead to such heavy black hole mergers. We show that, even in the presence of contamination from other merger channels, next-generation detectors will measure the location of the upper end of the mass gap with a relative precision close to at 90% CL, where is the number of detected mergers with both members beyond the gap. These future observations could reduce current uncertainties in nuclear and astrophysical processes controlling the location of the gap. Published by the American Physical Society2024 
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                            - Award ID(s):
- 2207502
- PAR ID:
- 10599401
- Publisher / Repository:
- Phys.Rev.D
- Date Published:
- Journal Name:
- Physical Review D
- Volume:
- 110
- Issue:
- 2
- ISSN:
- 2470-0010
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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