Pith Number

pith:XPR4IMOJ

pith:2026:XPR4IMOJ7SO6N7CLIHZDDX47DU

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Recoil corrections to $\mu$H hyperfine splitting

Andrzej Maro\'n, Krzysztof Pachucki, Mateusz Pa\'ntak

The full theory of muonic hydrogen hyperfine splitting, with direct recoil and QED corrections and proton structure taken from ordinary hydrogen, yields 182626(5) μeV for the ground state.

arxiv:2604.06930 v2 · 2026-04-08 · physics.atom-ph

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\pithnumber{XPR4IMOJ7SO6N7CLIHZDDX47DU}

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The resulting theoretical prediction for the ground state of μH is E_hfs = 182626(5) μeV.

C2weakest assumption

The proton structure correction extracted from ordinary hydrogen hyperfine splitting can be applied to muonic hydrogen with only the quoted 5 μeV uncertainty and without additional model-dependent errors from the different reduced-mass and wave-function regimes.

C3one line summary

The ground-state hyperfine splitting in muonic hydrogen is predicted as 182626(5) μeV after including all contributions above 1 ppm.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Hadronic vacuum polarization in hydrogen-like atoms and ions amid the interplay of recoil and finite-size effects

Receipt and verification

First computed	2026-06-19T16:10:37.209821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbe3c431c9fc9de6fc4b41f231df9f1d04923732f9b86b49eeea74710a4e618b

Aliases

arxiv: 2604.06930 · arxiv_version: 2604.06930v2 · doi: 10.48550/arxiv.2604.06930 · pith_short_12: XPR4IMOJ7SO6 · pith_short_16: XPR4IMOJ7SO6N7CL · pith_short_8: XPR4IMOJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XPR4IMOJ7SO6N7CLIHZDDX47DU \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: bbe3c431c9fc9de6fc4b41f231df9f1d04923732f9b86b49eeea74710a4e618b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "549b15ad4c0921e6ae5e69cd37843d79145f81b61835458f1bf5ee9ceafeb041",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.atom-ph",
    "submitted_at": "2026-04-08T10:43:04Z",
    "title_canon_sha256": "b67fb6118c6b6d96bdba0f0655c3ecf3e1f3e13797f8c011ce3e782056038ecd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.06930",
    "kind": "arxiv",
    "version": 2
  }
}