Pith Number

pith:OQVMNW62

pith:2026:OQVMNW62LJYC522OLUZIEMPJCW

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Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization

Masaki J. S. Yang

An explicit rephasing transformation converts any unitary mixing matrix to the Fritzsch-Xing parametrization, and under the approximations U13^e=0 and U23^e=0 the FX phase simplifies to the sum of the neutrino-intrinsic phase and the 1-2 re

arxiv:2602.14513 v2 · 2026-02-16 · hep-ph

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Claims

C1strongest claim

We construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch--Xing (FX) parametrization... With an additional approximation U_{23}^{e} = 0, the FX phase becomes highly simplified, reducing to a sum of the neutrino-intrinsic FX phase δ^ν_FX and the contribution from the relative phase ρ'_1 - ρ'_2.

C2weakest assumption

The approximations U_{13}^e = 0 and U_{23}^e = 0, where the 1-3 and 2-3 elements of the charged-lepton diagonalization matrix are neglected; these are invoked to obtain the compact expression for δ_FX.

C3one line summary

Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.

References

56 extracted · 56 resolved · 26 Pith anchors

[1] Before proceeding to the general situation, let us consider another simplified scenario, in whichU e 23 = 0 is imposed by sacrificing the conditionU ν 13 = 0. The mixing matrix is then given by U=  

[2] If|U e 23|is sufficiently small, we can perturbatively expand the expression ofδ FX

[3] C. Jarlskog, Phys. Rev. Lett.55, 1039 (1985) 1985

[4] D.-d. Wu, Phys. Rev. D33, 860 (1986) 1986

[5] J. Bernabeu, G. C. Branco, and M. Gronau, Phys. Lett. B169, 243 (1986) 1986

Receipt and verification

First computed	2026-05-17T23:39:16.132840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

742ac6dbda5a702eeb4e5d328231e915b99f89499bef05bb408ecd9a8c4f7c22

Aliases

arxiv: 2602.14513 · arxiv_version: 2602.14513v2 · doi: 10.48550/arxiv.2602.14513 · pith_short_12: OQVMNW62LJYC · pith_short_16: OQVMNW62LJYC522O · pith_short_8: OQVMNW62

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OQVMNW62LJYC522OLUZIEMPJCW \
  | 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: 742ac6dbda5a702eeb4e5d328231e915b99f89499bef05bb408ecd9a8c4f7c22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff3e7e27e58f1fb78d32d9688b9d9993dc506033414758e308e5906548191e17",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-02-16T06:51:23Z",
    "title_canon_sha256": "e5d0ec64f8d00af165816ff927feb8de7a1b047cd7d17e3b676a0d1f731f1755"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.14513",
    "kind": "arxiv",
    "version": 2
  }
}