AI 中文总结
该研究在对称质量生成模型中为半代费米子赋予显式马约拉纳质量，发现轻质量项需自发对称破缺，且源被屏蔽时未观察到跷跷板混合，临界行为呈饱和交叉。
AI 中文摘要
费米子质量将一个场与一个共轭电荷的伙伴配对：基本（希格斯-狄拉克）、自共轭（跷跷板）或三费米子复合（对称质量生成，SMG）。我们在一个四维SMG模型中给半个Spin(10)类似代赋予显式马约拉纳质量，并询问在无凝聚相中另一半的行为。当源开启时，未加源半代的所有质量型项在源作用量的对称群下平均为零，因此轻质量项以及跷跷板的轻-重混合需要自发对称破缺；这在格点上精确成立，且是一个一般性命题。该源是颜色民主的（对每种味道的右手味道双重态施加Delta_R型质量）；单个nu_R分裂位于所使用的正性类之外，但在对称性陈述之内。测量至8^4：(i)在对称能隙相中，当源被屏蔽至自由值的至多1.1%时，未加源半代的单费米子读出保持在自由值的0.3%，而其配对磁化率在h=2时从0.2%上升至1.2-1.7%；在相似模式集上，它随体积下降，在(4^4,8^4)上，没有不等价的轻质量通道比自由场增长更快，且对称性破缺在L<=8时未被分辨；(ii)在临界点，显式质量坍缩了临界sigma通道，并将轻半代推向自由场，表现为饱和交叉而非幂律；方向测试（按其预注册字母为MIXED）与临界耦合随质量增加一致；y_c(h)未被定位。轻传播子在p->0处的极点与零点未被测量。结果是在预注册测试后的读数，这些测试大多未给出裁决。此外：在L<=8处合并跃迁无一级相变特征，一个Z_4奇响应被交给格点复合体，以及正性类的味道民主。每个声明都有证据类别和可运行检查。
英文摘要
A fermion mass pairs a field with a partner of conjugate charge: elementary (Higgs-Dirac), self-conjugate (seesaw) or a three-fermion composite (symmetric mass generation, SMG). We give half of a Spin(10)-like generation an explicit Majorana mass in a four-dimensional SMG model and ask what the other half does in a phase with no condensate. With the source on, every mass-type term of the unsourced half averages to zero under the symmetry group of the sourced action, so a light mass term, and a seesaw's light-heavy mixing, requires a spontaneously broken symmetry; exact on the lattice and a general proposition. The source is colour-democratic (a Delta_R-type mass on every flavour's right-handed taste doublet); the single-nu_R split lies outside the positivity class used but inside the symmetry statement. Measured up to 8^4: (i) in the symmetric-gap phase, with the source screened to at most 1.1% of free, the unsourced half's single-fermion readout stays at 0.3% of free while its pair susceptibility rises from 0.2% to 1.2-1.7% at h=2; on like mode sets it falls with the volume, on (4^4,8^4) no inequivalent light mass channel grows faster than free, and symmetry breaking is not resolved at L<=8; (ii) at the critical point the explicit mass collapses the critical sigma channel and moves the light half toward free as a saturating crossover, not a power law; direction tests (MIXED by their pre-registered letter) are consistent with a critical coupling rising with the mass; y_c(h) is not located. Pole versus zero of the light propagator at p->0 is not measured. The outcomes are readings after pre-registered tests that mostly returned no verdict. Also: no first-order signature of the merged transition at L<=8, a Z_4-odd response handed to a lattice composite, and flavour democracy of the positivity class. Every claim has an evidence class and a runnable check.
Comments21 pages, 4 figures, 17 tables; code and machine-checked claims at https://github.com/PiotrTopa/mass-as-pairing (v1.0.1, DOI 10.5281/zenodo.23178329), data DOI 10.5281/zenodo.23117210
