论文标题
质子稳定性：从标准模型到超越大统一
Proton Stability: From the Standard Model to Beyond Grand Unification
论文作者
论文摘要
质子以其长寿而闻名，但是它的生命是什么？虽然许多宏伟的统一理论预测了质子衰变，但我们表明，标准模型（SM）和某些版本的超统一版（它们用新的外来散布/间隙/间隙的无菌中微子代替无菌中微子，例如，在全球隔离型下，拓扑或完美的领域，拓扑或完美的田地理论）用baryon and baryon plaryon pluse synmtry synmtry synmtry stat a stat a stat a stat a stat a stat a stat a stemtry。对于与15或16个Weyl fermions的$ N_F $的4D SM，除了连续的Baryon Minus Lepton U（1）$ _ {\ bf b -l} $对称性，还有一个兼容的离散Baryon Baryon Plus Lepton Plus Lepton $ \ MathBB {Z} _} _ _ {2n_f，\ l} $ \ mathbb {z} _ {2n_f，\ bf b + l} $由于BPST SU（2）Instanton下的ABJ异常，因此是离散的。虽然u（1）$ _ {\ bf b -l} $和$ \ m m mathbb {z} _ {2n_f，\ bf b + l} $ symmetries在动态的sm仪上是无异常的，在动态的sm仪领域下，在重力范围和更高的对象方面是否有指控的对象（是否具有自动化的对象）（是否具有自动化对象）（WIR WIR）。 SM。我们还可以用离散的变体$ \ mathbb {z} _ {z} _ {4，x} $替换u（1）$ _ {\ bf b- l} $，for $ x \ equiv 5（{\ bf b -l} $ for $ x} $我们通过控制SM的变形类别的COOBORDISM理论探讨了4D SM的候选局部局部和非扰动全局异常的系统分类，包括所有这些仪表和引力背景。我们在存在离散$ {\ bf b + l} $对称保护的情况下，特别是（u（u（1）$ _ {\ bf b -l} \ times \ times \ mathbb {z} _ {2n_f，\ bf b + l}）{ f}} $或$（\ mathbb {z} _ {4，x} \ times \ times \ mathbb {z} _ {2n_f，\ bf b + l}） $ \ mathbb {z} _2^{\ rm f} $。
A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of Ultra Unification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4d SM with $N_f$ families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry. The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ symmetries are anomaly-free under the dynamical SM gauge field, it is important to check whether they have mixed anomalies with the gravitational background field and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)$_{\bf B - L}$ with a discrete variant $\mathbb{Z}_{4,X}$ for $X \equiv 5({\bf B - L})-\frac{2}{3} {\tilde Y}$ of electroweak hypercharge ${\tilde Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of discrete ${\bf B + L}$ symmetry protection, in particular (U(1)$_{\bf B - L} \times \mathbb{Z}_{2N_f,\bf B + L})/{\mathbb{Z}_2^{\rm F}}$ or $(\mathbb{Z}_{4,X} \times \mathbb{Z}_{2N_f, \bf B + L})/{\mathbb{Z}_2^{\rm F}}$ symmetry with the fermion parity $\mathbb{Z}_2^{\rm F}$.
