Nucleon cosmological constant term and flavor structure of the gravitational form factors

The gravitational form factors furnish information on the mechanics of the nucleon. It is essential to compute the generalized isovector-vector form factors to examine the flavor structure of the gravitational form factors. The flavor-decomposed form factors reveal the internal structure of the nucleon. The up quark dominates over the down quark for the mass and spin of the nucleon, whereas the down quark takes over the up quark for the $D$-term form factor. We investigate for the first time the isovector cosmological constant term of the nucleon and its physical implications. The flavor-decomposed cosmological constant terms of the nucleon unveil how the up-quark contribution is exactly canceled by the down-quark contribution inside a nucleon within the framework of the pion mean-field approach. While the nucleon cosmological constant term does not contribute to the nucleon mass, its flavor structure sheds light on how the strong force fields due to the cosmological constant term characterize the stability of the nucleon.