The Higgs Trilinear Coupling and the Scale of New Physics for the SM-Axion-Seesaw-Higgs portal inflation (SMASH) Model

Comment: (1) Abstract written in better form,
(2) Last line added to abstract,
(3) In section: Introduction in the first paragraph we added new references
including our Institute, JINR's recent works on RGE,
(4) In section: Introduction in the third paragraph, recent references added
for HL-LHC and FCC,
(5) Eq. 3 little bit extended,
(6) Boxes around Eq. 8 removed and divided by two formulas, i.e. Eq. 8 and Eq. 9,
(7) Boxes around Eq. 13 removed,
(8) As per Feynman rules Eq. 15 corrected and proper co-efficients added,
(9) After Eq. 16 new line added for new diagram Fig. 3,
(10) All m_\sigma replaced by m_\rho to make consistent with the notation,
(11) In the paragraph after Eq. 16, second and third line "Specifically, the ... HL-LHC." added to explain Eq. 15 properly,
(12) Fig. 3 added for One-loop SM triple Higgs coupling correction diagram with a cubic vertex and a quartic vertex,
(13) Eq. 17 corrected,
(14) Footnote 1 added for Eq. 17,
(15) After Eq. 21 in the paragraph: "It is possible ... [74].", we mentioned cosmological upper mass bound for sum of neutrino masses with references and lower mass bound from theoretical calculations with one reference,
(16) A new Eq. 23 added to explain Eq. 22 properly,
(17) In the Eq. 23 paragraph we have added "After removing ... m_i=Cy_i^2/Y_i.", to explain we assumed normal mass ordering,
(18) In Table 1, we remove typos to make it consistent with the notation of the Yukawas,
(19) We also removed typos to make notations of the Yukawas consistent throughout the manuscript,
(20) A new Eq. 25 added to explain \eta,
(21) And a few lines added at the end of the paragraph of Eq. 25, "To achieve ... is in Fig. 4", to explain lepton asymmetry for SMASH,
(22) Table 3 became Table 2 and Table 2 became Table 3, due to priority in appearance in the text,
(23) In Table 2, in the 5th column the neutrino mass bound is explained with references including table caption,
(24) Just before the section: Methods, we mentioned one paragraph about our future course of analysis, " We will investigate ... SMASH framework.",
(25) In the second paragraph of the section: Methods, the notation of the Yukawas consistent with other parts of the manuscript,
(26) At the end of section: Methods, one more bullet point added "avoid the overproduction ... (requiring \lambda_{H\sigma} < 0),"
(27) One more Eq. 28 added for stability conditions,
(28) In the seventh paragraph of section: Results, Yukawa notations are consistent with text,
(29) In the seventh paragraph of section: Results, a new line added "Note that all ... GeV [30-32].",
(30) The eighth paragraph of section: Results, is a new paragraph,
(31) A new line "According to PDG ... channel alone." added to the ninth paragraph of section: Results, to explain \lambda_{HHH},
(32) A footnote 3 is added to the ninth paragraph of the section: Results,
(33) In section: Conclusions, in the second paragraph few more references added,
(34) In section: Conclusions, in the second paragraph last line " The lepton asymmetry ... for the SMASH framework." added,
(35) In Acknowledgments, one more line added,
(36) In Table 3 in the caption reference added for SM inputs,
(37) A new Fig. 4 added for the evolution of the lepton asymmetry,
(38) In section: Methods, in the third paragraph references added for SM inputs,
(39) In Fig. 6, the fonts for contour numbers have been increased,
(40) In Fig. 10, the fonts for contour numbers have been increased,
(41) There are over all increase of around 30 references to accommodate recent and update works,
(42) Grammar and spelling mistakes have been resolved, and some sentences are now better written,
(43) Keywords after abstract has been added,
(44) In Fig.1 we put the missing factor 2 in both Feynman diagram (-i2\lambda...),
(45) Minor issues like all lambda_S have been corrected to lambda_\sigma,
(46) PDG references updated with newer version,
(47) In the results section, second to last paragraph, last four lines added.