Mordred

To better understand the Weinberg mixing angles with regards to the CKMS matrix and to further examine the aspects of the seesaw mechanism of the Higgs field. Assuming supersymmetry though you would have supersymmetric Higgs partners as well. Supersymmetry though hasn't been disproven yet and is still viable. However our colliders are still too low an energy level to produce a supersymmetric particle. Were on the minimal border line however. From what I see the supersymmetric partners do not work in the current CKMS matrix so you would need a different matrix to account for them. That is what I'm confirming. I was correct you need a super-CKMS matrix for supersymmetry. Details here https://arxiv.org/pdf/0810.1613.pdfc Bose Einstein QFT format. \[|\vec{k_1}\vec{k_2}\rangle\hat{a}^\dagger(\vec{k_1})\hat{a}^\dagger(\vec{k_2})|0\rangle\] \[\Rightarrow |\vec{k_1}\vec{k_2}\rangle= |\vec{k_2}\vec{k_1}\rangle\] number operator \[\hat{N}=\hat{a}^\dagger(\vec{k})\hat{a}\vec{k})\] Hamilton operator \[\hat{H}=\int d^3k\omega_k[\hat{N}(\vec{k})+\frac{1}{2}]\] momentum of field \[\hat{P}=\int d^3k\vec{k}[\hat{N}(\vec{k})+\frac{1}{2}]\] renormlized Hamilton \[\hat{H_r}=\int d^3 k\omega_k\hat{a}^\dagger(\vec{k})\hat{a}(\vec{k})\]

Leptogenesis and baryogenesis would occur at the initial electroweak symmetry breaking stages prior to the dark ages where the mean free path of photons due to overall density is less than 10^-30 metres. The CMB data would unlikely be able to preserve any evidence as the expansion and slow roll stages of inflation would cause supercooling followed btmy reheating. However I'm not trying to solve either leptogenesis and baryogenesis. I already know the cross scatterings show that the right neutrino mixing angles would be insufficient in quantity via the Higgs seesaw to account for either That possibility is already well researched. However there is current research studying neutrino oscillations itself that may or may not provide insight to the above.

Uh huh and yet every particle of the standard model today was predicted using the methodologies you describe as old fashioned.There is a reason those models stick around to this day. They work extremely well in making testable predictions. Anyways that's really your hangup and opinion not mine. I stick to what I know has been successful and is still capable of being sucessful. Using proven successful methodologies. Thus far this thread has been far more claim than proving your mathematics work. So your not presenting anything convincing. Words and claims are essentially meaningless.

True however one must also factor in the luminosity relations. If you spread the infalling material over a wider area with the outgoing material also spread over a larger area. The material won't be as energized and subsequently a lower temperature. So the mean average frequency is lower. So both the luminosity and apparent magnitude would be reduced as opposed to a single confined outgoing accretion jet.

All good, it took me several months studying various literature directly relating to CKMS for me to finally fill in the blanks and be comfortable working with it. It has been one of my goals in this thread. (Still is but now that I figured out how the cross sections connect to to the CKMS for both left and right hand particles. I can now look at the supersymmetric partners.

Higgsstralung with k in c.m momentum of Higgs boson \[\sigma(g_i\overline{q}_j)\rightarrow=\frac{\pi \alpha^2 |V_{ij}|^2}{36sin^4\theta_W}\frac{2k}{\sqrt{s}}\frac{k^2+3m^2_W}{(s-m^2_W)^2}\] \[\sigma(f\acute{f}\rightarrow ZH)=\frac{2\pi\alpha^2|v_{ij}|^2(\ell^2_f+r^2_f)}{48n_csin^4\theta_Wcos_W^2}\frac{2k}{\sqrt{s}}\frac{k^2+3m_Z^2}{(s-m^2_Z)^2}\] note last equation shows all quarks contribute to ZZ fusion process. V denotes the CKM matrix usage [latex]\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}[/latex] [latex]V_{ckm}=V^\dagger_{\mu L} V_{dL}[/latex] the CKM mixing angles correlates the cross section between the mass eigenstates and the weak interaction eigenstates. Involves CP violations and chirality relations. Kk cool the first 2 equations show how the cross section correlates to the CKMS with the Higgs already factored in on the partial widths. The partial widths correlate to the detector channels. @GenadyI'm going to need the MSSM chiral operators. Simply as I have the supersymmetric cross sections and would like to examine them further.

Lol the aliens with tentacles might object in favor of the binary system.

Better to ask the aliens assuming they even use the decimal system lol. In all seriousness the more you describe your theory Baron the wilder and more unlikely it becomes.

SO(3,1) universal cover SL(2C) spin1/2 Lie group Pauli matrices \[SL(2\mathbb{C})={M\in Mat(2\mathbb{C});det(M)=1}\] \[(X= 2*2) Hermitian-matrices \begin{pmatrix}x^2+x^3&x^1-ix^2\\x^1+ix^2&x^0-x^3\end{pmatrix}\] \[\sigma_0=\begin{pmatrix}1&0\\0&1\end{pmatrix}\] \[\sigma_1=\begin{pmatrix}0&1\\1&0\end{pmatrix}\] \[\sigma_2=\begin{pmatrix}0&i\\-i&0\end{pmatrix}\] \[\sigma_3=\begin{pmatrix}1&0\\0&-1\end{pmatrix}\] \[det(x)=x_0^2-x_1^2-x_2^2-x_3^2\] \[\Psi=\begin{pmatrix}\Psi+\\\Psi-\end{pmatrix}\in\mathbb{C}^2\] \[(M,\Psi)\rightarrow M\cdot\Psi\] where Dirac spinors consist of 2 Weyl spinors

Higgs cross sections partial width's \[\Gamma(H\rightarrow f\bar{f})=\frac{G_Fm_f^2m_HN_c}{4\pi \sqrt{2}}(1-4m^2_f/m^2_H)^{3/2}\] \[\Gamma(H\rightarrow W^+ W^-)=\frac{GF M^3_H\beta_W}{32\pi\sqrt{2}}(4-4a_w+3a_W^2)\] \[\Gamma(H\rightarrow ZZ)=\frac{GF M^3_H\beta_z}{64\pi\sqrt{2}}(4-4a_Z+3a_Z^2)\] \[N_c=3\] for quarks 1 for leptons \[a_w=1-\beta^2_W=\frac{4m^2_w}{m^2_H}\] \[a_Z=1-\beta^2_Z=\frac{4m^2_Z}{m^2_H}\] explicitely \[\Gamma(H\longrightarrow gg)=\frac{\alpha_s^2G_FM^3_H}{36\pi^3\sqrt{2}}|\sum_q I(\frac{m^2_q}{m^2_H}|^2\] Higgsstralung with k in c.m momentum of Higgs boson \[\sigma(g_i\overline{q}_j)\rightarrow=\frac{\pi \alpha^2 |V_{ij}|^2}{36sin^4\theta_W}\frac{2k}{\sqrt{s}}\frac{k^2+3m^2_W}{(s-m^2_W)^2}\] \[\sigma(f\acute{f}\rightarrow ZH)=\frac{2\pi\alpha^2|v_{ij}|^2(\ell^2_f+r^2_f)}{48n_csin^4\theta_Wcos_W^2}\frac{2k}{\sqrt{s}}\frac{k^2+3m_Z^2}{(s-m^2_Z)^2}\] note last equation shows all quarks contribute to ZZ fusion process

You know you keep stating Physics in stuck in the 60"s and yet I could show you a universe model that applies known physics where the universe can arise from in essence positive matter energy. and negative gravity energy. That was designed back in the 60's. The model employs mathematics developed initially in 1920's Relativity and the FLRW metric 1939. Work still continues to this very day with papers still being written about it. The point you do not seem to grasp is that science never ever closed the book on a given viable theory. Every viable theory will always develop and improve each and every year. They do so with known physics they do not need to reinvent physics. As new research leads to new discoveries those discoveries get included into the applicable theories. You evidently do not seem to be aware of this detail and as such scorn the scientific process as a result. You claim you do not have the funds to get interest from the scientific community. Yet one doesn't require any funds to get a professional Peer reviewed paper published on arxiv or even require a degree. Provided you can convince a PH.D to sponsor your work anyone can get a peer review. This however doesn't mean the paper is correct. It simply means that the paper conforms with its standards and is on the topic being described. I could post papers describing numerous pre-universe models that have 11 dimensions. The Strong pre-universe, the gravitational pre-universe, the Charged pre-universe, the four stage universe. The universe from nothing, the zero energy- universe, the universe from a BH (countless numbers of those) same for the universe from white holes. The time reversal\time forward multiverse pair. The list is literally endless. All of them however have one thing in common. They are all viable in the mathematics they show with known physics. They all deploy a collection of formulas from a collection of any related theories and models. Thermodynamics, the FLRW metric, relativity, QM/QFT some with string theories some without. Some are schotastic other conformal or canonical. However none of them ever saw the need to reinvent any known and well tested physics. so no matter what you claim you never convince me physics is stuck in the 60's. Your wasting your breath on that score. I've watched too many theories develop from one form to later improvements in nearly every theory I have ever studied. That is the very essence of the scientific process and if you believe the idea of the SM particles arising from gravity is something new well that is essence of string theory. Its entire fundamental process applies the graviton as the fundamental string. This was the initial development long before M theory. lol the FLRW metric today isn't even in its original form... Lets take an example exercise. at 10^-43 seconds. The observable universe if you reverse expansion is less than an atom in volume. Actually much smaller than that. Yet we know its an extremely hot, dense state of low entropy. Now myself I would describe this state by the only meaningful mathematics. How would curvature even apply in such a miniscule volume. Why would gravity even be a factor with such a limited volume ? So really the only applicable geometry is simply \[ds^2=g_{ij}dq^idq^j\] which is simply denoting the Kronecker Delta under Cartesian coordinates. At that volume you wouldn't have any time dilation. Everything else is in thermal equilibrium (thermodynamics). So the only other meaningful detail is literally the temperature. Temperature is part of the EM field so one can employ gauge photons as the mediator. Now I can bet dollars to donuts your going to claim differently as from what you described that is not your model. Yet that is how the majority of the physics experts in cosmology will describe the state at that time. One could also use a generalized spacetime (coordinate independant form) ie Euclid, Polar, spherical, Cylindrical. \[ds^2=g_{\alpha\beta}dx^\alpha dx^\beta\] but that is an arbitrary choice with the given volume just a side note on unusual mathematical treatments in older models (still under development to this very day) is to describe particles in binary lattice space. \[|\Psi\rangle=\sum^n_{i=1}|\phi_i\rangle\] where the dimensions can b any arbitrary number from 4 to 11. (part of the zero energy universe model, or one of the numerous variations of the same theme). This equation then works with the nilpotent Dirac equation where the sum of energy, momentum, time and space=0. The model also has specific formulas for particles arising from those factors. for example the fermion mass formula given by that model is \[M_{d,a}=\sum_{M_f}\frac{3M_{b_{d-1,0}}}{2}\sum^a_{a=0}a^4\] this is work once presented by Bohr_Sommerfeld. In essence it is a universe from nothing model where particles arise from spacetime where spacetime equates the potential and kinetic energy terms via the nilpotent Dirac equation and the sum of the potential energy and kinetic energy terms is balanced at zero. Hope that gives you an idea of just a few of the NOT FOUND in textbooks professionally peer reviewed models your competing against. here is the reference for further detail. It is merely 1 out of literal hundreds of professional peer reviewed universe creation models I have come across https://arxiv.org/ftp/hep-th/papers/0201/0201115.pdf I have greater faith in this model that what I have seen of yours simply because there are no grandiose claims that are made. Not that I accept this paper as one I would fully trust this particular paper either. It is simply 1 variation of the theme. I've seen far better variations of zero energy universe treatments.

Likely the easiest way to answer the above is to recognize that in QFT. You don't think of particles as little billiard balls. In QFT all particles are field excitations. An excitation is a waveform however it is not a sinusoidal waveform as you have in your pictures. It would look more like a momentary spike. That momentary spike can be localized with definable boundaries whereas you cannot do the same with a sinusoidal. As all particles are states that encompass the particles wavefunctions you will require the complex conjugates you do in QM. Also you will invariably will applying density functions. You listed two of them but another extremely important one is the probability density functions In the Langrangian you apply any field related details under the potential energy term (coupling constants etc) the momentum terms is the kinetic energy terms. Both of these will vary uncertainty, flux, harmonic oscillator, field variations etc can be and usually is factored in. There is no single langrene formula, one can arbitrarily apply their own Langrene to anything involving kinematic motion. This includes scatterings aka Feymann Integrals as one example. Flux, density and mass are unavoidable terms when your talking field excitations. Mass is simply resistance to inertia change or acceleration. In essence QFT literally describes how the field varies (perturbs) where particles are localized field variations.

Funny part is the specific QFT equation I'm referring to is very rudimentary. QFT uses normalized units and directly applies the energy momentum equation E^2=P^2+m^2. (In normalized units) For field position you apply the coordinate in x^4 which breaks down to x^0=t, ×^1=x, x^2=y, x^3=z. Nice thing about that is it works well with time derivatives as well. Where the complexity starts to develop is when you add probability for the principle of least action (path taken) and quantum harmonic oscillator. That's where the Euler-Langrangian gets incorporated. Geometry related details gets detailed under the Poincare group. While particle details are under their Lorentz invariant gauge group.

If you apply the Klein Gordon equation you will be Lorentz invariant regardless of geometry changes of spacetime. That is the primary reason why the Klein Gordon equation was developed. The equation directly applies the 4 momentum and four velocity.

Under GR all events are inertial. The geodesic equations include this detail. The Euler Langranian equations are capable of handling wave equations with particle paths. The entire body of QFT incorporate that.

So you believe I for one have never come across a single physics related system or state in neither cosmology or particle physics that I cannot model. So I have never seen the point in attempting to rewrite physics at any stage.

Thanks For pointing that out. I will make the corrections once I get a chance though I may just change that section to a more standardized notation. +1 for catching that appreciate it. edit: Yeah I see what you mean I am going to change it to a more standardized format. Thanks again for the catch. I had pulled it from some old note I had put together a few years back. Likely an older format for the Majorana basis there is better and clearer methods. It was from my older notes when I was studying Majorana. yeah figured out what is the issue is I couldn't recall why I needed the identity matrix [latex]\mathbb{I}[/latex] the format pertains to MSSM where the identity matrix is a requirement. I won't be using this format so will change it to the MSM format with the modern tilde to denote Majorona fields. Its from back when I was studying Majorona under Pati-Salam. Its required for the supersymmetric partner identities. Completely forgot about that lmao

right hand neutrino details to examine in particular 3 LH neutrinos with 4 https://arxiv.org/pdf/1911.05092.pdf https://arxiv.org/pdf/1901.00151.pdf https://arxiv.org/pdf/2109.00767v2.pdf question to examine how many seesaw mechanism would 3 doublet 4 singlet Higgs entail and would this lead to Pati-Salam solutions pertaining to SO(10 MSSM). needs further examination Mikheyev–Smirnov–Wolfenstein (MSW) potential 3.5 KeV xray anomoly https://arxiv.org/abs/1402.2301 requirements sterile neutrino mass terms must be in the KeV range to satisfy sterile neutrinos as a DM candidate

The only thing missing from a GUT is how to keep gravity renormalizable. That may sound easy but merely quantizing spacetime or applying a regulator operator hasn't worked. There are valid SM model theories for DM and DE. What is lacking is the ability to verify the theories. However their are countless viable theories waiting for verification. Inflation is another good example. The Aspic library has tested over 70 viable inflationary models. Narrowing down which ones fit observational data the best via Monte Carlo as well as datasets. One essential step in a successful GUT involves "running of the coupling constants " it is a critical step. Particularly to match thermal equilibrium data. Just because I don't require a new mathematical method and use existing gauge groups via SO(10) does not inhibit my ability to make new findings. If anything it improves my chances by simply looking at each particles thermal equilibrium dropout and projected number density with regards to the expansion history of our universe and trace evidence in the CMB. If I cannot produce accuracy to current datasets then I know something is still missing. I will only be successful if I can match current datasets. Simply claiming to do so isn't sufficient. I must ensure any other person can take my work and reproduce the same results with nothing more than the mathematics and zero verbal explanation. Other than identifying any used variables etc. Hence the necessary mathematical proofs, This simulation for example simply tested our models for accuracy. https://www.illustris-project.org/ So consider this metal exercise take BB at \[10^-43\] seconds. You have a temperature roughly 10^19 Kelvin. the volume is so miniscule that you couldn't have any spacetime curvature aka gravity. How do you have curvature with a volume approximately one Planck length ? How would gravity even make sense ? Literally you can describe that state simply by its temperature and volume everything is in thermal equilibrium so one can apply the Bose-Einstein statistic for photon number density at Blackbody temperature 10^19 Kelvin. You should get roughly 10^90 photons. That is how that calculation comes about that is oft included in Cosmology textbooks. Another interesting detail is neutrinos today. Our universe has a blackbody temperature of 2.7 Kelvin. so ask yourself what the Blackbody of neutrinos are today? Now I can answer that question using nothing more that QM and classical physics ? can your model produce the correct answer? As you have already mentioned the required formula possibly but is that formula an integral aspect of your model or simply employing it to fill the gaps of what your GUT doesn't produce ? I really don't know as I know of 3 different methods to get the correct answer in 3 different theorem. All three are part of the standard model. Now it doesn't really matter if you choose to answer or not. That isn't the point. he point is a good GUT needs to be able to match observational evidence but also be able to match results at ATLAS and other particle accelerators. Given that why would I want any NON standard theory when my very goal is to match data that directly applies Standard theory. aka those Wilson coefficients I mentioned which apply to the QCD range not strictly Higgs. The datasets I need employ them so I need to be able to do so as well

The most commonly method to estimate DM rotation curve due to DM is the NFW profile. It a mass power law method. The essence that it shows is that in order to avoid Kelper curve you must have a uniform distribution of mass surrounding a Galaxy in particular spiral galaxies to offset the bulge. I can't recall the name of the most common DM modelling for early LSS formation beyond it involving Jean's instability.

just setting reminder equations that I find handy, in this case the Langrene that correlates the action of the various particle interations ( close to a unification....lol also reminds me how to do some interesting latex techniques... [latex] \mathcal{L}=\underbrace{\mathbb{R}}_{GR}-\overbrace{\underbrace{\frac{1}{4}F_{\mu\nu}F^{\mu\nu}}_{Yang-Mills}}^{Maxwell}+\underbrace{i\overline{\psi}\gamma^\mu D_\mu \psi}_{Dirac}+\underbrace{|D_\mu h|^2-V(|h|)}_{Higgs}+\underbrace{h\overline{\psi}\psi}_{Yukawa}[/latex] [latex]D_\mu[/latex] minimally coupled gauge covariant derivative. h Higg's bosonic field [latex] \chi[/latex] is the Goldstone boson (not shown above) Goldstone no longer applies after spontaneous symmetry breaking [latex]\overline{\psi}[/latex] is the adjoint spinor [latex]\mathcal{L}_h=|D\mu|^2-\lambda(|h|^2-\frac{v^2}{2})^2[/latex] [latex]D_\mu=\partial_\mu-ie A_\mu[/latex] where [latex] A_\mu[/latex] is the electromagnetic four potential QCD gauge covariant derivative [latex] D_\mu=\partial_\mu \pm ig_s t_a \mathcal{A}^a_\mu[/latex] matrix A represents each scalar gluon field Single Dirac Field [latex]\mathcal{L}=\overline{\psi}I\gamma^\mu\partial_\mu-m)\psi[/latex] under U(1) EM fermion field equates to [latex]\psi\rightarrow\acute{\psi}=e^{I\alpha(x)Q}\psi[/latex] due to invariance requirement of the Langrene above and with the last equation leads to the gauge field [latex]A_\mu[/latex] [latex] \partial_\mu[/latex] is replaced by the covariant derivitave [latex]\partial_\mu\rightarrow D_\mu=\partial_\mu+ieQA_\mu[/latex] where [latex]A_\mu[/latex] transforms as [latex]A_\mu+\frac{1}{e}\partial_\mu\alpha[/latex] Single Gauge field U(1) [latex]\mathcal{L}=\frac{1}{4}F_{\mu\nu}F^{\mu\nu}[/latex] [latex]F_{\mu\nu}=\partial_\nu A_\mu-\partial_\mu A_\nu[/latex] add mass which violates local gauge invariance above [latex]\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\frac{1}{2}m^2A_\mu A^\mu[/latex] guage invariance demands photon be massless to repair gauge invariance add a single complex scalar field [latex]\phi=\frac{1}{\sqrt{2}}(\phi_1+i\phi_2[/latex] Langrene becomes [latex] \mathcal{L}=\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+|D_\mu \phi|^2-V_\phi[/latex] where [latex]D_\mu=\partial_\mu-ieA_\mu[/latex] [latex]V_\phi=\mu^2|\phi^2|+\lambda(|\phi^2|)^2[/latex] [latex]\overline{\psi}=\psi^\dagger \gamma^0[/latex] where [latex]\psi^\dagger[/latex] is the hermitean adjoint and [latex]\gamma^0 [/latex] is the timelike gamma matrix the four contravariant matrix are as follows [latex]\gamma^0=\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&-1&0\\0&0&0&-1\end{pmatrix}[/latex] [latex]\gamma^1=\begin{pmatrix}0&0&0&1\\0&0&1&0\\0&0&-1&0\\-1&0&0&0\end{pmatrix}[/latex] [latex]\gamma^2=\begin{pmatrix}0&0&0&-i\\0&0&i&0\\0&i&0&0\\-i&0&0&0\end{pmatrix}[/latex] [latex]\gamma^3=\begin{pmatrix}0&0&1&0\\0&0&0&-1\\-1&0&0&0\\0&1&0&0\end{pmatrix}[/latex] where [latex] \gamma^0[/latex] is timelike rest are spacelike V denotes the CKM matrix usage [latex]\begin{pmatrix}\acute{d}\\\acute{s}\\\acute{b}\end{pmatrix}\begin{pmatrix}V_{ud}&V_{us}&V_{ub}\\V_{cd}&V_{cs}&V_{cb}\\V_{td}&V_{ts}&V_{tb}\end{pmatrix}\begin{pmatrix}d\\s\\b\end{pmatrix}[/latex] [latex]V_{ckm}=V^\dagger_{\mu L} V_{dL}[/latex] the CKM mixing angles correlates the cross section between the mass eigenstates and the weak interaction eigenstates. Involves CP violations and chirality relations. Dirac 4 component spinor fields [latex]\gamma^5=i\gamma_0,\gamma_1,\gamma_2,\gamma_3[/latex] 4 component Minkowskii with above 4 component Dirac Spinor and 4 component Dirac gamma matrixes are defined as [latex] {\gamma^\mu\gamma^\nu}=2g^{\mu\nu}\mathbb{I}[/latex] where [latex]\mathbb{I}[/latex] is the identity matrix. (required under MSSM electroweak symmetry break} in Chiral basis [latex]\gamma^5[/latex] is diagonal in [latex]2\otimes 2[/latex] the gamma matrixes are [latex]\begin{pmatrix}0&\sigma^\mu_{\alpha\beta}\\\overline{\sigma^{\mu\dot{\alpha}\beta}}&0\end{pmatrix}[/latex] [latex]\gamma^5=i{\gamma_0,\gamma_1,\gamma_2,\gamma_3}=\begin{pmatrix}-\delta_\alpha^\beta&0\\0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] [latex]\mathbb{I}=\begin{pmatrix}\delta_\alpha^\beta&0\\0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] Lorentz group identifiers in [latex](\frac{1}{2},0)\otimes(0,\frac{1}{2})[/latex] [latex]\sigma\frac{I}{4}=(\gamma^\mu\gamma^\nu)=\begin{pmatrix}\sigma^{\mu\nu\beta}_{\alpha}&0\\0&-\sigma^{\mu\nu\dot{\alpha}}_{\dot{\beta}}\end{pmatrix}[/latex] [latex]\sigma^{\mu\nu}[/latex] duality satisfies [latex]\gamma_5\sigma^{\mu\nu}=\frac{1}{2}I\epsilon^{\mu\nu\rho\tau}\sigma_{\rho\tau}[/latex] a 4 component Spinor Dirac field is made up of two mass degenerate Dirac spinor fields U(1) helicity [latex](\chi_\alpha(x)),(\eta_\beta(x))[/latex] [latex]\psi(x)=\begin{pmatrix}\chi^{\alpha\beta}(x)\\ \eta^{\dagger \dot{\alpha}}(x)\end{pmatrix}[/latex] the [latex](\alpha\beta)=(\frac{1}{2},0)[/latex] while the [latex](\dot{\alpha}\dot{\beta})=(0,\frac{1}{2})[/latex] this section relates the SO(4) double cover of the SU(2) gauge requiring the chiral projection operator next. chiral projections operator [latex]P_L=\frac{1}{2}(\mathbb{I}-\gamma_5=\begin{pmatrix}\delta_\alpha^\beta&0\\0&0\end{pmatrix}[/latex] [latex]P_R=\frac{1}{2}(\mathbb{I}+\gamma_5=\begin{pmatrix}0&0\\ 0&\delta^\dot{\alpha}_\dot{\beta}\end{pmatrix}[/latex] Weyl spinors [latex]\psi_L(x)=P_L\psi(x)=\begin{pmatrix}\chi_\alpha(x)\\0\end{pmatrix}[/latex] [latex]\psi_R(x)=P_R\psi(x)=\begin{pmatrix}0\\ \eta^{\dagger\dot{a}}(x)\end{pmatrix}[/latex] also requires Yukawa couplings...SU(2) matrixes given by [latex]diag(Y_{u1},Y_{u2},Y_{u3})=diag(Y_u,Y_c,Y_t)=diag(L^t_u,\mathbb{Y}_u,R_u)[/latex] [latex]diag(Y_{d1},Y_{d2},Y_{d3})=diag(Y_d,Y_s,Y_b)=diag(L^t_d,\mathbb{Y}_d,R_d[/latex] [latex]diag(Y_{\ell 1},Y_{\ell 2},Y_{\ell3})=diag(Y_e,Y_\mu,Y_\tau)=diag(L^T_\ell,\mathbb{Y}_\ell,R_\ell)[/latex] the fermion masses [latex]Y_{ui}=m_{ui}/V_u[/latex] [latex]Y_{di}=m_{di}/V_d[/latex] [latex]Y_{\ell i}=m_{\ell i}/V_\ell[/latex] Reminder notes: Dirac is massive 1/2 fermions, Weyl the massless. Majorona fermion has its own antiparticle pair while Dirac and Weyl do not. The RH neutrino would be more massive than the LH neutrino, same for the corresponding LH antineutrino and RH Neutrino via seesaw mechanism which is used with the seesaw mechanism under MSM. Under MSSM with different Higgs/higglets can be numerous seesaws. The Majorona method has conservation violations also these fermions must be electric charge neutral. (must be antiparticles of themselves) the CKM and PMNS are different mixing angels in distinction from on another. However they operate much the same way. CKM is more commonly used as its better tested to higher precision levels atm. Quark family is Dirac fermions due to electric charge cannot be its own antiparticle. Same applies to the charged lepton family. Neutrinos are members of the charge neutral lepton family CKM is also a different parametrisation than the Wolfenstein Parametrization in what way (next study) Lorentz group Lorentz transformations list spherical coordinates (rotation along the z axis through an angle ) \[\theta\] \[(x^0,x^1,x^2,x^3)=(ct,r,\theta\phi)\] \[(x_0,x_1,x_2,x_3)=(-ct,r,r^2,\theta,[r^2\sin^2\theta]\phi)\] \[\acute{x}=x\cos\theta+y\sin\theta,,,\acute{y}=-x\sin\theta+y \cos\theta\] \[\Lambda^\mu_\nu=\begin{pmatrix}1&0&0&0\\0&\cos\theta&\sin\theta&0\\0&\sin\theta&\cos\theta&0\\0&0&0&1\end{pmatrix}\] generator along z axis \[k_z=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}\] generator of boost along x axis:: \[k_x=\frac{1\partial\phi}{i\partial\phi}|_{\phi=0}=-i\begin{pmatrix}0&1&0&0\\1&0&0&0\\0&0&0&0\\0&0&0&0 \end{pmatrix}\] boost along y axis\ \[k_y=-i\begin{pmatrix}0&0&1&0\\0&0&0&0\\1&0&0&0\\0&0&0&0 \end{pmatrix}\] generator of boost along z direction \[k_z=-i\begin{pmatrix}0&0&0&1\\0&0&0&0\\0&0&0&0\\1&0&0&0 \end{pmatrix}\] the above is the generator of boosts below is the generator of rotations. \[J_z=\frac{1\partial\Lambda}{i\partial\theta}|_{\theta=0}\] \[J_x=-i\begin{pmatrix}0&0&0&0\\0&0&0&0\\0&0&0&1\\0&0&-1&0 \end{pmatrix}\] \[J_y=-i\begin{pmatrix}0&0&0&0\\0&0&0&-1\\0&0&1&0\\0&0&0&0 \end{pmatrix}\] \[J_z=-i\begin{pmatrix}0&0&0&0\\0&0&1&0\\0&-1&0&0\\0&0&0&0 \end{pmatrix}\] there is the boosts and rotations we will need and they obey commutations \[[A,B]=AB-BA\] SO(3) Rotations list set x,y,z rotation as \[\varphi,\Phi\phi\] \[R_x(\varphi)=\begin{pmatrix}1&0&0\\0&\cos\varphi&\sin\varphi\\o&-sin\varphi&cos\varphi \end{pmatrix}\] \[R_y(\phi)=\begin{pmatrix}cos\Phi&0&\sin\Phi\\0&1&0\\-sin\Phi&0&cos\Phi\end{pmatrix}\] \[R_z(\phi)=\begin{pmatrix}cos\theta&sin\theta&0\\-sin\theta&\cos\theta&o\\o&0&1 \end{pmatrix}\] Generators for each non commutative group. \[J_x=-i\frac{dR_x}{d\varphi}|_{\varphi=0}=\begin{pmatrix}0&0&0\\0&0&-i\\o&i&0\end{pmatrix}\] \[J_y=-i\frac{dR_y}{d\Phi}|_{\Phi=0}=\begin{pmatrix}0&0&-i\\0&0&0\\i&i&0\end{pmatrix}\] \[J_z=-i\frac{dR_z}{d\phi}|_{\phi=0}=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] with angular momentum operator \[{J_i,J_J}=i\epsilon_{ijk}J_k\] with Levi-Civita \[\varepsilon_{123}=\varepsilon_{312}=\varepsilon_{231}=+1\] \[\varepsilon_{123}=\varepsilon_{321}=\varepsilon_{213}=-1\] SU(3) generators Gell Mann matrix's \[\lambda_1=\begin{pmatrix}0&-1&0\\1&0&0\\0&0&0\end{pmatrix}\] \[\lambda_2=\begin{pmatrix}0&-i&0\\i&0&0\\0&0&0\end{pmatrix}\] \[\lambda_3=\begin{pmatrix}1&0&0\\0&-1&0\\0&0&0\end{pmatrix}\] \[\lambda_4=\begin{pmatrix}0&0&1\\0&0&0\\1&0&0\end{pmatrix}\] \[\lambda_5=\begin{pmatrix}0&0&-i\\0&0&0\\i&0&0\end{pmatrix}\] \[\lambda_6=\begin{pmatrix}0&0&0\\0&0&1\\0&1&0\end{pmatrix}\] \[\lambda_7=\begin{pmatrix}0&0&0\\0&0&-i\\0&i&0\end{pmatrix}\] \[\lambda_8=\frac{1}{\sqrt{3}}\begin{pmatrix}1&0&0\\0&1&0\\0&0&-2\end{pmatrix}\] commutation relations \[[\lambda_i\lambda_j]=2i\sum^8_{k=1}f_{ijk}\lambda_k\] with algebraic structure \[f_{123}=1,f_{147}=f_{165}=f_{246}=f_{246}=f_{257}=f_{345}=f_{376}=\frac{1}{2},f_{458}=f_{678}=\frac{3}{2}\] with Casimer Operator \[\vec{J}^2=J_x^2+J_y^2+j_z^2\]

Some of the aspects, I came across by doing the calculations and I will use Hydrogen thermal equilibrium dropout as an example. If one employs the Saha equations instead of relying on literature. One discovers that the hydrogen dropout value of 3000 kelvin only represents the value at the 75% mark. Hydrogen will begin drop out previous to that. At 6000 kelvin the % is 25%, at 4500 Kelvin the percentage is at 50%. It is details such as this that become apparent when one looks beyond literature, performs his own calculations and doesn't rely on merely verbal descriptions. Another example is that by applying the Langrangian creation and annihilation operators one can get a more exacting value for number density (albiet its a probability density) that applying Maxwell Boltzmann. Which is the more common methodology. Both are equally valid, but each method has its pros and cons. Maxwell Boltzmann is a far easier method but is more an first order approximation comparatively. Where as the former method makes it far easier to cross check with collider datasets for key aspects and works well with Feymann integrals

Trust me there will be very little comparison between your model and ideas and mine lol. Everything in my models use the standardized physics methodologies. I didn't have to create a single formula beyond deriving the elements I require out of them from the mathematical proofs of the existing formulas. These threads I have been using as a sort of whiteboard with regards to some of the formulas I am deploying. https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/ Orion and I spent some time breaking apart the Covariant derivative form of the SM Langrangian mainly to cross check its validity while Orion worked on the relativity portion. wish he was still around as he excelled at applying Maxwell Boltzmann applications. one of the tools I will be using for cross check accuracy is \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&T (Gy)&R (Gly)&D_{now} (Gly)&Temp(K) \\ \hline 2.00e+4&1.86e-6&3.49e-6&4.62e+1&5.45e+4\\ \hline 1.73e+4&2.45e-6&4.62e-6&4.62e+1&4.71e+4\\ \hline 1.49e+4&3.23e-6&6.10e-6&4.62e+1&4.07e+4\\ \hline 1.29e+4&4.25e-6&8.04e-6&4.61e+1&3.52e+4\\ \hline 1.12e+4&5.60e-6&1.06e-5&4.61e+1&3.04e+4\\ \hline 9.66e+3&7.37e-6&1.39e-5&4.61e+1&2.63e+4\\ \hline 8.35e+3&9.70e-6&1.83e-5&4.61e+1&2.27e+4\\ \hline 7.21e+3&1.28e-5&2.39e-5&4.61e+1&1.97e+4\\ \hline 6.24e+3&1.68e-5&3.12e-5&4.60e+1&1.70e+4\\ \hline 5.39e+3&2.20e-5&4.07e-5&4.60e+1&1.47e+4\\ \hline 4.66e+3&2.87e-5&5.29e-5&4.60e+1&1.27e+4\\ \hline 4.03e+3&3.75e-5&6.85e-5&4.59e+1&1.10e+4\\ \hline 3.48e+3&4.89e-5&8.86e-5&4.59e+1&9.49e+3\\ \hline 3.01e+3&6.36e-5&1.14e-4&4.58e+1&8.21e+3\\ \hline 2.60e+3&8.25e-5&1.47e-4&4.58e+1&7.09e+3\\ \hline 2.25e+3&1.07e-4&1.88e-4&4.57e+1&6.13e+3\\ \hline 1.94e+3&1.38e-4&2.41e-4&4.57e+1&5.30e+3\\ \hline 1.68e+3&1.78e-4&3.08e-4&4.56e+1&4.58e+3\\ \hline 1.45e+3&2.28e-4&3.92e-4&4.55e+1&3.96e+3\\ \hline 1.26e+3&2.93e-4&4.98e-4&4.54e+1&3.42e+3\\ \hline 1.09e+3&3.75e-4&6.31e-4&4.53e+1&2.96e+3\\ \hline 9.38e+2&4.78e-4&7.98e-4&4.52e+1&2.56e+3\\ \hline 8.11e+2&6.09e-4&1.01e-3&4.51e+1&2.21e+3\\ \hline 7.01e+2&7.74e-4&1.27e-3&4.50e+1&1.91e+3\\ \hline 6.06e+2&9.83e-4&1.60e-3&4.49e+1&1.65e+3\\ \hline 5.24e+2&1.24e-3&2.01e-3&4.47e+1&1.43e+3\\ \hline 4.52e+2&1.57e-3&2.53e-3&4.46e+1&1.24e+3\\ \hline 3.91e+2&1.99e-3&3.17e-3&4.44e+1&1.07e+3\\ \hline 3.38e+2&2.50e-3&3.97e-3&4.42e+1&9.23e+2\\ \hline 2.92e+2&3.15e-3&4.97e-3&4.40e+1&7.98e+2\\ \hline 2.52e+2&3.96e-3&6.22e-3&4.38e+1&6.90e+2\\ \hline 2.18e+2&4.98e-3&7.77e-3&4.35e+1&5.97e+2\\ \hline 1.88e+2&6.25e-3&9.71e-3&4.33e+1&5.16e+2\\ \hline 1.63e+2&7.83e-3&1.21e-2&4.30e+1&4.46e+2\\ \hline 1.40e+2&9.81e-3&1.51e-2&4.27e+1&3.85e+2\\ \hline 1.21e+2&1.23e-2&1.89e-2&4.24e+1&3.33e+2\\ \hline 1.05e+2&1.53e-2&2.35e-2&4.20e+1&2.88e+2\\ \hline 9.04e+1&1.92e-2&2.94e-2&4.16e+1&2.49e+2\\ \hline 7.80e+1&2.40e-2&3.66e-2&4.12e+1&2.15e+2\\ \hline 6.73e+1&2.99e-2&4.56e-2&4.08e+1&1.86e+2\\ \hline 5.80e+1&3.74e-2&5.68e-2&4.03e+1&1.61e+2\\ \hline 5.00e+1&4.66e-2&7.07e-2&3.98e+1&1.39e+2\\ \hline 4.31e+1&5.81e-2&8.81e-2&3.93e+1&1.20e+2\\ \hline 3.71e+1&7.25e-2&1.10e-1&3.87e+1&1.04e+2\\ \hline 3.20e+1&9.03e-2&1.37e-1&3.81e+1&8.98e+1\\ \hline 2.75e+1&1.13e-1&1.70e-1&3.74e+1&7.76e+1\\ \hline 2.36e+1&1.40e-1&2.12e-1&3.66e+1&6.71e+1\\ \hline 2.03e+1&1.75e-1&2.63e-1&3.59e+1&5.80e+1\\ \hline 1.74e+1&2.18e-1&3.28e-1&3.50e+1&5.02e+1\\ \hline 1.49e+1&2.71e-1&4.08e-1&3.41e+1&4.34e+1\\ \hline 1.28e+1&3.37e-1&5.08e-1&3.31e+1&3.75e+1\\ \hline 1.09e+1&4.20e-1&6.32e-1&3.21e+1&3.24e+1\\ \hline 9.28e+0&5.23e-1&7.86e-1&3.09e+1&2.80e+1\\ \hline 7.89e+0&6.51e-1&9.78e-1&2.97e+1&2.42e+1\\ \hline 6.68e+0&8.10e-1&1.22e+0&2.84e+1&2.09e+1\\ \hline 5.64e+0&1.01e+0&1.51e+0&2.70e+1&1.81e+1\\ \hline 4.74e+0&1.25e+0&1.88e+0&2.55e+1&1.56e+1\\ \hline 3.96e+0&1.56e+0&2.33e+0&2.38e+1&1.35e+1\\ \hline 3.29e+0&1.94e+0&2.88e+0&2.21e+1&1.17e+1\\ \hline 2.71e+0&2.40e+0&3.56e+0&2.02e+1&1.01e+1\\ \hline 2.21e+0&2.98e+0&4.38e+0&1.83e+1&8.74e+0\\ \hline 1.77e+0&3.69e+0&5.35e+0&1.62e+1&7.55e+0\\ \hline 1.40e+0&4.55e+0&6.49e+0&1.39e+1&6.53e+0\\ \hline 1.07e+0&5.58e+0&7.79e+0&1.16e+1&5.64e+0\\ \hline 7.91e-1&6.82e+0&9.19e+0&9.25e+0&4.88e+0\\ \hline 5.48e-1&8.27e+0&1.07e+1&6.85e+0&4.22e+0\\ \hline 3.38e-1&9.92e+0&1.21e+1&4.47e+0&3.65e+0\\ \hline 1.57e-1&1.18e+1&1.34e+1&2.16e+0&3.15e+0\\ \hline 0.00e+0&1.38e+1&1.44e+1&0.00e+0&2.73e+0\\ \hline -1.36e-1&1.60e+1&1.53e+1&2.03e+0&2.36e+0\\ \hline -2.48e-1&1.81e+1&1.59e+1&3.79e+0&2.05e+0\\ \hline -3.46e-1&2.04e+1&1.64e+1&5.37e+0&1.78e+0\\ \hline -4.31e-1&2.27e+1&1.67e+1&6.77e+0&1.55e+0\\ \hline -5.05e-1&2.50e+1&1.69e+1&8.02e+0&1.35e+0\\ \hline -5.69e-1&2.74e+1&1.71e+1&9.11e+0&1.17e+0\\ \hline -6.25e-1&2.98e+1&1.72e+1&1.01e+1&1.02e+0\\ \hline -6.74e-1&3.22e+1&1.72e+1&1.09e+1&8.88e-1\\ \hline -7.16e-1&3.46e+1&1.73e+1&1.16e+1&7.73e-1\\ \hline -7.53e-1&3.70e+1&1.73e+1&1.23e+1&6.72e-1\\ \hline -7.85e-1&3.94e+1&1.73e+1&1.28e+1&5.85e-1\\ \hline -8.13e-1&4.18e+1&1.73e+1&1.33e+1&5.09e-1\\ \hline -8.38e-1&4.43e+1&1.74e+1&1.37e+1&4.42e-1\\ \hline -8.59e-1&4.67e+1&1.74e+1&1.41e+1&3.85e-1\\ \hline -8.77e-1&4.91e+1&1.74e+1&1.44e+1&3.35e-1\\ \hline -8.93e-1&5.15e+1&1.74e+1&1.47e+1&2.91e-1\\ \hline -9.07e-1&5.39e+1&1.74e+1&1.49e+1&2.53e-1\\ \hline -9.19e-1&5.64e+1&1.74e+1&1.52e+1&2.20e-1\\ \hline -9.30e-1&5.88e+1&1.74e+1&1.53e+1&1.92e-1\\ \hline -9.39e-1&6.12e+1&1.74e+1&1.55e+1&1.67e-1\\ \hline -9.47e-1&6.36e+1&1.74e+1&1.56e+1&1.45e-1\\ \hline -9.54e-1&6.60e+1&1.74e+1&1.58e+1&1.26e-1\\ \hline -9.60e-1&6.85e+1&1.74e+1&1.59e+1&1.10e-1\\ \hline -9.65e-1&7.09e+1&1.74e+1&1.60e+1&9.55e-2\\ \hline -9.70e-1&7.33e+1&1.74e+1&1.60e+1&8.31e-2\\ \hline -9.73e-1&7.57e+1&1.74e+1&1.61e+1&7.23e-2\\ \hline -9.77e-1&7.81e+1&1.74e+1&1.62e+1&6.29e-2\\ \hline -9.80e-1&8.06e+1&1.74e+1&1.62e+1&5.47e-2\\ \hline -9.83e-1&8.30e+1&1.74e+1&1.63e+1&4.76e-2\\ \hline -9.85e-1&8.54e+1&1.74e+1&1.63e+1&4.14e-2\\ \hline -9.87e-1&8.78e+1&1.74e+1&1.63e+1&3.60e-2\\ \hline -9.89e-1&9.02e+1&1.74e+1&1.64e+1&3.13e-2\\ \hline -9.90e-1&9.27e+1&1.74e+1&1.64e+1&2.73e-2\\ \hline \end{array}}\] Jorrie and Cuthberd must be adding features I will have to contact them its not allowing the full column selection range at least not with the latex options. It does for the standard format. Likely they are working on the glitch already but will check p and make sure they are aware of it. \[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&H(t)&Temp(K) \\ \hline 1.09e+3&9.17e-4&3.72e-4&6.27e-4&4.53e+1&4.16e-2&5.67e-2&8.52e-4&1.55e+6&2.97e+3\\ \hline 3.39e+2&2.94e-3&2.49e-3&3.95e-3&4.42e+1&1.30e-1&1.79e-1&6.11e-3&2.46e+5&9.27e+2\\ \hline 1.05e+2&9.44e-3&1.53e-2&2.34e-2&4.20e+1&3.97e-1&5.53e-1&4.01e-2&4.15e+4&2.89e+2\\ \hline 3.20e+1&3.03e-2&9.01e-2&1.36e-1&3.81e+1&1.15e+0&1.65e+0&2.48e-1&7.15e+3&9.00e+1\\ \hline 9.29e+0&9.71e-2&5.22e-1&7.84e-1&3.09e+1&3.00e+0&4.61e+0&1.49e+0&1.24e+3&2.81e+1\\ \hline 2.21e+0&3.12e-1&2.98e+0&4.37e+0&1.83e+1&5.69e+0&1.09e+1&8.73e+0&2.23e+2&8.74e+0\\ \hline 0.00e+0&1.00e+0&1.38e+1&1.44e+1&0.00e+0&0.00e+0&1.65e+1&4.63e+1&6.74e+1&2.73e+0\\ \hline -6.88e-1&3.21e+0&3.30e+1&1.73e+1&1.12e+1&3.58e+1&1.73e+1&1.84e+2&5.64e+1&8.49e-1\\ \hline -8.68e-1&7.58e+0&4.79e+1&1.74e+1&1.43e+1&1.08e+2&1.74e+1&4.59e+2&5.61e+1&3.59e-1\\ \hline -9.44e-1&1.79e+1&6.28e+1&1.74e+1&1.56e+1&2.79e+2&1.74e+1&1.11e+3&5.60e+1&1.52e-1\\ \hline -9.76e-1&4.23e+1&7.77e+1&1.74e+1&1.61e+1&6.84e+2&1.74e+1&2.64e+3&5.60e+1&6.44e-2\\ \hline -9.90e-1&1.00e+2&9.27e+1&1.74e+1&1.64e+1&1.64e+3&1.74e+1&6.27e+3&5.60e+1&2.73e-2\\ \hline \end{array}}\] Anyways The above calculator which Myself, Jorrie, Cuthberd and Markus were involved in the development though in my case it was mainly error checking and writing up some of the guides to how to use it while Jorrie and Cuthberd handled the programming aspects. Markus mainly did his best on advertising and aiding others in using it as well as crosschecks. Unfortunately he passed away a few years back. Its is a handy tool as one can apply any dataset to it and it greatly saves on calculations using the primary formulas of the FLRW metric. The nucleosynthesis thread has the major formulas I will be employing along with the SM Langrange. I am currently working on the family generations aspects. Already have the required math just need to cross check a few details. Needless to say I'm not developing a GUT I am applying SO(10) MSM, the FLRW metric, QFT and GR. The calculator uses the methodology by Lineweaver and Davies in particular stretch, (inverse of scale factor, which coincidentally also gives temperature. Much of the methodology I will be using is covered in the following articles http://www.wiese.itp.unibe.ch/lectures/universe.pdf http://arxiv.org/pdf/hep-th/0503203.pdf in essence I am simply attempting more exacting solutions with more modern datasets and methodologies,

Very accurate assessment love the analogy. At the same time I'm getting a handle on the methods Baron used instead of being forced to cut and paste pages and pages of details from the work he has already done.

Specific timings, number densities of the SM particle thermal equilibrium dropout stages and subsequently BB nucleosynthesis for metalicity percentages of hydrogen, deuterium, lithium. In essence updating the actual values of each stage. From 10^-43 seconds to surface of last scattering up to z=1100. Ok that helps clarify a few details. The Higgs related details I'm waiting for is directly related to finer precision on mass values which directly correlate to thermal equilibrium dropout values