Approximate <i>SU</i>(5) Fine Structure Constants
We fit the three finestructure constants of the Standard Model, in which the first approximation of theoretically estimable parameters include (1) a “unified scale”, turning out <i>not</i> equal to the Planck scale and thus only estimable by a very speculative story, the second includes...
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| description | We fit the three finestructure constants of the Standard Model, in which the first approximation of theoretically estimable parameters include (1) a “unified scale”, turning out <i>not</i> equal to the Planck scale and thus only estimable by a very speculative story, the second includes (2) a “number of layers” being a priori the number of families, and the third is (3) a unified coupling related to a critical coupling on a lattice. So formally, we postdict the three fine structure constants! In the philosophy of our model, there is a physical lattice theory with link variables taking values in a (or in the various) “small” representation(s) of the standard model <b>Group</b>. We argue for that these representations function in the first approximation based on the theory of a genuine <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></mrow></semantics></math></inline-formula> theory. Next, we take into account fluctuation of the gauge fields in the lattice and obtain a correction to the a priori <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></mrow></semantics></math></inline-formula> approximation, because of course the link fluctuations not corresponding to any standard model Lie algebra, but only to the SU(5), do not exist. The model is a development of our old anti-grand-unification model having as its genuine gauge group, close to fundamental scale, a cross-product of the standard model group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula> with itself, with there being one Cartesian product factor for each family. In our old works, we included the hypothesis of the “multiple point criticallity principle”, which here effectively means the coupling constants are critical on the lattice. Counted relative to the Higgs scale, we suggest in our sense that the“unified scale” (where the deviations between the inverse fine structure constants deviate by quantum fluctuations being only from standard model groups, not SU(5)) makes up the 2/3rd power of the Planck scale relative to the Higgs scale or the topquarkmass scale. |
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| spelling | doaj-art-186e1f57aa5d49a69af585a7df8bbdad2025-08-20T02:45:41ZengMDPI AGUniverse2218-19972025-01-011123210.3390/universe11020032Approximate <i>SU</i>(5) Fine Structure ConstantsHolger B. Nielsen0Niels Bohr Institute, Jagtvej 155 a, DK 2200 Copenhagen, DenmarkWe fit the three finestructure constants of the Standard Model, in which the first approximation of theoretically estimable parameters include (1) a “unified scale”, turning out <i>not</i> equal to the Planck scale and thus only estimable by a very speculative story, the second includes (2) a “number of layers” being a priori the number of families, and the third is (3) a unified coupling related to a critical coupling on a lattice. So formally, we postdict the three fine structure constants! In the philosophy of our model, there is a physical lattice theory with link variables taking values in a (or in the various) “small” representation(s) of the standard model <b>Group</b>. We argue for that these representations function in the first approximation based on the theory of a genuine <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></mrow></semantics></math></inline-formula> theory. Next, we take into account fluctuation of the gauge fields in the lattice and obtain a correction to the a priori <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></mrow></semantics></math></inline-formula> approximation, because of course the link fluctuations not corresponding to any standard model Lie algebra, but only to the SU(5), do not exist. The model is a development of our old anti-grand-unification model having as its genuine gauge group, close to fundamental scale, a cross-product of the standard model group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula> with itself, with there being one Cartesian product factor for each family. In our old works, we included the hypothesis of the “multiple point criticallity principle”, which here effectively means the coupling constants are critical on the lattice. Counted relative to the Higgs scale, we suggest in our sense that the“unified scale” (where the deviations between the inverse fine structure constants deviate by quantum fluctuations being only from standard model groups, not SU(5)) makes up the 2/3rd power of the Planck scale relative to the Higgs scale or the topquarkmass scale.https://www.mdpi.com/2218-1997/11/2/32grand unfication SU(5)lattice theoryrunning couplingsanti-GUTstandard model <b>group</b>critical coupling |
| spellingShingle | Holger B. Nielsen Approximate <i>SU</i>(5) Fine Structure Constants Universe grand unfication SU(5) lattice theory running couplings anti-GUT standard model <b>group</b> critical coupling |
| title | Approximate <i>SU</i>(5) Fine Structure Constants |
| title_full | Approximate <i>SU</i>(5) Fine Structure Constants |
| title_fullStr | Approximate <i>SU</i>(5) Fine Structure Constants |
| title_full_unstemmed | Approximate <i>SU</i>(5) Fine Structure Constants |
| title_short | Approximate <i>SU</i>(5) Fine Structure Constants |
| title_sort | approximate i su i 5 fine structure constants |
| topic | grand unfication SU(5) lattice theory running couplings anti-GUT standard model <b>group</b> critical coupling |
| url | https://www.mdpi.com/2218-1997/11/2/32 |
| work_keys_str_mv | AT holgerbnielsen approximateisui5finestructureconstants |