Gauge Couplings calculated from Multiple Point Criticality yield $α^{-1}=136._8\pm 9$: At Last the Elusive Case of $U(1)$

D. L. Bennett; H. B. Nielsen

doi:10.1142/S0217751X9900155X

paper

Gauge Couplings calculated from Multiple Point Criticality yield $α^{- 1} = 136 ._{8} \pm 9$ : At Last the Elusive Case of $U (1)$

arXiv:hep-ph/9607278 · doi:10.1142/S0217751X9900155X

Abstract

We calculate the $U (1)$ continuum gauge coupling using the values of action parameters at the multiple point in the phase diagram of a lattice gauge theory. The multiple point is where a maximum number of phases convene. We obtain for the running inverse finestructure constant the values $α_{1}^{- 1} = 56 \pm 5$ and $α_{1}^{- 1} = 99 \pm 5$ at respectively the Planck scale and the $M_{Z}$ scale. The gauge group underlying the phase diagram in which we seek multiple point values of action parameters is what we call the Anti Grand Unified Theory (AGUT) gauge group $S M G^{3}$ which is the Cartesian product of 3 standard model groups (SMGs). There is one SMG factor for each of the $N_{g e n} = 3$ generations of quarks and leptons. In our model, this gauge group $S M G^{3}$ is the predecessor to the usual standard model group. The latter arises as the diagonal subgroup surviving the Planck scale breakdown of $S M G^{3} . T hi s b r e ak d o w n l e a d s t o a w e ak e nin g o f t h e$ U(1) $co u pl in g b y a$ N_{gen} $- r e l a t e df a c t or . T h e m os t im p or t an t cor r ec t i o n o b t ain e df r o m u s in g m u l t i pl e p o in tp a r am e t er v a l u es (inam u l t i - p a r am e t er p ha se d ia g r amin s t e a d o f t h es in g l ecr i t i c a l p a r am e t er v a l u eo b t ain e d s a y in t h e 1 - d im e n s i o na l p ha se d ia g r am o f aW i l so na c t i o n) co m es f r o min c l u d in g t h e in f l u e n ceo f ha v in g p ha sesco n f in e d so l e l y w . r . t . d i scr e t es u b g r o u p s . I n p a r t i c u l a r, w ha t ma tt er s i s t ha tt h e d e g r eeo f f i r s t - or d er n ess i s t ak e nin t o a cco u n t inmak in g t h e t r an s i t i o n f r o m t h ese l a tt er p ha ses a tt h e m u l t i pl e p o in tt o t h e t o t a l l y C o u l o mb - l ik e p ha se . C o mbin e d w i t h t h er es u l t so f e a r l i er w or k o n t h e n o n - A b e l ian g a ug eco u pl in g s, t h er es u l t s p r ese n t e d h er e l e a d t oo u r p r e d i c t i o n o f$ α^{-1}=136._8\pm 9$ as the value for the fine-structure constant at low energies.

4 figures, 85 pages, accepted for publication in Intl. J. Mod. Phys. A, this is a second replacement that should correct the lack of references in the original version

Gauge Couplings calculated from Multiple Point Criticality yield $α^{- 1} = 136 ._{8} \pm 9$ : At Last the Elusive Case of $U (1)$

Abstract

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Gauge Couplings calculated from Multiple Point Criticality yield α−1=136.8​±9: At Last the Elusive Case of U(1)

Abstract

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Cited by in corpus (27)

Gauge Couplings calculated from Multiple Point Criticality yield $α^{- 1} = 136 ._{8} \pm 9$ : At Last the Elusive Case of $U (1)$