RUNNING COUPLING CONSTANTS AND GRAND UNIFICATION MODELS

1991 ◽  
Vol 06 (19) ◽  
pp. 1745-1755 ◽  
Author(s):  
C. GIUNTI ◽  
C. W. KIM ◽  
U. W. LEE

The evolution of the gauge coupling constants in the SU (N) and SO (N) grand unification models is examined. It is shown that the three coupling constants αs, α2, α1 in the minimal SU(5) model do not merge into one at 99% confidence level when they are extrapolated from the values at the mass scale MZ, whereas in its supersymmetric version, the coupling constants do merge into one within one standard deviation. In the SU (N) (with N > 5) models with a two-step symmetry breaking the coupling constants can merge into one, but these models are ruled out by the constraint imposed on the unification mass scale from the absence of proton decay. The SO (N) models with N ≥ 10 are shown to be consistent with the proton decay constraint. In particular, the unification scale for the SO(10) model is shown to be 1015~1016 GeV and the intermediate energy scale is 1013~1014 GeV .

2017 ◽  
Vol 32 (09) ◽  
pp. 1741013 ◽  
Author(s):  
Jogesh C. Pati

By way of paying tribute to Abdus Salam, I first recall the ideas of higher unification which the two of us introduced in 1972–73 to remove certain shortcomings in the status of particle physics prevailing then, and then present their current role in theory as well as experiments. These attempts initiated the idea of grand unification and provided the core symmetry-structure [Formula: see text]-color towards such a unification. Embodied with quark-lepton unification and left-right symmetry, the symmetry [Formula: see text] is uniquely chosen as being the minimal one that permits members of a family to belong to a single multiplet. The minimal extension of [Formula: see text] to a simple group is given by the attractive SO(10)-symmetry that was suggested a year later. The new concepts, and the many advantages introduced by this core symmetry (which are, of course, retained by SO(10) as well) are noted. These include explanations of the observed: (i) (rather weird) electroweak and color quantum numbers of the members of a family; (ii) quantization of electric charge; (iii) electron-proton charge-ratio being [Formula: see text]; (iv) the co-existence of quarks and leptons; (v) likewise that of the three basic forces — the weak, electromagnetic and strong; (vi) the non-trivial cancelation of the triangle anomalies within each family; and opening the door for (vii) the appealing concept of parity being an exact symmetry of nature at the fundamental level. In addition, as a distinguishing feature, both because of SU(4)-color and independently because of [Formula: see text] as well, the symmetry [Formula: see text] introduced, to my knowledge, for the first time in the literature: (viii) a new kind of matter — the right-handed (RH) neutrino [Formula: see text] — as a compelling member of each family, and together with it; (ix) (B-L) as a local symmetry. The RH neutrions — contrary to prejudices held in the 1970’s against neutrinos being massive and thereby against the existence of [Formula: see text]’s as well — have in fact turned out to be an asset. They are needed to (a) understand naturally the tiny mass-scales observed in neutrino oscillations by combining the seesaw mechanism together with the unification ideas based on the symmetry SU(4)-color, and also (b) to implement the attractive mechanism of baryogenesis via leptogenesis. The quantitative success of the attempts as regards understanding both (a) and (b) are discussed in Sec. 6. These provide a clear support simultaneously for the following three features: (i) the seesaw mechanism, (ii) the SU(4)-color route to higher unification based on a symmetry like SO(10) or a string-derived [Formula: see text] symmetry in 4D, as opposed to alternative symmetries like SU(5) or even [SU(3)]3, and (iii) the (B-L)-breaking scale being close to the unification scale [Formula: see text] GeV. The observed dramatic meeting of the three gauge couplings in the context of low-energy supersymmetry, at a scale [Formula: see text] GeV, providing strong evidence in favor of the ideas of both grand unification and supersymmetry, is discussed in Sec. 3. The implications of such a meeting in the context of string-unification are briefly mentioned. Weighing the possibility of a stringy origin of gauge coupling unification versus the familiar problem of doublet-triplet splitting in supersymmetric SO(10) (or SU(5)), I discuss the common advantages as well as relative merits and demerits of an effective SO(10) versus a string-derived [Formula: see text] symmetry in 4D. In Sec. 7, I discuss the hallmark prediction of grand unification, viz. proton decay, which is a generic feature of most models of grand unification. I present results of works carried out in collaboration with Babu and Wilczek and most recently with Babu and Tavartkiladze on expectations for decay modes and lifetimes for proton decay, including upper limits for such lifetimes, in the context of a well-motivated class of supersymmetric SO(10)-models. In view of such expectations, I stress the pressing need for having the next-generation large underground detectors — like DUNE and HyperKamiokande — coupled to long-baseline neutrino beams to search simultaneously with high sensitivity for (a) proton decay, (b) neutrino oscillations and (c) supernova neutrinos. It is remarked that the potential for major discoveries through these searches would be high. Some concluding remarks on the invaluable roles of neutrinos and especially of proton decay in probing physics at the highest energy scales are made in the last section. The remarkable success of a class of supersymmetric grand unification models (discussed here) in explaining a large set of distinct phenomena is summarized. Noticing such a success and yet its limitations in addressing some fundamental issues within its premises, such as an understanding of the origin of the three families, and most importantly, the realization of a well-understood unified quantum theory of gravity describing reality, some wishes are expressed on the possible emergence and the desirable role of a string-derived grand-unified bridge between string/M-theory in higher dimensions and the world of phenomena at low energies.


2000 ◽  
Vol 15 (18) ◽  
pp. 2917-2932
Author(s):  
S. K. SRIVASTAVA

Using higher-derivative gravitational action in (4+D)-dimensional space–time, Lagrangian density of riccion is obtained with the quartic self-interacting potential. It is found that after compactification to four-dimensional space–time the resulting theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the energy mass scale showing that these dimensions increase with the increasing mass scale, (ii) phase transition at 1.76×1016 GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space–time above 1.76×1016 GeV should be fractal.


JETP Letters ◽  
2005 ◽  
Vol 81 (11) ◽  
pp. 551-555 ◽  
Author(s):  
F. R. Klinkhamer ◽  
G. E. Volovik

2007 ◽  
Vol 22 (10) ◽  
pp. 1849-1874 ◽  
Author(s):  
RODOLFO A. DIAZ ◽  
D. GALLEGO ◽  
R. MARTINEZ

By making a renormalization group analysis we explore the possibility of having a 331 model as the only intermediate gauge group between the standard model and the scale of unification of the three coupling constants. We shall assume that necessarily there is no group of grand unification at the scale of convergence of the couplings. With this scenario, different 331 models and their corresponding supersymmetric versions are considered, and we find the versions that allow the symmetry breaking described above. Besides, the allowed interval for the 331 symmetry breaking scale, and the behavior of the running coupling constants are obtained. It is worth saying that some of the supersymmetric scenarios could be natural frameworks for split supersymmetry. Finally, we look for possible 331 models with a simple group at the grand unification scale that could fit the symmetry breaking scheme described above.


2001 ◽  
Vol 16 (16) ◽  
pp. 2873-2894 ◽  
Author(s):  
GUANG-JIONG NI ◽  
GUO-HONG YANG ◽  
RONG-TANG FU ◽  
HAIBIN WANG

Based on a simple but effective regularization-renormalization method (RRM), the running coupling constants (RCC) of fermions with masses in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by renormalization group equation (RGE). Starting at Q=0 (Q being the momentum transfer), the RCC in QED increases with the increase of Q whereas the RCCs for different flavors of quarks with masses in QCD are different and they increase with the decrease of Q to reach a maximum at low Q for each flavor of quark and then decreases to zero at Q→0. Thus a constraint on the mass of light quarks, the hadronization energy scale of quark–antiquark pairs are derived.


1992 ◽  
Vol 07 (16) ◽  
pp. 1485-1495 ◽  
Author(s):  
DAVID BAILIN ◽  
ALEX LOVE

The question of whether contributions of exotic multiplets of the gauge group to the running of gauge coupling constants from the string scale to low energy can lead to consistency with the precision low energy values of gauge couplings is discussed for theories with SO(6)×SO(4), SU(3)×SU(3)×SU(3) and flipped SU(5)×U(1) grand unification.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Maria Mehmood ◽  
Mansoor Ur Rehman ◽  
Qaisar Shafi

Abstract We explore proton decay in a class of realistic supersymmetric flipped SU(5) models supplemented by a U(1)R symmetry which plays an essential role in implementing hybrid inflation. Two distinct neutrino mass models, based on inverse seesaw and type I seesaw, are identified, with the latter arising from the breaking of U(1)R by nonrenormalizable superpotential terms. Depending on the neutrino mass model an appropriate set of intermediate scale color triplets from the Higgs superfields play a key role in proton decay channels that include p → (e+, μ+) π0, p → (e+, μ+) K0, p →$$ \overline{v}{\pi}^{+} $$ v ¯ π + , and p →$$ \overline{v}{K}^{+} $$ v ¯ K + . We identify regions of the parameter space that yield proton lifetime estimates which are testable at Hyper-Kamiokande and other next generation experiments. We discuss how gauge coupling unification in the presence of intermediate scale particles is realized, and a Z4 symmetry is utilized to show how such intermediate scales can arise in flipped SU(5). Finally, we compare our predictions for proton decay with previous work based on SU(5) and flipped SU(5).


2010 ◽  
Vol 25 (04) ◽  
pp. 283-293 ◽  
Author(s):  
JITESH R. BHATT ◽  
SUDHANWA PATRA ◽  
UTPAL SARKAR

The gravitational corrections to the gauge coupling constants of Abelian and non-Abelian gauge theories have been shown to diverge quadratically. Since this result will have interesting consequences, this has been analyzed by several authors from different approaches. We propose to discuss this issue from a phenomenological approach. We analyze the SU(5) gauge coupling unification and argue that the gravitational corrections to gauge coupling constants may not vanish when higher dimensional non-renormalizable terms are included in the problem.


2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.


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