The beat particle physics' heart almost skipped

Non supersymmetric grand unification with Pati-Salam intermediate scale and minimal fermion spectrum
This spring and early summer 2015 have witnessed a blooming of beyond standard model speculations related to potential anomalies reported in data from LHC1 (see former posts).
Now the heart of sunny season can also be time for (re)visiting older and less fashionable pathways. This is precisely what Professor K. S. Babu and his student Saki Khan have courageously undertaken:
The crucial point about SO(10) Grand Unified Theories is that if we change our current attitude about fine-tuning, yet keep it at the minimal level by adopting philosophy like extended survival hypothesis, we realize that even without supersymmetry, SO(10) symmetry has the potential to be the gauge symmetry of nature on its own right, atleast upto the GUT scale (∼1016 GeV).
The absence of low energy supersymmetry might be the reality of our universe, taking away primary motivation to introduce supersymmetry. Thus it becomes mandatory to revisit the non-supersymmetric version of SO(10) GUTs with a more open attitude.
..

Evolution of gauge couplings using one-loop RGE with threshold corrections determined by the scalar mass spectrum given in Table 3. The unification scale determined here is compatible with the current experimental limit on proton lifetime. The small black circles correspond to the various scalar masses changing the β function coefficients and inflicting changes in the slope of the graphs. The vertical dashed lines correspond to gauge boson masses that stay at intermediate scale and unification scale
In this work, the philosophy of minimality was applied in the choice Higgs representation and that resulted in a breaking pattern with minimal number of intermediate scale (namely one) making the model truly minimal and predictive... 
Such a minimal model ended up relying on threshold corrections to escape from the wrath of experimental bounds on proton lifetime. The issue of threshold corrections deserves particular attention here. On one hand, one should not discard a model without taking into account the threshold corrections, on the other hand, one should not expect that threshold corrections can rescue any model before performing detailed calculation.

The non-SUSY SO(10) GUT presented here managed to unify the gauge couplings at a scale high enough to comply with the current experimental bound of proton lifetime. The Yukawa sector of the model provided a realistic description of fermion masses and mixings. The Peccei-Quinn-phase transition introduced axion as the dark matter candidate that can explain the dark matter abundance in the universe, while also solving the strong CP problem. Leptogenesis finds a natural place in SO(10) with seesaw mechanism and the Yukawa sector of the model has the potential to procure the right amount. Physics of inflation may reside outside the scope of the model or within the model where one (or more) SM singlets already present may provide the necessary ingredients.

One should emphasis the claim that the SM spectrum is completed by the recently discovered light Higgs and LHC should fail to find any other new physics, as the next scale of physics lies at the energy scale of 1010 GeV. 
Before getting demoralized one also needs to realize that the model generally predicts a proton lifetime less than a few times 1035 yrs. So Super-Kamiokande or next generation proton decay detectors and axion search experiments has the potential to discover the essential phenomenological proof of the model.
(Submitted on 24 Jul 2015)

/last new edition August 8, 2015: the graph has been added to underline the very precise work done to evaluate threshold corrections on the running of the gauge coupling constants; a work required to escape from the wrath of experimental bounds on proton lifetime!

//last update August 21 2015
Some critical questions from the past still pertinent today
I find it is very interesting to compare the last reported article on a tentative minimal nonsupersymmetric extension of the standard model with the very first published work (to my knowledge) which proposed a fit of the gauge couplings in a minimal susy grand unification model:

Is it not trivial for 3 lines to meet in one point with two free parameters?
In general one can always find a crossing point with two free parameters (MSUSY and MGUT), except for some exceptional cases... However, in case of SUSY the interesting aspect is the small SUSY scale and the unification scale well below the Planck mass, which does not violate proton decay bounds (see below). All of these are nontrivial constraints... 

Can non-supersymmetric models yield unification?

As shown, SUSY models yield unification consistent with the proton lifetime limit. It is easy to find other simple models which yield unification, like the SM with 6 or more Higgs doublets [3] or 2 Higgs doublets and two pairs of leptoquarks [11]. However, the obtained values lead to proton lifetimes 2 orders of magnitude or more below the present experimental limits. More extensive models can indeed yield unification consistent with the proton lifetime limits, as demonstrated by a systematic search of 800 extensions of the SM by adding split real representations (10+10b) and (5+5b) in SU(5)[12]. From the 800 possible models only about 60 yield unification and about 20 have GUT scales consistent with [13]. The real representations are split between the TeV and GUT scale. In all cases the new neutrinos and leptons are heavy (i.e. masses close to MGUT), while the quarks are partially light (i.e. TeV range) [13]. The physical motivation for such split representations is the fact that they lead to unification. In contrast, SUSY particles are predicted from the requirement of symmetry between fermions and bosons, a symmetry not related at all to unification...


Can one extrapolate the coupling constants reliably over 14 orders of magnitude in energy?

The answer is yes, since in first order the slopes are "quantized" by the known number of particles in a given theory. Especially, the slopes are of the values of the coupling constants, at least in first order and the second order contributions are small...


What is the meaning of MSUSY?  

Far above and below the threshold for the SUSY particles, the slopes of the inverse coupling constants are well known. Extrapolating them linear into the narrow threshold region defines an effective mass scale , defined as the energy where the SM and MSSM slopes cross. Clearly, a single parameter is inadequate to parametrize the SUSY mass spectrum, as emphasized in Ref. [8]; to do so one needs a minimum of 5 parameters. However, from the unification of the 3 coupling constants, one cannot determine so many parameters. What then is the meaning of MSUSY? One knows that within the MSSM the spread in sparticle masses is small compared with MGUT[7]. Therefore, MSUSY, being some effective mass in this rather narrow threshold region, is the best estimate of the sparticle masses we have. Unfortunately, even this single parameter has large errors, since MSUSY enters only logarithmically into the extrapolation of the coupling constants. The 68% C.L. error spans already one order of magnitude, so the 95% C.L. error spans two order of magnitudes, i.e. 102<MSUSY<105GeV, a result agreeing with our previous results[3] and obtained later also in Ref. [14]. Nevertheless, one knows that within the MSSM at least one of the Higgs particles will have a mass below 170 GeV [15], which should certainly be within reach of the next generation of accelerators. 

What is real significance of these fits? 

Several features could be considered. E.g. is it:
- the fact that no unification can be obtained within the SM, so new physics is required for the unifi cation of all three forces?
-the fact that it is the first fit of MSUSY ?
- the fact that MGUT is larger than 2×1015 as required by the lower limit on the proton lifetime and that MSUSY comes out to be much smaller than MGUT, as required by supersymmetry?
-the prediction of many new particles with masses "around the corner", so that new accelerators have to be built?
-the fact that one gets uni cation so easily in the minimal [supersymmetric extension of the] SM without invoking e.g. a complicated Higgs sector?
Probably none of them can be called most significant, but it is the combination of all these arguments, which provide such an amazingly and puzzlingly consistent picture...


Ugo Amaldi , Wim de Boer , Hermann Furstenau
5 November 1991

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