**Guest blog by Paul Frampton**

Dear Luboš, here is my guest blog associated with my recent paper entitled

"Lepton Number Conservation, Long-Lived Quarks and Superweak Bileptonic Decays"posted at 1504.05877 [hep-ph] which suggests that LHC seek three additional quarks but, as promised, I shall include a general overview of what new particles might show up in Run II.

As is well known, discovery of the Higgs Boson in Run I completed the content of the standard model. Run II at \(13\TeV\), later expected to reach \(14\TeV\), is just beginning and what additional particle, if any, will be discovered is surely the central issue of particle phenomenology.

About the possible particle discoveries at LHC, there follow five subsections: (i) No new particle; (ii) A surprise particle; (iii) A super-partner and/or WIMP; (iv) Three additional quarks; (v) Discussion.

As a disclaimer, I shall assume as seems extremely likely that effects of extra dimensions are inaccessible at LHC energies.

(i)

**No new particle.**It is a logical possibility that running at its maximum \(14\TeV\) center of mass energy and even after accumulating an integrated luminosity of a few inverse attobarns no additional particle will be detected beyond the standard model. I believe everybody would agree it is more agreeable if Nature is not like this although one must keep an open mind.

(ii)

**A surprise particle.**The LHC may discover a new particle that nobody has predicted. By definition, it is hard to imagine what this could be and there is nothing further to discuss, except that in some ways this would be the most exciting possibility for stimulating theory.

(iii)

**A super-partner and/or WIMP.**The squark, slepton and gaugino super-partners predicted by supersymmetry (Susy) were expected to show up during Run I. Susy theory goes back to the 1970s and three empirical evidences indirectly supporting Susy have arisen from

- canceling the quadratic divergence associated with the Higgs scalar (1970s);
- a dark matter WIMP candidate (H. Goldberg, Phys. Rev. Lett.
**50**, 1419 (1983))

arising from R-parity as a mixture of gauging and higgsino; - improved accuracy in grand unification of the three gauge couplings (U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett.
**B260**, 447 (1991)) when super-partners are included. In my view, all of (a, b, c) as empirical motivations for Susy were somewhat eroded by their all appearing in nonsupersymmetric quiver theories during the 2000s. Nevertheless NMSSM is the most popular candidate to go beyond the standard model. Regarding dark matter (b), independently of Susy, there is reason to think there might be a WIMP in the Run II energy region because of the WIMP miracle which leads naturally to the correct relic density for dark matter. If such a WIMP is produced at LHC, it will be essential to confirm its cosmological role by direct terrestrial detection and/or indirect astrophysical detection. More generally, however, masses considered for dark matter range by almost a hundred orders of magnitude from a particle whose Bohr radius is the galactic size to an intermediate-mass black hole with a hundred thousand solar masses.

**Three additional quarks.**I finally come to my paper 1504.05877 which is an example of motivated gauge theory model building. In choosing the gauge group and chiral matter representations, a crucial constraint is the absence of triangle anomalies, see S.L. Adler, Phys. Rev.

**177**, 2426 (1979). This constraint led to the confident prediction of the charmed quark (C. Bouchiat, J. Iliopoulos and P. Meyer, Phys. Lett.

**B38**, 519 (1972); D.J. Gross and R. Jackiw, Phys. Rev.

**D6**, 477 (1972)) and, after the bottom quark was discovered, an equally confident prediction of the top quark.

In the standard model each family separately cancels the triangle anomaly in a nontrivial way but this does not constrain the number of families. The simplest extension which addresses this is the 331-model which was invented in Phys. Rev. Lett.

**69**, 2889 (1992) and independently by F.Pisano and V. Pleitez, Phys. Rev.

**D46**, 410 (1992). The electroweak \(SU(2)\) is enlarged to \(SU(3)\) and each family acquires one additional quark: \(D\) and \(S\) have \(Q=-4/3\) and \(T\) has \(Q=5/3\). There are five triangle anomalies in \(SU(3)_C \times SU(3)_L \times U(1)_X\) which are potentially troublesome:\[

(3_C)^3 \quad (3_C)^2 X \quad (3_L)^3 \quad (3_L)^2 X \quad X^3

\] in a self-explanatory notation. Each individual family possesses non-vanishing values for the 3rd, 4th and 5th anomalies which cancel among families only when the number of families equals three. Aside from this motivation of explaining the number of families, the 331 model contains a scale \(4\TeV\) below which the 331 symmetry must be broken to the SM, and thus the new physics is expected to be within reach of Run II.

There are five additional gauge bosons which include a \(Z\) prime and two pairs of bileptons \((Y^{++}, Y^+)\) and \((Y^{--}, Y^-)\) which carry lepton number \(L=-2\) and \(L=+2\) respectively. The three extra quarks carry \(L=+2\) (\(D\), \(S\)) and \(L=-2\) (\(T\)). This implies that these quarks decay are mediated by bileptons with a rate suppressed by the heavy mass of these gauge bosons. The decays are given explicitly in 1504.05877 but a key signature will be the displaced vertices caused by their long lifetime. Perhaps the silicon vertex detectors should have a radius bigger than the one meter selected.

It should be added that there exist variants of the 331-model achieved by changing the definition of the electric charge operator, see e.g. D. L. Anderson and M. Sher, Phys. Rev.

**D72**, 095014 (2005), although this becomes non-minimal by adding more leptons.

Long-lived quarks have been studied for a fourth family where the longevity is due to the very small mixing allowed with the first three families, see P.H. Frampton and P.Q. Hung, Phys. Rev.

**B58**, 057704 (1998) and H. Murayama, V. Rentala, J. Shu and T. Yangida, Phys. Lett.

**B705**, 208 (2011). Here the long lifetime has a different cause. Discovery of the 331-model would provide a complementary explanation of three families to that provided in M. Kobayashi and T. Maskawa, Prog. Theor. Phys.

**49**, 652 (1973). It might suggest that the gauge structure be further extended, for example so that the weak hypercharge U(1) is subsumed into a further SU(3) group.

(v)

**Discussion.**

I happen to be writing this in the mezzanine of the Andrew Wiles Building which houses the Oxford Mathematics Department so, especially as this is for Luboš, I would like to be able to write about string theory predictions for the LHC but string theory cannot now make any specific prediction. Further research on Calabi-Yau and other compactifications may succeed. Four-dimensional string compactifications generally aim at a Susy model of the type (iii) and hence string theorists hope that Susy shows up. Top-down compactifications do not, however, yield anything like (iv) which is an example of bottom-up model building which seems old fashioned but has been successful in the past.

The data which will emerge from Run II will be enlightening and tell us about how Nature really works.

So Luboš, that is my guest blog.

Best regards,

Paul Frampton

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