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Universal Landau Pole
Alexander Andrianov
Saint Petersburg State University and Insitut de Ciencies del Cosmos, UB in collab oration with: D.Espriu, M. Kurkov and F. Lizzi

based on: arXiv:1302.4321 (Phys. Rev. Lett. in print)

QFTHEP 2013, Repino, June 28


Outline:
· Do we really need asymptotic freedom? Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. Then grand unification in a large non-ab elian group naturally endowed with the prop erty of asymptotic freedom may also lose its motivation. · Singular unification: an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), at which all gauge couplings diverge. · Minimal working mo del of the Universal Landau Pole. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hyp ercharges identical to those of the Standard Mo del. · Stability of the Higgs Potential. The Higgs quartic coupling diverges while the Yukawa couplings vanish.


DO WE REALLY NEED ASYMPTOTIC FREEDOM?

· Simplicity: the less parameters the b etter unification.

· Asymptotic freedom (flat space-time): valid up to infinitely high energies.

the theory is

· BUT what ab out gravity?

· At the energies of order of Planck scale MPl 1019 GeV gravity b ecomes strongly coupled, concept of weakly interacting p oint-like fields lo oses its meaning!

· Simplicity + p ointless geometry singular unification.


SINGULAR UNIFICATION: UNIVERSAL LANDAU POLE · We prop ose a singular unification at the one should find such a generalization of Mo del, that under the renormalization gr gauge couplings meet their common Land Planck scale. g
1,2,3

Planck scale: the Standard oup flow ALL au p ole at the

(µ) at µ M

Pl

· Kinetic terms of ALL gauge fields vanish and they cannot propagate anymore. 1 F µ F g (µ)2
µ

0 at µ M

Pl

· ? UV fixed p oint and dimensional reduction of gauge fields ? F
µ

1 + g (µ)2 M

2 Pl

+ ···

F

µ

F

µ

M

2 Pl

F

µ

at µ M

Pl


MINIMAL ULP: REQUIREMENTS · Simplicity: the gauge group of SM S U (3) â S U (2) â U (1). We add only fermions. Enlarging the gauge group in principle could b e motivated by intro duction of a GUT group. However it leads to ULP at 1016 GeV [see V. A. Rubakov and S. V. Troitsky, hep-ph/0001213, for a review] much smaller than MPl. · Higgs sector: to remain unchanged. If the new particles are describ ed by 4-comp onent spinors with Dirac masses and vector-like gauge interactions no necessity for any Higgs fields. It fits well the recent LHC b ounds on the numb er of generations [see A. Lenz, Adv. High En. Phys. 2013 (2013) 910275 ] · NO pathological electric charges restrictions on the representations of new fermions. · Stability: quartic coupling of the Higgs field self interaction is always p ositive under the renormalization group flow. It discriminates a single scenario with four generations.


MINIMAL WORKING ULP: REALIZATION ¯ · We use Dirac mass terms M for new fermions and we are lo oking for a minimal numb er of them.

· New femions b elong to known representations of gauge gr oup L-quarkons: SU(3) - triplets, SU(2) - doublets, Y =
1 3 2 3

R-quarkons: SU(3) - triplets, SU(2) - singlets, Y = 4 , - 3 L-leptos: SU(3) - singlets, SU(2) - doublets, Y = -1 R-leptos: SU(3) - singlets, SU(2) - singlets, Y = -2, 0

· Remark: L- and R- notations do not imply left and right chiralities! They vector-like relatives.


MINIMAL WORKING ULP: REALIZATION The only new vertexes app earing in the theory couple Quarkons and Leptos to E-W gauge b osons and gluons.

And at one lo op level only b eta functions of gauge fields are mo dified due to presence of these diagramms:

g

g

g

g


MINIMAL WORKING ULP: THE ANSWER ULP can b e rendered within 4 identical "generations" of new vector-like massive fermions with different mass scales: · At 5.0 · 103 GeV L-quarkons (NL-quar · At 3.7 · 107 GeV R-quarkons (NR
kon

= 4). = 4).
os

-quarkon

· At 2.6 · 1014 GeV L and R-leptos (NL-lept

= NR

-leptos

= 4).


One(two)-lo op RG running of gauge couplings


One(two)-lo op RG running of top Yukawa coupling


One(two)-lo op RG running of Higgs b oson quartic coupling


ON THE STABILITY OF THE HIGGS POTENTIAL Now we clarify how our vector-like fermions save the Universe from instability, i.e. how they don't let RG flow to drive the quartic coupling (µ) to negative values.
( 1)

=

1 24 2-6 y 4+ 16 2 + -9 g 2 2 - 3 g 1 2 +

3 34 g2 + g 4 8 12 y 2 .

2

2

+g

1

22

Y

Y

g

g

Y

Y

g

g


UV completion It could well b e the case that the onset of gravity corrections renders the ULP non-singular. Indeed gravity b eing non-renormalizable will require higher-dimensional op erators with more derivatives to make the theory finite. In particular, we exp ect dimension six kinetic terms like tr (DµW 2 2MP
µ µ Dµ W ) + · · ·

This would corresp ond to a renormalization of the gauge coupling induced by gravity of the form
2 mP p2 1 0 log 2 + 2 g 2 (p 2 ) p mP

Thus gravitational corrections may drive the ULP towards a new fixed p oint [see, for instance, M. E. Shap oshnikov, Theor. Math. Phys. 170, 229 (2012) ].


CONCLUSIONS · An idea of singular unification of ALL gauge interactions at the Planck scale, can b e realized in the form of the Universal Landau Pole (ULP). · The minimal working mo del of ULP generalization of the SM is constructed. · Under the RG flow the top Yukawa coupling eventually go es to zero while the quartic coupling has a concordant singularity at the Planck scale. Such a RG b ehavior saves the Universe from instability problem.