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Is multiple tґ-quarks bound states possible due to Higgs exchange?

Oleg Pavlovsky and Maxim Ulybyshev (ITPM MSU & ITEP Moscow)


tґ-balls: to be or not to be?
4-th generation is a natural extension of the Standard Model. 4-th generation quarks have hypothetical mass about several hundred GeV. No bound states due to gluu--oon exchange (like charmonium or bottomonium)!

BUT! tґ-quark ­ Higgs strong-coupling interaction

Formation of tґ-quarks ­ Higgs non-topological solitons (analogous to light chiral hadrons, not to heavy one)


· tґ-quark ­ Higgs interaction


tґ-quark Yukawa coupling

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tґ coupling constant must be more than 1!


tґ- balls physics: analogous to light chiral hadrons

Analog of chiral quark lagrangian in TeV scale!


Main feature of strong coupling Fermion-Higgs system: possibility of formation of the "Bubbles" in Higgs condensate!


If Fermion-Higgs interaction is strong enough it is favorable for quasi-massless quarks to be inside "bubble"-like soliton than to be free and massive.


One-dimensional illustration:


Three-dimensional case

Spherically symmetrical field configurations

Equations of motion

Normalization


How many fermions in "bubble" could be?
No soliton for one top-quark and for toponium! Macpherson, Campbell, Phys.Lett.B306:379-385,1993. For multi top-quark bound states it's open question.

The more fermions one has in the "bubble", the more such fermion-soliton system becomes energetically favorable.

N


Numerical results: soliton-waves phase diagram.

Waves

Soliton

For Higgs mass around M(Higgs) = 140 GeV, soliton solution can be formed only for fermions with mass greater than M(tґ) > 390 GeV.


Numerical results: tґ energy in soliton "bubble".

For large asymptotical mass of tґ, the energy of the quark in the "bubble" becomes relatively smaller. Formation of the "bubble" becomes more and more favorable.


Numerical results: profiles of fields

Typical radius of the "bubble" is about 2 / VEV = 1 / M(W). It is a very essential for EW stability.


Conclusions:
Possibility of the generation of the non-topological "bubble"-like soliton in tґ-Higgs system was discussed . Critical value of tґ mass for tґ-ball generation was founded. Physical properties of such states was studied. New experimental dates about TeV-physics are expected from LHC!