Friday, February 20, 2015

Perspectives and Challenges in Lattice Gauge Theory, Day Five

Today's programme started with a talk by Santanu Mondal on baryons in the sextet gauge model, which is a technicolor-style SU(3) gauge theory with a doublet of technifermions in the sextet (two index symmetric) representation, and a minimal candidate for a technicolor-like model with an IR almost-fixed point. Using staggered fermions, he found that when setting the scale by putting the technipion's decay constant to the value derived from identifying the Higgs vacuum expectation value as the technicondensate, the baryons had masses in excess of 3 TeV, heavy enough to not yet have been discovered by the LHC, but to be within reach of the next run. However, the anomaly cancellation condition when embedding the theory into the Standard Model of the electroweak interactions requires charge assignments such that the lightest technibaryon (which would be a stable particle) would have a fractional electrical charge of 1/2, and while the cosmological relic density can be made small enough to evade detection, the technibaryons produced by the cosmic rays in the Earth's atmosphere should have been able to accumulate (there currently appear to be no specific experimental exclusions for charge-1/2 particles though).

Next was Nilmani Mathur speaking about mixed action simulations using overlap valence quarks on the MILC HISQ ensembles (which include the radiative corrections to the lattice gluon action from the quarks). Tuning the charm quark mass via the kinetic rather than rest mass of charmonium, the right charmonium hyperfine splitting is found, as well as generally correct charmonium spectra. Heavy-quark baryons (up to and including the Ωccc) have also been simulated, with results in good agreement with experimental ones where the latter exist. The mixed-action effects appear to be mild small in mixed-action χPT, and only half as large as those for domain-wall valence fermions on an asqtad sea.

In a brief note, Gunnar Bali encouraged the participants of the workshop to seek out opportunities for Indo-German research collaboration, of which there are still only a limited number of instances.

After the tea break, there were two more theoretical talks, both of them set in the framework of Hamiltonian lattice gauge theory: Indrakshi Raychowdhury presented a loop formulation of SU(2) lattice gauge theory based on the prepotential formalism, where both the gauge links and their conjugate electrical fields are constructed from harmonic oscillator variables living on the sites using the Schwinger construction. By some ingenious rearrangements in terms of "fusion variables", a representation of the perturbative series for Hamiltonian lattice gauge theory purely in terms of integer-valued quantum numbers in a geometric-combinatorial construction was derived.

Lastly, Sreeraj T.P. presented a derivation of an analogy between the Gauss constraint in Hamiltonian lattice gauge theory and the condition of equal "angular impulses" in the SU(2) x SU(2) description of the SO(4) symmetry of the Coulomb potential to derive a description of the Hilbert space of SU(2) lattice gauge theory in terms of hydrogen atom (n,l,m) variables located on the plaquettes subject only to the global constraint of vanishing total angular momentum, from where a variational ansatz for the ground state can be constructed.

The workshop closed with some well-deserved applause for the organisers and all of the supporting technical and administrative staff, who have ensured that this workshop ran very smoothly indeed. Another excellent lunch (I understand that our lunches have been a kind of culinary journey through India, starting out in the north on Monday and ending in Kerala today) concluded the very interesting workshop.

I will keep the small subset of my readers whom it may interest updated about my impressions from an excursion planned for tomorrow and my trip back.

No comments: