Information for 3+1 transverse lattice: glueballs

Assignment of multiplets associated with the 2 dimensional lattice

Multiplets are as follows:

 group    |                 Multiplet number                        
 element  | 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 
 ---------|---------------------------------------------------------
  E       | 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  P_1     |          1 -1  1 -1  1 -1  1 -1                         
  P_2     |          1 -1  1 -1 -1  1  1 -1              1 -1       
  R^2     |    1 -1  1  1  1  1 -1 -1  1  1  1 -1  1 -1             
          |                                                         
  P_1 R   |          1 -1 -1  1              1  1 -1 -1        1 -1 
  R       |          1  1 -1 -1                                     
  R^3     |          1  1 -1 -1                                     
  P_1 R^3 |          1 -1 -1  1              1 -1 -1  1             
 -------------------------------------------------------------------
  J_z^P_1 |         0+ 0- 2+ 2- 1+ 1-

 The multiplets have the following use:

  9,  8    P_perp = (c,0),    P_2 = +1
  7, 10    P_perp = (c,0),    P_2 = -1
  11,12    P_perp = (c,c),  P_1 R = +1
  14,13    P_perp = (c,c),  P_1 R = -1
  15       n = (c,0)          P_2 = +1       
  16       n = (c,0)          P_2 = -1
  17       n = (c,c)        P_1 R = +1
  18       n = (c,c)        P_1 R = -1

To produce these results, we wrote lots of C-code. This code is linked to standard packages BLAS, LAPACK, and (optionally) ARPACK along with some other standard routines, and a parallel lanczos solver.

Older data from 1998

Results from 1999

These are our most important results for glueballs.

Scaling trajectory for various methods.

For the mesons, one is forced to use periodic boundary conditions for the link fields.  This introduces some serious problems with convergence in K.

The due to finite-K errors, the couplings that produce the best Lorentz covariance are slightly shifted for different methods:

Compare methods

Plots of the results, comparing the various methods:

Entire spectrum

To find the entire spectrum, we find all the states for a given K with no additional truncation in particle number.  The coupling constants are from the best fit glueball data ttraj_1_composite.out.  In order to make the calculations manageable, the spectrum for each sector was calculated separately: Now calculate this for all the data in ttraj_1_composite.out
E-mail: bvds@pitt.edu
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