Standard Model in symmetric phase

The SMSP implements the SM in the symmetric phase:

\[\begin{split}\mathcal{L}_{SMSP} =& -\frac{1}{4} B^{\mu\nu}B_{\mu\nu} -\frac{1}{4} W^{i\mu\nu}W^{i}_{\mu\nu} -\frac{1}{4} G^{a\mu\nu}G^{a}_{\mu\nu} \\ &+ \mathrm{i} \overline{Q}_\mathrm{L} \gamma^\mu\mathrm{D}_\mu \overline{Q}_\mathrm{L} + \mathrm{i} \overline{L}_\mathrm{L} \gamma^\mu\mathrm{D}_\mu \overline{L}_\mathrm{L} + \mathrm{i} \overline{u}_\mathrm{R} \gamma^\mu\mathrm{D}_\mu \overline{u}_\mathrm{R} + \mathrm{i} \overline{d}_\mathrm{R} \gamma^\mu\mathrm{D}_\mu \overline{d}_\mathrm{R} + \mathrm{i} \overline{l}_\mathrm{R} \gamma^\mu\mathrm{D}_\mu \overline{l}_\mathrm{R}\\ &+ \left(\mathrm{D}_\mu\Phi\right)^\dagger \left(\mathrm{D}_\mu\Phi\right) ,\end{split}\]

with \(B\) being the U1 field, \(W\) being the SU2 field and \(G\) being the gluon field. The covariant derivative is defined as

\[D_\mu = \partial_\mu - \mathrm{i} g_2 I^a_W W^a_\mu + \mathrm{i} g_1 \frac{Y_W}{2} B_\mu\]

which implies for the hypercharges of the quark and lepton representations:

Field

\(Y_W\)

\(Q_\mathrm{L}\)

1/3

\(L_\mathrm{L}\)

-1

\(u_\mathrm{R}\)

4/3

\(d_\mathrm{R}\)

-2/3

\(l_\mathrm{R}\)

-1/3

The Yukawa couplings are disabled and there is no direct coupling between quarks and the higgs.

The fermionic fields of this model correspond to the ones in the SM. The gauge fields are as follows

Fields

Recola identifier

\(\mathrm{B}_0\), \(\mathrm{W}^+\), \(\mathrm{W}^-\), \(\mathrm{W}^3\)

'B0', 'W+', 'W-', 'W3'

Gluon

'g'

Power counting

The model has been implemented with a power counting (see SM power counting) in the gauge couplings as follows

Coupling

Order

\(g_1\)

\(\mathrm{GC1}\)

\(g_2\)

\(\mathrm{GC2}\)

\(g_s\)

\(\mathrm{QCD}\)

Snippet code

Python

from pyrecola import *

set_output_file_rcl('*')

set_print_level_squared_amplitude_rcl(2)
set_draw_level_branches_rcl(1)
set_print_level_parameters_rcl(1)

define_process_rcl(1, 'u u~ -> W+ W-', 'NLO')
define_process_rcl(2, 'u u~ -> W3 W3', 'NLO')

generate_processes_rcl()

s = 500.
p1 = [s/2, 0., 0., s/2]
p2 = [s/2, 0., 0.,-s/2]

psp = set_outgoing_momenta_rcl(1, [p1, p2])
compute_process_rcl(1,psp,'NLO')
psp = set_outgoing_momenta_rcl(2, [p1, p2])
compute_process_rcl(2,psp,'NLO')

reset_recola_rcl()

Releases

UFO model files

References