arXiv:hep-lat/9608061v1 13 Aug 1996
1
UTCCP-P-12
August 1996
Four-dimensional Simulation of the Hot Electroweak Phase Transition
with the SU(2) Gauge-Higgs Model ∗
Yasumichi Aokia
aCenter for Computational Physics, University of Tsukuba, Ibaraki 305, Japan
We study the ﬁnite-temperature phase transition of the four-dimensional SU(2) gauge-Higgs model for inter-
mediate values of the Higgs boson mass in the range 50<∼mH <∼100GeV on a lattice with the temporal lattice size
Nt = 2. The order of the transition is systematically examined using ﬁnite size scaling methods. Behavior of the
interface tension and the latent heat for an increasing Higgs boson mass is also investigated.
1. INTRODUCTION
The possibility that the baryon number asym-
metry of the Universe has been generated in the
course of the electroweak phase transition has
led to recent lattice investigations of the SU(2)
gauge-Higgs model by several groups[1]. Their
studies have shown that a ﬁrst-order phase tran-
sition takes place at a ﬁnite temperature in this
system for a light Higgs boson, which, however,
becomes rapidly weak as the Higgs boson mass
increases. A central question, relevant for the
baryon number asymmetry problem, is whether
the ﬁrst-order transition survives with a suﬃcient
strength for realistically large Higgs boson mass,
experimentally bounded by MH ≥ 64GeV[2].
To answer this question many studies have been
done within the perturbatively reduced three-
dimensional model[1]. On the other hand, only
a few studies with the original four-dimensional
model exist in this region of Higgs boson mass[1].
In this article, we report results of our simula-
tion of the four-dimensional model, aiming at a
systematic ﬁnite-size scaling analysis of the order
of the transition for the Higgs boson mass in the
range 50<∼mH <∼100GeV.
2. SIMULATION
We employ the standard action given by
S = ∑
n
{∑
µ>ν
β
2 TrUn,µν + ∑
µ
κTr(Φ†
nUn,µΦn+ˆµ)
− ρ2
n − λ(ρ2
n − 1)2}, (1)
∗Talk given at Lattice 96, St. Louis, USA.
with the complex 2 × 2 matrix Φ decomposed
as Φn = ρnαn, ρn ≥ 0; αn ∈ SU(2). All of
our simulations are made for the temporal ex-
tent Nt = 2. We set the gauge coupling β =
1/g2 = 8, and make simulations for 6 values of
the scalar self-coupling λ as listed in Table 1.
Also listed in the table are the zero-temperature
Higgs boson mass MH at the transition point of
Nt = 2 lattice, estimated by interpolating avail-
able data for MH [3–5] as a function of λ. For
each value of λ runs are made on an N 3
s ×2 lattice
with Ns = 8, 12, 16, 24, 32, and in addition with
Ns = 40 for λ = 0.001, 0.0017235, 0.003(MH =
67, 85, 102GeV ). Gauge and scalar ﬁelds are up-
dated with a combination of the heat bath[6] and
overrelaxation[7] algorithms in the ratio reported
to be the fastest in ref. [4]. For each parameter
point we make 105 iterations of the combined up-
dates.
3. FINITE-SIZE SCALING ANALYSIS
Let us deﬁne the angular part of the spatial
component of the hopping term in the action by
Λs ≡ 1
3N 3
s Nt
∑
n
3∑
j=1
[ 1
2 Tr(α†
nUn,j αn+ˆj )
]
. (2)
In Fig. 1 we show the volume dependence of the
maximum height of the susceptibility deﬁned by
χΛs ≡ V (〈Λ2
s 〉 − 〈Λs〉2) , (3)
with V = N 3
s , which is calculated by the stan-
dard reweighting technique. For 47 ≤ MH ≤

100%

Four-dimensional Simulation of the Hot Electroweak Phase Transition with the SU(2) Gauge-Higgs Model

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