Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Supersymmetric Grand Unified Theories: Two Loop Evolution of Gauge and
  Yukawa Couplings   We make a numerical study of gauge and Yukawa unification in supersymmetric
grand unified models and examine the quantitative implications of fermion mass
ans\"{a}tze at the grand unified scale. Integrating the renormalization group
equations with $\alpha _1(M_Z)$ and $\alpha _2(M_Z)$ as inputs, we find $\alpha
_3(M_Z)\simeq 0.111 (0.122)$ for $M_{SUSY}^{}=m_t$ and $\alpha _3(M_Z)\simeq
0.106 (0.116)$ for $M_{SUSY}^{}=1$ TeV at one-loop (two-loop) order. Including
$b$ and $\tau $ Yukawa couplings in the evolution, we find an upper limit
$m_t\ltap 200$ GeV from Yukawa unification. For given $m_t\ltap 175$ GeV, there
are two solutions for $\beta$, one with $\tan \beta > m_t/m_b$, and one with
$\sin \beta \simeq 0.78(m_t/150\;{\rm GeV})$. Taking a popular ansatz for the
mass matrices at the unified scale, we obtain a lower limit on the top quark
mass of $m_t\gtap 150 (115)$ GeV for $\alpha _3(M_Z)=0.11 (0.12)$ and an upper
limit on the supersymmetry parameter $\tan \beta \ltap 50$ if $\alpha
_3(M_Z)=0.11$. The evolution of the quark mixing matrix elements is also
evaluated.

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The categories of this paper are: funct-an
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph