$wp_customize->add_section( 'cd_button' , array(
      'title'      => 'The Button',
      'priority'   => 20,
  ) );

  $wp_customize->add_setting( 'cd_button_display' , array(
      'default'     => true,
      'transport'   => 'refresh',
  ) );

  $wp_customize->add_control( 'cd_button_display', array(
  'label' => 'Button Display',
  'section' => 'cd_button',
  'settings' => 'cd_button_display',
  'type' => 'radio',
  'choices' => array(
    'show' => 'Show Button',
    'hide' => 'Hide Button',
  ),
) );