The possible parameters that can be used in the query string are:
Queries:
category - Category to limit results to, specified by name.
  Can be provided multiple times, or as pipe- ("|") separated
  values list, to limit results to those with any of the specified categories.
  Added in version 20.1.  See Categories, here.requireAllCategories - Setting to Y requires each result to be in
  all specified categories, instead of any one of them.
  Added in version 20.1.  See Categories, here.cq - Category to limit results to, specified by number:
  cq=1 for first category, cq=2 for second, etc.  Can be
  provided multiple times or as a CSV to limit results to those with any of
  the specified categories.
  See Categories, here.
  Deprecated; use category instead.cqall - Setting to Y requires each result to be in
  all specified categories, instead of any one of them.
  See Categories, here.
  Deprecated; use requireAllCategories instead.dq - Maximum Depth query (e.g. dq=2 for results found at most 2 links away from Base URLs)mtq - Mime Type query. May be an exact literal (e.g. mtq=application/pdf) or have a * after the / for anything of the left type (e.g. mtq=text/*)query - Main search querysq - Site query (here)tq - Title-only query (same Metamorph syntax as keyword search)uq - URL query, match against the entire URL. Accepts wildcards * for any amount of anything and ? for any single character. (e.g. uq=https://www.example.com/dir/*)
Search control:
dateSource - What date to use, id or Modified (see below)mdgt - Modified Date Greater Than: Only results with a modified date
  less than this will be returned.mdlt - Modified Date Less Than: Only results with a modified date
  less than this will be returned.pr - Specifies the Parametric Search Appliance profileprox - Proximity: Only return results with the query
  words in the same line, sentence, paragraph, or
  page (default).  Sets the Proximity search option
  (here).order - Controls the sort order; this is the same variable
  that Result Order (here) controls.
  Valid values are r (relevance),
  dd (date descending: newest first), or da
  (date ascending: oldest first).  The date used for
  newest/oldest sorting is the Last-Modified date of the document
  (or date of walk if none); this can be changed via the dateSource
  parameter (here).
  In version 17.1 and later, rank may be given as an alias for
  r (relevance), date for dd (newest first),
  and size, visited or depth may also be given.
  For Parametric appliances, order may also be a comma-separated list of
  Parametric Fields (and/or any of the above values, if version 17.1
  or later) to sort by; see the Sortable checkbox for Parametric
  Search Options, here.rpp - Max number of results per page (up to permitted limit; see Max User Results Per Page
  search setting, here)sr - Max number of results per site (if permitted; see Results per Site search settings, here)sufs - Word forms (suffixes).  Values are 0 (Exact match),
  1 (Plurals & Possessives), 2 (Any word forms), or 3 (Custom)mu - For meta searches: each value is a target profile
  (display name) to search.  Can be used to narrow down target profile
  search list.  Only respected if User Selection
  (here) is Y.
Rank Knobs: control the influence of ranking factors. Unless otherwise specified, each is an integer value, from off (0) to maximum (1000), to indicate the relative weight of that factor. Medium (500) is the default.
rorder - Word ordering: Favors results with query terms
  in the same order as the query; overrides Word Ordering
  (here)rprox - Word proximity: Favors results with query terms
  close together; overrides Word Proximity
  (here)rdfreq Database frequency: Favors results with query
  terms more rare across the entire profile; overrides Database
    Frequency (here)rwfreq - Document frequency: Favors results with query
  terms repeated more often in the document; overrides Document
    Frequency (here)rlead - Position in text: Favors results with query terms
  earlier in the document; overrides Position in Text
  (here)rdepth - Depth in site: "Shallower" results (fewer clicks
  from the Base URL) are better; overrides Depth in Site
  (here)rdatebiasWeight - Date bias weight: Favors "newer"
  results (closer to rdatebiasAnchor i.e. now).
  Additional parameters:
rdatebiasHalfLife - Date bias decay rate: time for
      rdatebiasWeight to be halved, in secondsrdatebiasAnchor - Date bias reference point: "best"
      date for maximum rank; can be lastWalkFinished for
      completion date of last successful walk, or Texis-parseable daterdatebiasField - Date bias field: date field to use for
      computing document age (default Modified)
  All of these override the equivalent Date Bias value in Search Settings (here).
rankBias - Rank Bias: Parametric field to add to rank (bias
  some results up or down); overrides Rank Bias
  (here)
Parametric Fields and related:
gb - restrict the Group Bys performed to one or more named
  fields.  The Group Bys must still be configured in the admin interface (see
  here), but the gb parameter allows you to further
  restrict Group Bys to fewer than would be performed otherwise.
See also Parametric Search Queries (here) for information on searching parametric fields, and specifying parametric search details.
dateSource: id vs modified
The dateSource parameter allows you to determine which date
associated with the URL gets used for display, sorting, etc.
Modified  date
would be a year ago, but the id date would be last night.
id is the default dateSource when requesting an RSS feed of a
search.
Other Variables
dropXSL - When Results Style
    (here) is set to XSL
    Stylesheet, or the search request URL is search/main.xml
    (note the .xml extension), the dropXSL query variable
    controls how the XSL is applied.  It may have one of the following
    values:
dropXSL is set based on the search/main.ext
    file extension in the URL: no if .xml was given,
    html otherwise.