You can sue the dog groomer for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable dog groomer would have exercised under the same or similar circumstances to prevent foreseeable harm).  A reasonable dog greoomer would have watched your dog to prevent it from being lost or harmed.Your damages (the amount of monetary compensation you are seeking in your lawsuit) would include the value of the dog and emotional distress for the loss of your dog.