How to send Cloudwatch log details via email?

The diagram below is what I am trying to achieve. In brief, to send CloudTrail logs to CloudWatch log group then scan it for certain events and finally send email alerts if there is an concerting event.

I am following this official documentation which also has a sample CloudFormation templates: http://docs.aws.amazon.com/awscloudtrail/latest/userguide/use-cloudformation-template-to-create-cloudwatch-alarms.html

Using the CloudFormation templates above, I have been able to send the email alerts. However the alerts are very basic; it does not send key information like which user initiated this event, when did it occur etc.

Logically thinking AWS::Logs::MetricFilter should pass the value to AWS::CloudWatch::Alarm which would then send the information. I have looked at the documentation of both MetricFilter and Alarm services. Dimension comes closer to what I want but not yet able to read the information from logs.

I would have thought this is a common use case and there would be documentation. Am I missing something glaringly obvious here? Has anyone here solved this issue?

AWS::Logs::MetricFilter block:

"AuthorizationFailuresMetricFilter": {
    "Type": "AWS::Logs::MetricFilter",
    "Properties": {
        "LogGroupName": { "Ref" : "LogGroupName" },
        "FilterPattern": "{ ($.errorCode = \"*UnauthorizedOperation\") || ($.errorCode = \"AccessDenied*\") }",
        "MetricTransformations": [
            {
                "MetricNamespace": "CloudTrailMetrics",
                "MetricName": "AuthorizationFailureCount",
                "MetricValue": "1"
            }
        ]
    }
},

AWS::CloudWatch::Alarm block

  "AuthorizationFailuresAlarm": {
      "Type": "AWS::CloudWatch::Alarm",
      "Properties": {
          "AlarmName" : "CloudTrailAuthorizationFailures",
          "AlarmDescription" : "Alarms when an unauthorized API call is made.",
          "AlarmActions" : [{ "Ref" : "AlarmNotificationTopic" }],
          "Dimensions": [
             {
                "Name": "errorCode",
                "Value": ""
             },
             {
                "Name": "userIdentity",
                "Value": ""
             }
          ],
          "MetricName" : "AuthorizationFailureCount",
          "Namespace" : "CloudTrailMetrics",
          "ComparisonOperator" : "GreaterThanOrEqualToThreshold",
          "EvaluationPeriods" : "1",
          "Period" : "300",
          "Statistic" : "Sum",
          "Threshold" : "1"

      }
  },