Thank you for your detailled answer.
But i'd really like to understand with adding score information on aggregation is so slow
This is profiling information
Aggregation with score
{
    "category": {
        "terms": {
            "field": "category",
            "size": 100
        },
        "aggs": {
            "score": {
                "max": {
                    "script": {
                        "lang": "painless",
                        "inline": "_score"
                    }
                }
            }
        }
    }
}
Profile result :
{
    "type": "org.elasticsearch.search.aggregations.bucket.terms.GlobalOrdinalsStringTermsAggregator$WithHash",
    "description": "category",
    "time": "97.76644000ms",
    "breakdown": {
        "reduce": 0,
        "build_aggregation": 90977021,
        "build_aggregation_count": 1,
        "initialize": 1760,
        "initialize_count": 1,
        "reduce_count": 0,
        "collect": 6773280,
        "collect_count": 14377
    },
    "children": [{
        "type": "org.elasticsearch.search.aggregations.metrics.max.MaxAggregator",
        "description": "score",
        "time": "4.316251000ms",
        "breakdown": {
            "reduce": 0,
            "build_aggregation": 5004,
            "build_aggregation_count": 125,
            "initialize": 315,
            "initialize_count": 1,
            "reduce_count": 0,
            "collect": 4296429,
            "collect_count": 14377
        }
    }]
}
Aggregation with field
{
    "category": {
        "terms": {
            "field": "category",
            "size": 100
        },
        "aggs": {
            "score": {
                "max": {
                    "field": "product_id"
                }
            }
        }
    }
}
Profile result :
{
    "type": "org.elasticsearch.search.aggregations.bucket.terms.GlobalOrdinalsStringTermsAggregator$WithHash",
    "description": "category",
    "time": "6.224784000ms",
    "breakdown": {
        "reduce": 0,
        "build_aggregation": 1436553,
        "build_aggregation_count": 1,
        "initialize": 1825,
        "initialize_count": 1,
        "reduce_count": 0,
        "collect": 4771863,
        "collect_count": 14541
    },
    "children": [{
        "type": "org.elasticsearch.search.aggregations.metrics.max.MaxAggregator",
        "description": "score",
        "time": "0.4531270000ms",
        "breakdown": {
            "reduce": 0,
            "build_aggregation": 7501,
            "build_aggregation_count": 123,
            "initialize": 298,
            "initialize_count": 1,
            "reduce_count": 0,
            "collect": 430663,
            "collect_count": 14541
        }
    }]
}