## 1 Introduction  
In France, each year, around 3.5 million cattle are slaughtered for meat production, which represents 1.3 million tons of beef carcasses [1]. Most of this meat is distributed in large and medium-sized stores and alone accounts for 75% of purchases of fresh red meat in France [2]. One in two consumers buy fresh red meat based on color [3]. However, if the red meat does not meet the consumer's requirements (a beautiful color and a good smell), the latter does not buy it, which leads to food waste. In 2016, waste due to organoleptic defects in beef was estimated at 3.4% of production or 45,000 tons of beef carcasses [4]. Microbiological contamination and color are the two major causes of observed defect in beef meat.  
The color of the meat is due to the presence of myoglobin. Myoglobin is a water-soluble intramuscular protein that binds to oxygen and allows cellular respiration in the muscle [5]. It is made up of globin and a prosthetic group called heme. At the center of the heme is an iron atom with its six coordination sites. The sixth coordination site makes it possible to bind a ligand such as dioxygen or even water [6]. Depending on the oxidation state of iron (ferrous Fe\({}^{2+}\) or ferric Fe\({}^{3+}\)) and the bound ligand, myoglobin is commonly found in 3 forms: deoxymyoglobin, oxymyoglobin, or metmyglobin [7]. Each redox form of myoglobin, when it is mainly present in meat, generates different colors. Deoxymyoglobin is purplish in color and is combined with a vacuum product or immediately cut. Oxymyoglobin is bright red in color and is associated with good quality red meat in trays, while metmyoglobin, brown in color on meat, and results in consumer rejection of the product. Indeed, there is a dynamic of interconversions (redox reactions) between these three forms of myoglobin [7]. Initially, myoglobin or deoxymyoglobin undergoes oxygenation or blooming by binding to oxygen and becomes red-colored oxymyoglobin. Under low partial oxygen pressure such as during cellular respiration by muscle tissue, oxymyoglobin can revert to deoxymyoglobin, which is sensitive to oxidation. This oxidation at the level of the iron atom in the center of the heme causes the passage of the deoxymyoglobin of purplish color in metmyoglobin of brown color.  
The aim of this study is to carry out a rapid and instant measurement of the redox potential, E\({}_{h}\), directly on a carcass (without slowing down the slaughter line), at the separation between forequarter and hindquarter in order to evaluate the time necessary for meat color to change from red to brown. To the best of the authors' knowledge, there is no technology to date to measure color and/or redox potential directly on slaughter lines. This would allow carcasses to be classified upstream in order to sort them. Indeed, a carcass whose E\({}_{h}\) value would indicate an early transfer would then be sent to a line of processed products, while a carcass whose E\({}_{h}\) value would indicate a later transfer would be distributed in large and medium-sized stores and offered in cut and packaged meat. However, since meat is a complex medium and redox probes for semi-solid media do not exist, the use of a mimetic medium such as meat juice (i.e., meat exsudate) has been proposed as a first approach.  
The strategy applied in this work consisted in simultaneously measuring the color of a beef meat juice and the E\({}_{h}\) in order to search for a relationship between these two variables. The main sources of variability have been identified in order to limit their effect. A validation of the relationship on beef meat was also performed.