We report a quantitative calorimetric study of ${\mathrm{UTe}}_2$ under pressure with a direct measurement of the Sommerfeld $\gamma$ coefficient, showing a threefold enhancement of electronic effective mass when approaching the critical pressure where superconductivity is suppressed and ordered states occur. We analyze the evolution of $\gamma$ with the amplitude of the jumps in the specific heat at the two superconducting transitions, and the superconducting critical temperature with pressure. This analysis would suggest that the high pressure superconducting phase nucleates only on a fraction of the Fermi surface. It also points to the possible major role of a quantum critical point of the unidentified phase that has been called weak magnetic order, rather than to the critical pressure of the antiferromagnetic phase. Just at the border of long-range antiferromagnetic order, where superconductivity emerges from the weak magnetic order phase, a significant increase in the specific heat jump for both superconducting transitions is found, accompanied by a noticeable change of their shapes.

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• Magnetic order
• Magnetic phase transitions
• Pairing mechanisms
• Quantum phase transitions
• Spin-triplet pairing
• Superconductivity