Context. A longstanding challenge for understanding classical Cepheids is the Cepheid mass discrepancy, where theoretical mass estimates using stellar evolution and stellar pulsation calculations have been found to differ by approximately 10 - 20%. Aims. We study the role of pulsation-driven mass loss during the Cepheid stage of evolution as a possible solution to this mass discrepancy. Methods. We computed stellar evolution models with a Cepheid mass-loss prescription and various amounts of convective core overshooting. The contribution of mass loss towards the mass discrepancy is determined using these models, Results. Pulsation-driven mass loss is found to trap Cepheid evolution on the instability strip, allowing them to lose about 5 - 10% of their total mass when moderate convective core overshooting, an amount consistent with observations of other stars, is included in the stellar models. Conclusions. We find that the combination of moderate convective core overshooting and pulsation-driven mass loss can solve the Cepheid mass discrepancy.Comment: 4 pages, 2 figures and 2 tables. Accepted for publication A&A Letter
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