This letter reports a first quantitative analysis of the contribution of higher partial waves in the charge symmetry breaking reaction $dd \to {}^4\pi^0$ using the WASA-at-COSY detector setup at an excess energy of MeV. The determined differential cross section can be parametrized as , where is the production angle of the pion in the center-of-mass coordinate system, and the results for the parameters are $a = \left(1.55 \pm 0.46 () ^{+0.32}{-0.8} () \right)b = \left(13.1 \pm 2.1 () ^{+1.0}{-2.7} ()\right)$ pb/sr. The data are compatible with vanishing p-waves and a sizable d-wave contribution. This finding should strongly constrain the contribution of the isobar to the reaction and is, therefore, crucial for a quantitative understanding of quark mass effects in nuclear production reactions.

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