Constraints on anomalous dimensions from the positivity of the S matrix

Abstract

I am thankful to Guilherme Guedes, Mario Herrero-Valea, Maria Ramos, and Jose Santiago for useful discussions. This work is supported by SRA under Grants No. PID2019–106087GB-C21 and No. PID2021-128396NB-I00, by the Junta de Andalucía grants No. FQM 101, No. A-FQM-211-UGR18, No. P21-00199, and No. P18-FR-4314 (FEDER), as well as by the Spanish MINECO under the Ramón y Cajal programme MCIN/AEI /10.13039/501100011033 with Grant No. RYC2019-027155-I and by Grant CNS2022-136024 funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR.We show that the analyticity and crossing symmetry of the S matrix, together with the optical theorem, impose restrictions on the renormalization group evolution of dimension-8 operators in the Standard Model effective field theory. Moreover, in the appropriate basis of operators, the latter manifest as zeros in the anomalous dimension matrix that, to the best of our knowledge, have not been anticipated anywhere else in the literature. Our results can be trivially extended to other effective field theories.European Union NextGenerationEU/PRTRSRA PID2019–106087GB-C21, PID2021-128396NB-I00FEDERMinisterio de Economía y Competitividad CNS2022-136024, MCIN/AEI/10.13039/501100011033, RYC2019-027155-I MINECOJunta de Andalucía A-FQM-211-UGR18, FQM 101, P18-FR-4314, P21-0019