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์ค๋ฅ ์ ๊ณ ํ๊ธฐํด๋น ํ์ด์ง ๋ด ์ ๋ชฉยท์ ์ยท๋ชฉ์ฐจยทํ์ด์ง์ ๋ณด๊ฐ ์๋ชป๋ ๊ฒฝ์ฐ ์๋ ค์ฃผ์ธ์!
๋ ผ๋ฌธ ๊ธฐ๋ณธ ์ ๋ณด
- ์ ์์ ๋ณด
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์ด๋กยทํค์๋
A bstract In the electroweak sector of the Standard Model, CP violation arises through a very particular interplay between the three quark generations, as described by the Cabibbo-Kobayashi-Maskawa (CKM) mechanism and the single Jarlskog invariant J 4 . Once generalized to the Standard Model Effective Field Theory (SMEFT), this peculiar pattern gets modified by higher-dimensional operators, whose associated Wilson coefficients are usually split into CP-even and odd parts. However, CP violation at dimension four, i.e., at the lowest order in the EFT expansion, blurs this distinction: any Wilson coefficient can interfere with J 4 and mediate CP violation. In this paper, we study such interferences at first order in the SMEFT expansion, ๐ช(1 / ฮ 2 ), and we capture their associated parameter space via a set of 1551 linear CP-odd flavor invariants. This construction describes both new, genuinely CP-violating quantities as well as the interference between J 4 and CP-conserving ones. We call this latter possibility opportunistic CP violation . Relying on an appropriate extension of the matrix rank to Taylor expansions, which we dub Taylor rank , we define a procedure to organize the invariants in terms of their magnitude, so as to retain only the relevant ones at a given precision. We explore how this characterization changes when different assumptions are made on the flavor structure of the SMEFT coefficients. Interestingly, some of the CP-odd invariants turn out to be less suppressed than J 4 , even when they capture opportunistic CPV, demonstrating that CP-violation in the SM, at dimension 4, is accidentally small.
๋ณธ๋ฌธยท๋ชฉ์ฐจ
์ธ๊ณต์ง๋ฅ ๋ฌธ์ ์ธ์ ๋ชจ๋ธ์ ํตํด ์ถ์ถ๋ ํ
์คํธ๋ก, ์ผ๋ถ ์คํ๋ ์ค๋ฅ๊ฐ ํฌํจ๋ ์ ์์ผ๋ ์ง์์ ์ผ๋ก ๊ฐ์ ์ค์
๋๋ค.
์ค๋ฅ๋ฅผ ๋ฐ๊ฒฌํ์ จ๋ค๋ฉด ํด๋น ๋ถ๋ถ์ ๋๋๊ทธํ ํ ' ๋ฅผ ํตํด ์ ๊ณ ํด์ฃผ์ธ์.
์ค๋ฅ๋ฅผ ๋ฐ๊ฒฌํ์ จ๋ค๋ฉด ํด๋น ๋ถ๋ถ์ ๋๋๊ทธํ ํ ' ๋ฅผ ํตํด ์ ๊ณ ํด์ฃผ์ธ์.
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