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1. Opportunistic CP violation

   https://doi.org/10.1007/JHEP06(2023)141  

   Bonnefoy, Quentin; Gendy, Emanuele; Grojean, Christophe; Ruderman, Joshua T. (June 2023, Journal of High Energy Physics)

   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, 𝒪(1 / Λ 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. 

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2. Higgs Parity, strong CP and dark matter

   https://doi.org/10.1007/JHEP07(2019)016  

   Dunsky, David; Hall, Lawrence J.; Harigaya, Keisuke (July 2019, Journal of High Energy Physics)
3. Nonlinear and non-CP gates for Bloch vector amplification

   https://doi.org/10.1088/1572-9494/acf304  

   Geller, Michael R (September 2023, Communications in Theoretical Physics)

   Abstract Any stater= (x,y,z) of a qubit, written in the Pauli basis and initialized in the pure stater= (0, 0, 1), can be prepared by composing three quantum operations: two unitary rotation gates to reach a pure state $\mathit{r}={\left(x^2+y^2+z^2\right)}^{-\frac{1}{2}}\times (x,y,z)$on the Bloch sphere, followed by a depolarization gate to decrease ∣r∣. Here we discuss the complementary state-preparation protocol for qubits initialized at the center of the Bloch ball,r=0, based on increasing or amplifying ∣r∣ to its desired value, then rotating. Bloch vector amplification increases purity and decreases entropy. Amplification can be achieved with a linear Markovian completely positive trace-preserving (CPTP) channel by placing the channel’s fixed point away fromr=0, making it nonunital, but the resulting gate suffers from a critical slowing down as that fixed point is approached. Here we consider alternative designs based on linear and nonlinear Markovian PTP channels, which offer benefits relative to linear CPTP channels, namely fast Bloch vector amplification without deceleration. These gates simulate a reversal of the thermodynamic arrow of time for the qubit and would provide striking experimental demonstrations of non-CP dynamics. 

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4. Uniform Random Generation and Dominance Testing for CP-Nets

   Allen, Thomas E; Goldsmith, Judy; Justice, Hayden Elizabeth; Mattei, Nicholas; Raines, Kayla (August 2017, Journal of artificial intelligence research)

   The generation of preferences represented as CP-nets for experiments and empirical testing has typically been done in an ad hoc manner that may have introduced a large statistical bias in previous experimental work. We present novel polynomial-time algorithms for generating CP-nets with n nodes and maximum in-degree c uniformly at random. We extend this result to several statistical cultures commonly used in the social choice and preference reasoning literature. A CP-net is composed of both a graph and underlying cp-statements; our algorithm is the first to provably generate both the graph structure and cp-statements, and hence the underlying preference orders themselves, uniformly at random. We have released this code as a free and open source project. We use the uniform generation algorithm to investigate the maximum and expected flipping lengths, i.e., the maximum length over all outcomes o1 and o2, of a minimal proof that o1 is preferred to o2. Using our new statistical evidence, we conjecture that, for CP-nets with binary variables and complete conditional preference tables, the expected flipping length is polynomial in the number of preference variables. This has positive implications for the usability of CP-nets as compact preference models. 

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5. Renormalization and running in the 2D CP (1) model

   https://doi.org/10.1007/JHEP02(2025)146  

   Buccio, Diego; Donoghue, John F; Menezes, Gabriel; Percacci, Roberto (February 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We calculate the scattering amplitude in the two dimensionalCP(1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to theO(N) model, for allN. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories. 

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