A U-spin anomaly in charm CP violation

Abstract

A bstract Recent LHCb data shows that the direct CP asymmetries of the decay modes D 0 → π + π − and D 0 → K + K − have the same sign, violating an improved U -spin limit sum rule in an unexpected way at 2 . 1 σ . From the new data, we determine for the first time the imaginary part of the CKM-subleading, U -spin breaking ∆ U = 1 correction to the U -spin limit ∆ U = 0 amplitude. The imaginary part of the ∆ U = 0 amplitude is determined by $$ \Delta {a}_{\textrm{CP}}^{\textrm{dir}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>CP</mml:mi> <mml:mi>dir</mml:mi> </mml:msubsup> </mml:math> . The corresponding strong phases are yet unknown and could be extracted in the future from time-dependent measurements. Assuming $$ \mathcal{O}(1) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mn>1</mml:mn> </mml:mfenced> </mml:math> strong phases due to non-perturbative rescattering, we find the ratio of U -spin breaking to U -spin limit contributions to the CKM-subleading amplitudes to be $$ \left({173}_{\hbox{--} 74}^{+85}\right)\% $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:msubsup> <mml:mn>173</mml:mn> <mml:mrow> <mml:mo>–</mml:mo> <mml:mn>74</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>85</mml:mn> </mml:mrow> </mml:msubsup> </mml:mfenced> <mml:mo>%</mml:mo> </mml:math> . This highly exceeds the Standard Model (SM) expectation of ~ 30% U -spin breaking, with a significance of 1 . 95 σ . If this puzzle is confirmed with more data in the future, in the SM it would imply the breakdown of the U -spin expansion in CKM-subleading amplitudes of charm decays. The other solution are new physics models that generate an additional ∆ U = 1 operator, leaving the U -spin power expansion intact. Examples for the latter option are an extended scalar sector or flavorful Z′ models.