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We propose the K → πγ decay mode as a signature of the violation of the Lorentz invariance and the appearance of new physics via space-time noncommutativity.PACS numbers: 12.39Dc, In this proposal we assume space-time noncommutativity (NC) to compute the K → πγ decay forbidden by the Lorentz invariance.The dynamics of the standard model (SM) forbidden flavor-changing weak decays is described in the framework of the noncommutative SM (NCSM), where the content of particles and symmetries is the same as in the usual commutative space-time. Gauge symmetry is included in an infinitesimal form, thus SU(N) gauge symmetry is implementable. All NC fields are expressed in terms of the usual fields via the Seiberg-Witten (SW) map by expansion up to first order in the NC parameter θ µν . As in other particle physics models on noncommutative space-time, a general feature of the NCSM action is the violation of space-time symmetries, in particular of angular momentum conservation and discrete symmetries like P, CP, and possibly even CPT. This symmetry breaking is spontaneous in the sense that it is broken with respect to a fixed noncommutative background.The method for implementing non-Abelian SU(N) theories on noncommutative space-time, based on the Seiberg-Witten map [1], has been proposed in [2]. In [3,4,5,6] this method has been applied to the standard model of particle physics resulting in the noncommutative extension of the SM, called NCSM action, with the same structure group SU(3) c × SU(2) L × U(1) Y and with the same fields and number of coupling parameters as in the original SM. It represents a θ µν -expanded effective actionvalid at very short distances, that leads to an anomaly free theory [7]. For expressions of particular contributions we refer to [5,6]. The θ µν = c µν /Λ 2 NC is the constant, antisymmetric tensor, where c µν are dimensionless coefficients of order unity and Λ NC is the scale of noncommutativity. The matter sector of the action (1), relevant to this work, is not affected by the freedom of choosing traces in the gauge kinetic part; the quark-gauge boson interactions remain the same [5,6]. The above action is symmetric under ordinary gauge transformations in addition to noncommutative ones.An alternative NCSM proposal was presented in [8].Signatures of noncommutativity have been discussed within collider physics [9,10,11,12], SM forbidden decays [4,13,14,15,16], neutrino astrophysics [17,18], in [19], as well as for low-energy non-accelerator experiments [20,21,22,24]. This paper represents an estimate of the K → πγ decay branching ratio, based on the complete analysis of the S NCSM action presented in [5]. From S Higgs we find the contribution proportional to the M 2while explicit expressions containing important Yukawa terms forq (i) q (j) γ andq (i) q (j) γW + vertices are given by Eqs. (76), (78) and (86) of Ref. [5]. There is also an additional contribution to the vertex (2) from Eq. (89) in [5], but owing to the symmetry this term vanishes. The free quark amplitude M contributing to the K ...

In this letter we propose a possible mechanism of left-and right-handed neutrino couplings to photons, which arises quite naturally in non-commutative gauge field theory. We estimate the predicted additional energy-loss in stars induced by space-time non-commutativity. The usual requirement that any new energy-loss mechanism in globular stellar clusters should not excessively exceed the standard neutrino losses implies a scale of non-commutative gauge theory above the scale of weak interactions.