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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク CKM Matrix ： ウィキペディア英語版 Cabibbo–Kobayashi–Maskawa matrix In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix (CKM matrix, quark mixing matrix, sometimes also called KM matrix) is a unitary matrix which contains information on the strength of flavour-changing weak decays. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks. ==The matrix== In 1963, Nicola Cabibbo introduced the Cabibbo angle (θc) to preserve the universality of the weak interaction.〔 〕 Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy,〔 〕 on the effectively rotated nonstrange and strange vector and axial weak currents, which he references.〔 〕 In light of current knowledge (quarks were not yet theorized), the Cabibbo angle is related to the relative probability that down and strange quarks decay into up quarks (|''V''ud|2 and |''V''us|2 respectively). In particle physics parlance, the object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks, here denoted by ''d′''.〔 〕 Mathematically this is: :$d^\backslash prime\; =\; V\_\; d\; +\; V\_\; s,$ or using the Cabbibo angle: :$d^\backslash prime\; =\; \backslash cos\; \backslash theta\_\backslash mathrm\; d\; +\; \backslash sin\; \backslash theta\_\backslash mathrm\; s\; .$ Using the currently accepted values for |''V''ud| and |''V''us| (see below), the Cabbibo angle can be calculated using :$\backslash tan\backslash theta\_\backslash mathrm=\backslash frac=\backslash frac\; \backslash rarr\; \backslash theta\_\backslash mathrm=\; ~13.02^\backslash circ.$ When the charm quark was discovered in 1974, it was noticed that the down and strange quark could decay into either the up or charm quark, leading to two sets of equations: :$d^\backslash prime\; =\; V\_\; d\; +\; V\_\; s\; ;$ :$s^\backslash prime\; =\; V\_\; d\; +\; V\_\; s,$ or using the Cabibbo angle: :$d^\backslash prime\; =\; \backslash cos\}\; s;$ :$s^\backslash prime\; =\; -\backslash sin\}\; s.$ This can also be written in matrix notation as: :$$ \begin d^\prime \\ s^\prime \end = \begin V_ & V_ \\ V_ & V_\\ \end \begin d \\ s \end, or using the Cabibbo angle :$$ \begin d^\prime \\ s^\prime \end = \begin \cos} \\ -\sin}\\ \end \begin d \\ s \end, where the various |''Vij''|2 represent the probability that the quark of ''j'' flavor decays into a quark of ''i'' flavor. This 2 × 2 rotation matrix is called the Cabibbo matrix. Observing that CP-violation could not be explained in a four-quark model, Kobayashi and Maskawa generalized the Cabbibo matrix into the Cabibbo–Kobayashi–Maskawa matrix (or CKM matrix) to keep track of the weak decays of three generations of quarks:〔 〕 : On the left is the weak interaction doublet partners of up-type quarks, and on the right is the CKM matrix along with a vector of mass eigenstates of down-type quarks. The CKM matrix describes the probability of a transition from one quark ''i'' to another quark ''j''. These transitions are proportional to |''Vij''|2. Currently, the best determination of the magnitudes of the CKM matrix elements is:〔 〕 :$$ \begin |V_| & |V_| & |V_| \\ |V_| & |V_| & |V_| \\ |V_| & |V_| & |V_| \end = \begin 0.97427 \pm 0.00015 & 0.22534 \pm 0.00065 & 0.00351^_ \\ 0.22520 \pm 0.00065 & 0.97344 \pm 0.00016 & 0.0412^_ \\ 0.00867^_ & 0.0404^_ & 0.999146^_ \end. Note that the choice of usage of down-type quarks in the definition is purely arbitrary and does not represent some sort of deep physical asymmetry between up-type and down-type quarks. We could just as easily define the matrix the other way around, describing weak interaction partners of mass eigenstates of up-type quarks, ''u′'', ''c′'' and ''t′'', in terms of ''u'', ''c'', and ''t''. Since the CKM matrix is unitary (and therefore its inverse is the same as its conjugate transpose), we would obtain essentially the same matrix. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cabibbo–Kobayashi–Maskawa matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.