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The application of effective field theory in strong disruptors of heavy corks

Number of pages: 92 File Format: word File Code: 32572
Year: Not Specified University Degree: Not Specified Category: Facilities - Mechanics
Tags/Keywords: Effective field - Heavy corks - on interaction - Particles - quark - Weak interactions
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  • Summary of The application of effective field theory in strong disruptors of heavy corks

    At the end, we investigated the weak interactions of particles and their standard parameterization. We used ta operators in the expansion of operators in weak decays. We used the weak effective Hamiltonian for the decays of the B meson and the K meson. We have calculated the Wilson coefficients related to them and applied them to several decays, and then we studied the heavy quark effective theory and used different states for heavy quark B mesons. The group

    has been studied to break spontaneously. And the above symbol is the weak charge and electric charge generators, and in place, which will be discussed in more detail in the next section.

    Let us recall certain features of the electroweak part of the standard model that will be important for considerations.

    Leptons and left-handed quarks are in pairs, as follows:

    There is a weak electro-weak interaction of warks and leptons by means of the weak measure of bosons and

    photon A, which is summarized by the following Lagrangian:

    where

    which describes the charge current interaction and

    describes the neutral current interaction where e is the QED coupling constant and is the coupling constant and the Weinberg angle. The currents are presented as follows: rtl;"> 

     

     

     

     

     

    respectively It represents the charge and the third component of the weak iso-spin left-round fermion. In weak decay the Fermi constant plays an important role, which has the following values:

    Other dependent parameter values ??will be collected in Appendix A. Interactions between quantum bosons are standard and can be found in any textbook of quantum theory. The prime in (2-1) shows that the eigenstate of the weak state is not equivalent to the eigenstate of the mass state corresponding to , but the linear combination of the latter is expressed through the following relation.

    in which the unit matrix connecting and relating two sets of states is the Kubibo-Kubaya-Moskawa (CKM) matrix. Many parameters of this matrix have been proposed in the literature. In this review, we use two types of parameterization. Standard parameterization recommended by particle data group and Wolfenstein parameterization

    1-2- Standard parameterization

    We consider the following notation:

                 then the standard parameterization is as follows:

    where The phase required for CP violation is and can be chosen positive and may vary within the range, however, the measurement of CP violation in the energy decay of K will result in being within the range. The extensive phenomenology of recent years shows that and ,

    are small numbers in the order of and , respectively, and therefore with excellent accuracy
    and the four independent parameters are as follows: rtl;"> with phase extracted from the transmission of CP violations with processes sensitive to .The next one is based on the observations for as well as the analysis of CP violation and there is a one-to-one correspondence as follows. style="direction: rtl;">One ??of the most useful relationships that provides the condition of the matrix being unique for CKM is:

    At different levels, the relationship (1-16) can be used as a unique triangle [1] (UT) It is called, it is discussed. It is interesting to know this triangle, if there is currently a wide debate about the simultaneous entry of elements, in the usual UT analysis, only the term in (1-16) is kept, but still we directly consider the "major term". First, we mention that: is, exists. We keep the correction and replace all terms (1-16) with , we have: style="direction: rtl;">

    Therefore, figure 1 can be represented as a unitary triangle in the complex plane. The length of CB, which lies on the real axis, is equivalent to one when the equation is replaced by Accuracy is relevant. But in the future, the accuracy and accuracy of the experimental results and theoretical calculations may improve significantly, so the formulation presented here will be appropriate.          

    Using simple trigonometry, we have:

    The length of CA and BA on a smaller scale in the triangle of Figure 1 are symbolized by and respectively, which are:

    and expressions with a good approximation according to presented, which can be clearly determined by two angles, we have:

    1-4- QCD normalization

    As mentioned in the preface, QCD plays an important role in the phenomenology of the weak decay of hadrons. QCD is the most difficult and extensive part. In this section, the basic features of QCD disorder and its renormalization should be briefly mentioned, as a result, we focus on the aspects that will be needed to investigate QCD disorder and its renormalization. Also, the opportunity to provide a reference for the expressions of the coupling function of the mass function and corresponding to the group of renormalization functions will be provided. The QCD Lagrangian density is as follows:

    -mq)q+?a*?????a

    Here are the triple colors of the quark flavor. g is the QCD coupling.

    is the gluon field and is the virtual field or phantom field.  The parameter is the measure and the generators which are constants of the structure.

  • Contents & References of The application of effective field theory in strong disruptors of heavy corks

    List:

    Chapter 1: Weak interactions 1

    1-1- Particles and interactions 2

    1-2-Standard parameterization. 5

    1-3-first order unitary triangle. 6

    1-4- Normal QCD again. 9

    Chapter 2: Operators in weak decays 16

    2-1- Expansion of operators in weak decays. 17

    2-2- Expansion of QCD operators and short-range effects. 22

    2-3-Invoicing scale. 32

    Chapter 3: 33

    Effective Hamiltonian in weak interactions 33

    3-1- Effective Hamiltonian. 34

    3-2- Effective Hamiltonian operators. 35

    3-3- Wilson coefficients. 40

    3-4- Effective Hamiltonian including QCD penguin operators. 47

    3-5- Effective Hamiltonian in QCD. 49

    3-6- Wilson coefficients in QCD. 51

    3-7-Hamiltonian in electroweak penguin operators. 52

    3-8- Effective Hamiltonian in electroweak penguin operators. 53

    3-10-Wilson's coefficients in penguin weak electro. 57

    Chapter 4: 59

    Weak decays of B and K mesons 59

    4-1- Hamiltonian effective in decay. 60

    4-2- Hamiltonian effective in decay. 62

    4-3-Hamiltonian effective in rare decays of K and B mesons. 63

    4-4- Decay. 67

    4-5- Second order Hamiltonian effective in decay. 70

    4-6-Decompositions of , , and . 73

    Chapter 5: 74

    Effective heavy quark theory 74

    5-1- Introduction. 75

    5-2- Effective heavy quark theory. 75

    5-3- Heavy currents. 79

    5-4- Phenomenology of weak decays of heavy meson B. 83

    5-5- Heavy quark decay modes b 86

    Source:

     

     

     

    [1] B.R. Webber”,HADRONIZATION”,B361(1991)93, added 30 Nov 1994.

    [2] N.G. Deshpande, and Xiao-Gang He, A Method for Determining CP Violating Phase, Rev. Lett 75 3064-3067(1995). [3]. N.G. Deshpande, G. Eilam, Xiao-Gang He, and JosipTrampetic,"The NonresonantCabibbo Suppressed Decay and Signal for CP Violation", ref: Phys.Rev.D52:5354-                   5357,1995.

    [4] N.G. Deshpande and Xiao-Gang He, "Penguin B Decays and ”, OITS-                           555, 1994.

    [5] Robert Fleischer, "Mixing-induced CP Violation in the Decay within the Standard               Model", Ref: Phys. Lett. B341:205-212, 1994.

    [6] J. Fleischer, O. V. Tarasov,"Two-loop gluon-condensate contributions to heavy-quark currentcorrelators: exact results and approximations", Ref: Phys.Lett.B329:103-110,1994. Phys.Lett.B326:145-153,1994.

    [8] Wolfgang Kilian and Thomas Mannel,”Unimagined Imaginary Parts in Heavy Quark Effective Field Theory”, Phys.Lett.B304:311-317,1993.

    [9] J M Flynn and N Isgur,”Heavy quark symmetry: ideas and applications”. J.Phys.G18:1627-                      1644,1992.

    [10] C.R. Allton, H. Duong, C.T. Sachrajda,"Quenched Hadrons using Wilson and O(a)-Improved Fermion Actions at = 6.2", Phys.Lett.B284:377-383,1992. [11] Matthias Neubert, "Theoretical Update on the Model-Independent Determination of Using Heavy Quark Symmetry". Phys.Lett.B338:84-91,1994.

    [12]Wolfgang Kilian Thomas Mannel,"QCD Corrected   Contributions to                            ",Phys.Lett. B301 382-392 (1993).

    [13] D. J. BROADHURST, A. G. GROZIN,”Two-loop renormalization of the effective field theory of a           static quark”, Phys.Lett.B267:105-110, 1991.

    [14] I.I.Bigi,”Nonperturbative Corrections to Inclusive Beauty and Charm. Decays: QCD versus Phenomenological Models”, Phys.Lett.B293:430-436,1992; ERRATUM-ibid.B297:477,1993.

    [15] IkarosBigi,"The Baffling Semileptonic Branching Ratio of B Mesons",Phys.Lett. B323 408-416 (1994). [16] Aneesh V. Manohar, Mark B.Wise,"Inclusive Semileptonic B and Polarized _b Decays from QCD", Phys.Rev.D49:1310-1329,1994. [17] Thomas Mannel and Matthias Neubert, "Resummation of Nonperturbative Corrections to the Lepton Spectrum in Inclusive Decays". Phys.Rev.D50:2037-2047,(1994).

    [18 ] Adam F. Falk,”Another Source of Baryons in B Meson Decays”,Phys.Rev.Lett. 73 1075-1078                 (1994).

    [19] I.I. Bigi,"On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays", Int.J.Mod.Phys. A9 2467-2504 (1994).

    [20] Adam F. Falk and Alexander Kyatkin,"Instantons and the endpoint of the lepton energy spectrum in

           charmlesssemileptonic B decays", Phys.Rev.D52:5049-5055,1995.

    [21] I. Bigia, b, M. Shifman c. N. Uraltseva, d, A. Vainshtein, "Heavy Quark Distribution Function in QCD and the AC2M2 Model", : Phys. Lett. B328 431-440 (1994).

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The application of effective field theory in strong disruptors of heavy corks
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