Fermion mixing renormalization and gauge invariance

Gambino, Paolo; Grassi, Pietro Antonio; Madricardo, Fantina

doi:10.1016/s0370-2693(99)00321-4

Cited by 71 publications

(176 citation statements)

References 26 publications

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“…A similar problem of gauge-dependence may arise if one tries to define the mixing parameters in the quark sector in terms of two-point functions only, instead of relying on physical amplitudes [15]. It follows that, if physical amplitudes are not directly employed like in Eq.…”

Section: The Nielsen Identities In the Smmentioning

confidence: 99%

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Nielsen identities of the SM and the definition of mass

2000

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In a generic gauge theory the gauge parameter dependence of individual Green functions is controlled by the Nielsen identities, which originate from an enlarged BRST symmetry. We give a practical introduction to the Nielsen identities of the Standard Model (SM) and to their renormalization and illustrate the power of this elegant formalism in the case of the problem of the definition of mass. We prove to all orders in perturbation theory the gauge-independence of the complex pole of the propagator for all physical fields of the SM, in the most general case with mixing and CP violation. At the amplitude level, the formalism provides an intuitive and general understanding of the gauge recombinations which makes it particularly useful at higher orders. We also include in an appendix the explicit expressions for the fermionic two-point functions in a generic R ξ gauge.

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Section: The Nielsen Identities In the Smmentioning

confidence: 99%

“…In general, it does not seem possible to form gauge-independent quantities on the basis of two-point functions only, i.e. of Γ φ , and to employ them to renormalize the mixing parameters [15]. On the other hand, the mixing parameters can be safely defined in terms of physical observables such as mesonic decay rates.…”

Section: The Scalar Sectormentioning

confidence: 99%

Nielsen identities of the SM and the definition of mass

2000

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“…It has been point out that in order to keep the gauge independence of the CKM matrix the CKM renormalization prescription must keep the unitarity of the CKM matrix [13,8]. But this conclusion is only a hypothesis.…”

Section: Relationship Between the Unitarity And The Gauge Indepenmentioning

confidence: 99%

“…In the on-shell renormalization framework, the early prescription [6] used the SU L (2) symmetry of SM to relate the CKM counterterm with the quark's wave-function renormalization constants (WRC) [12]. Although it is a delicate and simple prescription, it reduces the physical amplitude involving quark mixing gauge dependent 1 [13][14][15]. A revised prescription is to replace the on-shell quark WRC in the CKM counterterms with the ones calculated at zero momentum [13].…”

Section: Introductionmentioning

confidence: 99%

“…Although it is a delicate and simple prescription, it reduces the physical amplitude involving quark mixing gauge dependent 1 [13][14][15]. A revised prescription is to replace the on-shell quark WRC in the CKM counterterms with the ones calculated at zero momentum [13]. Another revised prescription [15] is to rearrange the off-diagonal quark WRC in a manner similar to the pinch technique [16].…”

Section: Introductionmentioning

confidence: 99%

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Renormalization of the Cabibbo–Kobayashi–Maskawa matrix at one-loop level

Zhou

2004

J. Phys. G: Nucl. Part. Phys.

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We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix at one-loop level. We emphasize at one prescription which is formulated with reference to the case of no mixing of quark's generations and point out that it doesn't make the physical amplitude involving quark mixing ultraviolet finite. We then propose a revised prescription to solve this problem and simultaneously keep the unitarity of the CKM matrix. Through explicit calculations we also prove that in order to keep the CKM matrix gauge independent the unitarity of the CKM matrix must be preserved.11.10. Gh, 12.15.Lk, 12.15.Hh

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Practical Algebraic Renormalization

2001

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A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process $B \to X_s \gamma$.Comment: version to be published in Annals of Physic

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Fermion mixing renormalization and gauge invariance

Cited by 71 publications

References 26 publications

Nielsen identities of the SM and the definition of mass

Nielsen identities of the SM and the definition of mass

Renormalization of the Cabibbo–Kobayashi–Maskawa matrix at one-loop level

Practical Algebraic Renormalization

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