Elementary Particles and Their Interactions

Ho‐Kim, Q.; Pham, Xuan-Yem

doi:10.1007/978-3-662-03712-6

Cited by 60 publications

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“…An analogous result was first derived by Lee and Yang in the framework of nonlocal extensions of the Fermi theory [1]. Calling M and m the masses of the initial and final leptons, recent papers have included both the leading corrections, of OðM 2 =M 2 W Þ, as well as the subleading contributions, of Oðm 2 =M 2 W Þ, to the and leptonic decay rates [2][3][4].In the present paper, we evaluate the corrections to the and leptonic decay rates induced by the W-boson propagator in two cases: (i) in the limit m ¼ 0, we derive a closed expression, valid to all orders in M 2 =M 2 W , as well as a useful expansion in powers of M 2 =M 2 W ; (ii) in the corrections of Oðm 2 j =M 2 W Þ (m j ¼ M, m), we evaluate the leading contributions, of OðM 2 =M 2 W Þ, as well as the subleading ones, of Oðm 2 =M 2 W Þ. In the calculation of the latter, it is important to include the contribution of the Àq q =M 2 W term in the unitary-gauge W-boson propagator or, equivalently, in other gauges, that of the associated Goldstone boson.…”

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confidence: 79%

“…(18) and (20), one finds that the relation between G 2 F and G 2 is given by We would like to thank M. Passera for calling our attention to Ref. [2] and for useful discussions. The work of A. F. and Z.…”

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Contributions of theW-boson propagator to theμandτleptonic decay rates

et al. 2013

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We derive closed expressions and useful expansions for the contributions of the tree-level W-boson propagator to the muon and leptonic decay rates. Calling M and m the masses of the initial and final charged leptons, our results in the limit m ¼ 0 are valid to all orders in M 2 =M 2 W . In the terms of Oðm 2 j =M 2 W Þ (m j ¼ M, m), our leading corrections, of OðM 2 =M 2 W Þ, agree with the canonical value ð3=5ÞM 2 =M 2 W , while the coefficient of our subleading contributions, of Oðm 2 =M 2 W Þ, differs from that reported in the recent literature. A possible explanation of the discrepancy is presented. The numerical effect of the Oðm 2 j =M 2 W Þ corrections is briefly discussed. A general expression, valid for arbitrary values of M W , M, and m in the range M W > M > m, is given in the Appendix. The paper also contains a review of the traditional definition and evaluation of the Fermi constant.The correction of Oðm 2 =M 2 W Þ to the muon decay rate, arising from the tree-level W-boson propagator, is well known in the literature and amounts to a correction factor 1 þ ð3=5Þm 2 =M 2 W . An analogous result was first derived by Lee and Yang in the framework of nonlocal extensions of the Fermi theory [1]. Calling M and m the masses of the initial and final leptons, recent papers have included both the leading corrections, of OðM 2 =M 2 W Þ, as well as the subleading contributions, of Oðm 2 =M 2 W Þ, to the and leptonic decay rates [2][3][4].In the present paper, we evaluate the corrections to the and leptonic decay rates induced by the W-boson propagator in two cases: (i) in the limit m ¼ 0, we derive a closed expression, valid to all orders in M 2 =M 2 W , as well as a useful expansion in powers of M 2 =M 2 W ; (ii) in the corrections of Oðm 2 j =M 2 W Þ (m j ¼ M, m), we evaluate the leading contributions, of OðM 2 =M 2 W Þ, as well as the subleading ones, of Oðm 2 =M 2 W Þ. In the calculation of the latter, it is important to include the contribution of the Àq q =M 2 W term in the unitary-gauge W-boson propagator or, equivalently, in other gauges, that of the associated Goldstone boson. In fact, this term leads to contributions of Oðm 2 =M 2 W Þ. Our result for (ii) is compared with those reported in the recent literature. In the Appendix we present expressions valid for arbitrary values of M W , M, and m in the range M W > M > m.We focus our attention on decay and later on we extend the results to the leptonic decay rates in a straightforward manner. Defining(1) the terms of Oðx n Þ (n ! 1) are very small. For this reason they are evaluated at the tree level, i.e. to zeroth order in .On the other hand, the QED correction to muon decay in the V-A Fermi theory is very important in the term of zeroth order in x. In order to obtain simple expressions, we follow the usual procedure of factorizing out the QED correction ½1 þ in all the terms of order x n (n ! 0) (see, for example, Ref.[5]). This factorization induces terms of Oðx n Þ (n ! 1), which are however extremely small. As a consistency check, we have carried ou...

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Contributions of theW-boson propagator to theμandτleptonic decay rates

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“…[52][53][54]) and ε being the direct CP violation parameter; the third order and higher orders in ε and ε 00 , ε +− are already neglected. We choose -analogously to previous section -the quasi spin states…”

Section: Wigner-type Inequalitiesmentioning

confidence: 99%

Bell inequalities for entangled kaons and their unitary time evolution

Bertlmann

Hiesmayr

2001

Phys. Rev. A

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We investigate Bell inequalities for neutral kaon systems from Φ resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, that means we also include all decay product states, in contrast to other authors. Only this guarantees the use of the complete Hilbert space. We develop a general formalism for Bell inequalities including both arbitrary "quasi spin" states and different times; finally we analyze Wigner-type inequalities. They contain an additional term, a correction function h, as compared to the spin 1/2 or photon case, which changes considerably the possibility of quantum mechanics to violate the Bell inequality. Examples for special "quasi spin" states are given, especially those which are sensitive to the CP parameters ε and ε .

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“…This non-leading correction can be obtained from the one-loop QCD correction to the well known e + e − → quark-pair cross-section, or the τ → ν τ + quark-pair decay rate found in the literature [12]; the only necessary change is the substitution α s ↔ 3α/4. Thus, in addition to Γ 1 , we have the non-leading contribution…”

Section: The Decay ν Hmentioning

confidence: 99%

The decays $\nu _H \rightarrow \nu_L \gamma$ and $\nu_H \rightarrow \nu_L e^+ e^-$ of massive neutrinos

Ho‐Kim

Machet²,

Pham³

2000

Eur. Phys. J. C

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Abstract:If, as recently reported by the Super-Kamiokande collaboration, the neutrinos are massive, the heaviest one ν H would not be stable and, though chargeless, could in particular decay into a lighter neutrino ν L and a photon by quantum loop effects. The corresponding rate is computed in the standard model with massive Dirac neutrinos as a function of the neutrino masses and mixing angles. The lifetime of the decaying neutrino is estimated to be ≈ 10 44 years for a mass ≈ 5 × 10 −2 eV.If kinematically possible, the ν H → ν L e + e − mode occurs at tree level and its one-loop radiative corrections get enhanced by a large logarithm of the electron mass acting as an infrared cutoff. Thus the ν H → ν L e + e − decay largely dominates the ν H → ν L γ one by several orders of magnitude, corresponding to a lifetime ≈ 10 −2 year for a mass ≈ 1.1 MeV. PACS

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Elementary Particles and Their Interactions

Abstract: Ho-Kim, Q. (Quang), 1938-Elementary particles and their interactions: concepts and phenomena / Quang Ho-Kim, Xuan-Yem Pham. p. cm. Includes bibliographical references and index. ISBN 3-540-63667-6 (alk. paper) 1. Particles (Nuclear physics) 2.. Nuclear reactions. I.

Cited by 60 publications

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Contributions of theW-boson propagator to theμandτleptonic decay rates

Contributions of theW-boson propagator to theμandτleptonic decay rates

Bell inequalities for entangled kaons and their unitary time evolution

The decays $\nu _H \rightarrow \nu_L \gamma$ and $\nu_H \rightarrow \nu_L e^+ e^-$ of massive neutrinos

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