Renormalization group equations for the CKM matrix

Kielanowski, P.

doi:10.1103/physrevd.78.116010

Cited by 11 publications

(8 citation statements)

References 14 publications

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“…Note that the first term on the right-hand side of Eq. (11) is rephasing-dependent, and it can be arranged to vanish in a special phase convention without altering any physical results [24], as one has noticed in deriving the RGEs of quark flavor mixing parameters [25]. We shall confirm that the terms associated with αV αi V * αi can always be cancelled out in our subsequent calculations.…”

Section: Renormalization-group Equationssupporting

confidence: 62%

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

Zhang

Zhou

2018

J. High Energ. Phys.

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Abstract:We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter a ≡ 2 √ 2 G F N e E to be an arbitrary scale-like variable with N e being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses m i (for i = 1, 2, 3). Given the standard parametrization of V , the RGEs for { θ 12 , θ 13 , θ 23 , δ} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial µ-τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.

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Section: Renormalization-group Equationssupporting

confidence: 62%

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

Zhang

Zhou

2018

J. High Energ. Phys.

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“…holds (for α = u, c, t and i = d, s, b) as a direct consequence of the differentiation of 287,512,513]. Therefore, a sum of the expression…”

Section: Differential Equations Of Umentioning

confidence: 96%

Flavor structures of charged fermions and massive neutrinos

Xing

2019

Preprint

116

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Most of the free parameters in the Standard Model (SM) -a quantum field theory which has successfully elucidated the behaviors of strong, weak and electromagnetic interactions of all the known fundamental particles, come from the lepton and quark flavors. The discovery of neutrino oscillations has proved that the SM is incomplete, at least in its lepton sector; and thus the door of opportunity is opened to exploring new physics beyond the SM and solving a number of flavor puzzles. In this review article we give an overview of important progress made in understanding the mass spectra, flavor mixing patterns, CP-violating effects and underlying flavor structures of charged leptons, neutrinos and quarks in the past twenty years. After introducing the standard pictures of fermion mass generation, flavor mixing and CP violation in the SM extended with the presence of massive Dirac or Majorana neutrinos, we briefly summarize current experimental knowledge about the flavor parameters of quarks and leptons. Various ways of describing flavor mixing and CP violation are discussed, the renormalization-group evolution of flavor parameters is illuminated, and the matter effects on neutrino oscillations are interpreted. Taking account of possible extra neutrino species, we propose a standard parametrization of the 6 × 6 flavor mixing matrix and comment on the phenomenological aspects of heavy, keV-scale and light sterile neutrinos. We pay particular attention to those novel and essentially model-independent ideas or approaches regarding how to determine the Yukawa textures of Dirac fermions and the effective mass matrix of Majorana neutrinos, including simple discrete and continuous flavor symmetries. An outlook to the future development in unravelling the mysteries of flavor structures is also given.

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“…The scale dependence of Eqs. (A.9) and (A.10) can be used to derive unambiguously the flow of the absolute values of the CKM matrix elements [137][138][139][140]. We use the unitarity of the rotation matrices and the fact that V = U † L D L to write…”

Section: T)mentioning

confidence: 99%

Flavor anomalies from asymptotically safe gravity

2021

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We use the framework of asymptotically safe quantum gravity to derive predictions for scalar leptoquark solutions to the $$b\rightarrow s$$ b → s and $$b\rightarrow c$$ b → c flavor anomalies. The presence of an interactive UV fixed point in the system of gauge and Yukawa couplings imposes a set of boundary conditions at the Planck scale, which allows one to determine low-energy values of the leptoquark Yukawa matrix elements. As a consequence, the allowed leptoquark mass range can be significantly narrowed down. We find that a consistent gravity-driven solution to the $$b\rightarrow s$$ b → s anomalies predicts a leptoquark with the mass of 4–7 $$\,\mathrm {TeV}$$ TeV , entirely within the reach of a future hadron-hadron collider with $$\sqrt{s}=100\,\mathrm {TeV}$$ s = 100 TeV . Conversely, in the case of the $$b\rightarrow c$$ b → c anomalies the asymptotically safe gravity framework predicts a leptoquark mass at the edge of the current LHC bounds. Complementary signatures appear in flavor observables, namely the (semi)leptonic decays of B and D mesons and kaons.

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Renormalization group equations for the CKM matrix

Cited by 11 publications

References 14 publications

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

Renormalization-group equations of neutrino masses and flavor mixing parameters in matter

Flavor structures of charged fermions and massive neutrinos

Flavor anomalies from asymptotically safe gravity

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