Running Fermion Masses - Institut für Physik

Theoretical Predictions of Fermion MassesFermion Masses Extracted from Experimental DataFermion masses from the PDG 2006HQET, LQCD, SRRunning Massesm(μ)χPT, Lattice QCD, Sum RulesDirect measurements′t Hooft scaleManohar & Sachrajda, 2008Review on Quark Masses, PDGPole Masses

Remarks:1. Unlike the leptons, quarks are confined in hadrons. Therefore,quark masses cannot be measured directly. They are indirectlydetermined from their influence on the properties of hadrons.2. When talking about quark masses, one should keep in mind thatthey are defined in a specific theoretical framework, and thusscheme-dependent. For example, the constituent quark massesin the quark models.

Leutwyler, arXiv: 0911.1416

Leutwyler, arXiv: 0911.1416

Running Fermion Masses: below the EW scaleGoal: running quark and lepton masses m(μ) at the EW scale μ=MzFormula: (1) RGEs for the strong coupling constant and quark masses‘t Hoof, 1972Number of active quarksGross & Wilczek, 1973; Politzer, 1973van Ritbergen, Vermaseren & Larin, 1997Chetyrkin, 1997;van Ritbergen, Vermaseren & Larin, 1997

Formula: (1) RGEs for the strong coupling constant and quark massesSolution of quark massesChetyrkin, 1997; Chetyrkin & Steinhauser, 1999;Melnikov & van Ritbergen, 2000Formula: (2) Matching conditions for the strong coupling and massesMz=91.2 GeVμ=mb(mb) = 4.2 GeVμ=2 GeVnq = 5 nq = 4Flavor thresholdμ=mc(mc) = 1.25 GeV

Formula: (2) Matching conditions for the strong coupling and massesChetyrkin, Kniehl & Steinhauser, 1998;Chetyrkin, Kuehn & Steinhauser, 2000

Formula: (3) Relation between running mq(μ) and pole masses MqChetyrkin & Steinhauser, 1999;Melnikov & van Ritbergen, 2000K (2)c = 11.21 K (2)b = 10.17 K (2)t = 9.13K (3)c = 123.8K (3)b = 101.5K (3)t = 80.4Formula: (4) RGEs for α and running masses of charged leptonsm (μ)lArason et al., 1992

Strategy: (1) Input values from the PDG 2006; (2) Runningmatching-runningscheme for the evaluation of quark massesμ(5)=mb(mb) = 4.20 GeVMz=91.186 GeVμ(4)=mc(mc) = 1.25 GeVnq = 4μ(5)=mb(mb) = 4.20 GeVMz=91.186 GeVnq = 5nq = 6

Running Fermion Masses: above the EW scaleGoal: running fermion masses m(μ) at the TeV scale, the seesaw scaleand the GUT scale, both in the SM and in the MSSM(1) We adopt the seesaw model for neutrino masses, so neutrinos areassumed to be Majorana particles;(2) Above the EW scale, we define fermion masses as mf = yf v, where yfare the eigenvalues of Yukawa couplings and v is the vev;(3) We use two-loop RGEs for Yu, Yd, Yl, but one-loop RGE for effectiveneutrino coupling matrix κ.mq(Mz)Yu & YdMachack & Vaughn, 1984; Antusch et al.,2002, 2005; Mei & Xing, 2004; Mei, 2005GaugecouplingsYl & κθ12 = 33.8 degθ23 = 45.0 degθ13 ~ 0δ=ρ=σ = 0(A) m1 = 0.001 eV, m1 < m2 < m3(B) m1 = 0.2 eV, m1< m2 < m3

Xing, Zhang & Zhou, Phys. Rev. D 77, 113016 (2008)Mathematica code RunDec, by Chetyrkin, Kuehn & Steinhauser, 2000

Xing, Zhang & Zhou, Phys. Rev. D 77, 113016 (2008)In the SM with MH = 140 GeV

Xing, Zhang & Zhou, Phys. Rev. D 77, 113016 (2008)In the SM with MH = 140 GeV

MSSM with tan β = 10MSSM with tan β = 50

Summary1. The origin of fermion masses, the fermion mass hierarchyand flavor mixing patterns are still big puzzles in particlephysics. New physics beyond the SM is expected so much.2. The models for fermion masses are usually constructed atthe high-energy scales, e.g. the TeV and GUT scales. Thepredictions should be confronted with experimental data.3. Starting with the latest values given by PDG, we haveevaluated the running quark and lepton masses at theEW, TeV, Seesaw, GUT scales, in the SM and MSSM.