The Standard Model Prediction for Muon g-2
The present Standard Model prediction for muon g-2 is reviewed. Emphasis is put in discussing the main hadronic uncertainties at present.
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arXiv subjects
Joaquim Prades
Publications and source records attributed to Joaquim Prades.
Comment on the Pion Pole Part of the Light-by-Light Contribution to the Muon $g-2$
We comment on the recent calculations of the pion pole part of the light-by-light contribution to the muon anomalous magnetic moment and we point out where the analysis in our previous work was mistaken.
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Matching the Electroweak Penguins $Q_7$, $Q_8$ and Spectral Correlators
Exact analytical expressions for the $ΔS=1$ coupling $\im G_E$ in terms of observable spectral functions are given. This coupling determines the size of the $ΔI=3/2$ contribution to $ε'$. We show analytically how the scheme-dependence and scale dependences vanish to all orders in $1/N_c$ and NLO in $α_S$ explicitly both for $Q_7$ and $Q_8$. Numerical results are derived for both $Q_7$ and $Q_8$ from the $τ$-data and known results on the scalar spectral functions. In particular we study the effect of all higher dimension operators. The coefficients of the leading operators in the OPE of the needed correlators are derived to NLO in $α_S$.
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Chiral Limit Prediction for epsilon'/epsilon at NLO in 1/N_c
We report on a calculation of $ε_K'/ε_K$ at next-to-leading in the $1/N_c$ expansion and to lowest order in Chiral Perturbation Theory. We discuss the short-distance matching, the scale and scheme dependence as well as the long-distance short-distance matching. We include the two known chiral corrections to our result and discuss further order $p^4$ corrections to it.
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epsilon'/epsilon at next-to-leading in 1/N_c and to lowest order CHPT
We report on a calculation of epsilon'/epsilon at next-to-leading in the 1/N_c expansion and to lowest order in Chiral Perturbation Theory. We also discuss the chiral corrections to our results and give the result of including the two known chiral corrections.
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Epsilon'/Epsilon in the Chiral Limit using Large N_c
The K to pi pi system is analyzed in the chiral limit and at NLO in 1/N_c. The Delta I = 1/2 rule is reproduced and we obtain a large value for epsilon' / epsilon.
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epsilon'/epsilon in the Chiral Limit
The $K\toππ$ system is analyzed in the chiral limit within the Standard Model. We discuss how to connect the short-distance running in the $|ΔS|=1$ case to the matrix-elements calculated in a low-energy approximation in a scheme-independent fashion. We calculate this correction and the resulting Wilson Coefficients. The matrix elements are calculated to next-to-leading order in the $1/N_c$ expansion and combined with the Wilson coefficients to calculate the two isospin amplitudes and $ε_K^\prime$. The $ΔI=1/2$ rule is reproduced within expected errors and we obtain a substantially larger value for $ε_K^\prime/ε_K$ than most other analysises. We discuss the reasons for this difference. We also suggest that the $X$-boson method is an option for lattice QCD calculations.
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Scheme Dependence of Weak Matrix Elements in the $1/N_c$ Expansion
We show how the scheme- and scale-dependence of the short-distance operator product expansion with four-quark operators can be correctly accounted for in the framework of the $1/N_c$-expansion once the hadronization of two-quark currents has been fixed. We show formulas explicitly in the case of the $B_K$-parameter. We then use them with our earlier estimates of the long-distance effects. We compare Chiral Perturbation Theory at Leading- and Next-to-Leading-Order with the ENJL model results in the chiral limit. Good matching between the long- and short-distance regimes is obtained and our final value for the physical scheme independent $\hat B_K$ is $0.77\pm0.05\pm0.05$.
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The $ΔI=1/2$ Rule for Kaons
We report on recent advances at understanding the $ΔI= 1/2$ rule for kaons. We get reasonable matching between short-- and long--distances for scales between between 0.6 and 1.0 GeV and reproduce the $ΔI=1/2$ rule huge enhancement in the chiral limit. A detailed analysis of the different contributions to the relevant octet and 27-plet couplings is done. For the $B_6^{(1/2)}(μ) \equiv < (ππ)_0 | Q_6 | K > / [< (ππ)_0 | Q_6 | K > {\Large|}_{N_c}]$ parameter, we get in the chiral limit $B_6^{(1/2)}(μ) = 2.2 \pm 0.5$ for scales $μ\in [0.6, 1.0]$ GeV.
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Strange Quark Mass Determination from Cabibbo-Suppressed Tau Decays
We present a general analysis of SU(3) breaking effects in the semi-inclusive tau hadronic width. The recent ALEPH measurements of the inclusive Cabibbo--suppressed decay width of the tau and several moments of its invariant mass distribution are used to determine the value of the strange quark mass. We obtain, in the MS scheme, m_s(M_τ^2) = (119\pm 24) MeV to O(α_s^3), which corresponds to m_s (1 GeV^2) = (164 \pm 33) MeV, m_s(4 GeV^2) = (114\pm 23) MeV .
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The $ΔI=1/2$ Rule in the Chiral Limit
We discuss the matching between long-distance and short-distance at next-to-leading in $1/N_c$ and show how the scheme-dependence from the two-loop renormalization group running can be treated. We then use this method to study the three $O(p^2)$ terms contributing to non-leptonic kaon decays, namely the usual octet and 27-plet derivative terms as well as the weak mass term using the Extended Nambu--Jona-Lasinio model as the low energy approximation. We also discuss subtleties in the momentum routing in the low energy theory and a problem in separating factorizable and non-factorizable contributions from the $Q_6$ operator in the chiral limit. We update our earlier results on the $B_K$ parameter as well.
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Strange Quark Mass Dependence of the Tau Hadronic Width
The perturbative quark mass corrections to the tau hadronic width are studied to O(alpha_s^3 m_q^2). Including up to dimension four corrections, we get m_s(4 GeV^2)=(143 \pm 42) MeV [m_s(1 GeV^2)=(193 \pm 59) MeV ]. Possible improvements to reduce the theoretical uncertainty are pointed out.
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Perturbative Quark Mass Corrections to the Tau Hadronic Width
The perturbative quark-mass corrections to the $τ$ hadronic width are analysed to $O(α_s^3 m_q^2)$, using the presently available theoretical information. The behaviour of the perturbative series is investigated in order to assess the associated uncertainties. The implications for the determination of the strange quark mass from $τ$ decay data are discussed.
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Obtaining K to pi pi from Off-Shell K to pi Amplitudes
We properly define off-shell $K\toπ$ transition amplitudes and use them to extract information for on-shell $K\toππ$ amplitudes within Chiral Perturbation Theory. At order $p^2$ in the chiral expansion all three parameters of weak interaction can be determined. At order $p^4$ we are able to fix eleven additional constants out of thirteen contributing to off-shell $K\toπ$ transitions, which leaves four undetermined constants in the on-shell $K\toππ$ amplitudes. All ${\cal O}(p^4)$ contributions have been exactly derived with $m_π^2\ne 0$. We finally discuss the weak mass term issue and find contributions to on-shell $ΔS=\pm 1$ Kaon decays, in particular to transitions like $K_L \to γγ$, $K_L \to μ^+ μ^-$ and $K_S \to π^0 γγ$ at the lowest non-zero order.
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m_u + m_d from QCD-Hadron Duality
The value of the light quark masses combination $m_u + m_d$ is analized using QCD-Hadron Duality. A detailed analysis of both the perturbative QCD [to four-loops] and the hadronic parametrization needed is done. The result we get is $[m_u + m_d] (1 GeV^2) = (12.8 \pm 2.5)$ MeV ($[m_u + m_d] (4 GeV^2) = (9.8 \pm 1.9)$ MeV) in the $\barMS$ scheme.
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Kaon Polarizabilities in Chiral Perturbation Theory
We study the kaon polarizabilities in the framework of Chiral Perturbation Theory to order $p^4$. For the neutral kaon we find that them vanish and they have the first non-zero contribution to order $p^6$. We also emphasize the theoretical potential of an eventual measuremnet of the kaon polarizabilities, in particular of the neutral kaon ones.
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Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities
The unknown constants in Chiral Perturbation Theory needed for an all orders analysis of the polarizabilities and electromagnetic corrections to the masses of the pseudo-Goldstone bosons are estimated at leading order in $1/N_c$. We organize the calculation in an $1/N_c$-expansion and separate long- and short-distance physics contributions by introducing an Euclidean cut-off. The long-distance part is evaluated using the ENJL model and the short-distance part using perturbative QCD and factorization. We obtain very good matching between both. We then include these estimates in a full Chiral Perturbation Theory calculation to order $e^2$ $p^2$ for the masses and $p^6$ for the polarizabilities. For the electromagnetic corrections to the masses, we confirm a large violation of Dashen's theorem getting a more precise value for this violation. We make comparison with earlier related work. Some phenomenological consequences are discussed too.
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Analysis of the Hadronic Light-by-Light Contributions to the Muon $g-2$
We calculate the hadronic light-by-light contributions to the muon $g-2$. We use both $1/N_c$ and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the $1/N_c$ expansion low energy contributions using the Extended Nambu--Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon $g-2$ are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon $g-2$ is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is $a_μ^{\rm light-by-light}= (-9.2\pm3.2 ) \cdot 10^{-10}$. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon $g-2$ experiment.
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