For any inelastic process $v_{\ell} + I \to \ell^- + F$ with $m_{\ell} = 0$, the cross section at $θ_{\ell} = 0$ is given by Adler's PCAC theorem. Inclusion of the lepton mass has a dynamical effect (``PCAC-screening'') caused by interference of spin-zero ($π^+$) and spin-one exchanges. This effect may be relevant to the forward suppression reported in recent experiments.
Restrictions on the Hadronic Contribution to the Muon $(g-2)$-factor and to the Pion Electromagnetic Formfactor from Analytical Properties of the Pion Electromagnetic Formfactor
This thesis investigates the Hadronic Light by Light (HLL) scattering contribution to the muon $g-2$, which is one of the most important low energy hadronic effects and consists mainly of the quark loop, the pion pole and the charged pion and kaon loops. In this work the charged pion loop has been investigated more closely. After reviewing the subject a preliminary introduction to Chiral Perturbation Theory (ChPT), Hidden Local Symmetry (HLS) model and the full Vector Meson Dominance (VMD) model is given, and they are used to calculate the pion loop HLL scattering contribution to the muon anom…
The largest error in the theoretical determination of the muon anomalous magnetic moment is due to the low-energy hadronic vacuum polarization, which cannot be calculated by perturbative QCD and requires nonperturbative techniques. Recently, an accurate determination of the low-energy two-pion contribution to muon $g-2$ has been obtained by a parametrization-free analytic continuation of the pion vector form factor from other kinematical regions. In this work we compare the results of the analytic continuation with direct determinations at low momenta from experiment and lattice QCD. We also e…
This paper contains some new results on the hadronic light-by-light contribution (HLbL) to the muon $g-2$. The first part argues that we can expect large effects from disconnected diagrams in present and future calculations by lattice QCD of HLbL. The argument is based on the dominance of pseudo-scalar meson exchange. In the second part, we revisit the pion loop HLbL contribution to the muon anomalous magnetic moment. We study it in the framework of some models studied earlier, pure pion loop, full VMD and hidden local symmetry for inclusion of vector mesons. In addition we study possible ways…
Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g-2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g-2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which …
We summarize our recent new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in a_μwhich relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a_μ(LbyL;π^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for t…
We describe a possibility to explain the $2.6σ$ deviation from lepton flavour universality observed by the LHCb collaboration in $B^+\to K^+\ell^+\ell^-$ decays in the context of minimal composite Higgs models. We find that a sizable degree of compositeness of partially composite muons can lead to a good agreement with the experimental data. Our construction predicts a new physics contribution to $B_s$-$\bar{B}_s$ mixing. Additionally, it accounts for the deficit in the invisible $Z$ width measured at LEP.
In the present work, we investigate several theoretical models of the pion vector form factor and aim at getting the best fit for the two-pion cross sections to reduce the uncertainties of the calculation of two-pion contribution to the muon anomalous magnetic moment. Combined with a polynomial description to the pion vector form factor, we obtain the best fit from the Gounaris-Sakurai (or Kühn-Santamaria) model for the experimental data up to 1 GeV. By product, the branching ratio of $ω\to ππ$ can be extracted as $\text{Br}(ω\toππ)=(1.52\pm 0.06) \%$, which is consistent with the one of Parti…
We discuss, how planned measurements at KLOE-2 of the (pi^0 -> gamma gamma) decay width and the (gamma^* gamma -> pi^0) transition form factor can improve estimates for the numerically dominant pion-exchange contribution to hadronic light-by-light scattering in the muon g-2 and what are the limitations related to the modelling of the off-shellness of the pion.
We review the recent measurements of the rare pion decays: Pi+ -> Pi0 e+ Nu [pion beta, Pi_(e3), or Pi_beta decay], radiative decay Pi+ -> e+ Nu Gamma [Pi_(e2Gamma) or RPD], and Pi+ -> e+ Nu [Pi_(e2)] decay, as well as the radiative muon decay, Mu -> e Nu Nu-bar Gamma, their theoretical implications, and prospects for further improvement.
In the internal shock model of gamma ray bursts ultrahigh energy muons, pions, neutrons and kaons are likely to be produced in the interactions of shock accelerated relativistic protons with low energy photons (KeV-MeV). These particles subsequently decay to high energy neutrinos/antineutrinos and other secondaries. In the high internal magnetic fields of gamma ray bursts, the ultrahigh energy charged particles ($μ^+$, $π^+$, $K^+$) lose energy significantly due to synchrotron radiations before decaying into secondary high energy neutrinos and antineutrinos. The relativistic neutrons decay to …
We compute the charged pion loop contribution to the muon anomalous magnetic moment $a_μ$, taking into account the effect of the charged pion polarizability, $(α_1-β_1)_{π^+}$. We evaluate this contribution using two different models that are consistent with the requirements of chiral symmetry in the low-momentum regime and perturbative quantum chromodynamics in the asymptotic region. The result increases the disagreement between the present experimental value for $a_μ$ and the theoretical, Standard Model prediction by as much as $\sim 60\times 10^{-11}$, depending on the value of $(α_1-β_1)_{…
Based on the simple phenomenological $σππ$, $σN N$ and $ππγ$ interactions, we estimate the $σ$ exchange effect in the Lamb shift of muonic hydrogen. We at first calculate the effective couplings of $σμμ$ by two photons and two pions exchange, then calculate the corresponding corrections to the energy shift of the 2S/2P states of muonic hydrogen. We find the correction to the energy shift of 2S state is about -14$μ$eV by the current used parameters, which is about $44\%$ of the usual two photons exchange contribution, and is larger than the current experimental precision, and should be consider…
We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the $48^3 \times 96$ ensemble generated with a physical-pion-mass and a 5.5 fm spatial extent by the RBC and UKQCD collaborations using the chiral, domain wall fermion (DWF) formulation. We find $a_μ^{\text{HLbL}} = 5.35 (1.35) \times 10^{- 10}$, where th…
We extend our previous calculations of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment in holographic QCD to models with finite quark masses and a tower of massive pions. Analysing the role of the latter in the Wess-Zumino-Witten action, we show that the Melnikov-Vainshtein short-distance constraint is satisfied solely by the summation of contributions from the infinite tower of axial vector meson contributions. There is also an enhancement of the asymptotic behavior of pseudoscalar contributions when their infinite tower of excitations is summed, but …
We have computed the hadronic light-by-light (LbL) contribution to the muon anomalous magnetic moment $a_μ$ in the frame of Chiral Perturbation Theory with the inclusion of the lightest resonance multiplets as dynamical fields (R$χ$T). It is essential to give a more accurate prediction of this hadronic contribution due to the future projects of J-Parc and FNAL on reducing the uncertainty in this observable. We, therefore, computed the pseudoscalar transition form factor and proposed the measurement of the $e^+e^-\toμ^+μ^-π^0$ cross section and dimuon invariant mass spectrum to determine more a…
A lattice computation of the leading-order hadronic contribution to the muon anomalous magnetic moment can potentially help reduce the error on the Standard Model prediction for this quantity, if sufficient control of all systematic errors affecting such a computation can be achieved. One of these systematic errors is that associated with the extrapolation to the physical pion mass from values on the lattice larger than the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 200 to 400MeV with the help of two-loop chiral perturbation theory, and f…
We examine the Cerenkov-like emission of $e^+ e^-$ from muon super-luminal muon neutrinos assuming a quadratic energy dependence of the neutrino velocity arising from Lorentz violating interactions. We find that with the OPERA result for the neutrino-photon velocity difference, the decay length for the process $ν_μ\rightarrow ν_μe^+ e^-$ is 17,039 km which is much larger than the OPERA neutrinos path length of 730 km. We also calculate the pion rate for super-luminal outgoing neutrinos, and we find that the deviation of the pion decay length from the standard Lorentz conserving case at the OPE…
There exists a longstanding disagreement between bubble chamber measurements of the single pion production channel $ν_μp\rightarrow μ^{-}pπ^{+}$ from the Argonne and Brookhaven National Laboratories. We digitize and reanalyse data from both experiments to produce cross-section ratios for various interaction channels, for which the flux uncertainties cancel, and find good agreement between the experiments. By multiplying the cross-section ratio by the well-understood charged current quasi-elastic cross-section on free nucleons, we extract single-pion production cross-sections which do not depen…
Simple dynamics, few available decay channels, and extremely well controlled radiative and loop corrections, make pion and muon decays a sensitive means for testing the underlying symmetries, the universality of weak fermion couplings, as well as for study of pion structure and chiral dynamics. We review the current state of experimental study of the allowed rare decays of charged pions: (a) electronic, $π^+ \to e^+ν_e$, or $π_{e2}$, (b) radiative, $π^+ \to e^+ν_eγ$, or $π_{e2γ}$, and (c) semileptonic, $π^+\to π^0 e^+ ν$, or $π_{e3}$, as well as muon radiative decay, $μ^+\to e^+ ν_{\text{e}}\b…
We present results for single pseudoscalar meson pole contributions and pion box contributions to the hadronic light-by-light (LBL) correction of the muon's anomalous magnetic moment. We follow the recently developed dispersive approach to LBL, where these contributions are evaluated with intermediate mesons on-shell. However, the space-like electromagnetic and transition form factors are not determined from analytic continuation of time-like data, but directly calculated within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. This strategy allows for a system…
Extensive Air Showers are complex macroscopic objects initiated by single ultra-high energy particles. They are the result of millions of high energy reactions in the atmosphere and can be described as the superposition of hadronic and electromagnetic cascades. The hadronic cascade is the air shower backbone, and it is mainly made of pions. Decays of neutral pions initiate electromagnetic cascades, while the decays of charged pions produce muons which leave the hadronic core and travel many kilometers almost unaffected. Muons are smoking guns of the hadronic cascade: the energy, transverse mom…
