ChPT Predictions Research Articles

Lattice QCD calculation of K→ℓνℓℓ′+ℓ′− decay width

We develop a methodology for the computation of the $K\to \ell\nu_\ell \ell'^+ \ell'^-$ decay width using lattice QCD and present an exploratory study here. We use a scalar function method to account for the momentum dependence of the decay amplitude and adopt the infinite volume reconstruction method to reduce the systematic errors such as the temporal truncation effects and the finite-volume effects. We then perform a four-body phase-space integral to obtain the decay width. The only remaining technical problem is the possible power-law finite-volume effects associated with the process of $K\to\pi\pi \ell\nu_\ell\to \ell\nu_\ell \ell'^+ \ell'^-$, where the intermediate state involves multiple hadrons. In this work, we use a gauge ensemble of twisted mass fermion with a pion mass $m_\pi=352$ MeV and a nearly-physical kaon mass. At this kinematics, the $\pi\pi$ in the intermediate state cannot be on shell simultaneously as $2m_\pi>m_K$ and the finite-volume effects associated with $\pi\pi$ state are exponentially suppressed. Using the developed methods mentioned above, we calculate the branching ratios for four channels of $K\to \ell\nu_\ell\ell'^+ \ell'^-$, and obtain the results comparable to the experimental measurements and ChPT predictions. Our work demonstrates the capability of lattice QCD to improve Standard Model prediction in $K\to \ell\nu_\ell \ell'^+ \ell'^-$ decay width.

Lattice study of thermodynamic properties of dense QC2D

In this paper we study thermodynamic properties of dense cold $SU(2)$ QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond to ${N}_{f}=2$ quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the region $\ensuremath{\mu}\ensuremath{\in}(0,2000)\text{ }\text{ }\mathrm{MeV}$. It is found that in the region $\ensuremath{\mu}\ensuremath{\in}(0,540)\text{ }\text{ }\mathrm{MeV}$ the system is well described by the ChPT predictions. In the region $\ensuremath{\mu}>540\text{ }\text{ }\mathrm{MeV}$ the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical potentials $\ensuremath{\mu}>900\text{ }\text{ }\mathrm{MeV}$ we observe formation of the Fermi sphere, and the system is similar to the one described by the Bardeen-Cooper-Schrieffer theory where the diquarks play a role of Cooper pairs. In order to study how nonzero baryon density influences the gluon background we calculate chromoelectric and chromomagnetic fields, as well as the topological susceptibility. We find that the chromoelectric field and the topological susceptibility decrease, whereas the chromomagnetic field increases with rising of baryon chemical potential. Finally we study the equation of state of dense two-color quark matter.

Recent NA48/2 results on rare kaon decays

NA48/2 results contributing to ChPT testing are presented. A sample of 1663 events of the rare decay $ K^ \pm \to \mu ^ \pm ve^ + e^ - $ has been selected with a minimume+e−effective mass of 140 MeV. The measured model independent decay rate is in agreement with ChPT predictions. The branching ratio of the $ K^ \pm \to \mu ^ \pm ve^ + e^ - $ decay, never observed so far, has been obtained from a sample of about 5000 candidates with less than 6% background, also in agreement with ChPT predictions. In addition, a most precise measurement of the charged kaon semileptonic formfactors has been obtained from 4.4 millionKe3and 2.3 millionKµ3events collected in 2004.

Lattice simulation of two-color QCD with Nf = 2 at non-zero baryon density

We present the results of lattice simulations of two-color QCD with two fermion flavors and non-zero chemical potential. Dependencies of the chiral condensate and baryon number density on the quark chemical potential were studied. We found that an increase of the quark chemical potential leads to chiral symmetry restoration. At small values of chemical potential, our results for the baryon density agree with ChPT predictions.

Formula omitted] measurements with NA48/NA62

The NA48/2 collaboration has analysed more than one million K±→π+π−e±ν decays, resulting in the improved determination of branching fraction by a factor of 3 and high precision form factor measurements. Concurrently, about 45000 K±→π0π0e±ν decays have been analyzed. Background contamination below the percent level and very good π0 reconstruction allow the first accurate measurement of the branching fraction and decay form factor at the percent level. The achieved precision makes possible the observation of small effects such as π+π−→π0π0 re-scattering. Both Ke4 modes decay properties bring new precise inputs to Low Energy QCD studies and can provide strong tests of ChPT predictions. Future prospects include the observation of several thousand decays in similar muonic modes K±→π0π0μ±ν and K±→π+π−μ±ν, that could be studied also in the forthcoming NA62 experiment.

Chiral Perturbation Theory from Charged Kaon Decays at NA48/2

Chiral Perturbation Theory, as a low-energy effective field theory of strong interactions, is a very useful tool to study the interactions of kaons. The NA48/2 experiment, whose primary goal was the measurement of direct CP violation in the decays of charged kaons, has however collected enough statistics to check the ChPT predictions for several decay modes of charged kaons.

Precision tests with Kl3 and Kl2 decays

In 2000, the analysis indicated that the unitarity relation, |Vud|2 + |Vus|2 + |Vub|2 = 1, might be broken at the 2.3σ level. At that time, however, the |Vus| was inferred from the old experimental data. Since then, a great experimental and theoretical effort has been invested to understand the source of that deviation. Thanks to the new and improved measurements by BNL-E865, KLOE, KTeV, ISTRA+ and NA48 the old Kl3 decay rate got shifted so that the new |Vus| is now consistent with unitarity. On the theory side, much progress in the lattice QCD community has been made in order to tame the systematic uncertainties related to the computation of the Kl3 form factors.This joint progress allowed to assess the validity of the CKM unitarity relation at the level less than 1%. Undergoing lattice studies will corroborate and improve this scenario. The key challenge will be to simulate lighter pions in the region in which ChPT predictions apply. Also interesting is the recent progress in accurately computing the kaon and pion decay constants on the lattice, which then give us access to |Vus| and |Vud| from the corresponding leptonic decays.In addition, we argue that the Kl3 and Kl2 decays offer the possibility to test various scenarios of physics beyond Standard Model.