Pion Beta Decay Research Articles

An LGAD-Based Full Active Target for the PIONEER Experiment

PIONEER is a next-generation experiment to measure the charged pion branching ratios to electrons vs. muons Re/μ=Γπ+→e+ν(γ)Γπ+→μ+ν(γ) and pion beta decay (Pib) π+→π0eν. The pion to muon decay (π→μ→e) has four orders of magnitude higher probability than the pion to electron decay (π→eν). To achieve the necessary branching-ratio precision it is crucial to suppress the π→μ→e energy spectrum that overlaps with the low energy tail of π→eν. A high granularity active target (ATAR) is being designed to suppress the muon decay background sufficiently so that this tail can be directly measured. In addition, ATAR will provide detailed 4D tracking information to separate the energy deposits of the pion decay products in both position and time. This will suppress other significant systematic uncertainties (pulse pile-up, decay in flight of slow pions) to <0.01%, allowing the overall uncertainty in to be reduced to O (0.01%). The chosen technology for the ATAR is Low Gain Avalanche Detector (LGAD). These are thin silicon detectors (down to 50 μm in thickness or less) with moderate internal signal amplification and great time resolution. To achieve a 100% active region several emerging technologies are being evaluated, such as AC-LGADs and TI-LGADs. A dynamic range from MiP (positron) to several MeV (pion/muon) of deposited charge is expected, the detection and separation of close-by hits in such a wide dynamic range will be a main challenge. Furthermore, the compactness and the requirement of low inactive material of the ATAR present challenges for the readout system, forcing the amplifier chip and digitizer to be positioned away from the active region.

The pion beta and radiative electronic decays

As the lightest meson, pion offers unique opportunities for measuring parameters and testing limits of the Standard Model (SM). The PiBeta experiment, carried out at PSI, focused on SM tests accessible through the pion beta, \pi^+ \to \pi^0e^+\nu_e(\gamma)π+→π0e+νe(γ), and electronic radiative, \pi^+ \to e^+\nu_e\gammaπ+→e+νeγ, decay channels. We review the PiBeta experiment, and update the pion beta decay branching ratio B^{\text{exp}}_{\pi\beta}=1.038(6)_{\text{tot}}\times10^{-8}Bπβexp=1.038(6)tot×10−8, along with the corresponding derived value of the Cabibbo-Kobayashi-Maskawa matrix element V_{ud} = 0.9738(28)Vud=0.9738(28).

Constraints on sterile neutrinos in the MeV to GeV mass range

A detailed discussion is given of the analysis of recent data to obtain improved upper bounds on the couplings $|{U}_{e4}{|}^{2}$ and $|{U}_{\ensuremath{\mu}4}{|}^{2}$ for a mainly sterile neutrino mass eigenstate ${\ensuremath{\nu}}_{4}$. Using the excellent agreement among the $\mathcal{F}t$ values (products of kinematic rate factors times half-lives with radiative corrections included) for superallowed nuclear beta decays, an improved upper limit is derived for emission of a ${\ensuremath{\nu}}_{4}$. The agreement of the ratios of branching ratios ${R}_{e/\ensuremath{\mu}}^{(\ensuremath{\pi})}=\mathrm{BR}({\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e})/\mathrm{BR}({\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})$, ${R}_{e/\ensuremath{\mu}}^{(K)}$, ${R}_{e/\ensuremath{\tau}}^{({D}_{s})}$, ${R}_{\ensuremath{\mu}/\ensuremath{\tau}}^{({D}_{s})}$, and ${R}_{e/\ensuremath{\tau}}^{(D)}$, and the branching ratios $\mathrm{BR}({B}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e})$ and $\mathrm{BR}({B}^{+}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}})$ decays with predictions of the Standard Model is utilized to derive new constraints on ${\ensuremath{\nu}}_{4}$ emission covering the ${\ensuremath{\nu}}_{4}$ mass range from MeV to GeV. We also discuss constraints from peak search experiments probing for emission of a ${\ensuremath{\nu}}_{4}$ via lepton mixing, as well as constraints from pion beta decay, CKM unitarity, $\ensuremath{\mu}$ decay, leptonic $\ensuremath{\tau}$ decay, and other experimental inputs.

Investigation of Rare Pion Decays with the PIBETA Spectrometer

Experimental results on pion decays obtained with the PIBETA spectrometer at the Paul Scherrer Institute (PSI) are reviewed. For pion beta decay π+ → π0е+ν (πβ), a precision measurement of relative probability yields Г(πβ) = [1.036 ± 0.004(stat) ± 0.004(syst) ± 0.003(π+→е+ν)] × 10–8, which implies Vud = 0.9728(30) for the corresponding element of the Cabibbo–Kobayashi–Maskawa mixing matrix. Using a sample of 65 × 103 events, relative probability of the π+→е+νγ radiative pion decay (RPD) in the kinematic region of Eγ > 10 MeV and θeγ > 40° is measured as Bexp = 73.86(54) × 10–8. A statistical analysis of measured Ee+ and Eγ distributions for this decay yield the values FV = 0.0258(17) and FA = 0.0117(17) for the pion weak formfactors. Assuming that FV linearly depends on the е+ν invariant mass q2 as FV(q2) = FV(0)(1 + aq2), the slope parameter is extracted as а = 0.10(6). The pion polarizability and neutral-pion lifetime are estimated as αE = 2.78(10) × 10–4 fm3 and τ(π0) = (8.5 ± 1.1) × 10–17 s, respectively. The data for decays π+→ е+ ν and $${\mu ^ + } \to {e^ + }v\bar v\gamma $$ have been collected and are being processed. The follow-up PEN experiment aims at reducing the uncertainty on the π+ → е+ ν relative probability by almost an order of magnitude (to 5 × 10–4).

Form factor of the longitudinal component of weak vector current in pion beta decay

The form factor f- of the longitudinal component of the weak vector current in pion β-decay is derived using the generalized Ward identity. The form factor is expressed through the pion mass difference and mean-square radii in the channels with angular momenta J = 1, 0 and isospins T = 1, 2.

Gauge boson mass generation–without Higgs–in the scalar strong interaction hadron theory

It is shown that the gauge boson mass is natu-rally generated–without Higgs–in the pion beta decay using the scalar strong interaction had-ron theory. This mass generation is made pos-sible by the presence of relative time between quarks in the pion in a fully Lorentz covariant formalism.

|Vud| from T = 1/2 mirror transitions and the role of atom and ion traps

Precision correlation measurements in nuclear beta decay using atom and ion traps have made significant progress since the last ENAM2004 Conference. We review here the achievements and plans of different projects and discuss for each of them their potential to contribute to the determination of the Vud element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. This matrix element has traditionally been determined from the analysis of data in nuclear superallowed 0+\( \rightarrow\) 0+ transitions, neutron decay and pion beta decay but can also independently be determined from data in nuclear mirror transitions. This requires the measurement of correlation parameters in such decays to determine the Gamow-Teller to Fermi mixing ratio which, in most cases, dominates the error on the extracted value of | Vud| .

Test of the Conserved Vector Current Hypothesis inT=1/2Mirror Transitions and New Determination of|Vud|

The V{ud} element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix has traditionally been determined from the analysis of data in nuclear superallowed 0;{+}-->0;{+} transitions, neutron decay, and pion beta decay. After providing a new test of the conserved vector current hypothesis, we present here a new independent determination of |V{ud}| from a set of five T=1/2 nuclear mirror transitions. The extracted value, |V{ud}|=0.9719+/-0.0017, is at 1.2 combined standard deviations from the value obtained from superallowed 0;{+}-->0;{+} transitions and has a precision comparable to the value obtained from neutron decay experiments.

OnVuddetermination from kaon decays

The pion beta decay pi^+ -> pi^0 e^+ nu proceeds through pure weak vector hadronic currents and, therefore, the theoretical prediction for it is more reliable than for the processes with axial-vector current contribution. For example, recently the pion beta decay has been used for V_ud determination. The main aim of this letter is to point that kaon beta decay K^0 -> K^+(pi^+ pi^0) e^- nu-bar analogously can be used for this purpose.

A REVIEW OF RARE PION AND MUON DECAYS

After a decade of no measurements of pion and muon rare decays, PIBETA, a new experimental program is producing its first results. We report on a new experimental study of the pion beta decay, π+→π0e+ν, the πe2γ radiative decay, π+→e+νγ, and muon radiative decay, [Formula: see text]. The new results represent four- to six-fold improvements in precision over the previous measurements. Excellent agreement with Standard Model predictions is observed in all channels except for one kinematic region of the πe2γ radiative decay involving energetic photons and lower-energy positrons.

Design, commissioning and performance of the PIBETA detector at PSI

We describe the design, construction and performance of the PIBETA detector built for the precise measurement of the branching ratio of pion beta decay, π +→π 0e +ν e, at the Paul Scherrer Institute. The central part of the detector is a 240-module spherical pure CsI calorimeter covering ∼3 π sr solid angle. The calorimeter is supplemented with an active collimator/beam degrader system, an active segmented plastic target, a pair of low-mass cylindrical wire chambers and a 20-element cylindrical plastic scintillator hodoscope. The whole detector system is housed inside a temperature-controlled lead brick enclosure, which in turn is lined with cosmic muon plastic veto counters. Commissioning and calibration data were taken during two 3-month beam periods in 1999/2000 with π + stopping rates between 1.3·10 3 π +/ s and 1.3·10 6 π +/ s . We examine the timing, energy and angular detector resolution for photons, positrons and protons in the energy range of 5– 150 MeV , as well as the response of the detector to cosmic muons. We illustrate the detector signatures for the assorted rare pion and muon decays and their associated backgrounds.

The evaluation of Vud, experiment and theory

The value of the Vud matrix element of the Cabibbo–Kobayashi–Maskawa (CKM) matrix can be derived from nuclear superallowed beta decays, neutron decay and pion beta decay. We survey current world data for all three. Today, the most precise value of Vud comes from the nuclear decays; however, the precision is limited not by experimental error but by the estimated uncertainty in theoretical corrections. Experimental uncertainty does limit the neutron-decay result, which, though statistically consistent with the nuclear result, is approximately a factor of three poorer in precision. The value obtained for Vud leads to a result that differs at the 98% confidence level from the unitarity condition for the CKM matrix. We examine the reliability of the small calculated corrections that have been applied to the data, and assess the likelihood of even higher quality nuclear data becoming available to confirm or deny the discrepancy. Some of the required experiments depend upon the availability of intense radioactive beams. Others are possible today.

Radiative corrections ofO(α)for pion beta decay in the light-front quark model

If the CKM matrix element ${V}_{\mathrm{ud}}$ that can be derived from superallowed nuclear decays, neutron decay and pion beta decay is used for a precision test of the unitarity of the CKM matrix, the combination of the present world data seems to indicate a small violation of the unitarity condition for the first row. While an accurate calculation of the radiative corrections (RC) of $O(\ensuremath{\alpha})$ is crucial in order to determine the value of ${V}_{\mathrm{ud}}$ as precisely as possible, the theoretical analysis has been limited in the past by the rather crude estimate of the effect of the hadronic structure. Only the contribution due to the axial vector current depends on the hadronic environment. We develop a strategy to deal with the influence of the hadronic structure on the decay properties of the simplest hadron, the pion, and calculate the contribution of the axial vector current to the RC, using a light-front model for the pion. Its $q\overline{q}$ bound state structure is well described by two parameters, the constituent quark mass and confinement scale, that have been fixed by a comparison with the data. We take into consideration three different groups of two-loop diagrams, and derive their light-front representations. We discuss the associated zero-mode problem and show that the respective light-front amplitudes are free of spurious contributions. There is only a small model dependent uncertainty of the final result for the RC for pion beta decay.

Erratum: Radiative corrections to the pion beta decay [JETP 59, No. 10, 671–676 (25 May 1994)

Erratum: Radiative corrections to the pion beta decay [JETP 59, No. 10, 671–676 (25 May 1994)

Measurement of the rate for pion beta decay.

The conserved-vector-current hypothesis, together with measured nuclear beta-decay rates, predicts a value of the rate for the decay ${\ensuremath{\pi}}^{+}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{0}$${e}^{+}$\ensuremath{\nu} of 0.4027\ifmmode\pm\else\textpm\fi{}0.0018 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. Using a decay-in-flight technique we have made the most precise measurement to date of this rate, obtaining the value 0.394\ifmmode\pm\else\textpm\fi{}0.015 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, in good agreement with the prediction. This differs slightly from the value previously reported in W. K. McFarlane et al., Phys. Rev. Lett. 51, 249 (1983).

New Measurement of the Rate for Pion Beta Decay

The conserved-vector-current hypothesis, together with measured nuclear-beta-decay rates, predicts a value of the rate for the decay ..pi../sup +/..--> pi../sup 0/e/sup +/..nu.. of 0.4027 +- 0.0018 s/sup -1/. With use of a decay-in-flight technique the authors have made the most precise measurement to date of this rate, obtaining the value 0.398 +- 0.015 s/sup -1/, in good agreement with the prediction.

On current algebra and CVC in pion beta-decay

It is observed that in pion beta decay the coupling constants are dictated by current algebra and PDDAC, independently of CVC.

Radiative Corrections toKl3±Decays

The radiative corrections to the lepton spectrum and decay rate for ${{K}_{l3}}^{\ifmmode\pm\else\textpm\fi{}}$ decays are calculated, assuming a phenomenological weak $K\ensuremath{-}\ensuremath{\pi}$ vertex and using perturbation theory. The answer depends logarithmically on a cutoff. The result applied to pion beta decay yields a fractional change in lifetime of -1.2% and is not sensitive to reasonable variations in the cutoff. The radiative correction to the electron spectrum from ${{K}_{e3}}^{\ifmmode\pm\else\textpm\fi{}}$ decays at rest is substantial, averaging about 5% in absolute magnitude over most of the measurable energy range, and is insensitive to the cutoff. The correction to the ${{K}_{e3}}^{\ifmmode\pm\else\textpm\fi{}}$ lifetime, the ${{K}_{\ensuremath{\mu}3}}^{\ifmmode\pm\else\textpm\fi{}}$ lifetime and muon spectrum is probably small (a fraction of a percent) although the numerical estimates are sensitive to the cutoff.

Measurements of the Rates of the Decayπ+→π0+e++νand ofπ−Capture in LiH, CH2, and CH

We have measured the branching ratio for ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{+}+\ensuremath{\nu}$. Our method exploited the near anticollinearity of the two $\ensuremath{\gamma}$ rays resulting from the subsequent decay of the ${\ensuremath{\pi}}^{0}$. The detection of these $\ensuremath{\gamma}$ rays using spark chambers, together with the identification of the positron in a scintillation target detector, enabled us to identify the pion beta-decay process in a manner which was effectively free from background. On the basis of 39 events, of which 3 are attributed to background, and an independent calibration of the over-all efficiency of the apparatus, we deduce for the branching ratio (0.97\ifmmode\pm\else\textpm\fi{}0.020)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$, in agreement with previous measurements and the prediction of the conserved-vector-current hypothesis. Using the same apparatus, we have also measured $W$, the fraction of stopped ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons captured by hydrogen nuclei bound in chemical compounds. We find ${W}_{\mathrm{LiH}}=(40\ifmmode\pm\else\textpm\fi{}4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, ${W}_{\mathrm{C}\mathrm{H}2}=(17.9\ifmmode\pm\else\textpm\fi{}1.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and ${W}_{\mathrm{CH}}=(5.5\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. Negative pion capture in ${\mathrm{H}}_{2}$-${\mathrm{N}}_{2}$ and ${\mathrm{H}}_{2}$-He gas mixtures has also been briefly studied.

On the vector form factor in pion beta decay

The pion vector form factor in the decay π ±→ π 0+ e ±± ν is calculated without the assumption of a conserved vector current in the weak interaction Lagrangian by assuming the vector form factor to satisfy an unsubtracted dispersion relation. In the approximation that only the π-π and N- N intermediate states are considered, a set of coupled integral equations for the pion and nucleon weak vector form factors is derived. These integral equations are solved numerically with a simple trial function chosen to make the integrals converge. The pion vector form factor obtained is comparable to that obtained unequivocally from the conserved vector current theory.