Form Factor Slope Research Articles

Pauli Radius of the ProtonSupported by the National Natural Science Foundation of China (Grant Nos. 12135007 and 11805097), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20180323), and STRONG-2020, “the strong interaction at the frontier of knowledge: fundamental research and applications” which received funding from the European Union’s Horizon 2020 Research and Innovation Programme (Grant No. 824093).

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyze proton magnetic form factor data obtained via electron+proton scattering on Q 2 ∈ [0.027, 0.55] GeV2 with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto Q 2 ≃ 0 for extraction of the form factor slope. In this way, we find r M = 0.817(27) fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, F 1,2(Q 2), are not truly independent observables; to wit, the difference , viz., the proton Foldy term.

Neutral pion form factor measurement by the NA62 experiment

The NA62 experiment at CERN collected a large sample of charged kaon decays with a highly efficient trigger for decays into electrons in 2007. The kaon beam represents a source of tagged neutral pion decays in vacuum. A measurement of the electromagnetic transition form factor slope of the neutral pion in the time-like region from ∼1 million fully reconstructed π0 Dalitz decay is presented. The limits on dark photon production in π0 decays from the earlier kaon experiment at CERN, NA48/2, are also reported.

Measurement of the π0 electromagnetic transition form factor slope

The NA62 experiment collected a large sample of charged kaon decays in 2007 with a highly efficient trigger for decays into electrons. A measurement of the π0 electromagnetic transition form factor slope parameter from 1.11×106 fully reconstructed K±→π±πD0, πD0→e+e−γ events is reported. The measured value a=(3.68±0.57)×10−2 is in good agreement with theoretical expectations and previous measurements, and represents the most precise experimental determination of the slope in the time-like momentum transfer region.

Search for Dark Photon at NA48/2, and measurement of π0 form factor

The NA48/2 experiment at CERN performed a search for the dark photon (A′) via the decay chain π0 → γA′, A′ → e+e−. Using a sample of ∼ 1.7 · 107 neutral pions tagged from and decays collected in 2003-04 no signal is observed. The limits in the plane dark photon mixing parameter ε2 versus its mass mA′ are reported. The NA62-RK experiment collected, during the 2007 data taking, a large sample of neutral pion Dalitz decays with a trigger optimised for electrons final states with respect to NA48/2 one. We report the measurement of the π0 electromagnetic transition form factor (TFF) slope parameter (a) based on a sample of decays. The preliminary measured value a = (3.70 ± 0.53stat ± 0.36syst) · 10−2 is compatible with theoretical expectations and previous measurements.

Study of π0 Dalitz decays in the NA62 and NA48/2 experiments

The NA62 experiment at CERN collected a large sample of charged kaon decays with a highly efficient trigger for decays into electrons in 2007. The kaon beam represents a source of tagged neutral pion decays in vacuum. A measurement of the electromagnetic transition form factor slope of the neutral pion in the time-like region from ∼1 million fully reconstructed π0 Dalitz decay is presented. The limits on dark photon production in π0 decays from the earlier kaon experiment at CERN, NA48/2, are also reported.

The neutral pion form factor at NA62

In 2007 the NA62 experiment at CERN collected a large sample of charged kaon decays with a highly efficient trigger selecting events with electrons in the final state. The kaon beam represents a rich source of tagged neutral pion decays in vacuum. The electromagnetic transition form factor slope of the π0 in the time-like region has been measured from about 106 fully reconstructed π0 Dalitz decays collected in 2007. The preliminary result a = (3.68 ± 0.51stat ± 0.25syst) × 10-2 is the most precise to date. This value is compatible with theoretical expectations and consistent with the previous measurements.

Kaon experiments at CERN: recent results and prospects

The NA48/2 and NA62-$R_K$ experiments at the CERN SPS collected large samples of charged kaon decays in flight in 2003--07. The data analysis is still on-going (with over 20 publications produced so far); the recent results from these experiments are presented. A new upper limit on the rate of a lepton number violating decay $K^\pm\to\pi^\mp\mu^\pm\mu^\pm$ is reported: $\mathcal{B} < 8.6\times 10^{-11}$ at 90\% CL. Searches for heavy sterile neutrino $N_4$ and neutral scalar resonances ($\chi$) in $K^\pm\to\pi\mu\mu$ decays are reported. Upper limits on the products $\mathcal{B}(K^\pm\to\mu^\pm N_4)\mathcal{B}(N_4\to\pi^\mp\mu^\pm)$ and $\mathcal{B}(K^\pm\to\pi^\pm \chi)\mathcal{B}(\chi\to\mu^+\mu^-)$ are set in the range $10^{-10}$ to $10^{-9}$ for resonance lifetimes up to 100~ps. A preliminary measurement of the electromagnetic transition form factor slope of the $\pi^0$ from $1.05\times 10^6$ fully reconstructed $\pi^0\to\gamma e^+e^-$ decays is presented: the obtained result $a = (3.70 \pm 0.53_\text{stat} \pm 0.36_\text{syst})\times 10^{-2}$ represents the first observation of a non-zero slope in the time-like region of momentum transfer.

Recent results and prospects from NA62

A large sample of charged kaon decays in 2007 has been collected by the NA62 experiment at CERN SPS using the experimental setup of the former NA48 experiment. Its intense kaon beam provides an abundant source of tagged neutral pions in vacuum. A measurement of the electromagnetic transition form factor slope of the neutral pion from 1:05 × 106 fully reconstructed π0 Dalitz decays is presented. The obtained preliminary value a = (3.70 ± 0.53stat ± 0.36syst ) × 10−2 is the first 5.8σ observation of a non-zero slope in the time-like region of momentum transfer.K + → π+ vv is a theoretically very clean decay where indirect effects of new physics may be detectable. The NA62 apparatus has been significantly upgraded between 2008 and 2014 in order to measure the branching ratio of this decay with 10% precision. The NA62 experiment took data with the new setup in pilot runs in 2014 and 2015, reaching the design beam intensity. Results of first data quality studies in view of the 2016-2017 physics runs are presented.

CONSTRAINTS ON B→π, K TRANSITION FORM-FACTORS FROM EXCLUSIVE SEMILEPTONIC D-MESON DECAYS

According to the heavy-quark flavor symmetry, the B→π, K transition form-factors could be related to the corresponding ones of D-meson decays near the zero recoil point. With the recent precisely measured exclusive semileptonic decays D →πℓν and D→K ℓν, we perform a phenomenological study of B →π, K transition form-factors based on this symmetry. Using BK, BZ and Series Expansion parametrizations of the form-factor slope, we extrapolate B →π, K transition form-factors from [Formula: see text] to q2 = 0. It is found that, although being consistent with each other within error bars, the central values of our results for B →π, K form-factors at q2 = 0, [Formula: see text], are smaller than predictions of the QCD light-cone sum rules, but are in good agreements with the ones extracted from hadronic B-meson decays within the SCET framework. Moreover, smaller form-factors are also favored by the QCD factorization approach for hadronic B-meson decays.

Measurement of|Vcb|and the Form-Factor Slope inB¯→Dℓ−ν¯ℓDecays in Events Tagged by a Fully ReconstructedBMeson

We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element |V(cb)| and the form-factor slope rho2 in B --> Dl- nu(l) decays based on 460x10(6) BB events recorded at the Upsilon(4S) resonance with the BABAR detector. B --> Dl- nu(l) decays are selected in events in which a hadronic decay of the second B meson is fully reconstructed. We measure B(B- --> D0 l- nu(l))/B(B- --> Xl- nu(l)) = (0.255+/-0.009+/-0.009) and B(B0 --> D+ l- nu(l))/B(B0 --> Xl- nu(l)) = (0.230+/-0.011+/-0.011), along with the differential decay distribution in B --> Dl- nu(l) decays. We then determine G(1)|V(cb)| = (42.3+/-1.9+/-1.4)x10(-3) and rho2 = 1.20+/-0.09+/-0.04, where G(1) is the hadronic form factor at the point of zero recoil.

High energy inelastic electron-hadron scattering in peripheral kinematics: Sum rules for hadron form factors

Relations between differential cross section for inelastic scattering of electrons on hadrons and hadron form factors (sum rules) are derived on the basis of analytical properties of heavy photon forward Compton scattering on hadrons. Sum rules relating the slope of form factors at zero momentum transfer and anomalous magnetic moments of hadrons with some integrals on photoproduction on a hadron are obtained as well. The convergency of these integrals is provided by the difference of individual sum rules for different hadrons. The universal interaction of the Pomeron with nucleons is assumed. We derive the explicit formulas for the processes of electroproduction on proton and light isobar nuclei. Sudakov's parametrization of momenta for peripheral kinematics, relevant here, is used. The light-cone form of differential cross sections is also discussed. The accuracy of sum rules estimated in frames of pointlike hadrons and it is shown to be at the level of precision achievable by experiments. Suggestions and predictions for future experiments are also given.

Study of the branching ratio and charge asymmetry for the decay [formula omitted] with the KLOE detector

Among some 400 million KSKL pairs produced in e+e− annihilations at DAΦNE, ∼6500 each of KS→π+e−ν¯ and KS→π−e+ν decays have been observed with the KLOE detector. From these, the ratio Γ(KS→πeν)/Γ(KS→π+π−)=(10.19±0.13)×10−4 is obtained, improving the accuracy on BR(KS→πeν) by a factor of four and providing the most precise test of the ΔS=ΔQ rule. From the partial width Γ(KS→πeν), a value for f+K0(0)×Vus is obtained that is in agreement with unitarity of the quark-mixing matrix. The lepton charge asymmetry AS=(1.5±9.6stat±2.9syst)×10−3 is compatible with the requirements of CPT invariance. The form-factor slope agrees with recent results from semileptonic KL and K+ decays. These are the first measurements of the charge asymmetry and form-factor slope for semileptonic KS decays.

Measurement of |V cb | using the semileptonic decay $\overline{\rm {B^{0}_{d}}} \rightarrow {\rm D}^* \ell^- \overline{\nu}_{\ell}$

Data from Z decays in DELPHI have been searched for anti-B0d -> D*+ l- anti-nu_l with the D*+ decaying to D0 pi+ and D0 -> K- pi+, K- pi+ pi+ pi- or K- pi+ (pi0). These events are used to measure the CKM matrix element |V_cb| and the form factor slope, rho_{A_1}^2: F_D*(1)|Vcb| = 0.0392 +/- 0.0018 +/- 0.0023; rho_{A_1}^2 = 1.32 +/- 0.15 +/- 0.33 corresponding to a branching fraction: BR(anti-B0d -> D*+ l- anti-nu_l) = (5.90 +/- 0.22 +/- 0.50)%. Combining these and previous DELPHI measurements gives: F_D*(1)|Vcb| = 0.0377 +/- 0.0011 +/- 0.0019, rho_{A_1}^2 = 1.39 +/- 0.10 +/- 0.33 and BR(anti-B0d -> D*+ l- anti-nu_l) = (5.39 +/- 0.11 +/- 0.34)%. Using F_{D*}(1) = 0.91 +/- 0.04, yields: |Vcb| = 0.0414 +/- 0.0012(stat.) +/- 0.0021(syst.) +/- 0.0018(theory). The b-quark semileptonic branching fraction into a D*+ emitted from higher mass charmed excited states has also been measured to be: BR(b -> D*+ X l- anti-nu_l) = (0.67 +/- 0.08 +/- 0.10)%.

Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory

We apply Pauli-Villars regularization and discretized light-cone quantization to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a single-fermion truncation. Three heavy scalars, including two with negative norm, are used to regulate the theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of a new, indefinite-metric Lanczos algorithm. Various observables are extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope.

Semileptonic form factors: A model-independent approach

We demonstrate that the $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}l\ensuremath{\nu}$ form factors can be accurately predicted given the slope parameter ${\ensuremath{\rho}}^{2}$ of the Isgur-Wise function. Only weak assumptions, consistent with lattice results, on the wave function for the light degrees of freedom are required to establish this result. We observe that the QCD and ${1/m}_{Q}$ corrections can be systematically represented by an effective Isgur-Wise function of shifted slope. This greatly simplifies the analysis of semileptonic B decay. We also investigate what the available semileptonic data can tell us about lattice QCD and heavy quark effective theory. A rigorous identity relating the form factor slope difference ${\ensuremath{\rho}}_{{D}^{*}}^{2}\ensuremath{-}{\ensuremath{\rho}}_{{A}_{1}}^{2}$ to a combination of form factor intercepts is found. The identity provides a means of checking theoretically evaluated intercepts with experiment.

Contributions of orderO(mquark2)toKl3form factors and unitarity of the CKM matrix

The form factors for the ${K}_{l3}$ semileptonic decay are computed to order $\mathcal{O}{(p}^{4})$ in generalized chiral perturbation theory. The main difference with the standard $\mathcal{O}{(p}^{4})$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, ${A}_{3}.$ A new simultaneous analysis is presented for the CKM matrix element ${V}_{\mathrm{us}},$ the ratio ${F}_{K}{/F}_{\ensuremath{\pi}}, {K}_{l3}$ decay rates and the scalar form factor slope ${\ensuremath{\lambda}}_{0}.$ This framework easily accommodates the precise value for ${V}_{\mathrm{ud}}$ deduced from superallowed nuclear \ensuremath{\beta} decays.

The quark-photon vertex and meson electromagnetic form factors

The ladder Bethe-Salpeter solution for the dressed photon-quark vertex is used to study the low-momentum behavior of the pion electromagnetic and the $\gamma^\star \pi^0 \gamma$ transition form factors. With model parameters previously fixed by light meson masses and decay constants, the low-momentum slope of both form factors is in excellent agreement with the data. In comparison, the often-used Ball-Chiu Ansatz for the vertex is found to be deficient; less than half of the obtained $r_\pi^2$ is generated by that Ansatz while the remainder of the charge radius could be attributed to the tail of the $\rho$ resonance.

Application of Pauli-Villars regularization and discretized light-cone quantization to a(3+1)-dimensional model

We apply Pauli-Villars regularization and discrete light-cone quantization to the nonperturbative solution of a $(3+1)$-dimensional model field theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of the complex symmetric Lanczos algorithm. This permits the calculation of each Fock-sector wave function, and from these we obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form factor slope.

Measurement of theB¯→Dlν¯Partial Width and Form Factor Parameters

We have studied the decay $\bar{B} \to D\ell\bar{\nu}$, where $\ell=e or \mu$. From a fit to the differential decay rate $d\Gamma/dw$ we measure the rate normalization ${\cal F}_D(1)|V_{cb}|$ and form factor slope $\hat{\rho}^2_D$, and, using measured values of $\tau_B$, find $\Gamma(\bar{B} \to D\ell\bar{\nu}) = (12.0 \pm 0.9 \pm 2.1) ns^{-1}$. The resulting branching fractions are ${\cal B}(\bar{B}^0 \to D^+\ell^-\bar{\nu})=(1.87 \pm 0.15 \pm 0.32)%$ and ${\cal B}(B^- \to D^0\ell^-\bar{\nu})=(1.94 \pm 0.15 \pm 0.34)%$. The form factor parameters are in agreement with those measured in $\bar{B} \to D^*\ell\bar{\nu}$ decays, as predicted by heavy quark effective theory.

Measurements of | Vcb|, form factors and branching fractions in the decays [formula omitted] and [formula omitted

Two samples of exclusive semileptonic decays, 579 B 0 → D ∗+ℓ − ν ℓ events and 261 B 0 → D +ℓ − ν ℓ events, are selected from approximately 3.9 million hadronic Z decays collected by the ALEPH detector at LEP. From the reconstructed differential decay rate of each sample, the product of the hadronic form factor F (ω) at zero recoil of the D (∗)+ meson and the CKM matrix element | V cb| are measured to be F D ∗+ (1)|V cb | = (31.9 ± 1.8 stat ± 1.9 syst ) × 10 −3 , F D + (1)| V cb| = (27.8 ± 6.8 stat ± 6.5 syst) × 10 −3. The ratio of the form factors F D + (1) and F D ∗+ (1) is measured to be F D + (1) F D ∗+ (1) = 0.87 ± 0.22 stat ± 0.21 syst . A value of | V cb| is extracted from the two samples, using theoretical constraints on the slope and curvature of the hadronic form factors and their normalization at zero recoil, with the result | V cb| = (34.4 ± 1.6 stat ± 2.3 syst ± 1.4 th) × 10 −3. The branching fractions are measured from the two integrated spectra to be Br( B 0 → D ∗+ℓ − ν ℓ) = (5.53 ± 0.26 stat ±0.52 syst ) %, Br( B 0 → D ∗+ℓ − ν ℓ) = (2.35 ± 0.20 stat ± 0.44 syst ) %.