PCAC Hypothesis Research Articles

Some Phenomenological Aspects of Kaon Photoproduction in the Extreme Kinematics

We have investigated phenomenological aspects of kaon photoproduction in three different extreme kinematics. The first kinematics of interest is the threshold region. At the threshold we have investigated the convergence of kaon photoproduction amplitude by expanding the square of the amplitude in terms of the ratio $m_K/m$, where $m_K$ is the mass of kaon and $m$ is the averaged mass of nucleon and $\Lambda$-hyperon. The amplitude is calculated from the appropriate Feynman diagrams by using the pseudovector theory. The contact diagram as a consequence of the PCAC hypothesis is also taken into account in the amplitude. Our finding indicates that the convergence can be only achieved if the amplitude was expanded up to at least $12^{\rm th}$ order. As a consequence, applications of some theoretical calculations based on the expansion the scattering amplitude, such as the Low Energy Theorem or Soft Kaon Approximation, cannot be easily managed in kaon photoproduction. The second kinematics is the forward region, where we could assume only $t$-channel contributes to the process. Here we have investigated the effect of amplitude expansion on the extraction of the coupling constants $g_{K^+\Lambda p}$ and $g^V_{K_1^+\Lambda p}$. The last kinematics is the backward region, where we have also assumed that only $u$-channel survives and we could extract the leading coupling constants $g_{K^+\Lambda p} $ and $g_{K^+\Sigma^0 p}$.

Measurement of total and differential cross sections of neutrino and antineutrino coherent π± production on carbon

Neutrino induced coherent charged pion production on nuclei, $\overline{\nu}_\mu A\to\mu^\pm\pi^\mp A$, is a rare inelastic interaction in which the four-momentum squared transfered to the nucleus is nearly zero, leaving it intact. We identify such events in the scintillator of MINERvA by reconstructing |t| from the final state pion and muon momenta and by removing events with evidence of energetic nuclear recoil or production of other final state particles. We measure the total neutrino and antineutrino cross sections as a function of neutrino energy between 2 and 20 GeV and measure flux integrated differential cross sections as a function of $Q^2$, $E_\pi$ and $\theta_\pi$. The $Q^2$ dependence and equality of the neutrino and anti-neutrino cross-sections at finite $Q^2$ provide a confirmation of Adler's PCAC hypothesis.

One pion production in neutrino–nucleon scattering and the different parameterizations of the weak [formula omitted] vertex

The N→Δ weak vertex provides an important contribution to the one pion production in neutrino–nucleon and neutrino–nucleus scattering for πN invariant masses below 1.4 GeV. Beyond its interest as a tool in neutrino detection and their background analyses, one pion production in neutrino–nucleon scattering is useful to test predictions based on the quark model and other internal symmetries of strong interactions. Here we try to establish a connection between two commonly used parameterizations of the weak N→Δ vertex and form factors (FF) and we study their effects on the determination of the axial coupling C5A(0), the common normalization of the axial FF, which is predicted to hold 1.2 by using the PCAC hypothesis. Predictions for the νμp→μ−pπ+ total cross sections within the two approaches, which include the resonant Δ++ and other background contributions in a coherent way, are compared to experimental data.

Neutrino-induced forward meson-production reactions in nucleon resonance region

As a first step toward developing a reaction model that enables a comprehensive description of neutrino-nucleon reactions in the nucleon resonance region, we have applied for the first time a dynamical coupled-channels model, which successfully describes \pi N, \gamma N --> \pi N, \eta N, \pi \pi N, K\Lambda, K\Sigma reactions up to W = 2 GeV, to predict the neutrino-induced meson-production reactions with \Delta S = 0 at the forward angle limit. This has been achieved by relating the divergence of the axial-current matrix elements at Q^2 = 0 to the \pi N --> X reaction amplitudes through the PCAC hypothesis. We present the contributions from each of the \pi N, \eta N, \pi \pi N, K\Lambda, K\Sigma channels to the F_2 structure function at Q^2 --> 0 limit up to W = 2 GeV.

PCAC and shadowing of low energy neutrinos

The Adler relation between reactions initiated by neutrinos and pions is easy to misinterpret as a manifestation of the pion pole dominance. An axial current, however, cannot fluctuate into a pion, but only to heavy axial-vector states, since the lepton current is transverse. This is the miracle of the PCAC hypothesis which dictates a specific conspiracy between the heavy fluctuations, so that all together they mock the pion pole. Indeed, the observed Q^2 dependence of the axial form factor is controlled by the effective mass m_A \sim 1 GeV, rather than the pion mass. On the contrary, the onset of nuclear shadowing is governed by the small pion mass, rather than by the large axial mass scale. This is in variance with the conventional wisdom which equates the fluctuation lifetime and the coherence time. For the case of axial current they are different by almost two orders of magnitude. As a result, neutrino interactions are shadowed at very low energies of few hundred MeV, while energy of about 10 GeV is needed to access nuclear shadowing for the vector current. On the contrary to naive expectations, nuclear absorption enhances, rather than suppresses the cross section of coherent neutrino-production of pions which is the strongest channel (half of the total cross section) in the black disc limit.

Doppler-broadening of gamma rays following muon capture: search for scalar coupling

A precision measurement of the 277 keV γ ray produced by capturing muons in gaseous oxygen was performed using high-resolution HPGe detectors. The Doppler-broadened shape of this line is sensitive to the possible admixture into muon capture of genuine scalar interaction. This experiment complements, in the muon sector, in principle, similar ones undertaken recently in nuclear β decay. Using a procedure discussed in earlier papers, a fit to the experimental line-shape allowed us to obtain for the recoil–gamma correlation coefficient the value of a 1 2=0.096±0.041 (95% CL). The available evaluations of the contributing nuclear matrix elements, performed in the impulse approximation in the absence of scalar interaction, produce correlation coefficients in disagreement with our result. These evaluations are independent of the induced pseudoscalar coupling and so of the validity of the PCAC hypothesis, but their reliability and model dependence remain to be investigated.

PCAC and Modifications in Hadron Properties in Nuclear Medium

It is known that the Adler zero condition when imposed on pion amplitudes leads to several relations between hadron masses through the dual resonance formula of Lovelace, Shapiro and Veneziano. In particular the Lovelace quantization condition leads to the relation [Formula: see text] which is well satisfied experimentally. The Regge slope parameter α′ can be related to the gluon condensate. The latter is modified in the nuclear medium as compared to its value in the QCD vacuum. Combining the PCAC hypothesis with changes in gluon condensate leads to lowering of vector masses in the nuclear medium. It also leads to predictions regarding, nucleon isobar mass differences, pion decay constant in the medium, pion amplitudes and transverse momentum distribution of secondaries in heavy ion collisions.

Coherent single charged pion production by neutrinos

We report on a measurement of coherent single charged pion production in neutrino-nucleus scattering. The analysis is based on data taken with the CHARM II detector in beams of muon-neutrinos and -antineutrinos. The event numbers amount to N(μ−π) = 748 and N(μ+π) = 631. Cross sections and their dependence on the neutrino energy are determined. The results are in agreement with the predictions of models based on the PCAC hypothesis.

LOW Q2, HIGH ν NEUTRINO PHYSICS (CVC, PCAC, HADRON DOMINANCE)

A critical review is given of the main theoretical bases and of the experimental results of neutrino physics at low four-momentum transfer (Q2≤1 GeV 2) and high energy transfer (ν≥a few GeV). The theoretical predictions for the vector current are first presented, using the CVC hypothesis and the hadron dominance model of Piketty and Stodolsky. The predictions for the axial current at very small Q2 values are discussed on the basis of the PCAC hypothesis (Adler’s theorem), and extended for Q2≲1 GeV 2 in the lines of hadron dominance; the structure of the longitudinal component of the axial current is particularly discussed. Experimental data on neutrino and antineutrino interactions on nucleons are reviewed, in particular the total cross sections, which provide good tests of the PCAC hypothesis and of the model of Piketty and Stodolsky; also reviewed are the data on diffractive production of π, ρ and a1 mesons. The observation of shadowing, from the comparison of the total cross sections of neutrinos and antineutrinos on neon and deuterium nuclei, is discussed in detail with emphasis on the predictions of the PCAC hypothesis, in the framework of the Glauber-Gribov model. Finally a review is given of the results on coherent neutrino and antineutrino interactions on atomic nuclei: • π meson production, by charged and neutral currents in several experiments, providing a detailed test of the PCAC hypothesis; • ρ meson production, providing a test of the CVC hypothesis in weak interactions; • a1 meson or nonresonant ρπ system production, allowing the study of the weak axial current structure.

Experimental test of the PCAC hypothesis in the reactionsv ? p? ?? p?+ and $$ \bar v_\mu p \to \mu ^ + p\pi ^ - $$ in the?(1232) region

Data on the reactionsv μ p→ μ− pπ+ and\( \bar v_\mu p \to \mu ^ + p\pi ^ - \) in the Δ(1232) region are presented and a test of the PCAC hypothesis, using a modified version of the Adler model, is performed. The analysis is based on 1081 events in the neutrino and on 180 events in the antineutrino reaction, obtained in a bubble chamber experiment with BEBC at CERN. The experimental cross-sections for an invariant hadronic massW<1.4 GeV and an (anti-)neutrino energyE L v >10 GeV are determined to be (0.628±0.059)·10−38 cm2 for the neutrino and (0.168±0.023)·10−38 cm2 for the antineutrino reaction. TheQ 2 andW distributions, the density matrix elements of the Δ resonance, and moments of the pion angular distribution are discussed. The data are found to be in good agreement with the Adler model in theQ 2 region below 1 GeV2. A maximum likelihood fit for the axial massm A in the axial-vector form factor yields a value ofm A =1.31±0.12 GeV. At lowQ 2 the data confirm the PCAC hypothesis and the discrepancy, formerly observed between the experimental and theoretical cross-sections forv μ p→ μ− pπ+ at low momentum transfers (Q 2≲0.2 GeV2), is understood as being due to inadequate pion ‘off-mass-shell’ corrections.

About ω 0-exchange in the (γ, π 0) reaction on the proton near threshold

With the amplitudes obtained in the effective lagrangian (BL) and in the dispersion (BDW) methods the new data for the (γ, π 0) reaction on the proton near threshold are analysed. The inclusion of ω 0-meson exchange in the BDW amplitude removes the discrepancy with experimental data. The tensor and vector coupling constants which are consistent with the results of other analyses give the value of E 0+ multipole predicted by the PCAC hypothesis.

The long-distance s-d transition and K→2π decays

The author shows how one can build an off-diagonal off-shell non-perturbative s-d transition with the PCAC hypothesis after chiral symmetry breaking in QCD. The resulting effective Hamiltonian correctly reproduces almost the whole (up to 80%) of the a12/(K0 to 2 pi ) amplitude and therefore demonstrates the importance of long-distance contributions to the Delta I=1/2 rule.

The γ→3π coupling constant, the Goldberger-Treiman relation, vector mesons and the ω→3π contact term

The recent experimental measurement of the gamma to 3 pi coupling constant is compared with the prediction of an extended PCAC hypothesis. Consistency is then sought between the omega rho pi coupling constant, as obtained from an analogue of the GT relation for vector mesons, and what is predicted by the low-energy theorems. A remarkable relation for the dimensionless coupling constant g( rho pi pi ) emerges, mod g( rho pi pi ) mod =2 pi . The authors also find that the coupling constant g( omega rho 0 pi 0), as obtained from the GT relation for vector mesons, does not support an omega pi pi pi contact term.

Experimental test of the PCAC-hypothesis in charged current neutrino and antineutrino interactions on protons

Data obtained with the bubble chamber BEBC at CERN are used for the first significant test of Adler's prediction for the neutrino and antineutrino-proton scattering cross sections at vanishing four-momentum transfer squaredQ 2. An Extended Vector Meson Dominance Model (EVDM) is applied to extrapolate Adler's prediction to experimentally accessible values ofQ 2. The data show good agreement with Adler's prediction forQ 2→0 thus confirming the PCAC hypothesis in the kinematical region of high leptonic energy transfer ν>2 GeV. The good agreement of the data with the theoretical predictions also at higherQ 2, where the EVDM terms are dominant, also supports this model. However, an EVDM calculation without PCAC is clearly ruled out by the data.

Coherent single pion production by antineutrino charged current interactions and test of PCAC

The cross section for coherent production of a single π− meson in charged current antineutrino interactions on neon nuclei has been measured in BEBC to be (175±25) 10−40 cm2/neon nucleus, averaged over the energy spectrum of the antineutrino wide band beam at the CERN SPS; this corresponds to (0.9±0.1) % of the total charged current\(\bar v_\mu \) cross section. The distributions of kinematical variables are in agreement with theoretical predictions based on the PCAC hypothesis and the meson dominance model; in particular, theQ 2 dependence is well described by a propagator containing a massm=(1.35±0.18) GeV. The absolute value of the cross section is also in agreement with the model. This analysis thus provides a test of the PCAC hypothesis in the antineutrino energy range 5–150 GeV.

New pulsed-beam measurement of the average polarization of 12B (ground state) produced in the polarized-muon capture reaction 12C( μ−, vμ) 12B

The average polarization P av of the recoil nucleus 12B (bound states) produced in the polarized-muon capture reaction was measured by the muon spin resonance method in a pulsed beam at the BOOM muon facility. The polarization of 12B was maintained completely under a longitudinal magnetic field of 3kG in a Grafoil target. After correcting the observed result for excited-state contributions of 12B, P av (ground state) was deduced to be 0.462 ± 0.053. It yields g P / g A = 10.1 −2.6 +2.4, which is almost consistent with the prediction of the PCAC hypothesis of about 7.

Dynamic masses or quarks in quantum chromodynamics

Using Dyson-Schwinger equations we obtain an ultraviolet asymptotics for the dynamical mass of quark in QCD mD(p) = 〈qq〉 3 ḡ2(p2/μ2, g2 R) p2 ( ḡ2(p2/μ2, g2 R) g2 R )−d . We also determine a numerical value for the π meson decay constant fπ. Electronic version of the paper published in Russ. Phys. J. 25, 55 (1982). As is well known, strong interactions at high energies are approximately invariant with respect to the chiral symmetry group SUL(N) ⊗ SUR(N) (N is the number of different quark species). The Lagrangian of QCD – the most popular field-theoretical model of strong interactions – has the chiral symmetry group SUL(N)⊗ SUR(N) in approximation of massless quarks. The success of current algebra and PCAC hypothesis shows that the chiral symmetry SUL(N) ⊗ SUR(N) is spontaneously broken down to SU(N) symmetry. The spontaneous violation of the chiral symmetry reveals itself in nonvanishing vacuum expectation values 〈qq〉 and also in the appearance of dynamical mass for originally massless quarks. The problem of dynamical mass generation in massless theories has a long history. First, in refs. [1, 2] it has been shown in some concrete models that the generation of the dynamical mass can take place in quantum field theory. However, the consistent study of the problem of dynamical mass generation requires going beyond perturbation theory. It is obvious that this problem is rather nontrivial in the field theory because of the absence of the consistent methods different from perturbation theory. The purpose of the present paper is to investigate a possibility of generation of the dynamical mass of quarks in QCD. Using the Dyson-Schwinger equations we show that one can reliably determine the dependence of the dynamical mass of quarks m(p) on the momentum p in the ultraviolet domain due to the property of asymptotic freedom of strong interactions. In the following we will work in Euclidean space-time and in the transverse gauge (Landau gauge). The use of this gauge is convenient since the propagator of the massless quark is not renormalized in the leading logarithmic approximation. The Dyson-Schwinger equation for the quark propagator G(p) has the form G(p) = S(p) + g (2π)4 ∫ dk Γμ(p, k)G(k)Dμν(p− k)γν(λ /2). (1) Here S(p) is the propagator of free quarks, λ/2 are the generators of the fundamental representation of the group SU(N). Equation (1) is written for bare quantities. After performing the renormalization we find Z 2 G −1 R (p) = S (p) + g R (2π)4 ∫ dk Γ μ (p, k)GR(k)D R μν(p− k)γν(λ /2), where Z2 is the renormalization constant of the quark propagator. At the lowest order in g 2 R in the Landau gauge the renormalization constant of the quark propagator is equal to one Z2 = 1+O(g 4 R). Therefore in the leading logarithmic approximation we can set G(p) = m(p)−p. For the quantity m(p) we obtain the equation of the form m(p) = 4 (2π)4 ∫ dk m(k)ḡ((p− k)) (m2(k2) + k2)(p− k)2 where ḡ(p) = ḡ(p/μ, g R) = g 2 R/ ( 1 + (11− 2N/3) g R 16π2 ln p μ2 ) is the effective quark-gluon coupling constant. We split the region of integration into two subdomains determined by the requirements k > p (sub-domain (I)) and k < p (sub-domain (II))

S-wave pion-nucleon interaction and PCAC in nuclear matter

It is shown that the pion-nucleon σM-term contribution to the S-wave π-N interaction leads to a modification of the PCAC hypothesis in nuclear matter. Some experiments that enable one to obain directly the pion-nucleon σ-term, without any extrapolation to unphysical values of the kinematical variables, are discussed.

Two-component sigma-model and modified Goldberger-Treiman relation

A two-componentSU2×SU2 nonlinear σ-model with a general symmetry-breaking term is presented in which a symmetry of internal discrete transformations is introduced. In a redefined PCAC relation this model gives a modified Goldberger-Treiman relation with a free parameter to be determined by experiment. Using this model we have calculated the pseudoscalar form factorgp(q2) which is compared with the result of the single-component PCAC hypothesis. The two models lead to the same prediction ofgp(q2) forq2.

Nuclear Structure Effects on Weak Nuclear Form Factors of 0+-0- Transitions in A=16 System

The ratio of muon-capture rate to beta-decay rate in the trans1t10ns 160 (o+: ground) 1'N co-: 120 ke V) is calculated with realistic nuclear models and with an exact formalism for lepton wave functions. In contrast to the results with no ground-state correlation, the calculated ratio is strongly reduced in agreement with the experimental data. Our results are compatible with the PCAC hypothesis. The effects of the exchange currents are found to be not large. § l. Introduction Among vanous nuclear weak processes the o+ -0- transitions are unique transi­ tions which are governed completely by the nuclear axial vector current. Their rates are, therefore, sensitive to the detailed dynamics of this current, and the transitions between 160 co+: ground) and 16N co··: 120 ke V) are well-known. At the early time, the muon capture rate in 160 leading to 16N co-) was