Pion Pairs Research Articles

Studies of azimuthal modulations in two hadron fragmentation of a transversely polarised quark

We study the azimuthal modulations of dihadron fragmentation functions (DiFFs) of a transversely polarised quark using an NJL-jet based model that incorporates the Collins effect for single hadron emission. The DiFFs are extracted as Monte Carlo (MC) averages of corresponding multiplicities using their probabilistic interpretation. To simplify the model and highlight the possible mechanisms that create this modulation, we choose the elementary Collins function to be proportional to the elementary unpolarised fragmentation and a constant probability (PSF) for the quark to flip its spin after a single hadron emission. Moreover, as a leading order calculation, only one of the produced hadrons in the decay chain of the quark is produced with elementary Collins modulation. We calculate the dependence of the polarised DiFFs on various angles such as the azimuthal angle of the single hadron and the angle of the two-hadron production plane φR for several values of PSF. We observe that the polarised DiFFs for oppositely charged pion pairs exhibit a sin(φR) modulation. This effect is induced purely via the elementary Collins effect and persists even when the quark completely depolarises after a single hadron emission (PSF=0.5). Moreover, similar sine modulations are present in the distribution of pion pairs with respect to the azimuthal angle of their total transverse momentum, φT.

Complete QED NLO contributions to the reaction e + e − → μ + μ − γ and their implementation in the event generator PHOKHARA

KLOE and Babar have an observed discrepancy of 2% to 5% in the invariant pion pair production cross section. These measurements are based on approximate NLO $ \mu^+ \mu^- \gamma $ cross section predictions of the Monte Carlo event generator PHOKHARA7.0. In this article, the complete NLO radiative corrections to $ \mu^+ \mu^- \gamma $ production are calculated and implemented in the Monte Carlo event generator PHOKHARA9.0. Numerical reliability is guaranteed by two independent approaches to the real and the virtual corrections. The novel features include the contribution of pentagon diagrams in the virtual corrections, which form a gauge-invariant set when combined with their box diagram partners. They may contribute to certain distributions at the percent level. Also the real emission was complemented with two-photon final state emission contributions not included in the generator PHOKHARA7.0. We demonstrate that the numerical influence reaches, for realistic charge-averaged experimental setups, not more than 0.1% at KLOE and 0.3% at BaBar energies. As a result, we exclude the approximations in earlier versions of PHOKHARA as origin of the observed experimental discrepancy.

Collider signatures of Goldstone bosons

Recently Weinberg suggested that Goldstone bosons arising from the spontaneous breakdown of some global hidden symmetries can interact weakly in the early Universe and account for a fraction of the effective number of neutrino species N_eff, which has been reported persistently 1 \sigma away from its expected value of three. In this work, we study in some details a number of experimental constraints on this interesting idea based on the simplest possibility of a global U(1), as studied by Weinberg. We work out the decay branching ratios of the associated light scalar field $\sigma$ and suggest a possible collider signature at the Large Hadron Collider (LHC). In some corners of the parameter space, the scalar field \sigma can decay into a pair of pions with a branching ratio of order O(1)% while the rest is mostly a pair of Goldstone bosons. The collider signature would be gluon fusion into the standard model Higgs boson gg -> H or associated production with a W gauge boson q q'-bar -> H W, followed by H -> \sigma \sigma -> (\pi\pi) (\alpha\alpha), where \alpha is the Goldstone boson.

DETECTING CORRELATED DI-HADRON PAIRS: ABOUT THE EXTRACTION OF TRANSVERSITY AND BEYOND

We summarize the latest achievements about the extraction of the transversity parton distribution based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Recently released data for proton and deuteron targets by HERMES and COMPASS allow for a flavor separation of the valence components of transversity. This extraction relies on di-hadron fragmentation functions. The latter have been taken from the first recent analysis of the semi-inclusive production of two pion pairs in back-to-back jets in e+e- annihilation. We also comment on the possibility of isolating new azimuthally asymmetric correlations of opposite pion pairs, which could arise when a fragmenting quark crosses parity-odd domains localized in Minkowski space-time and induced by the topologically nontrivial QCD background (the so-called θ vacuum).

FRAGMENTATION FUNCTIONS AT BABAR

Inclusive hadron production cross section in e+e- annihilation shed light on fundamental questions of hadronization and fragmentation processes. We present measurements of inclusive spectra of charged pions, kaons, and protons (antiprotons) produced in e+e- collisions at the center-of-mass energy of 10.54 GeV, and tests of QCD predictions and hadronization models. We also report the results on the measurement of the azimuthal modulation induced by the Collins effect in inclusive production of charged pion pairs e+e- → ππX, where the two pions are produced in opposite hemispheres. These data allows the determination of the polarized Collins fragmentation functions.

Exclusive electromagnetic production of pion pairs in lead-lead collisions at LHC

The cross section for π+ π− and π 0 π 0 meson pairs production in peripheral ultrarelativistic heavy-ion collisions is calculated in the impact parameter space equivalent photon approximation. The cross section is calculated at the energy available at the CERN Large Hadron Collider, √s NN = 3.5 TeV. For the first time the world data for γ γ → ππ are described, both for the total cross section and for the angular distribution. This is obtained simultaneously for γ γ → π+ π− and γ γ → π 0 π 0 at all experimentally available energies.

QUASIFREE PHOTOPRODUCTION OF PION-PAIRS OF PROTONS AND NEUTRONS

Beam-helicity asymmetries and mass-differential cross sections have been measured at the MAMI accelerator in Mainz for the photoproduction of neutral and mixed-charge pion pairs in the reactions γp → nπ0π+ and γp → pπ0π0 off free protons and γd → (p)pπ0π-, γd → (n)pπ0π0 and γd → (n)nπ0π+, γd → (p)nπ0π0 off quasi-free nucleons bound in the deuteron for incident photon energies up to 1.4 GeV. Circularly polarized photons were produced in bremsstrahlung processes of longitudinally polarized electrons and tagged with the Glasgow-Mainz magnetic spectrometer. The decay products (photons, protons neutrons and charged pions) were detected in the 4π electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. Using a full kinematic reconstruction of the final state, excellent agreement was found between the results for free and quasi-free protons, indicate that the quasi-free neutron results are also a close approximation of the free-neutron results. Comparison of the results to predictions of model calculations portend that especially the reaction mechanisms in the production of the mixed-charge final states are still not well understood, in particular at low incident photon energies in the second nucleon resonance region.

Measurement of thepn→ppπ0π−reaction in search for the recently observed resonance structure indπ0π0anddπ+π−systems

Exclusive measurements of the quasi-free $pn \to pp\pi^0\pi^-$ reaction have been performed by means of $pd$ collisions at $T_p$ = 1.2 GeV using the WASA detector setup at COSY. Total and differential cross sections have been obtained covering the energy region $\sqrt s$ = (2.35 - 2.46) GeV, which includes the region of the ABC effect and its associated resonance structure. No ABC effect, {\it i.e.} low-mass enhancement is found in the $\pi^0\pi^-$-invariant mass spectrum -- in agreement with the constraint from Bose statistics that the isovector pion pair can not be in relative s-wave. At the upper end of the covered energy region $t$-channel processes for Roper, $\Delta(1600)$ and $\Delta\Delta$ excitations provide a reasonable description of the data, but at low energies the measured cross sections are much larger than predicted by such processes. Adding a resonance amplitude for the resonance at $m$=~2.37 GeV with $\Gamma$ =~70 MeV and $I(J^P)=~0(3^+)$ observed recently in $pn \to d\pi^0\pi^0$ and $pn \to d\pi^+\pi^-$ reactions leads to an agreement with the data also at low energies.

On Bose–Einstein correlations in AA collisions versus energy, transverse mass and momentum

The dependence of the Rlong dimension, obtained from the ππ Bose–Einstein correlations (BEC) in heavy ion collisions, on the average transverse momentum kT of the pion pair and on its corresponding transverse mass mT is found to be well described within the framework of the Heisenberg uncertainty relations. The rise of Rlong with the center of mass energy is independent of the atomic number of the colliding heavy ion pair and the selected kT range. The nuclear kinematic viscosity ν and its related shear viscosity η, associated with the time delay between the Pb–Pb collision and the outgoing hadrons, are estimated from the BEC at low center of mass energies to be ν ≃ (4.23 ± 1.70) × 1023 fm2 s−1 and η ≃ (0.007 ± 0.003) GeV3.

U-spin breaking in CP asymmetries in B decays

U-spin symmetry predicts equal CP rate asymmetries with opposite signs in pairs of ΔS=0 and ΔS=1B meson decays in which initial and final states are related by U-spin reflection. Of particular interest are six decay modes to final states with pairs of charged pions or kaons, including Bs→π+K− and Bs→K+K− for which asymmetries have been reported recently by the LHCb collaboration. After reviewing the current status of these predictions, highlighted by the precision of a relation between asymmetries in Bs→π+K− and B0→K+π−, we perform a perturbative study of U-spin breaking corrections, searching for relations among asymmetries which hold to first order. No such relation is found in these six decays, in two-body decays involving a neutral kaon, and in three-body B+ decays to charged pions and kaons.

Finite size of hadrons and Bose–Einstein correlations

It is observed that the finite size of hadrons produced in high energy collisions implies that their positions are correlated, since the probability to find two hadrons on top of each other is highly reduced. It is then shown that this effect can naturally explain the values of the correlation function below one, observed at LEP and LHC for pairs of identical pions.

Unified dispersive approach to real and virtual photon-photon scattering at low energy

Previous representations of pion pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitariy, chiral symmetry and soft photon constraints are generalized to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the $\pi\pi$ phase-shifts, on pion form factors and on pion polarizabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalized polarizabilies, to vector meson radiative decays, and to the $\sigma\gamma$ electromagnetic form factor. Finally, and evaluation of the contribution of $\gamma\pi\pi$ states in the hadronic vacuum polarization to the muon $g-2$ is given, which should be less model dependent than previous estimates.

The History of Cosmic Ray Studies after Hess

The discovery of cosmic rays by Victor Hess was confirmed with balloon flights at higher altitudes by Kolhörster. Soon the interest turned into questions about the nature of cosmic rays: gamma rays or particles? Subsequent investigations have established cosmic rays as the birthplace of elementary particle physics. The 1936 Nobel prize was shared between Victor Hess and Carl Anderson. Anderson discovered the positron in a cloud chamber. The positron was predicted by Dirac several years earlier. Many new results came now from studies with cloud chambers and nuclear emulsions. Anderson and Neddermeyer saw the muon, which for some time was considered to be a candidate for the Yukawa particle responsible for nuclear binding. Lattes, Powell, Occhialini and Muirhead clarified the situation by the discovery of the charged pions in cosmic rays. Rochester and Butler found Vʼs, which turned out to be short-lived neutral kaons decaying into a pair of charged pions. Λʼs, Σʼs and Ξʼs were found in cosmic rays using nuclear emulsions. After that period, accelerators and storage rings took over. The unexpected renaissance of cosmic rays started with the search for solar neutrinos and the observation of the supernova 1987A and other accelerators in the sky. With the observation of neutrino oscillations one began to look beyond the standard model of elementary particles. After 100 years of cosmic ray research we are again at the beginning of a new era, and cosmic rays may contribute to solve the many open questions, like dark matter and dark energy, by providing energies well beyond those of earth-bound accelerators.

Measurement of the beam-helicity asymmetry [formula omitted] in the photoproduction of [formula omitted]-pairs off the proton and off the neutron

Beam-helicity asymmetries have been measured at the MAMI accelerator in Mainz for the photoproduction of neutral pion pairs in the reactions γ→p→pπ0π0 and γ→d→(n)pπ0π0, γ→d→(p)nπ0π0 off free protons and off quasi-free nucleons bound in the deuteron for incident photon energies up to 1.4 GeV. Circularly polarized photons were produced from bremsstrahlung of longitudinally polarized electrons and tagged with the Glasgow magnetic spectrometer. Decay photons from the π0 mesons, recoil protons, and recoil neutrons were detected in the 4π covering electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. After kinematic reconstruction of the final state, excellent agreement was found between the results for free and quasi-free protons. This demonstrates that the free-nucleon behavior of such observables can be extracted from measurements with quasi-free nucleons, which is the only possibility for the neutron. Contrary to expectations, the measured asymmetries are very similar for reactions off protons and neutrons. The results are compared to the predictions from the Two-Pion MAID reaction model and (for the proton) also to the Bonn–Gatchina coupled channel analysis.

Search for di-muon decays of a low-mass Higgs boson in radiative decays of theΥ(1S)

We search for di-muon decays of a low-mass Higgs boson (A0) produced in radiative Υ(1S) decays. The Υ(1S) sample is selected by tagging the pion pair in the Υ(2S,3S)→π+π−Υ(1S) transitions, using a data sample of 92.8×106 Υ(2S) and 116.8×106 Υ(3S) events collected by the BABAR detector. We find no evidence for A0 production and set 90% confidence level upper limits on the product branching fraction B(Υ(1S)→γA0)×B(A0→μ+μ−) in the range of (0.28−9.7)×10−6 for 0.212≤mA0≤9.20 GeV/c2. The results are combined with our previous measurements of Υ(2S,3S)→γA0, A0→μ+μ− to set limits on the effective coupling of the b quark to the A0.Received 2 October 2012Corrected 21 February 2013DOI:https://doi.org/10.1103/PhysRevD.87.031102© 2013 American Physical Society

Energy dependence of theρresonance inππelastic scattering from lattice QCD

We determine the energy-dependent amplitude for elastic $\ensuremath{\pi}\ensuremath{\pi}$ $P$-wave scattering in isospin-1 by computing part of the discrete energy spectrum of QCD in finite cubic boxes. We observe a rapidly rising phase shift that can be well described by a single $\ensuremath{\rho}$ resonance. The spectrum is obtained from hadron correlators computed using lattice QCD with light quark masses corresponding to ${m}_{\ensuremath{\pi}}\ensuremath{\sim}400\text{ }\text{ }\mathrm{MeV}$. Variational analyses are performed with large bases of hadron interpolating fields including, as well as fermion bilinears that resemble $q\overline{q}$ constructions, also operators that resemble pairs of pions with definite relative and total momentum. We compute the spectrum for a range of center-of-mass momenta and in various irreducible representations of the relevant symmetry group. Hence we determine more than 30 values of the isospin-1 $P$-wave scattering phase shift in the elastic region, mapping out its energy dependence in unprecedented detail.

Early developments: Particle physics aspects of cosmic rays

Cosmic rays is the birthplace of elementary particle physics. The 1936 Nobel prize was shared between Victor Hess and Carl Anderson. Anderson discovered the positron in a cloud chamber. The positron was predicted by Dirac several years earlier. In subsequent cloud chamber investigations Anderson and Neddermeyer saw the muon, which for some time was considered to be a candidate for the Yukawa particle responsible for nuclear binding. Measurements with nuclear emulsions by Lattes, Powell, Occhialini and Muirhead clarified the situation by the discovery of the charged pions in cosmic rays. The cloud chamber continued to be a powerful instrument in cosmic ray studies. Rochester and Butler found V’s, which turned out to be shortlived neutral kaons decaying into a pair of charged pions. Also Λ’s, Σ’s, and Ξ’s were found in cosmic rays. But after that accelerators and storage rings took over. The unexpected renaissance of cosmic rays started with the search for solar neutrinos and the observation of the supernova 1987A. Cosmic ray neutrino results were best explained by the assumption of neutrino oscillations opening a view beyond the standard model of elementary particles. After 100years of cosmic ray research we are again at the beginning of a new era, and cosmic rays may contribute to solve the many open questions, like dark matter and dark energy, by providing energies well beyond those of accelerators.

τ− → π−π0ντ decay in the extended NJL model

The width of the decay $\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $\rho$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $\rho$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.

Search for Long-Lived Particles and Lepton-Jets with the ATLAS detector

Many extensions of the Standard Model include neutral weakly-coupled particles that can be long- lived. These long-lived particles occur in many models, included gauge-mediated extensions of the Minimal Supersymmetric Model (MSSM), MSSM with R-parity violation, inelastic dark matter and the Hidden Valley scenario. Results are presented on the ATLAS searches at the LHC for possible rare Higgs boson decays to pair of neutral, long-lived hidden-sector particles that lead to final states containing collimated lepton jets or fermion anti-fermion pairs. No excess of events above the expected background has been observed on data collected in 2011 at a center of mass energy of 7 TeV and limits on the cross sections are set. of the leptons increases with d mass, but decreases with d. In this model, d = 0.0, 0.1, and 0.3, and d masses (m ) of 150, 300, and 500 MeV are used. For m = 150 MeV, the d is below the + threshold and can only de- cay to electrons. With m 300 MeV, the d decays to electron and muon pairs. Additionally, for m = 500 MeV, 20% of the decays produce pion pairs. This analysis con- siders LJs in three signatures: single muon-jets with four or more muons, pairs of muon-jets each with two or more muons, and pairs of electron-jets each with two or more electrons. Events containing electron-jets (EJs) were selected using single-electron triggers with an online pT threshold of 20 or 22 GeV. To ensure proper modelling of the trigger ac- ceptance, events were required to contain at least one re- constructed electron with pT > 35 GeV, above which the trigger e ciency is constant. The reconstructed electron was required to match an electron reconstructed above the pT threshold in the trigger system with a separation R less than 0.2. The EJ candidates were built from elec- tromagnetic (EM) clusters. At least two tracks from the primary vertex (PV) with pT > 10 GeV were required to have R < 0.1 of the cluster position in the second sam- pling layer of the calorimeter. Additional requirements were made on the number of hits along the track in the silicon pixel and microstrip detectors to suppress back- grounds from photon conversions. The analysis required two LJ candidates in each event, with one cluster match- ing the electron reconstructed in the trigger system. The invariant mass of the two highest-pT tracks associated with each EJ had to be less than 2 GeV. To reduce the back- ground coming from multi-jet events, the electron cluster concentration (R 2), defined as the ratio of total energy in 3 7 cells to the total energy in 7 7 cells in , in the second sampling layer of the EM calorimeter (ECAL) was used, together with the electron cluster lateral shower width and number of TRT high threshold hits. A scaled

RevisitingD0−D¯0mixing using U-spin

We prove that ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$ mixing in the standard model occurs only at second order in U-spin breaking. The U-spin subgroup of SU(3) is found to be a powerful tool for analyzing the cancellation of intermediate-state contributions to the ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$ mixing parameter $y=\ensuremath{\Delta}\ensuremath{\Gamma}/(2\ensuremath{\Gamma})$. Cancellations due to states within a single U-spin triplet are shown to be valid to first order in U-spin breaking. Illustrations are given for triplets consisting of (a) pairs of charged pions and kaons; (b) pairs of neutral pseudoscalar members of the meson octet; (c) charged vector-pseudoscalar pairs, and (d) states of four charged kaons and pions.