The pion-nucleon scattering lengths from pionic deuterium

We use the framework of effective field theories to discuss the determination of the S-wave scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length is extracted from the data. Next, is related to the S-wave scattering lengths a ₊ and a _-. We discuss the use of this information for constraining the values of these scattering lengths in the full analysis, which also includes the input from the pionic hydrogen energy shift and width measurements, and thoroughly investigate the accuracy limits for this procedure. In this paper, we also give a detailed comparison to other effective field theory approaches, as well as to the earlier work on the subject, carried out within the potential model and multiple scattering framework. Received: 28 January 2005, Published online: 8 April 2005 PACS: 36.10.Gv, 12.39.Fe, 13.75.Cs, 13.75.Gx A. Rusetsky: On leave of absence from High Energy Physics Institute, Tbilisi State University, University St. 9, 380086 Tbilisi, Georgia. This research is part of the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078. Work supported in part by DFG (SFB/TR 16, “Subnuclear Structure of Matter”). An erratum to this article is available at .     

Electromagnetic corrections to deep inelastic scattering at HERA

The dominant electromagnetic radiative corrections to neutral current deep inelastic scattering at HERA energies have been calculated analytically in collinear approximation for unpolarized beams. The results may be used for the construction of an event generator and are applied to discuss the influence of cuts on the magnitude of the correction. For final state collinear photon emission the measurement of the resulting electromagnetic jet (electron plus collinear photon) reducesx-andy-dependence of the correction factor. Electromagnetic corrections to charged current interactions are discussed in leading logarithmic approximation.     

Comments on the calculation of the pion-nucleon coupling constant and s-wave scattering lengths

It is pointed out that Coulomb barrier effects above 300 MeV may have a significant effect on the calculation of f² and a₁ ? a₃ for pion-nucleon scattering. It is argued that Bugg et al. have overestimated the value of f². Uncertainties in their calculations, which cannot be included in the statistical error, are listed and discussed.     

Spectroscopic determination of the s-wave scattering lengths of 86Sr and 88Sr

We report the use of photoassociative spectroscopy to determine the ground-state s-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr and 88Sr. Photoassociative transitions are driven with a laser red detuned by up to 1400 GHz from the 1S0-1P1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr at -494 +/- 5 GHz allows us to determine the scattering lengths 610a0 < a86 < 2300a0 for 86Sr and a much smaller value of -1a0 < a88 < 13a0 for 88Sr.     

Electromagnetic radiative corrections in parity-violating electron-proton scattering

QED radiative corrections have been calculated for leptonic and hadronic variables in parity-violating elastic ep scattering. For the first time, the calculation of the asymmetry in the elastic radiative tail is performed without the peaking-approximation assumption in hadronic variables configuration. This method has been validated in a comparison with the PVA4 data. It has been also used to evaluate the radiative corrections to the parity-violating asymmetry measured in the G⁰ experiment. The results obtained are here presented.     

The S-wave pion–nucleon scattering lengths from pionic atoms using effective field theory

The pion–deuteron scattering length is computed to next-to-next-to-leading order in baryon chiral perturbation theory. A modified power-counting is then formulated which properly accounts for infrared enhancements engendered by the large size of the deuteron, as compared to the pion Compton wavelength. We use the precise experimental value of the real part of the pion–deuteron scattering length determined from the decay of pionic deuterium, together with constraints on pion–nucleon scattering lengths from the decay of pionic hydrogen, to extract the isovector and isoscalar S-wave pion–nucleon scattering lengths, a⁻ and a⁺, respectively. We find a⁻=[0.0936(±0.0011)]M_π⁻¹ and a⁺=[−0.0029(±0.0009)]M_π⁻¹.     

Kinetic energy distributions in pionic hydrogen

A framework for analyzing the Doppler broadening of the X-ray lines in pionic hydrogen is proposed. It is shown that the kinetic energy distributions at the instant of the (n = 2-4) radiative transitions are related to each other. In order to establish the connection, the collisional processes for pionic hydrogen scattering from hydrogen atoms and molecules have been calculated in different models. The proposed method can be used to determine reliably the strong interaction width of the ground state of pionic hydrogen from the X-ray line profiles measured recently at the Paul-Scherrer-Institut.Received: 6 August 2004, Published online: 28 September 2004PACS: 34.50.-s Scattering of atoms and molecules - 36.10.Gv Mesonic atoms and molecules, hyperonic atoms and molecules     

Radiative corrections to the Bhabha scattering

In this review we consider the high energy processes in QED frames in peripherical kinematics. The key feature of this kinematics is that processes have a large cross section which do not decrease with the increasing of the initial center of mass energy. Two purposes to study peripheral processes are: the background processes with large total cross sections and the structure of jets in the fragmentation region.     

Ground-state energy of pionic hydrogen to one loop

We investigate the ground-state energy of the atom (pionic hydrogen) in the framework of QCD + QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at next-to-leading order in the low-energy expansion in the framework of the relevant effective field theory. The result provides a relation between the strong energy shift and the pion-nucleon S-wave scattering lengths - evaluated in pure QCD - at next-to-leading order in isospin-breaking and in the low-energy expansion. We compare our result with available model calculations. Received: 11 June 2002 / Published online: 9 October 2002     

Two-loop corrections to Bhabha scattering

The two-loop radiative photonic corrections to Bhabha scattering are computed in the leading order of the small electron mass expansion up to the nonlogarithmic term. After including the soft photon bremsstrahlung, we obtain the infrared-finite result for the differential cross section, which can directly be applied to a precise luminosity determination of the present and future e+ e- colliders.     

Determination of the s-wave scattering length of chromium

We have measured the deca-triplet s-wave scattering length of the bosonic chromium isotopes 52Cr and 50Cr. From the time constants for cross-dimensional thermalization in ultracold atomic samples, we have determined the magnitudes |a(52Cr)|=(170+/-39)a(0) and |a(50Cr)|=(40+/-15)a(0), where a(0)=0.053 nm. By measuring the rethermalization rate of 52Cr over a wide temperature range and comparing the temperature dependence with the effective-range theory and numerical single-channel calculations, we have obtained strong evidence that the sign of a(52Cr) is positive. Rescaling our 52Cr model potential to 50Cr strongly suggests that a(50Cr) is positive also.     

Corrections to Weinberg's pion-pion scattering lengths

We derive twice subtracted dispersion sum rules for theππ scattering lengths. The subtraction constants are the Weinberg values, and the dispersion integrals yield small corrections in good agreement with other authors.     

Inner Coulomb corrections to pion-nucleus scattering

A semiclassical model for inner Coulomb corrections to pion-nucleus scattering in the Δ-resonance region is suggested. Its main consequence is a change of the nuclear radius R, giving $\text{R(π}{}^{\mathrm{?}}\text{)}\text{R(π}{}^{\mathrm{+}}\text{)}\text{= 1+2Z}\text{αE}\text{k}{}^2\text{R}$. The Glauber model can be extended to include these effects.     

Radiative corrections to high-energy neutrino scattering

Motivated by precise neutrino experiments, we reconsider the electromagnetic radiative corrections to the data. We investigate the usefulness and demonstrate the simplicity of the “leading log” approximation: the calculation to order α ln (Q/μ), α ln (Q/m_q). Here Q is an energy scale of the overall process, μ is the lepton mass and m_q is a hadronic mass, the effective quark mass in a parton model. We identify those questions the answers to which do not depend on unknown hadron parameters like quark masses. The leading log radiative corrections to dδ/dy distributions and to suitably interpreted dδ/dx distributions are quark-mass independent. We improve upon the conventional leading log approximation and compute explicitly the largest terms that lie beyond the leading log level. In practice this means that our model-independent formulae, though approximate, are likely to be excellent estimates everywhere except at low energy or very large y. We point out that radiative corrections to measurements of deviations from the Callan-Gross relation and to measurements of the “sea” constituency of nucleons are gigantic. The QCD inspired study of deviations from scaling is of particular interest. We compute, beyond the leading log level, the radiative corrections to the QCD predictions.     

Radiative corrections to pion nucleus scattering

The radiative corrections to elastic pion-nucleus scattering are evaluated for kinematical conditions pertaining to the pion spectrometer facilities at the newer meson factories, and are found to be experimentally relevant. A reasonably simple, experimentally useful approximation to the exact expression for the radiative correction is given.