Probing CP Violation with the Deuteron Electric Dipole Moment

We present an analysis of the electric dipole moment (EDM) of the deuteron as induced by CP-violating operators of dimension 4, 5 and 6 including theta QCD, the EDMs and color EDMs of quarks, four-quark interactions and the Weinberg operator. We demonstrate that the precision goal of the EDM Collaboration's proposal to search for the deuteron EDM, (1-3)\times 10^{-27} e cm, will provide an improvement in sensitivity to these sources of one-two orders of magnitude relative to the existing bounds. We consider in detail the level to which CP-odd phases can be probed within the MSSM.Comment: 5 pages, 4 figures; precision estimates clarified, to appear in Phys. Rev.

Matching functions for heavy particles

We introduce matching functions as a means of summing heavy-quark logarithms to any order. Our analysis is based on Witten's approach, where heavy quarks are decoupled one at a time in a mass-independent renormalization scheme. The outcome is a generalization of the matching conditions of Bernreuther and Wetzel: we show how to derive closed formulas for summed logarithms to any order, and present explicit expressions for leading order and next-to-leading order contributions. The decoupling of heavy quarks in theories lacking asymptotic freedom is also considered.Comment: Revised version to be published in Physical Review D; added section with application to decoupling of heavy particles in non-asymptotically free theorie

In search of the QCD-Gravity correspondence

Quantum Chromodynamics (QCD) is the fundamental theory of strong interactions. It describes the behavior of quarks and gluons which are the smallest known constituents of nuclear matter. The difficulties in solving the theory at low energies in the strongly interacting, non-perturbative regime have left unanswered many important questions in QCD, such as the nature of confinement or the mechanism of hadronization. In these lectures oriented towards the students we introduce two classes of dualities that attempt to reproduce many of the features of QCD, while making the treatment at strong coupling more tractable: (1) the AdS/CFT correspondence between a specific class of string theories and a conformal field theory and (2) an effective low-energy theory of QCD dual to classical QCD on a curved conformal gravitational background. The hope is that by applying these dualities to the evaluation of various properties of the strongly-interacting matter produced in heavy ion collisions one can understand how QCD behaves at strong coupling. We give an outline of the applications, with emphasis on two transport coefficients of QCD matter -- shear and bulk viscosities.Comment: 31 pages, 7 figures; Lectures delivered by D. Kharzeev at the International QGP Winter School, Jaipur, India, February 1-3, 200

Hadron Structure on the Lattice

A few chosen nucleon properties are described from a lattice QCD perspective: the nucleon sigma term and the scalar strangeness in the nucleon; the vector form factors in the nucleon, including the vector strangeness contribution, as well as parity breaking effects like the anapole and electric dipole moment; and finally the axial and tensor charges of the nucleon. The status of the lattice calculations is presented and their potential impact on phenomenology is discussed.Comment: 17 pages, 9 figures; proceedings of the Conclusive Symposium of the Collaborative Research Center 443 "Many-body structure of strongly interacting systems", Mainz, February 23-25, 201

Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation

The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested.Comment: 46 pages, 19 tables and 16 figures. A review article accepted for EPJ

What π−π\pi-\pi Scattering Tells Us About Chiral Perturbation Theory

We describe a rearrangement of the standard expansion of the symmetry breaking part of the QCD effective Lagrangian that includes into each order additional terms which in the standard chiral perturbation theory ($\chi$PT) are relegated to higher orders. The new expansion represents a systematic and unambiguous generalization of the standard $\chi$PT, and is more likely to converge rapidly. It provides a consistent framework for a measurement of the importance of additional ``higher order'' terms whose smallness is usually assumed but has never been checked. A method of measuring, among other quantities, the QCD parameters $\hat{m}\langle\bar{q}q\rangle$ and the quark mass ratio $m_s/\hat{m}$ is elaborated in detail. The method is illustrated using various sets of available data. Both of these parameters might be considerably smaller than their respective leading order standard $\chi$PT values. The importance of new, more accurate, experimental information on low-energy $\pi-\pi$ scattering is stressed.Comment: RevTeX 62 pages (6 figures not added, request from any author), IPNO/TH 92-106, PURD-TH-93-0

The reactions ππ→ππ\pi\pi \rightarrow \pi\pi π π → π π and γγ→ππ\gamma\gamma \rightarrow \pi\pi γ γ → π π in χ\chi χ PT with an isosinglet scalar resonance

The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $\sigma$ meson, also known as the $f_0(500)$. We augment SU(2) chiral perturbation theory ($\chi$PT) by including the $\sigma$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarr\'us and others. In this effective field theory, denoted $\chi$PT$_S$, the $\sigma$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $\mathcal{O}(p^4)$ another low-energy constant appears in the dressed $\sigma$-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $\pi\pi\rightarrow\pi\pi$ and $\gamma\gamma\rightarrow\pi\pi$ reactions to data from threshold through the energies at which the $\sigma$-meson resonance affects observables. The leading-order (LO) $\pi \pi$ amplitude reproduces the $\sigma$-meson pole position, the isoscalar $\pi \pi$ scattering lengths and $\pi \pi$ scattering and $\gamma \gamma \rightarrow \pi \pi$ data up to $\sqrt{s} \approx 0.5$ GeV. It also yields a $\gamma\gamma\rightarrow\pi\pi$ amplitude that obeys the Ward identity. The value obtained for the $\pi^0$ polarizability is, however, only slightly larger than that obtained in standard $\chi$PT.Comment: 17 pages, 7 figures. This version, which will be published in European Physical Journal A, contains clarification and more explanation of several points, as well as additional reference

The U(1)A Anomaly and QCD Phenomenology

The role of the U(1)A anomaly in QCD phenomenology is reviewed, focus- ing on the relation between quark dynamics and gluon topology. Topics covered include a generalisation of the Witten-Veneziano formula for the mass of the η′, the determina- tion of pseudoscalar meson decay constants, radiative pseudoscalar decays and the U(1)A Goldberger-Treiman relation. Sum rules are derived for the proton and photon structure functions g1p and g1γ measured in polarised deep-inelastic scattering. The first moment sum rule for g1p (the ‘proton spin’ problem) is confronted with new data from COMPASS and HERMES on the deuteron structure function and shown to be quantitatively explained in terms of topological charge screening. Proposals for experiments on semi-inclusive DIS and polarised two-photon physics at future ep and high-luminosity e+e− colliders are discussed