Probing Chiral Dynamics with photons Henry R. Weller Duke University and Triangle Universities Nuclear Laboratory HI γ S PROGRAM HUGS_4, June 2009
A wide variety of process can be used to study Chiral Dynamics , guided mainly by the results of CHPT, an expansion of the Lagrangian for low energy QCD about the chiral limit, m q =0. EXAMPLES: PrimEx at JLAB—a precision measurement of the π 0 lifetime. 1. Pion-electroproduction from the proton near threshold at Mainz and JLAB . ChPT at finite Q 2 . 2. N/ Δ Physics at Mainz : t he pion-cloud to quark-parton transition. 3. 4. Compton scattering from the deuteron at LUND—neutron polarizabilities. Precision measurements of the polarizabilities of the proton at HI γ S. 5. Obtain ~5% measurements of α p and β p . 6. Double-polarization measurements at LEGS using the HD target. 7. Spin-polarizability measurements for both p and n at HI γ S using polarized p, d and 3 He targets. Test ChPT and Lattice QCD results . Pion-threshold measurements at HI γ S using polarized beam and target. 8. HUGS_4, June 2009
References: International Workshop on Chiral Dynamics 2006 Organizers: H. Gao, B. Holstein, HRW www.tunl.duke.edu/events/cd2006/proceeding.html also Chiral Dynamics in Photopion Physics: Theory, Experiment and Future Studies at the HI γ S Facility Bernstein, Ahmed, Stave, Wu and Weller Ann. Rev. Nucl. Part. Sci. 2009 (to be published) HUGS_4, June 2009
These experiments will provide stringent tests of • The predictions of Chiral Perturbation Theory • Predictions of isospin breaking due to the mass differences of the up and down quarks. HUGS_4, June 2009
Chiral Dynamics and QCD QED– The neutral gauge bosons are photons. Neutral so photons don’t interact with photons. So only a single vertex is required: the coupling of a photon to a fermion. Coupling constant e is related to α = e 2 /4 π = 1/137. Smallness of α allows for perturbative treatment. QCD– A triplet of colour charges interact via exchange of colour gauge bosons (gluons). Coupling constant (g 2 /4 π ) ~ 1, so perturbative treatment isn’t possible. Since gauge bosons carry colour charge, in addition to fermion gluon vertex, now have 3 and 4 gluon vertices. Theory becomes highly non- linear. This has prevented a precise confrontation of experiment with rigorous QCD predictions. HUGS_4, June 2009
Exceptions 1. At very high energies when momentum transfer is large, g(q 2 ) approaches zero and can do perturbative QCD. 2. Can confront QCD with experimental tests using the symmetry of the QCD Lagrangian. Consider u,d,s quarks, whose masses are << Λ QCD . Their interactions can be analyzed by exploiting the Chiral Symmetry of the QCD Lagangian. Useful for E<<1 GeV. This low E method is called Chiral Perturbation Theory. HUGS_4, June 2009
Chiral Symmetry In the massless (high energy) limit, it can be shown that the chiral transformations which project left and right handed components of the wavefunction are identical to helicity. Also, for m=0, L QCD is invariant wrt. left and right handed rotations. This invariance is called chiral SU(3)XSU(3) symmetry. If Chiral Symmetry were realized in the conventional manner, there should exist a supermultiplet of 8 particles in the configurations demanded by SU(3), and corresponding 8 nearly degenerate opposite parity states. These don’t exist! Resolve this by postulating that the axial symmetry is spontaneously broken. HUGS_4, June 2009
Goldstone’s Theorem When a continuous symmetry is spontaneously broken, a massless boson is generated. When the axial charge acts on a single particle eigenstate one does not get an eigenstate of opposite parity in return. Instead, one generates massless bosons. So one expects that there should exist eight massles pseudoscalar states—the Goldsone bosons of QCD. NO such particles exist. But the piece of L QCD associated with quark mass explicity breaks the Chiral symmetry. So Goldstone’s theorem is violated and the bosons are not required to be massless. Their masses arise from the breaking of the symmetry. The eight Goldstone Bosons are identified as π 0,+,- , K 0, +, - , K 0 bar and η . HUGS_4, June 2009
Symmetry Breaking Explicity symmetry breaking —The symmetry violation is manifested in the LaGrangian itself. ie. a term appears which breaks the symmetry (eg. under spatial inversion). Spontaneous symmetry breaking —The LaGrangian possesses a symmetry, but this symmetry is broken by the nature of the ground (equilibrium) state of the system. Usually this arises from the history of the system as the critical velocity is approached. This determines the exact nature of the equilibrium state. HUGS_4, June 2009
Effective Field Theory Does not include all degrees of freedom of the “true” field theory. But not defective. Example—superconductivity. Free electrons + lattice of ions. Interaction of electron with lattice deforms lattice which has effect on nearby electron. Gives effective binding between electron pairs. Integrating the lattice out yields effective theory expressed in terms of electron pairs. A coefficient shows up which changes sign for T>T c vs T<T c . Effective potential displays a double well for T<T c which leads to spontaneous symmetry breaking. The ground state shifts in energy leading to Bose condensation—the electron pairs condense into the same state and superconductivity occurs. HUGS_4, June 2009
EFT in QCD Now electron pairs become quark-antiquark pairs which interact strongly with the colour gluons. The effective LaGrangian has the colour gluons integrated out, similar to the lattice in the case of superconductivity. The resulting effective LaGrangian encapsulates the relevant physics in terms of degrees of freedom which are relevant experimentally. Superconductivity QCD weakly bound strongly bound L eff for (e - e - ) L eff for (qq bar ) Lattice degrees of Gluon degrees of freedom freedom are gone are gone HUGS_4, June 2009
Chiral Perturbation Theory ChPT is a simultaneous expansion of the effective Lagrangian in powers of (external) momenta and explicit chiral symmetry breaking terms (light quark masses) where successive terms in the chiral expansion are suppressed by the inverse powers of the chiral symmetry breaking scale Λ x ~1 GeV. The small masses make the low-energy interaction weaker than a typical strong interaction, but not zero. It is important to measure the near-threshold interactions because they are an explicit effect of chiral symmetry breaking, and have been evaluated in ChPT. HUGS_4, June 2009
γ p � π 0 p The real part of the s-wave electric dipole amplitude for the γ p � π 0 p reaction has been measured at Mainz. The following figure shows their extracted results along with the predictions of ChPT and a model based on Unitarity. Good agreement. Also see projected data points for a proposed experiment at HI γ S, where each point is the result of running for 100 hours. More on this later. HUGS_4, June 2009
Simulations A full Monte Carlo simulation was performed using Geant4 , based on the predictions of ChPT. The π 0 s were detected using the CBx assembly. Beam on target was assumed to be 10 7 γ /s, and the polarized target thickness was 3.5 x 10 23 p/cm 2 . All observables were measured at all CM angles. Observables considered were σ, Σ, Τ, Ε, and F. Each was run for 100 hours at each energy (with σ constructed from the polarized data). HUGS_4, June 2009
HUGS_4, June 2009
The cross section measurements provide three coefficients: σ ( θ ) = A + B cos θ + C cos 2 θ A, B, and C can be written in terms of the four contributing amplitudes near threshold: E 0+ , P 1 , P 2 , and P 3 . Where P 1 = 3E 1+ + M 1+ - M 1- , P 2 = 3E 1+ - M 1+ + M 1- , and P 3 = 2M 1+ + M 1- . A fourth relationship is needed to solve these without invoking a model. Mainz has measured the photon asymmetry using a linearly polarized γ beam: HUGS_4, June 2009
Success of ChPT at pion-threshold Linearly Polarized Photon asymmetry for the γ p � π 0 p reaction at an average energy of 159.5 MeV MAINZ 2001 HUGS_4, June 2009
Motivation Isospin Symmetry Breaking A measurement of the imaginary part of the s-wave production + ) provides a determination of the charge exchange amplitude (E 0 scattering length a cex ( π + n � π 0 p). Requires measurement of the polarized target analyzing power T( θ ). T( θ )/ σ(θ) = Im[E 0+ (P 3 – P 2 ) sin( θ) 2 � Im(E 0+ ) HUGS_4, June 2009
Unitary cusp The ratio of the electric dipole amps for neutral and charged pion channels is ~ -20 (Kroll-Ruderman LET plus Mainz data). E 0+ ( γ p � π + n) ~ -20 E 0+ ( γ p � π 0 p) So the two-step reaction γ p � π + n � π 0 p is as strong as the direct path. Gives rise to a significant unitary cusp. The 3-channel S-matrix ( γ p, π 0 p, π + n) + Unitarity leads to a coupled channel result for the E 0+ ( γ p � π 0 p) amplitude expressed in terms of the “cusp parameter” β: β = Re[E 0+ ( γ p -> π + n)] a cex ( π + n -> π 0 p) HUGS_4, June 2009
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