Probing Chiral Dynamics with photons Henry R. Weller Duke - - PowerPoint PPT Presentation

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Probing Chiral Dynamics with photons

Henry R. Weller

Duke University and Triangle Universities Nuclear Laboratory

HIγS PROGRAM

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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, mq=0.

EXAMPLES:

1. PrimEx at JLAB—a precision measurement of the π0 lifetime. 2. Pion-electroproduction from the proton near threshold at Mainz and JLAB. ChPT at finite Q2. 3. N/Δ Physics at Mainz: the pion-cloud to quark-parton transition. 4. Compton scattering from the deuteron at LUND—neutron polarizabilities. 5. Precision measurements of the polarizabilities of the proton at HIγS. Obtain ~5% measurements of αp and βp. 6. Double-polarization measurements at LEGS using the HD target.

• 7. Spin-polarizability measurements for both p and n at HIγS using polarized p, d and 3He targets.

Test ChPT and Lattice QCD results . 8. Pion-threshold measurements at HIγS using polarized beam and target.

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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 HIγS Facility Bernstein, Ahmed, Stave, Wu and Weller

• Ann. Rev. Nucl. Part. Sci. 2009

(to be published)

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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.

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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 = e2/4π = 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 (g2/4π) ~ 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.

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Exceptions 1. At very high energies when momentum transfer is large, g(q2) 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 << ΛQCD. 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.

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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, LQCD 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.

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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 LQCD 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 π0,+,-, K0, +, -, K0

bar

and η.

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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.

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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

• f electron pairs.

A coefficient shows up which changes sign for T>Tc vs T<Tc. Effective potential displays a double well for T<Tc 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.

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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 Leff for (e-e-) Leff for (qqbar) Lattice degrees of Gluon degrees of freedom freedom are gone are gone

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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 Λx~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.

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γpπ0p

The real part of the s-wave electric dipole amplitude for the γpπ0p 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 HIγS, where each point is the result of running for 100

• hours. More on this later.

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Simulations

A full Monte Carlo simulation was performed using Geant4, based on the predictions of ChPT. The π0s were detected using the CBx assembly. Beam on target was assumed to be 107 γ/s, and the polarized target thickness was 3.5 x 1023 p/cm2. 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).

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The cross section measurements provide three coefficients: σ(θ) = A + B cosθ + C cos2θ A, B, and C can be written in terms of the four contributing amplitudes near threshold: E0+, P1, P2, and P3. Where P1 = 3E1+ + M1+ - M1-, P2 = 3E1+ - M1+ + M1- , and P3 = 2M1+ + M1- . A fourth relationship is needed to solve these without invoking a model. Mainz has measured the photon asymmetry using a linearly polarized γ beam:

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Success of ChPT at pion-threshold Linearly Polarized Photon asymmetry for the γpπ0p reaction at an average energy of 159.5 MeV MAINZ 2001

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A measurement of the imaginary part of the s-wave production amplitude (E0

+) provides a determination of the charge exchange

scattering length acex(π+nπ0p). Requires measurement of the polarized target analyzing power T(θ).

T(θ)/σ(θ) = Im[E0+(P3 – P2) sin(θ)2 Im(E0+)

Motivation Isospin Symmetry Breaking

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Unitary cusp

The ratio of the electric dipole amps for neutral and charged pion channels is ~ -20 (Kroll-Ruderman LET plus Mainz data). E0+(γpπ+n) ~ -20 E0+(γpπ0p) So the two-step reaction γpπ+n π0p is as strong as the direct path. Gives rise to a significant unitary cusp. The 3-channel S-matrix (γp, π0p, π+n) + Unitarity leads to a coupled channel result for the E0+(γpπ0p) amplitude expressed in terms of the “cusp parameter” β:

β = Re[E0+ (γp -> π+n)] acex (π+n -> π0p)

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Calculation of β from Unitarity

First we assume that isospin is conserved so that a(π+n π0p) = -a(π-p π0n) The observed width of the 1s state in pionic hydrogen (PSI) gives: a(π-p π0n) = -(0.122 +/- 0.002)/mπ Measurement of E0+(γpπ+n) => 28.06 +/- 0.27 +/- 0.45 This gives β = 3.43 +/- 0.08 (Unitarity) ChPT (at one loop O(q4) level gives β = 2.78. Discrepancy attributed to truncation. A measurement of β is needed.

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Our measurement will determine β to +/- 0.10, where Im[E0+(γp -> π0p)] = β pπ+/mπ and β = Re[E0+ (γp -> π+n)] acex (π+n -> π0p) Re[E0+ (γp -> π+n)] is well measured (=28.06 +/- 0.27 +/- 0.45), giving us acex (π+n -> π0p).

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Simulations

The results indicate that we can measure ImE0+ with a statistical uncertainty of 3.7% in 200 hours of actual data taking at 158 MeV. This gives us the value of acex (π+n -> π0p). Isospin conservation implies acex (π+n -> π0p) = -acex (π-p -> π0n). The latter is well known from the width of pionic hydrogen (0.1301 +/- 0.0059) after a decade of work. Our result will give a comparable accuracy for acex (π+n -> π0p).

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Four polarization observables will be measured:

For example—at 900 Σ(90) Linearly polarized beam on unpolarized target T(90) Unpolarized beam on transversely polarized target E(90) Circularly polarized beam on Longitudinally polarized target F(90) Circularly polarized beam on transversely polarized target

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P-wave amplitudes predicted for the HIγS experiment where 100 hrs of beam time is used at each energy in four different beam-target polarization

• configuration. Theory is ChPT of Bernard, Kaiser and Meissner.

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Isospin mixing due to u-d quark mass difference

Weinberg predicted a sizeable (~20%) effect of u-d quark mass difference on the value of the π0p scattering length. This quantity cannot be directly measured since π0 beams don’t exist. However, a measurement of the Analyzing power in the γpπ0p reaction using transversely polarized protons between π0 threshold (144.7 MeV) and π+ threshold (151.4 MeV) will give the imaginary part of the E0

+ amplitude.

This can be combined with the real part to give the phase. The Fermi- Watson theorem (unitarity) then gives the phase shift, which leads to the scattering length. This requires a beam of 109 γ/s. If available, a 1000 hr. experiment should determine a(π0p) with a statistical accuracy of ~10-3/mπ which should be adequate to test the 20% violation of isospin symmetry.

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Threshold pion-photoproduction from the proton @ HIγS p(γ,π0)p Co-spokesperson: Aron Bernstein

The first experiment: A measurement of the Target analyzing power at Eγ = 158 MeV.

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HIγS –A free-electron laser generated

γ-ray source

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Upgraded Facility

RF System with HOM Damping 1.2-GeV Booster Injector

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Resources at HIγS

Mirror development is the key to pion threshold Physics at HIγS.

Present mirrrors can take us up to 110 MeV. A development plan is in place for 150 nm mirrors which are needed to reach 160 MeV.

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• Extending Gamma Energy Range (4 kA Wiggler Op)
• Extending Wiggler Current 4 kA max
• Operational Concerns
• Saturated magnetic fields
• Additional power supplies
• Filter/bassbar system upgrades
• 1.2 GeV operation to reach 158 MeV with 150

nm mirrors

• 158 MeV

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Frozen Spin Polarized Deuterium Target

Butanol Polarization ~ 80 % Polarizing Field ~ 2.5 T Holding Field ~ 0.6 T—Saddle coil needed for transvers polarization (Pil Neyo-Seo e ~4 x 1023 p/cm2

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• Phase I
• Calorimetry Only
• 60 CsI Crystals
• All Phases
• Veto Scint.
• Phase II
• Tracking
• 2 BGO Layers +
• 2 Sets of MWPC
• 14 Plastic
• Scintillators

The Neutral Meson Spectrometer (NMS)

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The proposed HIγS NMS Consists of three refurbished (JLAB) arrays from the XTAL Box (LEGS) and two arrays from the LANL NMS. Mohammad will give details soon.

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Future Plans The 150 nm mirrors are under development and will be tested in the HIγS environment this year. The upgrade to 4 kA should be completed in 2010. The transverse polarized target is being built and should be operating by late 2010. All NMS parts are in house and will be assembled during 2010. Experiments should begin in 2011.

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End of Presentation

• Extra slides follow:

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190 nm mirrors have been proven to work in our environment…these will produce 110 MeV gammas. 165 nm mirrors will produce 140 MeV beams once OK-5 is

• perating at 4kA.

Schedule for FEL Cavity Mirror R&D

Date Milestone July 2006 Delivery of 1st mirror sets with coatings for 190, 180 and 165 nm May 2007 Intracavity evaluation of 1st set of 190, 180 and 165 nm mirrors

• Oct. 2007

Delivery of 2nd mirror sets with coatings for 180 and 165 nm

• Nov. 2007

Intracavity evaluation of 2nd set of 180 and 165 nm mirrors

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Recent results from Choudhury, Nogga and Phillips for elastic scattering from 3He

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Primakoff Effect

• The π0 photoproduction

from Coulomb field of the nucleus.

• Production (γγ*!π0) and

decay (π0!γγ) mechanisms imply the Primakoff cross section is proportional to the π0 lifetime.

( ) ( )

π π γγ π

θ β α σ

2 2 4 4 3 3 2

sin 8 Q F Q E m Z d d

em em P →

Γ = Ω

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π0 production on 208Pb

Events/0.04 deg

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Our measurement will determine β to +/- 0.10, where Im[E0+(γp -> π0p)] = β pπ+/mπ and β = Re[E0+ (γp -> π+n)] acex (π+n -> π0p) Re[E0+ (γp -> π+n)] is well measured (=28.06 +/- 0.27 +/- 0.45), giving us acex (π+n -> π0p). Isospin conservation implies acex (π+n -> π0p) = -acex (π-p -> π0n). The latter is well known from the width of pionic hydrogen (-0.1301 +/- 0.0059) after a decade of work. Our measurement will give a comparable accuracy for acex (π+n -> π0p).

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Recent (PRC C71, 044002 (2005)) HBChPT calculations of Choudhury and Phillips indicate appreciable sensitivity of Σx observed in Compton scattering from the deuteron to γ1n at 135 MeV. Test for consistency!

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Solid curve->αN = 12; βΝ = 3 Dashed curve->αN = 6; βN = 9

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How to disentangle the different spin polarizabilities assume the energy dependence of the dynamical polarizabilities given by dispersion relations which is in good agreement with predictions from SSE use the available experimental values for α, β, γ0 and γπ use double polarized Compton scattering and check the sensitivity to the remaining two unknown polarizabilities ( γE1E1 and γM1M1 , or equivalently, γE1M2 and γM1E2) with dispersion-relation calculation

γ0 = γE1E1 - γM1M1 - γM1E2 - γE1M2 = (-1.01 ± 0.13) ⋅10-4 fm4

GDH coll., PRL 87 (2001)

γπ = γE1E1 + γM1M1 + γM1E2 - γE1M2 = (-36.1 ± 2.2) ⋅10-4 fm4

MAMI, EPJ A10 (2001)

α + β = (13.8 ± 0.4) ⋅10-4 fm3

Baldin sum rule, EPJ A10 (2001)

α − β = (10.5 ± 0.9) ⋅10-4 fm3

MAMI, EPJ A10 (2001)

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