Elastic Neutrino-Nucleon Scattering

1. Elastic Neutrino-Nucleon Scattering Argonne, July 2002 C. J. Horowitz

2. Elastic Neutrino Scattering • Nothing in. • Nothing out. • Nothing happens.

3. Neutrino Elastic Scattering • Supernovae • Introduction • Opacity dominated by -n elastic • Detection via -p and -A elastic • Strange quark content of nucleon • Parity violating electron scattering • Contributions to nucleon spin • Past -p elastic measurements • Future exp: controlling systematics

4. Core collapse supernova >8M Star Envelope n July 5, 1054 Shock Crab nebula Hot bubble Proto-neutron star: hot, e rich

5. Opacity Dominated by -n Elastic • Energy transport mostly by x (´ , ) because twice as many as e and x without charged currents, have longer mean free path. • Opacity of x mostly from -n elastic. • Incorrect elastic cross sec caused Oak Ridge simulation to explode when it did not with correct one. • Uncertainty in -n cross sec from strange quarks very relevant for SN simulations.

6. Detecting Supernova  • Important to measure total energy radiated in neutrinos. This is binding E of proto-neutron star ~3/5 GM2/R. • Astrophysicists very interested in mass of proto-neutron star. Compactness, M/R, important for SN mechanism,  driven wind and nucleosynthesis. • Benchmark for  osc. measurements. • Most E in x because twice as many as e.

7. Need to Measure x • 20 anti-e detected from SN1987A via anti- + p ! n + e+. • To measure energy of x need two-body final states: -e, -p or -A elastic. • x-e has small cross sec, swamped by background from e-e. • -p elastic may be possible in Kamland [J. Beacom]. • -A has very large cross section.

8. Underground Laboratory • Underground lab. will facilitate low background, low threshold, large mass experiments. • Detecting low energy solar n, dark matter, and supernovae via n-A elastic scattering are complimentary. • Backgrounds for SN ¿ solar  or dark matter [Events in known ~10 sec. interval with ~ half in first sec.]

9. CLEAN (D. McKinsey) • Liquid Ne scintillator (¼ 100 tons) for low energy solar  via -e scattering. • Liquid is self cleaning of radioactive impurities for low backgrounds and thresholds. • Coherent x-Ne cross sec gives yields up to 4 events / ton for SN at 10 kpc (¸ 20 times anti-e+p in H2O). • Should yield large very clean x signal.

10. Recoil Spectrum

11. Strange quark content of nucleon • Three form factors • F1s, F2s, Gas • Low Q limits: • F1s(0)=0, dF1s/dQ2  strangeness radius s, • F1s=(s+s) Q2/4M2 for small Q2 • F2s(0)=s strange magnetic moment, • Gas(0)=s, fraction of nucleon spin carried by s

12. Assume good isospin • Assume strange quarks in proton same as in neutron: s is isoscalar. • Three observables: E+M form factor of proton, neutron and parity violating weak from factor of proton: allows separation of u, d, and s contribution. • Without assuming isospin, can’t separate d from s, even in principle, because they have same E+M and weak charge.

13. Parity Violating Electron Scattering • Measure asymmetry in cross section of right handed versus left handed electrons. A ¼ 1 ppm • Sensitive to interference between Z0 and  exchange. • Forward angles: F1s, back angles F2s • Little sensitivity to Gas because of small vec. weak coupling of electron (and radiative corrections). PV can’t get s!

14. Radiative Corrections • Lowest order matrix elem. Squared • Radiative correction e  Z0 p   Some PV

15. Radiative Corrections • Parity violation admixture in either initial or final wave function. Nucleon need not have good parity. • Parity violating coupling of photon to nucleon (anapole moment).  Example: photon couples to pion loop which has parity violating weak coupling to nucleon 

16. Sample Results • PV on H and D give both radiative corrections and s. • GMs (or s) consistent with zero put large errors. • Radiative corrections much larger then expected.

17. HAPPEX • Forward angle exp. at Jefferson Lab Hall A, Q2=0.5 Gev2. • Errors: stat., syst. and E+M form factors • SAMPLE:

18. Other PV Experiments • G0 will measure PV from H and D at front and back angles over large Q2 range. • A4 in Germany, PV from H at intermediate angles. • HAPPEX II: PV from H at more forward angle Q2=0.1 GeV2. • Low Q24He experiment isolates F1s • Elastic PV from Pb will measure neutron radius. [Weak chage of n À p]. • Qweak PV from H at low Q2 as standard model test. Also PV e-e exp. at SLAC.

19. Bring Me the Head of a Strange Quark • Can one measure s with accuracy much better than §0.3 ? • Can one find a significantly nonzero strange quark signal with PV?? • It may be very hard to improve significantly on the systematic errors of SAMPLE and G0.

20. Neutrino-Nucleon Elastic Scattering • Measure both s and s • Radiative corrections small. • Past experiments (BNL, LSND) • Present (BOONE) • Future ratio experiments very promising.

21. BNL Exp. With 170 ton detector in wide band beam (1986)

22. BNL cross sections Energy of recoil gives Q2, this + angle gives E

23. s=-1.26

24. CJH+S. Pollock, PRC48(’93)3078 Rel. Mean Field Calculations compared to BNL data. s or  strongly correlated with MA.

25. Sensitivity to Parameters

26. E=150 MeV

27. Ratio of p/n sensitive to s

28. Garvey, Kolbe, Langanke and Krewald • Continuum RPA calculation averaged over LSND’s decay in flight  beam. • Ratio very sensitive to s, some sensitivity to s.

29. Low E Sensitivity to Parameters

30. LSND had background problems Rex Tayloe

31. Mini Boone • In <E>¼ 800 MeV beamline. • Large tank of mineral oil (Both Cerenkov and scint. Light). • Will try and measure ratio of neutral to charged current. • However lack of segmentation will limit precision.

32. A Future -p Elastic Experiment • Physics goals are compelling: • Gas(Q2) and s. • F2s or s independent of PV radiative correcections. • Very attractive  fluxes at beam lines for long baseline -osc. experiments (NUMI, BOONE, KeK…)

33. Need to control systematic errors! • Beam flux and spectrum (measure a ratio) • Theory errors from: • MA (lower Q2, measure MA, look at a ratio), • s (lower Q2, also measure with anti-). • Detector efficiencies, backgrounds. • Inelastic contributions: Pions! (good particle id, segmented detector, lower beam energy) • Nuclear structure (Q2¸ 0.5 Gev2) • Two-body contributions to rxn. Mechanism.

34. Possible ratio measurements • Ratio of ejected neutrons to protons • Very sensitive to s. • Insensitive to beam flux. • Insensitive to “isoscalar” distortions. • Worry about neutron detection efficiency and two-body corrections to reaction mechanism. • At high Q2, neutron detection hard.

35. Ratio of Neutral to Charged Currents • Ratio of protons from:  + p ! + p to protons from:  + n !- + p. • Note, both are quasielastic scattering from an N=Z nucleus such as 12C. • Very simple observable: ratio of protons of a given E without muons to those with muons.  p p

36. Example: E=0.8 GeV, Q2=0.5 • R ¼ 0.14 • Assume Gas=s/(1+Q2/MA2)2 • Error in extracted s • 5% measurement of R 0.04 • §0.03 GeV uncer. in MA 0.01 • §0.3 uncer. in s 0.07 • §2 uncer. in s 0.002 • 5% ratio sensitive to s at §0.04 • Determine one combination of s and s from  and another from anti-.

37. Experimental Considerations • Many systematics, such as absolute flux, cancel in ratio. • Need to know spectrum but ratio only weakly depends on E. • Need to identify pions to separate elastic from inelastic events. [This may require a segmented detector.] • Want large acceptance for muons.

38. Ratio of Nucleon to Nucleus Elasitc • Consider a CH2 target. • -C elastic cross section is large and accurately known. Makes very good beam monitor. • Measure ratio of -p to -C elastic events. • Need to see low energy C recoils.

39. Measurement of Axial Form Factor • Needed to control systematic errors for extraction of s. • Accurate determination of MA possible with charged current quasielastic events. • Search for non dipole behavior? Look at large Q2 range: 0.5-2+GeV2. How to control systematic errors??

40. A Future -p Elastic Experiment • Physics goals are compelling: • Gas(Q2) and s. • F2s independent of PV radiative correc. • Ga(Q2) and Axial mass MA. • Very attractive  fluxes at beam lines for long baseline -oscillation exp. • Measuring ratio of neutral to charged currents is simple and controls many systematic errors.