Magnetic Moment of a  in a Nucleus H. Tamura Tohoku University 1. Introduction 2.  -ray spectroscopy of  hypernuclei and spin-flip B(M1) 3. Experiments at J-PARC 4. Summary

1.Introduction

Motivation for   in nucleus Nuclear medium effect is not well studied for baryons. Detection of the effect is not easy.  Magnetic moment of  in a hypernucleus Hyperons are free from Pauli effect  long lifetime (~0.2 ns), stays in 0s orbit (  and  short lifetime in medium by  N->  N,  N->  ) Partial restoration of chiral symmetry -> Reduction of mass ? Partial deconfinement? ->  N changes? No theoretical calculations -- Clue to understand the origin of baryon magnetic moment Constituent quark:  B looks OK with  q = eh 2mqc2mqc m q : constituent quark mass Nucleon spin = quark spin ( ~0.2) + gluon spin + L how to understand  B ?

Other effects for   in nucleus Pauli effect between quarks (“quark exchange current”) Changes  B in nucleus Sensitive to baryon size (b) Meson exchange current Rather small for  (OPE forbidden)  mixing Large for large T hypernuclei Quark Cluster Model Takeuchi et al., N.P. A481(1988) 639  /  : 4  He(1 + ) -1% ~ -2%, larger by  mixing 4  + Li(1 + ) -40% ~ -100% b = 0.6 fm -> 0.8 fm,  becomes twice large. Saito et al., N.P. A625 (1997) 95

Spin-flip B(M1) and g  in nucleus How to measure   in nucleus? Direct measurement of    : extremely difficult. “Dream Experiment” -- Planned at GSI using relativistic HI beams B(M1) of  -spin-flip M1 transition -> g  Established for “hypernuclear shrinkage” in 7  Li from B(E2) : PRL 86 (’01)1982 Doppler Shift Attenuation Method~100% Assume “Weak coupling” between a  and core

2.  -ray spectroscopy of  hypernuclei and spin-flip B(M1)

Hypernuclear  -ray data since 1998 “Table of Hyper-Isotopes” => Information on  N spin-dependent interactions Two-body  N effective interaction  = 0.4 S  = S N = -0.4 T = 0.03 MeV

Setup for A Z (  +,K +  ) A  Z at KEK Hyperball2 (2005~)

 -ray spectrum of 7  Li (KEK E419) H. Tamura et al., PRL 84 (2000) 5963  E ~ 2 MeV (FWHM)  E ~ 3 keV (FWHM)

Tanida et al., PRL 86 (2001) 1982 Lifetime measurement by Doppler shift attenuation method (DSAM) Hypernucleus in excited state γray emission before stop B ｒ = % /2 + 3/2 + 5/2 + Weak decay Lifetime γray emission after stop t stop ~ 12 ps Same order B(E2) = 3.6 ± e 2 fm “Shrinkage by  ” was confirmed. K. Tanida et al., PRL 86 (2001) 1982

7  Li  study from 10 B(K -,  - ) at BNL(E930) 10 B (K -,  -  ) 10  B*(3 + ) -> 7  Li* + 3 He 471 keV  coincidence  coin First  coincidence for hypernuclei All the bound states determined Ukai et al., PRC 73 (2006)

10  B*(3 + ) -> 7  Li*(3/2 + ) + 3 He 10 B (K -,  - ) 10  B*, simulation First data of g  in nucleus g  = -1.1  N preliminary (statistical error only) g  (free) =  N BNL E930(’01) 10 B (K -,  -  ) 10  B*(3 + ) -> 7  Li* + 3 He First  coincidence for hypernuclei All the bound states determined 471 keV  coincidence  coin M1 Spin-flip B(M1) in 7  Li (BNL E930) indirect population Indirect population => more background, ambiguities in production

Preliminary 11  B  rays from 12 C(  +,K + ) 12  C highly excited states region ±0.7 keV p  states region 261.6±0.2 keV Unfortunately, E  is too low -> 1/  ∝ E  3, then  >> t stop -> No broadening. DSAM unusable. Another attempt: using low density target (CH 2 :polyethylene) for DSAM  spin-spin int.

3. Experiments at J-PARC

J-PARC (Japan Proton Accelerator Research Complex) Tokai, Japan World-highest beam intensity : ~1 MW x10 of BNL-AGS, x100 of KEK-PS Material and Biological Science Facility 50 GeV Synchrotron (15  A) 400 MeV Linac (350m) 3 GeV Synchrotron (333  A) Neutrino Facility Hadron Hall 60m x 56m Under commissioning

K1.8 will run from the summer, 2009 J-PARC 50 GeV facility Tokai, Japan Handron Hall Beam Dump T1 target K1.8 K1.8BR K1.1 S-type KL K0.8 C-type 30GeV primary beam (phase 1) Hyperball-J production target (T1) SKS Hyperball2 (2005~) -> Hyperball-J

Proposed B(M1) measurement (E13) To avoid ambiguities, we will use the best-known hypernucleus, 7  Li. Energies of all the bound states and B(E2) were measured.  -ray background level was measured. Cross sections are reliably calculated.  = 0.5ps, t stop = 2-3 ps for 1.5 GeV/c (K -,  - ) and Li 2 O target Calc. by Motoba (K -,  - ) at 1.5 GeV/c PRL 84 (2000) 5963 PRC 73 (2006)

Weak coupling assumption is OK? B(M1) [  N 2 ] method  He+p+n cluster model (Hiyama et al.) shell model (Motoba et al.)  +d+  cluster model (Motoba, old) shell model (Gal, old) shell model (Gal, old) The variation gives a rough magnitude of nuclear effect. Theoretical predictions without exotic effects 7  Li (3/2 + ->1/2 + )

Expected yield and sensitivity Yield estimate N K = 0.5 x 10 6 /spill Target ( 7 Li in Li 2 O) = 20cm x 2.0g/cm 3 x 14/30 x / 7 x 6.02x10 23 ∫d  /d  (1/2;1)  x BR(1/2 + ;1->3/2 + ) = 0.84  b x 0.5  (Ge) x  (tracking) = 0.7 x 0.6 => Yield (3/2 + ->1/2 + ) = 7.3 /hr(1000 spill) = 3600 / 500 hrs Background estimated from E419 7  Li spectrum Fitting result: 0.478±0.027 ps Syst. error < 5% mainly from stopping time Stat. error  /  5.4%  |g  -g c | |g  -g c | ~ 3%=>

Future possibility If a large shift of B(M1) is observed,  and T dependence should be studied from various hypernuclei Meson-exchange current,  mixing => T dependence Restration of chiral symmetry =>  dependence  (M1) ~ t stop (condition for DSAM) cannot be often satisfied.  Heavier hypernuclei -> smaller doublet spacing  -> longer  (M1) ~  (weak decay)  Another method for longer  (M1) is necessary.

Proposed method: B(M1) measurement by  -weak coincidence 900 hours, 9x10 6 K - /spill at K1.1 (50 GeV full beam) -> 5% stat. error of B(M1) 12  C case

How to measure lifetimes for hypernuclear  transitions 1 W.u. 7  Li 4H4H 11  B 12  C Spin-flip M1 7  Li 9  Be E2

4. Summary Magnetic moment of a  in hypernuclei provides an opportunity to study nuclear medium effect of baryons. Theoretical predictions are welcome. g  can be studied from B(M1) of  -spin-flip M1 transition. B(M1) measurement is one of the most important subjects in our  spectroscopy project. Using Doppler shift attenuation method, the first B(M1) result was obtained for 7  Li with a large error. The new J-PARC experiment will provide us with B(M1) of 7  Li with accuracy of ~5%. Preparation is going on. For slow M1 transitions, B(M1) measurement with “  -weak coincidence method” is proposed.

Predicted by Motoba, Bando, Ikeda Prog.Theor.Phys. 70 (1983) He + d +  model ～ 20% shrinkage B(E2) ∝ | | 2 ∝ R 4 or (  ) 2 R  Hiyama et al. PRC 59 (1999) 2351, NPA684(2001)227 5  He + p + n, 4 He + p + n +  Shrink between 5  He – pn distance 22% shrinkage Confirmation of shrinking effect by 