Spin Filtering of Stored (Anti)Protons: from FILTEX to COSY to AD to FAIR

0.06 MB·English

by  N. Nikolaev

Spin Filtering of Stored (Anti)Protons:
from FILTEX to COSY to AD to FAIR 1
Nikolai Nikolaev and Fyodor Pavlov
InstitutfürKernphysik,ForschungszentrumJülich,52428Jülich,Germany
Abstract. Wereviewthetheoryofspinfilteringofstored(anti)protonsbymultiplepassagethrough
the polarizedinternaltarget(PIT).Implicationsfortheantiprotonpolarizationbuildupin the pro-
7 posedPAXexperimentatFAIRGSIarediscussed.
0
0 Keywords: Spinfiltering
2 PACS: 24.70.+s,29.27.Hj

n
a An ambitious physics program with polarized antiproton–polarized proton collider
J
hasbeenproposedrecentlybythePAXCollaboration[1]forFAIRatGSIinDarmstadt,

1
Germany [2]. Such a collider would give an unique access to the last leading–twist
2
missingpieceoftheQCDpartonicstructureofthenucleon—thetransversity—which

1 can only be investigated via double–polarized p¯p Drell–Yan production and without
v
which the spin tomography of the proton would be ever incomplete. At the core of
5
7 the PAX proposal is spin filtering of stored antiprotons by multiple passage through a
1 PolarizedInternalhydrogengasTarget(PIT)[1,3]—atechniquetestedbytheFILTEX
1
experimentat23MeVprotonTSR-ringinHeidelberg[4].Initsextensiontoantiprotons
0
7 thereremainopen issues,though.
0 In his theory of the FILTEX result, H. O. Meyer (i) obsreved that stored particles
/
h whichscatterelasticallyinPIT atangles withina storagering acceptance angleq are
acc
p
retainedinthebeamandtheirpolarizationcomplementsthepolarizationbytransmission
-
p and (ii) argued that the QED polarization transfer from polarized target electrons to
e
scattered protons [5] is crucial for the qunatitative understanding of the FILTEX result
h
: [6]. This prompted an idea to base the antiproton polarizer of the PAX on spin filtering
v
i bypolarized electronsin PIT [3].
X
After the PAX proposal, the interplay of the transmission and Scattering Within
r
a the Ring Acceptance Angle (SWRAA) mechanisms, and the feasibility of filtering on
electrons, became a major issue. Yu. Shatunov 2 was perhaps the first to question the
filtering by electrons. Eventually two groups of theorists — at the Budker Institute [7]
and IKP, Jülich [8] — came to a conclusion on the self-cancellation of the polarized
electroncontributiontothespinfilteringof(anti)protons.Herewepresentabriefreview
ofthisfinding anditsimplicationsforthePAX program.
There is an important hierarchy of scattering angles q in the proton-atom scattering.
First,theCoulombfieldsoftheprotonandatomicelectronscreeneachotherforscatter-
inganglesq <q =a m / 2m T ≈2·10−2 mrad(T =23MeV).Second,light
min em e p p p
electrons do not deflect protonps, q ≤ q =m /m ≈ 5·10−1 mrad. Third comes the
e e p
1 Presentedatthe17thIntl.SpinPhysicsSymposium,SPIN2006,Kyoto,Japan,October2-7,2006
2 Yu.Shatunov,privatecommunication
Colomb-Nuclear Interference (CNI) angle q ≈ 2pa /m T s pp ≈ 100mrad.
CNI em p p tot,nucl
q
FourthfortheTSRq =4.4 mrad,andq ≪q ≪q ≪q .Forimportantan-
acc min e acc CNI
glesq >q theprroton-atominteractionisdominatedbyquasielastic(QE)scattering,
min
p+atom→ p′ +e +p ,p′ +p +e (q is the momentum transfer,
scatt spect recoil scatt spect recoil
rˆ — thebeamspin-densitymatrix)):
dsˆ 1 1 1
QE = Fˆ(q)rˆFˆ†(q)= Fˆ (q)rˆFˆ†(q)+ Fˆ (q)rˆFˆ†(q)
d2q (4p )2 (4p )2 e e (4p )2 p p
In our normalization the forward scattering amplitude Fˆ(0) = Rˆ(0)+isˆ . For spin-1
tot 2
beam and target sˆ = s +s (s ·Q)+s (s ·k)(Q·k), where k is the beam axis, Q
tot 0 1 2
andP are thetarget and beam polarizations.
Let N be the volume density of atoms in PIT and z the integrated thickness of
the PIT for a circulating particle. The spin-momentum density matrix of the beam,
rˆ(p)= 1[I (p)+s s(p)],satisfies theevolutionequation
2 0
d 1 1
rˆ = i N Rˆrˆ(p)−rˆ(p)Rˆ − N sˆ rˆ(p)+rˆ(p)sˆ
tot tot
dz 2 (cid:16) (cid:17) 2 (cid:16) (cid:17)
Precessionintransmission Filteringby transmission
| W acc d{2zq } | {z }
+ N Fˆ(q)rˆ(p−q)Fˆ†(q) (1)
Z (4p )2
Feedback fromSWRAA
| {z }
The stable polarization are either normal to ring plane (the case in the FILTEX exper-
iment) or longitudinal if a ring is furnished with the Siberian Snakes. The precession
effects are very important in the polarized neutron optics but average out in our case.
Upon neglecting the precession terms (cid:181) Rˆ, Eq. (1) boils down to the kinetic equation
forspinpopulationnumbers.ForrealstorageringsEq.(1)furthersimplifiesbecausethe
angulardivergenceofthebeamatPITismuchsmallerthanq .TheFILTEXPITused
acc
thehyperfinestatewithparallel protonand electron polarizations.
The real issue is a pattern of a (partial) cancellation of transmission and
SWRAA effects in Eq. (1). Without spin-flip, the polarization buildup follows
P(z) = −tanh(Qs Nz) where s = s . Because only those particles which scatter
P P 1
in PIT at angles q > q are removed from the stored beam, Meyer argued that
acc
the transmission be evaluated taking sˆ = sˆ (q < q ). For all-angle nuclear
tot tot acc
interaction without CNI, the SAID phase shifts give s = 122 mb, upon the
1,nuclear
correction for CNI Meyer found s (CNI;q >q )=83 mb vs. the published FILTEX
1 acc
result s (FILTEX,1993) = 63±3 (stat.) mb. Next Meyer includes the polariza-
P
tion from SWRAA. In view of q ≪ q , the scattering off electrons is entirely
e acc
SWRAA and contributes ds ep(q < q ) = −70mb. SWRAA off protons contributes
1 acc
ds pp(q <q )=+52 mb.Meyer’snetresult forthepolarizationcross section[6],
1 acc
s =s (CNI;q >q )+ds pp+ds ep =135 mb+ds ep =65 mb, (2)
P 1 acc 1 1 1
is in perfect agreement with the published FILTEX result. A subsequent reanalysis of
the target density and polarization gave s (FILTEX,2004)= 72.5±5.8(stat.+sys.)
P
(F.Rathmann,see [1]).
The Budker and Jülich groups argue that sˆ in the transmission term must rather
tot
includeascatteringonatomsatallanglesq >q :sˆ =sˆ (q >q )=sˆ (q <
min tot tot min tot min
q < q )+sˆ (q < q ). Then one would readily find that the beam polarization-
acc tot acc
independent SWRAA cancels exactly the corresponding transmission effects from
sˆ (q < q < q ). For a polarized beam there is a mismatch between the spin-
tot min acc
filtering component in sˆ (q < q < q ) and the polarization feedback from
tot min acc
SWRAA. This mismatch is entirely due the spin-flip elastic proton-atom scattering at
anglesq <q .Thegenericsolutionforthepolarizationbuildupreads
acc
Q(s +D s )tanh(Qs Nz)
1 1 3
P(z)=− , (3)
Qs +0.5D s tanh(Qs Nz)
3 0 3
where D s are the proton spin-flip (SF) cross sections for an unpolarized and polar-
0,1
ized target, respectively, |D s | ≤ |D s |, and Qs = Q2s (s +D s )+D s 2/4. The
1 0 3 1 1 1 0
q
formulas for D s in terms of the two-spin observables are found in [7, 8]. In contrast
0,1
totheMeyerapproach,intheBudker-Jülichanalysistheelectron-to-protonpolarization
transferisentirelycanceledbytheelectroncontributiontothetransmissionfiltering.For
nuclear SF scattering at q ≤ q ≪ q CNI is arguable negligible and a crude esti-
acc CNI
mate is D s <s q 2 <10−4s . Within the Budker-Jülich approach, the small-time
0 ∼ tot acc ∼ tot
polarizationbuildupiscontrolledby(SAID-SP05 database)
s ≈−(s (CNI;q >q )+D s )=85.6mb. (4)
P 1 acc 1
The case of the pure electron target deserves a special consideration. Here s (q >
0
q )=0, s (q >q )=0, Qs =D s , the beam is not attenuated and the polar-
acc 1 acc 3 0
izationbuildupfollows
D s
P(z)=P(0)exp(−ND s z)+Q 1 1−exp(−ND s z) . (5)
0 D s 0
0n o
Spin filtering by electron coolers was discussedin the PAX TP withthe conclusionthat
theattainabletarget densitiesare toolow[1].Morerecently,Th. Walcheretal. 3 argued
that if the SF on electrons is comparable to the electron-to-proton spin transfer, then
filtering in apure electron target can be enhanced considerablyby a judiciouschoiceof
the non-relativisticrelativevelocity of the comoving electron and proton beams. At the
moment,basedonlyontheFILTEXresult,onecannotdiscriminatebetweentheMeyer
and Budker-Jülich treatments of theelectron contributionto filtering; as it is a common
practicewithconflictingtheories,theissuemustbeclarified experimentally.
First,thefilteringbySFhasneverbeentestedexperimentally.Ifthepolarizedelectron
target polarizes the initially unpolarized stored beam, the unpolarized electron target
depolarizes the stored proton beam, see Eq. 5. The required density of electrons is
provided by the 4He internal target, which has an advantage of the spin-0 nucleus.
Consequently,ausefulupperboundondepolarizationbyelectrons,i.e.,D s and|D s |≤
0 1
3 Th.Walcher,privatecommunication
3 30
2
1 20
0
-1 10
mb --23 mb 0
T,1 -4 L,1-10
s -5 s
---687 qqqaaacccccc===123mmmrrraaaddd --3200 qqqaaacccccc===123mmmrrraaaddd
-9 s1 tot=-(1/2)Ds T, SAID Expt. -(1/2)Ds L, SAID Expt.
-10 -40
100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800
T, MeV T, MeV
FIGURE1. PredictionsforspinfilteringofprotonsbynuclearinteractioninpolarizedhydrogenPITfor
transverse(T)andlongitudinal(L)polartizations.Thecurvesmarkedbybacksquaresareforpurenuclear
pp interaction,the three curvesfor differentrange acceptance angle are predictionswith allowance for
CNI.
|D s | can bededuced. Such an experiment,theidea ofwhich grew up from discussions
0
with H.O. Meyer, is being planned at COSY [9]. Second, filtering on electrons and on
protonshavea very distinctenergy dependence. In Fig. 1 we showthepredictionsfrom
the Budker-Jülich approach for the nuclear spin filtering cross section which can be
tested at COSY. The confirmation of this energy dependence would be a convincing
proof that spin filtering is dominated by nuclear interaction of a negligible filtering on
electrons.
We come to a summary. FILTEX experiment is an important proof of the principle
of spin filtering. The Meyer and Budker-Jülich approaches disagree in the treatment
of SWRAA and significance of the electron contribution to spin filtering. If the elec-
trons do not contribute (Budker-Jülich), then filtering of antiprotons would depend on
spin-dependence of p¯p,p¯D interactions. The existing models of N¯N interactions are
encouraging but not reliable because of a lack of double-spin observables to fix the
model parameters. The solution for PAX is to optimize the filtering energy with an-
tiprotons available at existing facilities (CERN AD) [9]. The experimental constraints
on the electron contribution to filtering can be obtained from proton depolarization and
energy-dependenceoffilteringofprotonsat COSY.
REFERENCES
1. PAX Technical Proposal for the HESR at FAIR, Jülich (2004), Spokespersons: P. Lenisa and F.
Rathmann.e-PrintArchive:hep-ex/0505054.Fortheupdateseehttp://www.fz-juelich.de/ikp/pax/
2. H.Ströher,theseProceedings.
3. F.Rathmannetal.,Phys.Rev.Lett.94,014801(2005).
4. F.Rathmannetal.,Phys.Rev.Lett.71,1379(1993).
5. C.J.HorowitzandH.O.Meyer,Phys.Rev.Lett.72,3981(1994).
6. H.O.Meyer,Phys.Rev.E50,1485(1994).
7. A.I.MilsteinandV.M.Strakhovenko,Phys.Rev.E72,066503(2005)
8. N.N.NikolaevandF.F.Pavlov,e-PrintArchive:hep-ph/0512051,hep-ph/0601184.
9. F.Rathmann,theseProceedings.