On Polarization of the Beam Extracted with the Bent Crystal
M. Ukhanov
IHEP Protvino
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 2
Outline
• Basics of the phenomenon
• Estimation of the effect
• Numerical example
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 3
Definition
P = 0A ≠ 0P ≠ 0
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 4
Junior hunter exercise
P = 0A ≠ 0P ≠ 0
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 5
Senior hunter exercise
P = 0A ≠ 0P ≠ 0
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 6
Consequence from the definition
Beam,
extracted by means of the bent crystal,
must be polarized
by definition.
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 7
Analyzing power at small |t|
hadflipnon
hadflip
hadflipnon
emflipN CCA *
2*
1
AN = AEM + AH
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 8
Analyzing power at small |t|
B.Z. Kopeliovich and T.L. Trueman, hep-ph/0012091
best fit withhadronic spin-flip
Kopeliovich –Truemann modelPRD64 (01) 034004hep-ph/0305085
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 9
What we can expect
NH
NH
NH
NH
tAtA
tAtAP
))(1())(1(
))(1())(1(
Critical channeling angle in Si
θ = 5 μrad / p½(TeV/c)½
@ p = 70 GeV/c => θ ≈ 20 μrad
100 mrad bend gives N = 5000
If AH(t) = A0 |t/t0|½
for very small –t < t0 = 10-3 GeV2
and A0 = AH(10-3 GeV2) = 0.005Then P ≈ 0.8
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 10
Dependence on the A0
AH(t) = A0 |t/t0|½
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 11
Conclusions
• Bent crystal extraction provides polarization in the resulted beam.
• The beam polarization could be measurable
• or even big enough for practical needs.
Kyoto 2-7 October 2006 M. Ukhanov IHEP Protvino 12
Analyzing power evolution at small t
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Independence on the channeling assumptions