Tensor structure Tensor structure in high-energy proton-deuteron in high-energy proton-deuteron reactions reactions September 25, September 25, 2009 2009 [email protected][email protected]http://research.kek.jp/ http://research.kek.jp/ people/kumanos/ people/kumanos/ KEK theory center workshop KEK theory center workshop on Short-range correlations and tensor structure at J- on Short-range correlations and tensor structure at J- PARC PARC Shunzo Kumano Shunzo Kumano High Energy Accelerator Research Organization (KEK) High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) Graduate University for Advanced Studies (GUAS) Based on works with Based on works with F. E. Close, S. Hino, T.-Y. Kimura, M. Miyama F. E. Close, S. Hino, T.-Y. Kimura, M. Miyama
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Tensor structure in high-energy proton-deuteron reactions
Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS). Tensor structure in high-energy proton-deuteron reactions. [email protected] http://research.kek.jp/people/kumanos/. Based on works with - PowerPoint PPT Presentation
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Tensor structureTensor structure
in high-energy proton-deuteron reactionsin high-energy proton-deuteron reactions
KEK theory center workshop KEK theory center workshop on Short-range correlations and tensor structure at J-PARCon Short-range correlations and tensor structure at J-PARC
Shunzo KumanoShunzo Kumano
High Energy Accelerator Research Organization (KEK)High Energy Accelerator Research Organization (KEK)
Graduate University for Advanced Studies (GUAS)Graduate University for Advanced Studies (GUAS)
Based on works with Based on works with F. E. Close, S. Hino, T.-Y. Kimura, M. MiyamaF. E. Close, S. Hino, T.-Y. Kimura, M. Miyama
ContentsContents
Introduction to tensor structure functionsIntroduction to tensor structure functions Tensor structure functions (Tensor structure functions (bb11, …, , …, bb44))
Sum rule, Projection to each structure function from WSum rule, Projection to each structure function from W
Note: The proton does not have to be polarized for Note: The proton does not have to be polarized for bb11..
If a polarized-deuteron target will becomes available at J-PARC or any other facilities, it is a possible experiment.
Introduction to Introduction to Tensor Structure FunctionsTensor Structure Functions
References on tensor structure function References on tensor structure function bb11
Theoretical formalism for polarized electron-deuteron Theoretical formalism for polarized electron-deuteron deep inelastic scatteringdeep inelastic scattering P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571. [ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]
HERMES experimental resultHERMES experimental result A. Airapetian et al., Phys. Rev. Lett. 95 (2005) 242001.
Our worksOur works
Sum rule for Sum rule for bb11
F. E. Close and SK, Phys. Rev. D 42 (1990) 2377.
Projections to Projections to bb11, …, , …, bb44 from from WW
T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.
MotivationMotivation
Spin structure of the spin-1/2 nucleonSpin structure of the spin-1/2 nucleon Nucleon spin puzzle:Nucleon spin puzzle: This issue is not solved yet, This issue is not solved yet,
but it is rather well studied theoretically and experimentally.but it is rather well studied theoretically and experimentally.
Spin-1 hadrons (e.g. deuteron)Spin-1 hadrons (e.g. deuteron) There are some theoretical studies especially on tensor structThere are some theoretical studies especially on tensor struct
ure ure in electron-deuteron deep inelastic scattering.in electron-deuteron deep inelastic scattering.
A few investigations have been done for polarizedA few investigations have been done for polarized proton-deuteron processes. proton-deuteron processes.
J-PARC experiment ?J-PARC experiment ?
Structure function Structure function bb11 in a simple example in a simple example
The The bb11 probes a dynamical aspect of hadron structure probes a dynamical aspect of hadron structure beyond simple expectations of a naive quark model.beyond simple expectations of a naive quark model. Description of tensor structure Description of tensor structure by quark-gluon degrees of freedomby quark-gluon degrees of freedom
Electron scattering from a spin-1 hadron Electron scattering from a spin-1 hadron
W =−F1g + F2
p p
+ g1
iελσqλsσ + g2
i 2 ελσqλ p⋅qsσ −s⋅qpσ( )
−b1r +16
b2 s + t +u( ) +12
b3 s −u( ) +12
b4 s −t( )
r =1 2 q⋅E∗q⋅E −
13 2κ⎛
⎝⎜⎞⎠⎟
g ,s =2 2 q⋅E∗q⋅E −
13 2κ⎛
⎝⎜⎞⎠⎟
p p
t =1
2 2 q⋅E∗p E +q⋅E∗p E +q⋅Ep E∗+q⋅Ep E
∗ −43 p p
⎛⎝⎜
⎞⎠⎟
u =1
E∗E + E
∗E +23
M 2g −23
p p⎛⎝⎜
⎞⎠⎟
=p ⋅q, κ = 1 + M 2 Q2 ν 2 , E2 = −M 2 , sσ = −i
M 2 ε σαβτ Eα∗Eβ pτ
P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571.[ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]
Note: Obvious factors from qW =qW =0arenotexplicitlywritten.
Projections to Projections to FF11, , FF22, …, , …, bb44 from W from W Calculate W inhadronmodels→ needtoextractstructurefunctionsb1 ,b2 ,⋅⋅⋅ProjectionoperatorsareneededtoextractthemfromthecalculatedW .ForF1 andF2 ,theyarewellknown:
Actual experimental proposals at J-PARC: P04, P24Actual experimental proposals at J-PARC: P04, P24
E866: existing measurements by the Fermilab-E866
E906: expected measurements by the Fermilab-E906
(from 2010)
J-PARC: proposal stage
It should be possible to use polarized proton-deuteron Drell-Yan processeIt should be possible to use polarized proton-deuteron Drell-Yan processess to measure the tensor polarized distributions.to measure the tensor polarized distributions.
+
–
q
qAntiquarkAntiquarkdistributionsdistributions
Polarized proton-deuteronPolarized proton-deuteronDrell-Yan process Drell-Yan process
rp +
rd→ +− + X
(p+rd→ +− + Xisenoughfortensorstructure)
ReferencesReferences • • General formalism for polarized Drell-Yan processesGeneral formalism for polarized Drell-Yan processes
with spin-1/2 and spin-1 hadronswith spin-1/2 and spin-1 hadrons M. Hino and SK, Phys. Rev. D59 (1999) 094026.
• • Parton-model analysis of polarized Drell-Yan processesParton-model analysis of polarized Drell-Yan processes with spin-1/2 and spin-1 hadronswith spin-1/2 and spin-1 hadrons M. Hino and SK, Phys. Rev. D60 (1999) 054018.
• • An application: Possible extraction of polarized An application: Possible extraction of polarized light-antiquark distributions from Drell-Yanlight-antiquark distributions from Drell-Yan SK and M. Miyama, Phys. Lett. B497 (2000) 149.
Comments on the situationComments on the situation
• There was a feasibility study for polarized deuteron beam at RHIC: E. D. Courant, BNL-report (1998).
• No acutual experimental progress with hadron facilities.
• Future: J-PARC, COMPASS, U70, GSI-FAIR, RHIC, …
Purposes of studying polarized deuteron reactions Purposes of studying polarized deuteron reactions (1) Neutron information
We use Fierz transformation for γ μ( ) jk γ ν( )li
so that the index summations are taken
separately in hadrons A and B.
Spin asymmetries in the parton modelSpin asymmetries in the parton modelunpolarized: qa , longitudinally polarized: Δqa,transverselypolarized:ΔT qa, tensorpolarized:δqa