Transversity – status and what we need in EIC
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EIC Workshop, Hampton, VA
May 21
Ralf Seidl (RBRC)
EIC workshop, May 21th 1R.Seidl: Transversity measurements at EIC
Outline
TransversityChiral-odd PDFSIDIS results Belle resultsglobal analysis
First global analysis Comparison to Lattice predictions Evolution of Collins
FF(?)What will be important after these first measurements
Higher scales kt-Moments , lower x to get to tensor charge
other measurements (IFF, )
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Transversity In helicity basis: helicity
distribution and momentum difference and sum of diagonal amplitudes
Transversity contains helicity flip and is not diagonal
Helicity is conserved quantity for (nearly) massless quarks
All interactions conserve helicity/chirality
Transversity cannot be observed in DIS
Unpol. DF
Helicity
Transversity
Transversity and friends
Sivers function
Boer-Mulders function
q(x)
q(x)
q(x)
Tf1
1h
Lh1
Th1
Tg1
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Transversity properties
Does not couple to gluons different QCD evolution than q(x)
Valence dominated Comparable to Lattice calculations, especially tensor charge:
Test relativistic nature of quarks in the nucleon
Positivity bound:
Soffer bound:
xqxδq
xqxqxδq 21
1
0
)()( xqxqdxgT
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How to access Transversity another chiral-odd function
Drell Yan: Combine two
Transversity distributions with each other
SIDIS: Combine
Transversity distributions with chiral-odd fragmentation function (FF)
Total process is chiral-even: OK
Possible Partners: Collins FF Interference FF Transverse L FF
Most require single spin asymmetries in the fragmentation
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First successful attempt at a global analysis for the transverse SIDIS and the BELLE Collins data
HERMES AUT p data
COMPASS AUT d data
Belle e+ e-
Collins dataKretzer FF
First extraction of transversity (up to a sign)
Anselmino et al: hep-ex 0701006
Tensor charges obtained from this fit (from Alexei Prokudin) at Q2= 2.4 GeV2:
0.340 +0.398 -
0.346 +0.392 -
189.0195.0
150.0203.0
0.236
0.569
166.0
403.0
du
du
d
u
Current problems in the global transversity analysisUniversaliy? Is the Collins function from e+e-
the same in SIDIS, how about pp? According to Bacchetta et al.
and Gamberg et al, yesEvolution?
Is the evolution of transversity understood? YesIs the evolution of the Collins function understood?
Not really – is this the reason for low transversity in the global fit so far?
Error treatment, first suggestions to start a CTEQ-like transversity global analysis group with contributors from Theory (Torino), COMPASS(Trieste),HERMES(Ferrara), Belle(Illinois, RBRC)
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Collins measurements IIK+ asymmetries
compatible with asymmetries (through u quark dominance)
K- asymmetries maybe slightly positive
Coming additions to global analysis
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arXiv:0802.2160
COMPASS full d data set,Charged , K and KS
In DY: TT
Further additionsBelle 547 fb-1 data set (submitted to PRD arXiv:0805.2975)
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New data to come
HERMES K data not yet used in fits
COMPASS K data not yet used
JLAB 6 and 12 GeVLow energies and
multiplicitiesHigher twist an issue?
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Very important Test: COMPASS proton data-
• Will it be consistent in the overlap with HERMES?
• Will they be different
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DY transversity measurements at RHIC, JPARC and FAIR
DY transverse double spin asymmetries golden channel to Transversity:
Requires both (anti)- protons transversely polarized
For mostly sensitive to u-quark transversity
For pp smaller asymmetries due to sea transversity , but for tensor charge absolutely necessary
)()( xqxqATT
pp
Q= 8GeV
Q= 3GeV
Q= 5GeV
Q=15GeV
RHIC @ √s=200GeV
JPARC @ √s=10 GeV
Kawamura et. alNucl.Phys.B777:203-225,2007.
Assuming Soffer bound
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Transversity access over DY in single spin asymmetries
Instead of double spin asymmetries measure single spin asymmetries
Advantage: only one proton polarized better FOM at RHIC, earlier feasible at JPARC and GSI
Disadvantage: first have to measure Boer-Mulders function with good precision
Also planned at COMPASS with pion beam
)()(1 xqxhAT
Q=2GeV
Q=3GeV
Q=4GeV
Q=6GeVGSI (collider option) @ √s=15 GeV
Kawamura et. alNucl.Phys.B777:203-225,2007.
Theory for ATT fairly well understood even at very low scales,
if there will be PAX, it will measure mostly u2 – until then already relatively well known only consistency test
Transversity over pp DY in double spin asymmetries
What is needed at EIC?
Larger x range measured b y existing experimentsCOMPASS ends at ~
0.01, go lower by almost one order of magnitude, but asymmetries become small
Have some overlap at intermediate x to test evolution of Collins function and higher twist but at higher Q2
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What is needed at EIC IIDetect SIDIS hadrons at z range 0.1 – 0.9 Have to be able to reject exclusive VMs
nearly hermetic detector, reasonable momentum resolution
Good e/h separation needed everywhere, good hadron PID needed in hadron acceptance
So far: No Ph moments measured yet, why?
Acceptance effects are very difficult to correctMake sure we have very good and uniform Ph
coverage , say cone of Ph
< 3 GeV Need generator capable to produce kT
dependent asymmetries Generalize gmc_trans
Other channels: IFFHERMES,COMPASS,pp, BELLE
COMPASS: zero on deuteron target proton date will be interesting
Possibility to measure IFF also at RHIC
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Other channels II: polarization
Measurements available from COMPASS on deuteron target,
Plan to measure it at Belle
IFF and polarimetry can also be probed with great precision at EIC
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SummaryTransversity:
First global analysis available, errors still huge, evolution of Collins function?Newer data not yet included in global analysis
from HERMES (K), COMPASS (K, proton data), JLAB
Large Belle Collins data now finalNew accesses over IFF, polarimetry soon
EIC needs to cover intermediate x range, z>0.2, Ph
< 3 GeV , good e/h separation and PID
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q(x), G(x)
Difference of quarks with parallel and antiparallel polarization relative to longitudinally polarized proton(known from fixed target (SI)DIS experiments)
q(x),G(x)Sum of quarks with parallel and antiparallel polarization relative to proton spin(well known from Collider DIS experiments)
q(x)
Quark distributions in spin bases
Difference of quarks with parallel and antiparallel polarization relative to transversely polarized proton(first results from HERMES and COMPASS – with the help of Belle)
Unpolarized distribution function q(x)
Helicity distribution function q(x)
Transversity distribution function q(x)
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