- Email: [email protected]
Future transversity measurements: experimental aspects
__ _Eli!
s!A
ELSEVIER
Future
Transversity
Nuclear
Physics
B (Proc. Suppl.)
Measurements:
SUPPLEMENTS 105 (2002) 71-75
Experimental
Aspects
M. Grosse Perdekamp” “RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA Recent experimental results from the HERMES collaboration at DESY and the SMC collaboration at CERN suggest that it may be possible to access nucleon transversity distributions through the measurement of transverse single spin asymmetries in semi-inclusive hard scattering processes. In this paper we review current and future experimental activities to measure transversity. We include a discussion of the measurement of the relevant fragmentation functions in e+e- annihilation.
1. Introduction High energy, deeply inelastic lepton-nucleon and hadron-hadron scattering cross sections can be described with the help of three independent nucleon helicity amplitudes. Measurements of the nucleon structure functions Fl(x, Q2) -the helicity average- and gi (2, Q2) -the helicity difference-, have explored the helicity conserving part of the cross sections with great experimental accuracy. In contrast, no information is presently available on the helicity flip amplitude. The absence of experimental measurements is a consequence of the chiral-odd nature of the helicity flip amplitude and the related “transversity quark distributions”, 6q(z, Q2), which prevents the appearance of helicity flip contributions at leading twist in inclusive DIS experiments. The experimental study of transversity distributions at leading twist requires observables which are the product of two objects with odd chirality. This was first discussed by Ralston and Soper [l] for Drell Yan scattering of two transversely polarized hadrons: The transverse double spin asymmetry, ATT, is proportional to 6q&j with even chirality. Transverse single spin asymmetries AT (e.g. unpolarized leptons on transversely polarized nucleon targets) in semi-inclusive DIS and pp scattering may offer an alternative way to observe helicity flip contributions at leading twist. This possibility relies on the presence of quark fragmentation functions (FF) which are sensitive to
the quark polarization in the final state and possess the necessary negative chirality. The asymmetries AT are proportional to C, Sq x af x FF, where a{ are the transversity dependent partonic initial-final-state asymmetries which can be calculated from pQCD. For example, Collins suggested that in semiinclusive single pion production the quark spin direction might be reflected in the azimuthal distribution of a final state pion [2]. Collins further demonstrated that the symmetry properties of the process do not require the proposed fragmentation function Hf to be identical to zero. The current interest in transversity distributions results from a recent HERMES result on azimuthal single spin asymmetries [3] and a preliminary SMC result [4], which suggest that Collins’s function Hk and the transversity distribution function 6q in fact are different from 0; see reference [5] for a detailed discussion. 2. Future
Transversity
Measurements
2.1. Drell Yan The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) at BNL has the capability to study spin dependent Drell Yan production with longitudinal and transverse spin orientations. PHENIX possesses excellent lepton detection capabilities within a limited geometric acceptance; for electrons at mid rapidity In] 5 0.35,34’ < 141< 124’ and for muons in the pseudo rapidity range 1.2 < 171< 2.4.
0920-5632/02/$ ~ see front matter 0 2002 Published by Elsevier Science B.V. PI1 SO920-5632(01)01954-S
72
A4. Grosse Perdekmnp/Nucleur
Physics
Originally the transverse double spin asymmetry, ATT, in Drell Yan was viewed as a good candidate for a measurement of the transversity distribution functions at RHIC, ATT N SqStj . However, a recent analysis by Martin et al. [6] - using PHENIX acceptances and the projected luminosities for pp-running at RHIC, 320pb_r/year at 200 GeV - estimates ATT to be about 1% with statistical errors comparable to the asymmetry itself for a projected measurement at RHIC.
Lepton Pair Moss [GeVI
Figure 1. Projected Drell Yan double spin asymmetries ATT for a RHIC upgrade luminosity of s,,,, Ldt = 8 fb-’ at 200 GeV.
Future luminosity upgrades at RHIC possibly can reach integrated luminosities of up to s,,,, Ldt = 8 fb-’ at 200GeV. The sensitivities for ATT in Drell Yan for &,,,
Ldt = 8 f&l
at
200 GeV are shown in Fig. (1). The plotted sensitivities are obtained by extrapolating the results from reference [6] to the higher integrated luminosities. A significant measurement appears to be possible. However, it should be noted that currently there are no plans to carry out the massive detector upgrades necessary (event selection and data acquisition) to capitalize on luminosities of several fb ‘.
B (Proc. SuppI.)
2.2.
IO5 (2002) 71-75
Semi Inclusive
Deep
Inelastic
Scatter-
ing
The HERMES experiment at DESY is expected to start measurements with transverse target polarization in late 2001. The observable is Collins’ single spin asymmetry for charged pion production in deep inelastic electron proton scattering: The azimuthal distribution of the final state pions with respect to the virtual photon axis carries information about the transverse quark spin orientation. In a partonic picture of the nucleon the transverse single spin asymmetry AT is related to the transversity distributions as follows:
where Htg is the Collins function for a quark of flavor q and 0: is the regular spin independent fragmentation function. Korotkov, Nowak and Oganessyan have proposed an analysis procedure for the HERMES transverse asymmetries that - under the assumption of u-quark dominance, 6d = 0 - results in the extraction of the shape for 6u(z) and the ratio Hi-/D;” [7]. As a normalization condition to fix the absolute size of &J(Z) and the fragmentation function ratio it is further assumed that SU(Z~ = 0.25) = Au(zc) at some soft scale, Qz M 0.4 GeV. Alternatively, it may be worthwhile to investigate if the ratio Hf/Dy can be determined from fragmentation function measurements in e+e- annihilation using LEP and b-factory data, see section (3). The HERMES measurement of 6u(z) between 0.02 < 5 < 0.7 is projected to result in a statistical error of about 6~ Z!Z0.3 at the lowest z and 6u kO.1 at highest 2 [7]. Systematic errors are expected to be of comparable size. A similar measurement will be attempted by the COMPASS collaboration at CERN. The higher beam energy, 100 - 200 GeV compared to 27.5 GeV may allow, for the first time, the exploitation of interference fragmentation processes. However, the ultimate experiments to measure transversity distributions and their first moments, the tensor charge, appeal to be two future high luminosity electron proton scattering experiments: At DESY a fixed target
M. Grosse Perdekump/Nuclear
experiment has been proposed for one arm of a possible future e+e- linear accelerator collider at DESY: TESLA-N; it is estimated that the first moment of bu can be measured to about one percent and for 6d to 6% (81. At BNL the prospects of a future electron ion collider (EIC) with luminosities reaching 4 fb-‘/year have been studied. [9]: A measurement with the statistical precision of the HERMES measurement but at lower 5 can be achieved in one day of running or 20 pb-’ ; see Fig. (2).
_
0.05
r
0
With the presently available luminosities and detectors the proposal of Collins et al. [lo] and Jaffe et al. [ll] to utilize chiral odd two pion interference fragmentation processes appears to be the most promising approach to measure transversity at RHIC. This channel also has been studied for the RAMPEX experiment at IHEP Protvino [12]. The relevant process is pion pair production in pp
I
Invariant
Mass
Resolution
0.3 and 0.5
I
RMS=
12MeV
1~_____,__*__~___~____t____~,
-0.05
r
-0.1
-
-0.15
z between
Interference fragmentation and Collins fragmentation in direct photon jet events.
l
l,l
0.1
73
Plq*sics B (Psoc. Suppl.) 105 (2002) 71-75
r I,,,,, 1o-3
I I111111 I Illil,, lo-*
I ,,,,I_ 10-l
1
XE3jorken
300
-
200
t -
Ott,,,“,‘,-0.1
-0.15
Figure 2. Projected sensitivities for the single spin asymmetries in single inclusive pion production at the EIC for Jday Ldt = 20pb-’ and 0.3 < z = En/E, < 0.5.
Single Spin Asymmetries in Polarized Proton Scattering In addition to the double spin asymmetry measurements in Drell Yan the following single spin asymmetry measurements have been suggested for polarized proton scattering experiments:
r
100 -
-r
-0.05
,I,,, 0
0.05
“‘I
0.1
m +-rn,_
“”
0.15
IGeVl
Figure 3. Simulation studies of two pion production in the pmass region for the PHENIX detector. The invariant mass resolution for pion pairs is shown in the pmass region.
2.3.
Single spin asymmetries ference fragmentation.
in two pion inter-
The measurement of azimuthal asymmetries in the production of pions around the jet-axis (Collins fragmentation function).
scattering with one proton transversely polarized. For example, in the p/g invariant mass region interference occurs between two pions in a superposition of s-wave and p-wave states. The spin analyzing power of this process is different from 0 in intervals of only a few 1OOMeV above and below the pmass and changes sign at the pmass (131. Therefore, it will be important for RHIC experiments to have sufficiently high invariant mass resolution to observe the invariant mass dependence of the analyzing power. The invariant mass
M. Gro.we Perdekamp/Nuclear
74
Physics B {Proc. SuppI,) 105 (2002) 71-75
Table 1 Present and future measurements of transversity distributions. Different processes are used to access transversity distributions: Collins fragmentation (CF), interference fragmentation (IF) and Drell Yan (DY). Note that PHOBOS and BRAHMS currently have no approved transversity program. However, in absence of spin rotators at their interaction points both experiments will be able to engage in transversity measurements well before STAR and PHENIX where the transverse spin program competes with measurements using longitudinal proton spin orientation. Experiment
Location
Process
4
[GeV]
year
HERMES
DESY/HERA
DIS: CF
7.5
2001
COMPASS
CERN/SPS
DIS: CF, IF(?)
14 - 20
2003
EIC-detector
BNL/EIC
DIS: CF, IF
65 - 100
2008+
DESY/TESLA
DIS: CF, IF
8 - 22
2010+
RAMPEX
IHEP Protvino
pp: IF
12
2001
BRAHMSPHOBOS
BNL/RHIC
pp: IF
50 - 500
2002
PHENIX,STAR
BNL/RHIC
pp: IF, CF, DY
50 - 500
2006
TESLA-fixed
target
resolution for pion pairs in the p-mass region is shown in the left plot of Fig. (3) for the example of the PHENIX experiment. The RMS of the distribution is 12MeV - 15MeV for STAR which easily meets the demands for an experimental determination of transversity distributions at RHIC. In STAR transversity measurements rely on the large acceptance, Ir]] < 2.0, time projection chamber for tracking and the electromagnetic calorimeter for triggering purposes. The PHENIX measurement will use the central detector arms which cover the pseudo rapidity interval ]T$ < 0.35. A combination of tracking chambers will give good momentum resolution: Ap/p x 2% at p = 10GeV. The electromagnetic calorimeter in combination with the ring imaging Cherenkov Counter will provide pion identification over are large momentum range, 4 < px < 12GeV. In order to estimate experimental sensitivities a first study was carried out at the event generator level including PHENIX detector acceptances and a parametrizations of the PHENIX central arm momentum resolution. The results using an integrated luminosity of 32 pb-’ (corresponding to one week of polarized proton running at RHIC) are compared to asymmetry projections from Tang [13] in Fig. (4). The error bars shown in the plot represent statistical errors only. The asymmetries in Fig. (4) were obtained using up-
per bounds for the relevant distribution and fragmentation functions and represent an optimistic upper limit [13]. More detailed studies with different model assumptions and a full simulation of the detector response are underway. Nevertheless, the high rates at RHIC and the excellent momentum resolution in STAR and PHENIX are well suited for a transversity measurement in two pion interference fragmentation and a run with 320pb-l integrated luminosity has been added to of the spin physics run plan [14].
3. Collins and Interference Functions in e+e-
Fragmentation
All future transversity measurements have in common that their success critically depends on the knowledge of the spin dependent and chiral odd fragmentation functions giving sensitivity to transverse quark spin in the final state. Atru and Collins have provided a detailed recipe how to extract interference fragmentation functions from light quark di-jet events in e+e- collisions [15]. Efremov , Smirnova and Tkachev have carried out first experimental studies using LEP data from DELPHI [16]. A recent discussion of the prospects of transversity measurements using future fragmentation function information from e+e- can be found in reference [17].
M. Grosse Perdekanlp/Nuclear
Asvmmetrv
vs Std.
P&sics B (Proc.
Errors
r
-T-
Suppl.)105 (2002) 71-75
z = Eh/Eq and for different state hadrons.
75
combinations
of final
REFERENCES 1.
i
t
t Statistical
Errors only
i
6. 7.
Figure 4. Simulation studies of two pion production in the pmass region for the PHENIX detector: Projected transverse single spin asymmetries versus the transverse momentum of the pion pair. The statistical errors correspond to an integrated luminosity of s Ldt = 32pb-l at fi = 200GeV.
Additional studies in e+e- have been proposed using the high statistic data sample of the Belle experiment at the KEK b-factory [18] with the goal to measure the two relevant fragmentation functions: l
l
The Collins function Hf : The fragmentation of a transversely polarized quark into a charged pion and the azimuthal distribution of the final state pion with respect to the initial quark momentum (jet-axis). fragmentation functions Interference @h&z: The fragmentation of transversely polarized quarks into pairs of hadrons in a state which is the superposition of two different partial wave amplitudes; e.g. n+, ?rrpairs in the p, c invariant mass region.
High luminosities at KEKB - presently the integrated luminosity is 36.4fb-’ - and Belle’s superior particle identification will allow fragmentation function measurements over a large range in
8. 9. 10.
11. 12. 13. 14.
15. 16.
17. 18.
Ralston J., Soper D.E., A&cl. Phys. B152, 109 (1979). Collins J.C., Nucl. Phys. B396, 161 (1993). Airapetian k. et al , Phys. Rev. Lett. 84, 4047 (2000). &a&r A., Nucl. Phys. (Proc. Suppl.) B79, 520 (1999). K.A. Oganessyan, N. Bianchi, E. De San&is, W.D. Nowak, hep-ph/OO 10261. Martin 0. et al., Phys. Rev. D60, 117502 (1999). Phys. Rev. D57, 5920 (1998). W.-D. Nowak, K.A. V.A. Korotkov, Oganessyan, Eur. Phy. J. Cl8 (2001)639. hepTESLA-N study group, ph/0011299(2000). EIC White Paper submitted to the NSAC LRP meeting, Santa Fe (2001). Collins J.C. , Heppelmann S.F. and Ladinsky G.A., N&. Phys. B420, 565 (1994); Collins J.C. and Ladinsky G.A., Preprint PSU-TH114, hep-ph/9411444; Collins J.C., Proceedings of the RHIC Spin Workshop, October 6 - 8, 1999, p. 158. Jaffe R.L., Jin X., Tang J. et al., Phys. Rev. Lett. f 80, 1166 (1998); Yu.1. Arestov, Proc of DIS2000, World Scientific (2001)247. Tang J., Preprint hep-ph/9807560 and Tang J., Thesis, MIT (1999). D. Boer et al., RHIC Spin Physics Program, White Paper submitted to the DNP Town Meeting at Jefferson Laboratory, December 1-4, 2000. X. Artru and J. Collins, Z. Phys. C69, 277(1996). A.V. Efremov, O.G. Smirnova, L.G. Tkachev, Nucl. Phys. Proc. Suppl. 74, 49 (1999), A.V. Efremov, L.G. Tkachev, Acta Physics Polonica B, Vol. 29 (1998)1385. D. Boer, hep_ph/0106206. M. Grosse Perdekamp, J. S. Lange, A. Ogawa, Letter of Intent to Belle Collaboration, unpublished (2001).
s!A
ELSEVIER
Future
Transversity
Nuclear
Physics
B (Proc. Suppl.)
Measurements:
SUPPLEMENTS 105 (2002) 71-75
Experimental
Aspects
M. Grosse Perdekamp” “RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA Recent experimental results from the HERMES collaboration at DESY and the SMC collaboration at CERN suggest that it may be possible to access nucleon transversity distributions through the measurement of transverse single spin asymmetries in semi-inclusive hard scattering processes. In this paper we review current and future experimental activities to measure transversity. We include a discussion of the measurement of the relevant fragmentation functions in e+e- annihilation.
1. Introduction High energy, deeply inelastic lepton-nucleon and hadron-hadron scattering cross sections can be described with the help of three independent nucleon helicity amplitudes. Measurements of the nucleon structure functions Fl(x, Q2) -the helicity average- and gi (2, Q2) -the helicity difference-, have explored the helicity conserving part of the cross sections with great experimental accuracy. In contrast, no information is presently available on the helicity flip amplitude. The absence of experimental measurements is a consequence of the chiral-odd nature of the helicity flip amplitude and the related “transversity quark distributions”, 6q(z, Q2), which prevents the appearance of helicity flip contributions at leading twist in inclusive DIS experiments. The experimental study of transversity distributions at leading twist requires observables which are the product of two objects with odd chirality. This was first discussed by Ralston and Soper [l] for Drell Yan scattering of two transversely polarized hadrons: The transverse double spin asymmetry, ATT, is proportional to 6q&j with even chirality. Transverse single spin asymmetries AT (e.g. unpolarized leptons on transversely polarized nucleon targets) in semi-inclusive DIS and pp scattering may offer an alternative way to observe helicity flip contributions at leading twist. This possibility relies on the presence of quark fragmentation functions (FF) which are sensitive to
the quark polarization in the final state and possess the necessary negative chirality. The asymmetries AT are proportional to C, Sq x af x FF, where a{ are the transversity dependent partonic initial-final-state asymmetries which can be calculated from pQCD. For example, Collins suggested that in semiinclusive single pion production the quark spin direction might be reflected in the azimuthal distribution of a final state pion [2]. Collins further demonstrated that the symmetry properties of the process do not require the proposed fragmentation function Hf to be identical to zero. The current interest in transversity distributions results from a recent HERMES result on azimuthal single spin asymmetries [3] and a preliminary SMC result [4], which suggest that Collins’s function Hk and the transversity distribution function 6q in fact are different from 0; see reference [5] for a detailed discussion. 2. Future
Transversity
Measurements
2.1. Drell Yan The PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) at BNL has the capability to study spin dependent Drell Yan production with longitudinal and transverse spin orientations. PHENIX possesses excellent lepton detection capabilities within a limited geometric acceptance; for electrons at mid rapidity In] 5 0.35,34’ < 141< 124’ and for muons in the pseudo rapidity range 1.2 < 171< 2.4.
0920-5632/02/$ ~ see front matter 0 2002 Published by Elsevier Science B.V. PI1 SO920-5632(01)01954-S
72
A4. Grosse Perdekmnp/Nucleur
Physics
Originally the transverse double spin asymmetry, ATT, in Drell Yan was viewed as a good candidate for a measurement of the transversity distribution functions at RHIC, ATT N SqStj . However, a recent analysis by Martin et al. [6] - using PHENIX acceptances and the projected luminosities for pp-running at RHIC, 320pb_r/year at 200 GeV - estimates ATT to be about 1% with statistical errors comparable to the asymmetry itself for a projected measurement at RHIC.
Lepton Pair Moss [GeVI
Figure 1. Projected Drell Yan double spin asymmetries ATT for a RHIC upgrade luminosity of s,,,, Ldt = 8 fb-’ at 200 GeV.
Future luminosity upgrades at RHIC possibly can reach integrated luminosities of up to s,,,, Ldt = 8 fb-’ at 200GeV. The sensitivities for ATT in Drell Yan for &,,,
Ldt = 8 f&l
at
200 GeV are shown in Fig. (1). The plotted sensitivities are obtained by extrapolating the results from reference [6] to the higher integrated luminosities. A significant measurement appears to be possible. However, it should be noted that currently there are no plans to carry out the massive detector upgrades necessary (event selection and data acquisition) to capitalize on luminosities of several fb ‘.
B (Proc. SuppI.)
2.2.
IO5 (2002) 71-75
Semi Inclusive
Deep
Inelastic
Scatter-
ing
The HERMES experiment at DESY is expected to start measurements with transverse target polarization in late 2001. The observable is Collins’ single spin asymmetry for charged pion production in deep inelastic electron proton scattering: The azimuthal distribution of the final state pions with respect to the virtual photon axis carries information about the transverse quark spin orientation. In a partonic picture of the nucleon the transverse single spin asymmetry AT is related to the transversity distributions as follows:
where Htg is the Collins function for a quark of flavor q and 0: is the regular spin independent fragmentation function. Korotkov, Nowak and Oganessyan have proposed an analysis procedure for the HERMES transverse asymmetries that - under the assumption of u-quark dominance, 6d = 0 - results in the extraction of the shape for 6u(z) and the ratio Hi-/D;” [7]. As a normalization condition to fix the absolute size of &J(Z) and the fragmentation function ratio it is further assumed that SU(Z~ = 0.25) = Au(zc) at some soft scale, Qz M 0.4 GeV. Alternatively, it may be worthwhile to investigate if the ratio Hf/Dy can be determined from fragmentation function measurements in e+e- annihilation using LEP and b-factory data, see section (3). The HERMES measurement of 6u(z) between 0.02 < 5 < 0.7 is projected to result in a statistical error of about 6~ Z!Z0.3 at the lowest z and 6u kO.1 at highest 2 [7]. Systematic errors are expected to be of comparable size. A similar measurement will be attempted by the COMPASS collaboration at CERN. The higher beam energy, 100 - 200 GeV compared to 27.5 GeV may allow, for the first time, the exploitation of interference fragmentation processes. However, the ultimate experiments to measure transversity distributions and their first moments, the tensor charge, appeal to be two future high luminosity electron proton scattering experiments: At DESY a fixed target
M. Grosse Perdekump/Nuclear
experiment has been proposed for one arm of a possible future e+e- linear accelerator collider at DESY: TESLA-N; it is estimated that the first moment of bu can be measured to about one percent and for 6d to 6% (81. At BNL the prospects of a future electron ion collider (EIC) with luminosities reaching 4 fb-‘/year have been studied. [9]: A measurement with the statistical precision of the HERMES measurement but at lower 5 can be achieved in one day of running or 20 pb-’ ; see Fig. (2).
_
0.05
r
0
With the presently available luminosities and detectors the proposal of Collins et al. [lo] and Jaffe et al. [ll] to utilize chiral odd two pion interference fragmentation processes appears to be the most promising approach to measure transversity at RHIC. This channel also has been studied for the RAMPEX experiment at IHEP Protvino [12]. The relevant process is pion pair production in pp
I
Invariant
Mass
Resolution
0.3 and 0.5
I
RMS=
12MeV
1~_____,__*__~___~____t____~,
-0.05
r
-0.1
-
-0.15
z between
Interference fragmentation and Collins fragmentation in direct photon jet events.
l
l,l
0.1
73
Plq*sics B (Psoc. Suppl.) 105 (2002) 71-75
r I,,,,, 1o-3
I I111111 I Illil,, lo-*
I ,,,,I_ 10-l
1
XE3jorken
300
-
200
t -
Ott,,,“,‘,-0.1
-0.15
Figure 2. Projected sensitivities for the single spin asymmetries in single inclusive pion production at the EIC for Jday Ldt = 20pb-’ and 0.3 < z = En/E, < 0.5.
Single Spin Asymmetries in Polarized Proton Scattering In addition to the double spin asymmetry measurements in Drell Yan the following single spin asymmetry measurements have been suggested for polarized proton scattering experiments:
r
100 -
-r
-0.05
,I,,, 0
0.05
“‘I
0.1
m +-rn,_
“”
0.15
IGeVl
Figure 3. Simulation studies of two pion production in the pmass region for the PHENIX detector. The invariant mass resolution for pion pairs is shown in the pmass region.
2.3.
Single spin asymmetries ference fragmentation.
in two pion inter-
The measurement of azimuthal asymmetries in the production of pions around the jet-axis (Collins fragmentation function).
scattering with one proton transversely polarized. For example, in the p/g invariant mass region interference occurs between two pions in a superposition of s-wave and p-wave states. The spin analyzing power of this process is different from 0 in intervals of only a few 1OOMeV above and below the pmass and changes sign at the pmass (131. Therefore, it will be important for RHIC experiments to have sufficiently high invariant mass resolution to observe the invariant mass dependence of the analyzing power. The invariant mass
M. Gro.we Perdekamp/Nuclear
74
Physics B {Proc. SuppI,) 105 (2002) 71-75
Table 1 Present and future measurements of transversity distributions. Different processes are used to access transversity distributions: Collins fragmentation (CF), interference fragmentation (IF) and Drell Yan (DY). Note that PHOBOS and BRAHMS currently have no approved transversity program. However, in absence of spin rotators at their interaction points both experiments will be able to engage in transversity measurements well before STAR and PHENIX where the transverse spin program competes with measurements using longitudinal proton spin orientation. Experiment
Location
Process
4
[GeV]
year
HERMES
DESY/HERA
DIS: CF
7.5
2001
COMPASS
CERN/SPS
DIS: CF, IF(?)
14 - 20
2003
EIC-detector
BNL/EIC
DIS: CF, IF
65 - 100
2008+
DESY/TESLA
DIS: CF, IF
8 - 22
2010+
RAMPEX
IHEP Protvino
pp: IF
12
2001
BRAHMSPHOBOS
BNL/RHIC
pp: IF
50 - 500
2002
PHENIX,STAR
BNL/RHIC
pp: IF, CF, DY
50 - 500
2006
TESLA-fixed
target
resolution for pion pairs in the p-mass region is shown in the left plot of Fig. (3) for the example of the PHENIX experiment. The RMS of the distribution is 12MeV - 15MeV for STAR which easily meets the demands for an experimental determination of transversity distributions at RHIC. In STAR transversity measurements rely on the large acceptance, Ir]] < 2.0, time projection chamber for tracking and the electromagnetic calorimeter for triggering purposes. The PHENIX measurement will use the central detector arms which cover the pseudo rapidity interval ]T$ < 0.35. A combination of tracking chambers will give good momentum resolution: Ap/p x 2% at p = 10GeV. The electromagnetic calorimeter in combination with the ring imaging Cherenkov Counter will provide pion identification over are large momentum range, 4 < px < 12GeV. In order to estimate experimental sensitivities a first study was carried out at the event generator level including PHENIX detector acceptances and a parametrizations of the PHENIX central arm momentum resolution. The results using an integrated luminosity of 32 pb-’ (corresponding to one week of polarized proton running at RHIC) are compared to asymmetry projections from Tang [13] in Fig. (4). The error bars shown in the plot represent statistical errors only. The asymmetries in Fig. (4) were obtained using up-
per bounds for the relevant distribution and fragmentation functions and represent an optimistic upper limit [13]. More detailed studies with different model assumptions and a full simulation of the detector response are underway. Nevertheless, the high rates at RHIC and the excellent momentum resolution in STAR and PHENIX are well suited for a transversity measurement in two pion interference fragmentation and a run with 320pb-l integrated luminosity has been added to of the spin physics run plan [14].
3. Collins and Interference Functions in e+e-
Fragmentation
All future transversity measurements have in common that their success critically depends on the knowledge of the spin dependent and chiral odd fragmentation functions giving sensitivity to transverse quark spin in the final state. Atru and Collins have provided a detailed recipe how to extract interference fragmentation functions from light quark di-jet events in e+e- collisions [15]. Efremov , Smirnova and Tkachev have carried out first experimental studies using LEP data from DELPHI [16]. A recent discussion of the prospects of transversity measurements using future fragmentation function information from e+e- can be found in reference [17].
M. Grosse Perdekanlp/Nuclear
Asvmmetrv
vs Std.
P&sics B (Proc.
Errors
r
-T-
Suppl.)105 (2002) 71-75
z = Eh/Eq and for different state hadrons.
75
combinations
of final
REFERENCES 1.
i
t
t Statistical
Errors only
i
6. 7.
Figure 4. Simulation studies of two pion production in the pmass region for the PHENIX detector: Projected transverse single spin asymmetries versus the transverse momentum of the pion pair. The statistical errors correspond to an integrated luminosity of s Ldt = 32pb-l at fi = 200GeV.
Additional studies in e+e- have been proposed using the high statistic data sample of the Belle experiment at the KEK b-factory [18] with the goal to measure the two relevant fragmentation functions: l
l
The Collins function Hf : The fragmentation of a transversely polarized quark into a charged pion and the azimuthal distribution of the final state pion with respect to the initial quark momentum (jet-axis). fragmentation functions Interference @h&z: The fragmentation of transversely polarized quarks into pairs of hadrons in a state which is the superposition of two different partial wave amplitudes; e.g. n+, ?rrpairs in the p, c invariant mass region.
High luminosities at KEKB - presently the integrated luminosity is 36.4fb-’ - and Belle’s superior particle identification will allow fragmentation function measurements over a large range in
8. 9. 10.
11. 12. 13. 14.
15. 16.
17. 18.
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