1. Villa Olmo (Como), 7−10th. September 2005
9/19/2018
Transverse Double Spin Asymmetries in Drell-Yan processes with antiprotons
Marco Guzzi Università di Lecce, Università dell’Insubria (collaboration with V.Barone, A. Cafarella, C. Corianò, P.G.Ratcliffe)
“Transversity 2005“
Villa Olmo (Como), 7−10th. September 2005
19/09/2018
M. Guzzi
M. Guzzi

2. The missing piece in the leading twist QCD description of
the nucleon is the transversity density
δq(x) = qhh(x) - qhi(x)
Given its chirally-odd nature, transversity may be accessed in collisions
between two transversely polarized nucleons.
Double polarized Drell-Yan production is the
cleanest process that probes the transversity distributions.
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3. Double-spin transverse asymmetries depend on quark and
antiquark transversity distributions only.
Measurement of is planned at RHIC but this
asymmetry is expected to be small (2-3%).
(Barone, Calarco, Drago 1997; O. Martin et al. 1998)
contains antiquark transversity distributions
RHIC kinematics (√s=200 GeV, M<10 GeV, x1 x2=M²/s <3×10­³) probes
the low x region where δq(x) is suppressed by QCD evolution compared
to q(x).
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4. This is the program of the PAX experiment at GSI
These problems may be avoided by measuring
at lower center of mass energies.
(Barone, Calarco, Drago 1997; Anselmino et al. 2004)
This is the program of the PAX experiment at GSI
(PAX Technical report, hep-ex/o5o5o54)
s=30 GeV² or 45 GeV² (fixed target)
up to 200 GeV ² (collider mode)
GSI kinematics
M>2 GeV
τ = x1 x2 = M²/s >0.1
(M is the dilepton invariant mass)
Double transverse pp Drell-Yan process probes the product δq × δq
of two quark distributions and the GSI kinematics is such that the
asymmetries are dominated by valence. ‾
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5. is found to be of order of 30% (Anselmino et al. 2004;
At leading order:
is found to be of order of 30% (Anselmino et al. 2004;
Efremov et al )
s=30 GeV²
____
s=45 GeV²
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6. and the hard scattering term is
At NLO the factorization formula for the cross section of transversely
polarized proton-antiproton scattering with dilepton production is
(O. Martin et al. 1999; Mukherjee et al. 2003)
and the hard scattering term is
(y is the rapidity variable and Ф is the azimuthal angle of the dilepton pair)
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7. To predict the asymmetries one has to make some assumption about the
transversity distributions. For instance:
Helicity = Transversity at low scale (as suggested by models)
δf(x, μ) = Δf(x, μ)
(“Minimal Bound”)
Saturation of Soffer’s inequality
2 δf(x, μ) ≤ [ f(x, μ) + Δf(x, μ) ]
We used GRV input distributions whose starting scale (at NLO) is
μ0=0.63 GeV. The relations between transversity and the GRV distributions
are set at this scale.
The transversity densities have been evolved by solving the appropriate
NLO DGLAP equations (Cafarella, Corianò 2004)
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8. We plot the ratio
NLO ATT with M integrated from 2 to 3 GeV using GRV input with the minimal bound δf(x, μ) = Δf(x, μ)
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9. ATT at NLO with M integrated from 2 to 3 GeV using GRV input saturating
the Soffer bound.
(Systematically larger than ATT obtained with the “minimal bound”)
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10. NLO ATT with M integrated from 4 to 7 GeV using GRV input with the
minimal bound δf(x, μ) = Δf(x, μ).
The asymmetry gets larger at larger M (but the cross section goes down rapidly)
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11. NLO vs. LO LO vs. NLO asymmetries generated using GRV input
with the minimal bound at M=4 GeV and s=45 GeV²
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12. LO vs. NLO asymmetries generated using GRV input with the minimal bound at M=4 GeV and s=200 GeV²
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13. NLO ATT/âTT integrated over M from 2 up to 3 GeV.
Setting the constraint δf(x, μ) = Δf(x, μ) at 1 GeV gives
slightly larger asymmetries
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14. Dilepton production via J/Ψ resonance in the GSI regime
To have a higher counting rate one can exploit the J/Ψ peak, where the
cross section is two orders of magnitude larger.
If the J/Ψ production is dominated by qq annhilation channel
the corresponding asymmetry has the same structure as in the continuum
region, since the J/Ψ is a vector particle and qq-J/Ψ coupling is similar to
qq-γ* coupling (M. Anselmino et al. 2004). ‾ ‾ ‾
Old SPS data show that the pp cross section for J/ Ψ production at s=80 GeV²
is about 10 times larger than the corresponding pp cross section, indicating the
dominance of the qq annhilation mechanism. ‾ ‾
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15. The helicity structure of the asymmetries is preserved. Replacing the
couplings:
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16. transversity the condition h1u(x)>>h1d(x) holds. Hence one gets
In the region of large x1 x2 only the u and d valence quarks dominate and the
coupling qq-J/Ψ is the same for u and d quarks. Thus the asymmetry for the
pp process is ‾ ‾
We can have a further simplification since at large x in all the models for
transversity the condition h1u(x)>>h1d(x) holds. Hence one gets
The J/Ψ asymmetry is essentially the DY asymmetry evaluated at MJ/Ψ
This remains true at NLO (that is considering gluon radiation) as far
as the gg fusion diagram can be neglected, as old pp data suggest. ‾
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17. Threshold Resummation (Shimizu et al. 2005)
Virtual and Real emission diagrams become
strongly unbalanced (real-gluon emission
is suppressed)
z = τ/(x1 x2) ≤ 1
There are large logarithmic higher-order corrections to the partonic
cross section of the form
The region z≈1 is dominant in the kinematic regime relevant for GSI,
hence large logarithmic contributions need to be resummed to all
orders in αs, (“threshold resummation”).
Resummation effects on ATT are less than 10% and rather dependent on the
infrared cut-off in the soft gluon emission.
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18. Conclusions
Drell-Yan double transverse asymmetries in the GSI regime are
sizable (ATT/âTT ≈0.3).
They are not spoiled by NLO (and resummation) effects.
Transverse asymmetries for J/Ψ production at moderate
energies are expected to be similar (with the advantage of much
higher counting rate).
Transversely polarized antiproton experiments at GSI will provide
an excellent window on the transversity of nucleons.
THANK YOU!
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M. Guzzi

19. Bibliography
[1] A. Cafarella, C. Corianò, V. Barone, M. Guzzi and P. Ratcliffe in preparation.
[2] Shimizu, Sterman, Vogelsang and Yokoya,
Phys. Rev. D 71, (2005)
[3] O. Martin, A. Schäfer, M. Stratmann, and W. Vogelsang
Phys. Rev. D (1999)
[4] A. Mukherjee, M. Stratmann, and W. Vogelsang
Phys. Rev. D (2003)
[5] J. Soffer, Phys. Rev. Lett (1995)
[6] Proton-Antiproton scattering experiments with polarization
(V. Barone et al.) hep-ex/
[7] M. Anselmino, V. Barone, A. Drago, N.N. Nikolaev,
Phys. Lett. B (2004)
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20. NLO vs. LO asymmetries plotted using GRV input evolved up to 1 GeV
and saturating the minimal bound with a fixed value of M=4 GeV.
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21. NLO transversely polarized cross section with M integrated from 2 to 3
GeV , with GRV input evolved up to 1 GeV and saturating the minimal
bound.
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22. NLO vs. LO transversely polarized cross section with M=4 GeV and
s= 45 GeV²
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M. Guzzi