Marco Guzzi Universit

1
Marco Guzzi Università di Lecce, Università
dellInsubria(collaboration with V.Barone, A.
Cafarella, C. Corianò, P.G.Ratcliffe)

• Transverse Double Spin Asymmetries in Drell-Yan
  processes with antiprotons

Transversity 2005 Villa Olmo (Como), 7-10th.
September 2005
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The missing piece in the leading twist QCD
description of the nucleon is the transversity
density
dq(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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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 (vs200 GeV, Mlt10 GeV, x1 x2M²/s
lt310³) probes the low x region where dq(x) is
suppressed by QCD evolution compared to q(x).
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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)
s30 GeV² or 45 GeV² (fixed target) up to
200 GeV ² (collider mode)
GSI kinematics
Mgt2 GeV t x1 x2 M²/s gt0.1
(M is the dilepton invariant mass)
Double transverse pp Drell-Yan process probes the
product dq dq of two quark distributions and
the GSI kinematics is such that the asymmetries
are dominated by valence.
?
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At leading order
is found to be of order of 30 (Anselmino et al.
2004 Efremov et al. 2004 )
- - - - - s30 GeV²
____
s45 GeV²
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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 ? is the
azimuthal angle of the dilepton pair)
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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)
df(x, µ) ?f(x, µ)
(Minimal Bound)
2 df(x, µ) f(x, µ) ?f(x, µ)
Saturation of Soffers inequality
We used GRV input distributions whose starting
scale (at NLO) is µ00.63 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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We plot the ratio
NLO ATT with M integrated from 2 to 3 GeV using
GRV input with the minimal bound df(x, µ) ?f(x,
µ)
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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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NLO ATT with M integrated from 4 to 7 GeV using
GRV input with the minimal bound df(x, µ)
?f(x, µ). The asymmetry gets larger at larger M
(but the cross section goes down rapidly)
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NLO vs. LO
LO vs. NLO asymmetries generated using GRV
input with the minimal bound at M4 GeV and s45
GeV²
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LO vs. NLO asymmetries generated using GRV input
with the minimal bound at M4 GeV and s200 GeV²
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NLO ATT/âTT integrated over M from 2 up to 3
GeV. Setting the constraint df(x, µ) ?f(x, µ)
at 1 GeV gives slightly larger asymmetries
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Dilepton production via J/? resonance in the GSI
regime
To have a higher counting rate one can exploit
the J/? peak, where the cross section is two
orders of magnitude larger. If the J/?
production is dominated by qq annhilation channel
the corresponding asymmetry has the same
structure as in the continuum region, since the
J/? is a vector particle and qq-J/? coupling is
similar to qq-? coupling (M. Anselmino et al.
2004).
?
?
?
Old SPS data show that the pp cross section for
J/ ? production at s80 GeV² is about 10 times
larger than the corresponding pp cross section,
indicating the dominance of the qq annhilation
mechanism.
?
?
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The helicity structure of the asymmetries is
preserved. Replacing the couplings
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In the region of large x1 x2 only the u and d
valence quarks dominate and the coupling qq-J/?
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)gtgth1d(x) holds. Hence one gets
The J/? asymmetry is essentially the DY asymmetry
evaluated at MJ/? 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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Threshold Resummation (Shimizu et al. 2005)
Virtual and Real emission diagrams
become strongly unbalanced (real-gluon emission
is suppressed)
z t/(x1 x2) 1
There are large logarithmic higher-order
corrections to the partonic cross section of the
form
The region z1 is dominant in the kinematic
regime relevant for GSI, hence large logarithmic
contributions need to be resummed to all orders
in as, (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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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/? 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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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, 114007 (2005)
• 3 O. Martin, A. Schäfer, M. Stratmann, and W.
  Vogelsang
• Phys. Rev. D 60 117502 (1999)
• 4 A. Mukherjee, M. Stratmann, and W. Vogelsang
• Phys. Rev. D 67 114006 (2003)
• 5 J. Soffer, Phys. Rev. Lett. 74 1292 (1995)
• 6 Proton-Antiproton scattering experiments with
  polarization
• (V. Barone et al.) hep-ex/0505054
• 7 M. Anselmino, V. Barone, A. Drago, N.N.
  Nikolaev,
• Phys. Lett. B 594 97 (2004)

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NLO vs. LO asymmetries plotted using GRV input
evolved up to 1 GeV and saturating the minimal
bound with a fixed value of M4 GeV.
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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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NLO vs. LO transversely polarized cross section
with M4 GeV and s 45 GeV²