f giordano: spin-dependent effects in spin-averaged dis
TRANSCRIPT
SPIN EFFECTS IN UNPOLARIZED SIDIS
PSHP2010, Frascati18th-21st October 2010
Kaon Azimuthal cosine modulationsin SIDIS unpolarized cross section Francesca GiordanoRebecca Lamb
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DIS 2009 Madrid, 26-30 April 2009
Monday, October 18, 2010
Francesca GiordanoSPIN 2012, Dubna, Russia
1
Francesca Giordano
Collinear case
targetpolarization
beam polarization virtual photon
polarization
d3⇤dxdydz = �2
xyQ2
�1 + ⇥2
2x
�{A(y)FUU,T +B(y)FUU,L}
SEMI-INCLUSIVE DIS
2
Francesca Giordano
targetpolarization
beam polarization virtual photon
polarization
SEMI-INCLUSIVE DIS
2
Francesca Giordano
targetpolarization
beam polarization virtual photon
polarization
SEMI-INCLUSIVE DIS
Negative squared4-momentum transfer to the targetFractional energy of the virtual photonParton fractional momentumFractional energy transfer to the produced hadron
2
TRANSVERSE MOMENTUM DEPENDENT FUNCTIONS
DF
!FF
3
TRANSVERSE MOMENTUM DEPENDENT FUNCTIONS
DF
!FF
distribution functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum3
TRANSVERSE MOMENTUM DEPENDENT FUNCTIONS
DF
!FF
distribution functions
fragmentation functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum3
TRANSVERSE MOMENTUM DEPENDENT FUNCTIONS
DF
!FF
distribution functions
fragmentation functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum3
TRANSVERSE MOMENTUM DEPENDENT FUNCTIONS
DF
!FF
distribution functions
fragmentation functions
Boer-Mulders DF
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum3
TRANSVERSE MOMENTUM DEPENDENT FUNCTIONS
DF
!FF
distribution functions
fragmentation functions
Boer-Mulders DFCollins FF
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum3
Francesca Giordano
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum
LEADING TWIST TERMS
implicit sum over quark flavors
distribution functions
fragmentation functions
4
Francesca Giordano
LEADING AND NEXT-TO-LEADING TWIST TERMS
implicit sum over quark flavors
distribution functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum
fragmentation functions
5
Francesca Giordano
LEADING AND NEXT-TO-LEADING TWIST TERMS
implicit sum over quark flavors
distribution functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum
fragmentation functions
5
Francesca Giordano
LEADING AND NEXT-TO-LEADING TWIST TERMS
implicit sum over quark flavorsinteraction dependent
terms neglected
distribution functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum
fragmentation functions
5
Francesca Giordano
LEADING AND NEXT-TO-LEADING TWIST TERMS
implicit sum over quark flavorsinteraction dependent
terms neglected
+M2
Q2 C [ �2T
M2 f1D1 + ...]
distribution functions
Chapter2
2.2. The interpretation of TMD
PDF probabilistic interpretation chiral properties
f q1 (x) chiral-even
gq1 (x) chiral-even
hq1 (x) chiral-odd
legendtransverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
Table 2.1.: Pictorial representation and chiral properties of the leading-twist PDF: The notation ofthe quark distribution functions uses the letters f ,g,h specifying the quark polarisationand a subscript indicating leading-twist (digit 1) or subleading-twist distributions (digit2). Unpolarised quarks are denoted as f , longitudinally (transversely) polarised quarks asg (h). The dependence of the PDF on the quark flavour is included as superscript q.
whereas the amplitude that defines the transversity distribution involves a helicity flip:
hq1 (x)⇥ℑ[A+�,�+]. (2.17)
The momentum distribution (figure 2.2) and the helicity distribution (figure 2.3) have been mea-sured accurately in a variety of experiments. The measurement of the transversity distribution ishampered by its chiral properties. In the infinite momentum frame, where quark masses can be ne-glected, helicity and chirality properties of quarks are identical. Thus, the transversity distribution isassociated with both a helicity and chirality flip and known as a chiral-odd function. Chiral symmetrycan be dynamically broken for quark distribution (or fragmentation) functions which are describedby non-perturbative QCD. But chirality is conserved for all perturbative QCD and electroweak pro-cesses such as inclusive measurements of deep-inelastic scattering. Hence, the transversity distribu-tion can only be studied in interactions involving another chiral-odd (distribution or fragmentation)function. One example is an analysis of the Collins mechanism which is sensitive to transversity inconjunction with a chiral-odd fragmentation function (section 2.3).Another consequence of the chiral properties is the simple scale-dependence of the transversity
distribution. A helicity flip of spin-1 gluons would require a change of the nucleons’ helicities by|Λ�Λ⇤| = 2. Thus, there is no analogon of transversity for gluons in a nucleon. Contrary to themomentum and helicity distributions, transversity does not mix with gluons under Q2-evolution, i.e.there is no sea-quark contribution and transversity decreases slowly towards zero with increasingQ2.
2.2. The interpretation of TMDLeading twist effects are associated with quark-quark correlations; quark-gluon correlations enter atsubleading twist. In section 2.1.3, the leading twist parametrisation of the nucleon structure is dis-cussed in terms of the momentum f q1 (x), helicity gq1 (x) and transversity h
q1 (x) distributions. Omit-
ting also here the weak scale dependence, the three parton distribution functions depend only on theBjorken scaling variable x, representing in the infinite momentum frame the longitudinal momentum
9
transverse longitudinalnucleon spin
parton spin
DY 2011, BNL - May 11th, 2011Gunar Schnell
TMDs - Probabilistic interpretation
4
f1 =
g1 =
h1 =
f�1T =
h�1 =
h�1T =
h�1L =
g1T =
parton with transverse or longitudinal spin
parton transverse momentum
nucleon with transverse or longitudinal spin
Proton goes out of the screen/ photon goes into the screen
[courtesy of A. Bacchetta]
Wednesday, May 11, 2011
parton transverse momentum
fragmentation functions
5
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
6
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
6
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
SPIN Effect!
6
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
chiral odd chiral odd
chiral even!
}correlations between quark transverse spin &
transverse momentum
h?1 H?
1
chiral odd functions
SPIN Effect!
6
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
chiral odd functions
naive Time reversal odd
SPIN Effect!
6
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
Final State Interactions
correlations between quark transverse spin & transverse momentum
chiral odd functions
naive Time reversal odd
SPIN Effect!
6
uFSI
u
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
Final State Interactions
correlations between quark transverse spin & transverse momentum
chiral odd functions
naive Time reversal oddSpatial distortions due to
spin-orbit correlations
SPIN Effect!
6
uFSI
u
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
Final State Interactions
correlations between quark transverse spin & transverse momentum
chiral odd functions
naive Time reversal oddSpatial distortions due to
spin-orbit correlations
Collins FF H1A(z,kT2) correlates transverse spin of fragmenting quark
and transverse momentum PhA of produced hadron h
““CollinsCollins--effect” effect”
h
h
q q
Æ left-right (azimuthal) asymmetry in the direction of the outgoing hadron
our observable: singleour observable: single--spin spin azimuthalazimuthal asymmetryasymmetry
Collins effect
SPIN Effect!
6
uFSI
u
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
Final State Interactions
correlations between quark transverse spin & transverse momentum
Spatial distortions due to spin-orbit correlations
Collins FF H1A(z,kT2) correlates transverse spin of fragmenting quark
and transverse momentum PhA of produced hadron h
““CollinsCollins--effect” effect”
h
h
q q
Æ left-right (azimuthal) asymmetry in the direction of the outgoing hadron
our observable: singleour observable: single--spin spin azimuthalazimuthal asymmetryasymmetry
Collins effect
SPIN Effect!
access to Collins effect
6
uFSI
u
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
Cahn effect / C [f1D1]
Ph?
Ph?kT
kT
SPIN Effect!
access to Collins effect
7
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
Cahn effect / C [f1D1]
Ph?
Ph?kT
kT
kinematic effect generated by parton intrinsic transverse motion
SPIN Effect!
access to Collins effect
7
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
Cahn effect / C [f1D1]
Ph?
Ph?kT
kT
kinematic effect generated by parton intrinsic transverse motion
hqT i ! cos�q
h ! cos�Hh
SPIN Effect!
access to Collins effect
7
Francesca Giordano
BOER-MULDERS EFFECT/ C [�h?
1 H?1 ]Boer-Mulders effect
kTkT
Ph?
Ph? sT
sT
correlations between quark transverse spin & transverse momentum
Cahn effect / C [f1D1]
Ph?
Ph?kT
kT
kinematic effect generated by parton intrinsic transverse motion
access to parton transverse momenta
hqT i ! cos�q
h ! cos�Hh
SPIN Effect!
access to Collins effect
7
Francesca GiordanoFrancesca Giordano
HERMES @ HERA
8
Francesca Giordano
DESY
Francesca Giordano
HERMES @ HERA
8
Francesca Giordano
DESY
Francesca Giordano
HERMES @ HERA
27.6 GeV (e+/e-) lepton beam off D/H target
8
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
!"#$%&'$()
*+,#-./'
0/$1(
1*2345
(,/6.(
*.!!07*
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9/&9<*+,#-./'
1$.!02*!,#9'
9/.'+&=./2>+5?
'(..!29!,(. *,!&/$#.(./
0/$1(2*+,#-./'
(/$66./2+&0&'*&9.2+3
" ! # % & ' ( ) * + !"
/$*+5@:2ABCD
5@:2ABCD
#"&%2+&0&'*&9.
=$0.2,%6!.
1/&%(
#"&%
+&0&
#,6%.(
$
$/&%2=,!!
EF
5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
RICH
RICH
DIPOLE
DIPOLE
9
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
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*+,#-./'
0/$1(
1*2345
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*.!!07*
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9/.'+&=./2>+5?
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=$0.2,%6!.
1/&%(
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EF
5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
27.6GeV e± beam
RICH
RICH
DIPOLE
DIPOLE
9
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
!"#$%&'$()
*+,#-./'
0/$1(
1*2345
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*.!!07*
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9/.'+&=./2>+5?
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0/$1(2*+,#-./'
(/$66./2+&0&'*&9.2+3
" ! # % & ' ( ) * + !"
/$*+5@:2ABCD
5@:2ABCD
#"&%2+&0&'*&9.
=$0.2,%6!.
1/&%(
#"&%
+&0&
#,6%.(
$
$/&%2=,!!
EF
5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
27.6GeV e± beam
H/D target
RICH
RICH
DIPOLE
DIPOLE
9
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
!"#$%&'$()
*+,#-./'
0/$1(
1*2345
(,/6.(
*.!!07*
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9/.'+&=./2>+5?
'(..!29!,(. *,!&/$#.(./
0/$1(2*+,#-./'
(/$66./2+&0&'*&9.2+3
" ! # % & ' ( ) * + !"
/$*+5@:2ABCD
5@:2ABCD
#"&%2+&0&'*&9.
=$0.2,%6!.
1/&%(
#"&%
+&0&
#,6%.(
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$/&%2=,!!
EF
5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
27.6GeV e± beam
H/D target
RICH
RICH
DIPOLE
DIPOLE
tracking detectors: momentum resolution <2.5%
9
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
!"#$%&'$()
*+,#-./'
0/$1(
1*2345
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*.!!07*
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9/&9<*+,#-./'
1$.!02*!,#9'
9/.'+&=./2>+5?
'(..!29!,(. *,!&/$#.(./
0/$1(2*+,#-./'
(/$66./2+&0&'*&9.2+3
" ! # % & ' ( ) * + !"
/$*+5@:2ABCD
5@:2ABCD
#"&%2+&0&'*&9.
=$0.2,%6!.
1/&%(
#"&%
+&0&
#,6%.(
$
$/&%2=,!!
EF
5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
27.6GeV e± beam
H/D targetparticle identification: lepton/hadron separation
RICH
RICH
DIPOLE
DIPOLE
tracking detectors: momentum resolution <2.5%
9
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
!"#$%&'$()
*+,#-./'
0/$1(
1*2345
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=$0.2,%6!.
1/&%(
#"&%
+&0&
#,6%.(
$
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EF
5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
27.6GeV e± beam
H/D target
RICH: discrimination between charged " / K / p
particle identification: lepton/hadron separation
RICH
RICH
DIPOLE
DIPOLE
tracking detectors: momentum resolution <2.5%
9
Francesca Giordano
HERMES
CIPANP San Diego, CA May 29, 2009Rebecca Lamb
The HERMES Spectrometer
6
!
"
#
!!
!#
$
!"#$%&'$()
*+,#-./'
0/$1(
1*2345
(,/6.(
*.!!07*
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9/&9<*+,#-./'
1$.!02*!,#9'
9/.'+&=./2>+5?
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0/$1(2*+,#-./'
(/$66./2+&0&'*&9.2+3
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/$*+5@:2ABCD
5@:2ABCD
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=$0.2,%6!.
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+&0&
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5@<G26E7
3;:2ABCD
3@:2ABCD
3@:2ABCD
3;:2ABCD
#"&%2+&0&'*&9.'
27.6GeV e± beam
H/D target
RICH: discrimination between charged " / K / p
particle identification: lepton/hadron separation
RICH
RICH
DIPOLE
DIPOLE
tracking detectors: momentum resolution <2.5%
9
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
�0w[1 + 2hcos�hiw + 2hcos 2�hiw]
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
34
MC
RAD
MCMCMC
accLn !!=MC
0"RAD
EXP
accLn !!" )1(0 +=
CAHNn
#h
#h
#h
#h
#h
)()( #!#!RADacc
)2coscos1( ## BA ++= LnEXP
0"CAHNn
0" )1(UUFA+
Generated in 4⇡
!"!#"!#!$ dLn MC
RAD
MCMCMCMC
acc ),(),()(0=
),(),( "!#"!#
RADacc)2cos)(cos)(1( "!"! BA ++= LnEXP )(0 !$ !d
%
Inside acceptanceMC
MC simulation of spectrometers to correct for acceptance/QED radiation
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
34
MC
RAD
MCMCMC
accLn !!=MC
0"RAD
EXP
accLn !!" )1(0 +=
CAHNn
#h
#h
#h
#h
#h
)()( #!#!RADacc
)2coscos1( ## BA ++= LnEXP
0"CAHNn
0" )1(UUFA+
Generated in 4⇡
!"!#"!#!$ dLn MC
RAD
MCMCMCMC
acc ),(),()(0=
),(),( "!#"!#
RADacc)2cos)(cos)(1( "!"! BA ++= LnEXP )(0 !$ !d
%
Inside acceptanceMC
MC simulation of spectrometers to correct for acceptance/QED radiation
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
n =
ZL⇥0
w�accw,�h
�radw,�hdw
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
34
MC
RAD
MCMCMC
accLn !!=MC
0"RAD
EXP
accLn !!" )1(0 +=
CAHNn
#h
#h
#h
#h
#h
)()( #!#!RADacc
)2coscos1( ## BA ++= LnEXP
0"CAHNn
0" )1(UUFA+
Generated in 4⇡
!"!#"!#!$ dLn MC
RAD
MCMCMCMC
acc ),(),()(0=
),(),( "!#"!#
RADacc)2cos)(cos)(1( "!"! BA ++= LnEXP )(0 !$ !d
%
Inside acceptanceMC
MC simulation of spectrometers to correct for acceptance/QED radiation
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
n =
ZL⇥0
w�accw,�h
�radw,�hdw
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
34
MC
RAD
MCMCMC
accLn !!=MC
0"RAD
EXP
accLn !!" )1(0 +=
CAHNn
#h
#h
#h
#h
#h
)()( #!#!RADacc
)2coscos1( ## BA ++= LnEXP
0"CAHNn
0" )1(UUFA+
Generated in 4⇡
!"!#"!#!$ dLn MC
RAD
MCMCMCMC
acc ),(),()(0=
),(),( "!#"!#
RADacc)2cos)(cos)(1( "!"! BA ++= LnEXP )(0 !$ !d
%
Inside acceptanceMC
Not allowed!
MC simulation of spectrometers to correct for acceptance/QED radiation
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
n =
ZL⇥0
w�accw,�h
�radw,�hdw
10
Francesca Giordano
ACCEPTANCE CORRECTIONw = (x, y, z, Ph?)
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
34
MC
RAD
MCMCMC
accLn !!=MC
0"RAD
EXP
accLn !!" )1(0 +=
CAHNn
#h
#h
#h
#h
#h
)()( #!#!RADacc
)2coscos1( ## BA ++= LnEXP
0"CAHNn
0" )1(UUFA+
Generated in 4⇡
!"!#"!#!$ dLn MC
RAD
MCMCMCMC
acc ),(),()(0=
),(),( "!#"!#
RADacc)2cos)(cos)(1( "!"! BA ++= LnEXP )(0 !$ !d
%
Inside acceptanceMC
Not allowed!
MC simulation of spectrometers to correct for acceptance/QED radiation
only if fully differential ratio (4D binning)and only in the limit of infinitely small bins
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
n =
ZL⇥0
w�accw,�h
�radw,�hdw
10
Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
ACCEPTANCE CORRECTION
�
11
Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
nborn
= S�1[n�B0]
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
ACCEPTANCE CORRECTION
�
11
Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
describes the acceptance & smearing between adjacent bins
events smeared in the sample from outside the acceptance
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
nborn
= S�1[n�B0]
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
ACCEPTANCE CORRECTION
�
11
Francesca Giordano
w = (x, y, z, Ph?)
(w)4-dimensional
describes the acceptance & smearing between adjacent bins
events smeared in the sample from outside the acceptance
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
A(1 +B cos�h + C cos 2�h)
nborn
= S�1[n�B0]
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
unfolding
ACCEPTANCE CORRECTION
�
11
Francesca Giordano
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
PION FIT & PROJECTIONw = (x, y, z, Ph?)
(w)4-dimensional
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
A(1 +B cos�h + C cos 2�h)
unfolding
�
z
xy
Ph?
12
Francesca Giordano
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
0.023 0.042 0.078 0.145 0.27
0.3 0.45 0.6 0.7 0.85
0.2 0.3 0.4 0.5 0.6 0.750.05 0.2 0.35 0.5 0.7 1
PION FIT & PROJECTIONw = (x, y, z, Ph?)
(w)4-dimensional
n =
ZL⇥0
w[1 + 2hcos⇤hiw + 2hcos 2⇤hiw]�accw,�h�radw,�h
dw
A(1 +B cos�h + C cos 2�h)
unfolding
�
z
xy
Ph?
12
Francesca Giordano
Boer-Mulders
Cahn
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
Boer-Mulders
Cahn
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
Gamberg, GoldsteinPhys. Rev. D77:094016, 2008
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
Zhang et alPhys. Rev. D78:034035, 2008
Gamberg, GoldsteinPhys. Rev. D77:094016, 2008
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
Barone et alPhys. Rev. D78:045022, 2008
Zhang et alPhys. Rev. D78:034035, 2008
Gamberg, GoldsteinPhys. Rev. D77:094016, 2008
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
SPIN Effect!13
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
Hydrogen vs Deuterium
SPIN Effect!14
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
Boer-Mulders
Cahn
COS2 : PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
h?,u1 ⇡ h?,d
1
Hydrogen vs Deuterium
SPIN Effect!14
arXiv:1204.4161
Francesca Giordano
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
COS : PIONS�Final!/ 2M
Q C [�h?1 H
?1
�f1D1 + ....]
15
arXiv:1204.4161
Francesca Giordano
Cahn
Boer-Mulders
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
COS : PIONS�Final!/ 2M
Q C [�h?1 H
?1
�f1D1 + ....]
15
arXiv:1204.4161
Francesca Giordano
Cahn
/01&"#2'3" 456785988:.#;88<=>?"#/01&"#@" $A67A5A.#;885
!"
x
-110
UU
!)h"
co
s(
#2
-0.2
-0.1
0
0.1$%+%
y
0.4 0.6 0.8
-0.2
-0.1
0
0.1 X% e &e p
z 0.4 0.6
-0.2
-0.1
0
0.1
[GeV]'h
P
0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1 HERMES preliminary
#$%"& '$()*+,-$. [ ]...2
1111
cos +$$( '' DfHhQ
MF h
UU C"
!"#$%&'()*%+#', -(".#/01&"#2'3" 456785988:.#;88<=>?"#/01&"#@" $A67A5A.#;885
F cos�h
UU / C [h?1
H?1
�f1
D1
+....]F cos�h
UU / C [h?1
H?1
�f1
D1
+....]
Cahn only
Too large!
x
-110
UU
!)h"
co
s(
#2
-0.2
-0.1
0
0.1$%+%
y
0.4 0.6 0.8
-0.2
-0.1
0
0.1 X% e &e p
z 0.4 0.6
-0.2
-0.1
0
0.1
[GeV]'h
P
0.2 0.4 0.6 0.8 1
-0.2
-0.1
0
0.1 HERMES preliminary
" [ ]...2
1111
cos +$$( '' DfHhQ
MF h
UU C"
Boer-Mulders
Cahn expected flavor blind
different / amplitudes Boer-Mulders effect
⇡+⇡�
COS : PIONS�Final!/ 2M
Q C [�h?1 H
?1
�f1D1 + ....]
15
arXiv:1204.4161
Francesca Giordano
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
KAON FIT & PROJECTION
(w)4-dimensional
A(1 +B cos�h + C cos 2�h)
unfolding
�
z
xy
Ph?
16
Francesca Giordano
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Binning900 kinematic bins x 12 -bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #x 0.023 0.042 0.078 0.145 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1.3 6Ph?
KAON FIT & PROJECTION
0.042 0.078 0.145 0.27
0.3 0.45 0.6 0.7
0.3 0.4 0.5 0.6
0.2 0.35 0.5 0.7
(w)4-dimensional
A(1 +B cos�h + C cos 2�h)
unfolding
�
z
xy
Ph?
16
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final! / C [�h?
1 H?1
+2T
Q2f1D1 + ....]
17
arXiv:1204.4161
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final!
Boer-Mulders
Cahn
/ C [�h?1 H
?1
+2T
Q2f1D1 + ....]
17
arXiv:1204.4161
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final!
Boer-Mulders
Cahn
/ C [�h?1 H
?1
+2T
Q2f1D1 + ....]
No predictions for Kaons!
17
arXiv:1204.4161
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final!
Boer-Mulders
Cahn
/ C [�h?1 H
?1
+2T
Q2f1D1 + ....]
No predictions for Kaons! Favored dominance for & .
same signK+ ⇡+ ?
17
arXiv:1204.4161
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final!
Boer-Mulders
Cahn
/ C [�h?1 H
?1
+2T
Q2f1D1 + ....]
No predictions for Kaons! Favored dominance for & .
same signK+ ⇡+ ?
fully sea object!both favored&unfavored fragmentation
K�
17
arXiv:1204.4161
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final!
Boer-Mulders
Cahn
/ C [�h?1 H
?1
+2T
Q2f1D1 + ....]
No predictions for Kaons! Favored dominance for & .
same signK+ ⇡+ ?
fully sea object!both favored&unfavored fragmentation
K�
Non trivial!17
arXiv:1204.4161
Francesca GiordanoFrancesca Giordano
COS2 KAONS & PIONS�Final!
Boer-Mulders
Cahn
/ C [�h?1 H
?1
+2T
Q2f1D1 + ....]
No predictions for Kaons! Favored dominance for & .
same signK+ ⇡+ ?
fully sea object!both favored&unfavored fragmentation
K�
Non trivial!
Collins FF for kaons soon from Belle
17
arXiv:1204.4161
Francesca Giordano
COS KAONS & PIONS�Final!
No predictions for Kaons!Similar trends for Pion-Kaon
/ 2MQ C [�h?
1 H?1
�f1D1 + ....]
18
arXiv:1204.4161
Francesca Giordano
COS KAONS & PIONS�Final!
No predictions for Kaons!Similar trends for Pion-Kaon ?
Cahn
Boer-Mulders
/ 2MQ C [�h?
1 H?1
�f1D1 + ....]
18
arXiv:1204.4161
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
19
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
3rd x bin
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
3rd x bin 4th x bin
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
3rd x bin 4th x bin 5th x bin
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
3rd x bin 4th x bin 5th x bin
HYDROGEN, .⇡+
DEUTERIUM, .⇡+
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
3rd x bin 4th x bin 5th x bin
HYDROGEN, .⇡+
HYDROGEN, .⇡�DEUTERIUM, .
⇡+DEUTERIUM, .⇡�
HYDROGEN, .K�HYDROGEN, .K+
DEUTERIUM, .K�DEUTERIUM, .K+
HYDROGEN, .HYDROGEN, .
DEUTERIUM, .DEUTERIUM, .
h+
h+h�
h�
20
Francesca Giordano
MULTI-D RESULTShttp://durpdg.dur.ac.uk
First 6 bins
1st x bin2nd x bin
3rd x bin 4th x bin 5th x bin
HYDROGEN, .⇡+
HYDROGEN, .⇡�DEUTERIUM, .
⇡+DEUTERIUM, .⇡�
HYDROGEN, .K�HYDROGEN, .K+
DEUTERIUM, .K�DEUTERIUM, .K+
HYDROGEN, .HYDROGEN, .
DEUTERIUM, .DEUTERIUM, .
THERE’S AN EASIER WAY!
h+
h+h�
h�
20
Francesca Giordano
A USEFUL TOOLhttp://www-hermes.desy.de/cosnphi/
New!
21
Francesca Giordano
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #
x 0.02 0.04 0.08 0.15 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1 6Ph?
�
A USEFUL TOOL
New!
z
xy
Ph?
22
Francesca Giordano
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #
x 0.02 0.04 0.08 0.15 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1 6Ph?
�
A USEFUL TOOL
New!
z
xy
Ph?
22
Francesca Giordano
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Binning900 kinematic bins x 12 - bins
Variable Bin limitsBin limitsBin limitsBin limitsBin limitsBin limitsBin limits #
x 0.02 0.04 0.08 0.15 0.27 0.6 5
y 0.2 0.3 0.45 0.6 0.7 0.85 5
z 0.2 0.3 0.4 0.5 0.6 0.75 1 6
0.05 0.2 0.35 0.5 0.7 1 1 6Ph?
�
A USEFUL TOOL
New!
z
xy
Ph?
22
Francesca Giordano
A USEFUL TOOL
New!23
Francesca Giordano
UU
�qco
s2�
2
-0.2
-0.1
0
0.1+h
x -110
UU
�qco
s2�
2
-0.2
-0.1
0
0.1-h
y 0.4 0.6 0.8
z 0.4 0.6 0.8
e h XAe p
[GeV]�hP0.2 0.4 0.6 0.8 1 1.2
Systematic errors not shown
Systematic errors not shown
A USEFUL TOOL
New!23
Francesca Giordano
UU
�qco
s2�
2
-0.2
-0.1
0
0.1+h
x -110
UU
�qco
s2�
2
-0.2
-0.1
0
0.1-h
y 0.4 0.6 0.8
z 0.4 0.6 0.8
e h XAe p
[GeV]�hP0.2 0.4 0.6 0.8 1 1.2
Systematic errors not shown
Systematic errors not shown
A USEFUL TOOL
New!23
Francesca Giordano
PIONS: MORE PROJECTIONSFull z-dependence
24
Francesca Giordano
PIONS: MORE PROJECTIONSFull z-dependence
24
Francesca Giordano
PIONS: MORE PROJECTIONSFull z-dependence Full -dependencePh?
24
Francesca Giordano
KAONS: MORE PROJECTIONSLarger z-dependence Larger -dependencePh?
25
Francesca Giordano
KAONS: MORE PROJECTIONSLarger z-dependence Larger -dependencePh?
25
Francesca Giordano
SUMMARYTo date provides the most complete data set available for Boer-Mulders and Cahn effects!
DIS 2009 Madrid, 26-30 April 2009
26
Francesca Giordano
Different behavior for with respect to pions:large signals and same sign for modulation: indication of same sign for favored/unfavored strange Collins fragmentation functions?
K+/K�
cos 2�h
SUMMARYTo date provides the most complete data set available for Boer-Mulders and Cahn effects!
DIS 2009 Madrid, 26-30 April 2009
26
Francesca Giordano
Different behavior for with respect to pions:large signals and same sign for modulation: indication of same sign for favored/unfavored strange Collins fragmentation functions?
K+/K�
cos 2�h
Differences between :evidence of a non-zero Boer-Mulders function: confirms opposite sign for favored and unfavored pion Collins fragmentation functions
�+/��
SUMMARYTo date provides the most complete data set available for Boer-Mulders and Cahn effects!
DIS 2009 Madrid, 26-30 April 2009
26
Francesca Giordano
Different behavior for with respect to pions:large signals and same sign for modulation: indication of same sign for favored/unfavored strange Collins fragmentation functions?
K+/K�
cos 2�h
Differences between :evidence of a non-zero Boer-Mulders function: confirms opposite sign for favored and unfavored pion Collins fragmentation functions
�+/��
Similar results for deuterium & hydrogen data suggest a Boer-Mulders function with same sign for u and d quark
SUMMARYTo date provides the most complete data set available for Boer-Mulders and Cahn effects!
DIS 2009 Madrid, 26-30 April 2009
26
Francesca Giordano
Different behavior for with respect to pions:large signals and same sign for modulation: indication of same sign for favored/unfavored strange Collins fragmentation functions?
K+/K�
cos 2�h
Differences between :evidence of a non-zero Boer-Mulders function: confirms opposite sign for favored and unfavored pion Collins fragmentation functions
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Thank you!Similar results for deuterium & hydrogen data suggest a Boer-Mulders function with same sign for u and d quark
SUMMARYTo date provides the most complete data set available for Boer-Mulders and Cahn effects!
DIS 2009 Madrid, 26-30 April 2009
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