Review of TMDs in SIDIS

1. Francesca Giordano
Riken, Wako, Japan, 30 June 2015
Exploring the proton
structure with TMDs in SIDIS
1
* from Symmetry Magazine

2. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
?

3. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
?
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!

4. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
?
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Large distances:
Non-Perturbative = Not calculable!
Fragmentation

5. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Large distances:
Non-Perturbative = Not calculable!
Fragmentation

6. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Large distances:
Non-Perturbative = Not calculable!
Fragmentation

7. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Large distances:
Non-Perturbative = Not calculable!
Fragmentation

8. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Large distances:
Non-Perturbative = Not calculable!
Fragmentation
Quarks
Gluons
Proton
Mass
~5%
~95%
Higgs
~1%

9. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Proton
Momentum
~50%
~50%
Large distances:
Non-Perturbative = Not calculable!
Fragmentation
Quarks
Gluons
Proton
Mass
~5%
~95%
Higgs
~1%

10. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Proton
Momentum
~50%
~50%
Proton
Spin
30%
?
Large distances:
Non-Perturbative = Not calculable!
Fragmentation
Quarks
Gluons
Proton
Mass
~5%
~95%
Higgs
~1%

11. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Proton
Momentum
~50%
~50%
Proton
Spin
30%
?
Large distances:
Non-Perturbative = Not calculable!
Fragmentation
Where is the Spin of the
Proton?
Quarks
Gluons
Proton
Mass
~5%
~95%
Higgs
~1%

12. Francesca Giordano
Proton Structure
2
1970s:
Quantum ChromoDynamics
2015:
still not able to describe QCD
fundamental state: the proton
Small distances:
Asymptotic freedom,
Perturbative theory= calculable!
Color confinement
Proton
Momentum
~50%
~50%
Proton
Spin
30%
?
Large distances:
Non-Perturbative = Not calculable!
Fragmentation
Where is the Spin of the
Proton?
How are Quarks and Gluons
distributed in the Proton?
Quarks
Gluons
Proton
Mass
~5%
~95%
Higgs
~1%

13. Francesca Giordano
Proton Structure
3
Inclusive DIS

14. Francesca Giordano
Proton Structure
3
Inclusive DIS
e-

15. Francesca Giordano
Proton Structure
3
Inclusive DIS
e-
X

16. Francesca Giordano
Proton Structure
d / Lµ⌫Wµ⌫
3
Inclusive DIS
e-
X

17. Francesca Giordano
Proton Structure
d / Lµ⌫Wµ⌫
Leptonic Tensor: describes
emission of single photon:
Calculable from QED
3
Inclusive DIS
e-
X

18. Francesca Giordano
Proton Structure
d / Lµ⌫Wµ⌫
Leptonic Tensor: describes
emission of single photon:
Calculable from QED
Hadronic Tensor: describes
internal proton structure
Not Calculable in QCD!
3
Inclusive DIS
e-
X

19. Francesca Giordano
Proton Structure
4
Inclusive DIS
Only basic symmetry arguments/
conservation laws: Gauge/Lorentz
invariance, parity conservation
No other assumption!
Negative squared
4-momentum transfer to the target
Fractional energy of the virtual photon
Parton fractional momentum
e-

20. Francesca Giordano
Proton Structure
5
Inclusive DIS
Only basic symmetry arguments/
conservation laws: Gauge/Lorentz
invariance, parity conservation
No other assumption!
Parton model:
Fi ➾ Σp parton distributions
Each Structure function
expanded in 1/Q serie
e-

21. Francesca Giordano
Parton Distribution Functions
Collinear case
6
Partonic Interpretation
Accessible in various reactions:
Universal!
Factorizable in the cross-section!
x-dependence=
1D!
PDF probabilistic interpreta
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
transverse an
transverse an
transverse longitudinal
nucleon spin
parton spin
PDFs Leading Twist Table

22. Francesca Giordano
Parton Distribution Functions
Collinear case
6
Partonic Interpretation
Accessible in various reactions:
Universal!
Factorizable in the cross-section!
x-dependence=
1D!
Need for Global
analyses!
PDF probabilistic interpreta
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
transverse an
transverse an
transverse longitudinal
nucleon spin
parton spin
PDFs Leading Twist Table

23. Francesca Giordano
Parton Distribution Functions
Collinear case
6
Partonic Interpretation
Accessible in various reactions:
Universal!
Factorizable in the cross-section!
x-dependence=
1D!
Need for Global
analyses!
DGLAP evolution
= different
energies
PDF probabilistic interpreta
f q
1 (x)
gq
1 (x)
hq
1 (x)
legend
transverse an
transverse an
transverse longitudinal
nucleon spin
parton spin
PDFs Leading Twist Table

24. Francesca Giordano 7
G
+
momentum frame, these number densities are related to the helicity distrib
the difference of the probability to find a quark polarised along or against t
eigenstate:
gq
1 (x) = q
!)
(x) q
!(
(x).
The momentum distribution measuring the spin average is given by the sum
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin eigen
transversity distribution hq
1 (x) measures the difference of the number dens
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is illust
Differences between the helicity and transversity distributions are a conseq
motion of the quarks within the nucleon. Euclidean rotations and Lorentz
and thus longitudinally polarised nucleons cannot be converted in transverse
infinite momentum. Only in case of non-relativistic quarks both distributions
Another difference emerges from an analysis of helicity amplitudes. F
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0) =
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleon
0 0
q
Momentum distribution
Collinear case
x = parton momentum fraction

25. Francesca Giordano
TABLE IV: Truncated first moments, ∆f
1,[0.001→1]
i ,
x-range in Eq. (35) Q2
[GeV2
] ∆u + ∆¯u ∆d
0.001-1.0 1 0.809 -
4 0.798 -
10 0.793 -
100 0.785 -
0.0-1.0 1 0.817 -
4 0.814 -
10 0.813 -
100 0.812 -
0
0.1
0.2
0.3
0.4
-0.15
-0.1
-0.05
0
0.05
-0.04
-0.02
0
0.02
-0.04
-0.02
0
0.02
-0.02
0
0.02
x(Δu + Δu
–
) x(Δd + Δd
–
)
DSSV
xΔu
–
xΔd
–
xΔs
–
xΔg
0
0.05
0.1
the virtual photon selects only quarks of one polarisation, measurements
anti-parallel (!() or parallel polarisations (!)) of lepton (!) and target nu
to number densities q of quarks polarised along or against the nucleon po
momentum frame, these number densities are related to the helicity distri
the difference of the probability to find a quark polarised along or against
eigenstate:
gq
1 (x) = q
!)
(x) q
!(
(x).
The momentum distribution measuring the spin average is given by the sum
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin eig
transversity distribution hq
1 (x) measures the difference of the number den
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is illu
Differences between the helicity and transversity distributions are a conse
motion of the quarks within the nucleon. Euclidean rotations and Lorentz
and thus longitudinally polarised nucleons cannot be converted in transvers
infinite momentum. Only in case of non-relativistic quarks both distributio8
G
G
q
G
q
Helicity distribution
Collinear case
x = parton momentum fraction

26. Francesca Giordano
TABLE IV: Truncated first moments, ∆f
1,[0.001→1]
i ,
x-range in Eq. (35) Q2
[GeV2
] ∆u + ∆¯u ∆d
0.001-1.0 1 0.809 -
4 0.798 -
10 0.793 -
100 0.785 -
0.0-1.0 1 0.817 -
4 0.814 -
10 0.813 -
100 0.812 -
0
0.1
0.2
0.3
0.4
-0.15
-0.1
-0.05
0
0.05
-0.04
-0.02
0
0.02
-0.04
-0.02
0
0.02
-0.02
0
0.02
x(Δu + Δu
–
) x(Δd + Δd
–
)
DSSV
xΔu
–
xΔd
–
xΔs
–
xΔg
0
0.05
0.1
the virtual photon selects only quarks of one polarisation, measurements
anti-parallel (!() or parallel polarisations (!)) of lepton (!) and target nu
to number densities q of quarks polarised along or against the nucleon po
momentum frame, these number densities are related to the helicity distri
the difference of the probability to find a quark polarised along or against
eigenstate:
gq
1 (x) = q
!)
(x) q
!(
(x).
The momentum distribution measuring the spin average is given by the sum
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin eig
transversity distribution hq
1 (x) measures the difference of the number den
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is illu
Differences between the helicity and transversity distributions are a conse
motion of the quarks within the nucleon. Euclidean rotations and Lorentz
and thus longitudinally polarised nucleons cannot be converted in transvers
infinite momentum. Only in case of non-relativistic quarks both distributio8
G
G
q
G
q
Helicity distribution
Collinear case
x = parton momentum fraction
Spin crisis!!
quarks only provide ≈ 30%
of the proton spin

27. Francesca Giordano
TABLE IV: Truncated first moments, ∆f
1,[0.001→1]
i ,
x-range in Eq. (35) Q2
[GeV2
] ∆u + ∆¯u ∆d
0.001-1.0 1 0.809 -
4 0.798 -
10 0.793 -
100 0.785 -
0.0-1.0 1 0.817 -
4 0.814 -
10 0.813 -
100 0.812 -
0
0.1
0.2
0.3
0.4
-0.15
-0.1
-0.05
0
0.05
-0.04
-0.02
0
0.02
-0.04
-0.02
0
0.02
-0.02
0
0.02
x(Δu + Δu
–
) x(Δd + Δd
–
)
DSSV
xΔu
–
xΔd
–
xΔs
–
xΔg
0
0.05
0.1
RHIC$
arXiv:1501.01220$
ProjecCons$for$inclusive$j
(p+p$200/500GeV)$
the virtual photon selects only quarks of one polarisation, measurements
anti-parallel (!() or parallel polarisations (!)) of lepton (!) and target nu
to number densities q of quarks polarised along or against the nucleon po
momentum frame, these number densities are related to the helicity distri
the difference of the probability to find a quark polarised along or against
eigenstate:
gq
1 (x) = q
!)
(x) q
!(
(x).
The momentum distribution measuring the spin average is given by the sum
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin eig
transversity distribution hq
1 (x) measures the difference of the number den
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is illu
Differences between the helicity and transversity distributions are a conse
motion of the quarks within the nucleon. Euclidean rotations and Lorentz
and thus longitudinally polarised nucleons cannot be converted in transvers
infinite momentum. Only in case of non-relativistic quarks both distributio8
G
G
q
G
q
Helicity distribution
Collinear case
x = parton momentum fraction
Spin crisis!!
quarks only provide ≈ 30%
of the proton spin
quark spins gluon spins
quark&gluon
orbital motion

28. Francesca Giordano
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu9
G
q
q
q
G
Transversity distribution
Collinear case
x = parton momentum fraction

29. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu10
in helicity basis
helicity flip!
G
q
q
q
G
Transversity is chiral-odd!
x = parton momentum fraction

30. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu11
in helicity basis
helicity flip!
G
q
q
q
G
Transversity is chiral-odd!
x = parton momentum fraction

31. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu12
in helicity basis
helicity flip!
G
q
q
q
G
Transversity is chiral-odd!
x = parton momentum fraction

32. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu13
G
q
q
q
G
x = parton momentum fraction
chiral oddchiral odd
}
chiral even
⇥ Hh1

33. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu13
G
q
q
q
G
x = parton momentum fraction
chiral oddchiral odd
}
chiral even
⇥ Hh1
DIS reaction:
semi inclusive DIS
Drell-Yan/pp

34. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu13
G
q
q
q
G
x = parton momentum fraction
chiral oddchiral odd
}
chiral even
⇥ Hh1
DIS reaction:
semi inclusive DIS
Drell-Yan/pp
? no gluon transversity (in proton)
and quark and gluon
transversities don’t mix!

35. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu13
G
q
q
q
G
x = parton momentum fraction
chiral oddchiral odd
}
chiral even
⇥ Hh1
DIS reaction:
semi inclusive DIS
Drell-Yan/pp
? no gluon transversity (in proton)
and quark and gluon
transversities don’t mix!

36. Francesca Giordano
Proton Structure
14
Semi-Inclusive DIS
e-
Dq
h
h
Dq
h
X
d3
⇤
dxdydz =
2
xyQ2 1 + ⇥2
2x {A(y)FUU,T + B(y)FUU,L}
Negative squared
4-momentum transfer to the target
Fractional energy of the virtual photon
Parton fractional momentum
Fractional energy transfer to the produced
hadron

37. Francesca Giordano
Proton Structure
14
Semi-Inclusive DIS
Parton model:
Fi ➾ Ủp parton
distributions
+
Fragmentation!
e-
Dq
h
h
Dq
h
X
d3
⇤
dxdydz =
2
xyQ2 1 + ⇥2
2x {A(y)FUU,T + B(y)FUU,L}

38. Francesca Giordano
Proton Structure
15
Semi-Inclusive DIS
e-
Dq
h
h
Dq
h
X
DF
σ
FF
Factorization of Non-
Perturbative Parts!

39. Francesca Giordano
Transversity distribution
Collinear case
f q
1 (x) = q
!)
(x)+q
!(
(x).
Transversely polarised nucleons In the basis of transverse spin ei
transversity distribution hq
1 (x) measures the difference of the number de
larised quarks aligned along or against the polarisation of the nucleon:
hq
1 (x) = q"*
(x) q"+
(x).
The probabilistic interpretation of these parton distribution functions is ill
Differences between the helicity and transversity distributions are a con
motion of the quarks within the nucleon. Euclidean rotations and Loren
and thus longitudinally polarised nucleons cannot be converted in transve
infinite momentum. Only in case of non-relativistic quarks both distributi
Another difference emerges from an analysis of helicity amplitudes
scattering amplitudes AΛlΛ0l0 , labelled by the helicities of quarks (l(0)
(Λ(0) = ±1
2 ⌘ ±), represent the absorption of a quark (l) from a nucleo
emission of the quark (l0) by the nucleon (Λ0). Due to conservation of
parity, AΛlΛ0l0 = A Λ l Λ0 l0 and time reversal there are exactly three i
A++,++, A+ ,+ A+ , +.
The optical theorem relates the forward quark-nucleon scattering amplitu16
G
q
q
q
G
x = parton momentum fraction
chiral oddchiral odd
}
chiral even
⇥ Hh1
DIS reaction:
semi inclusive DIS

40. Francesca Giordano
Transversity distribution
Collinear case
Interference Fragmentation
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collins Fragmentation
17

41. Francesca Giordano
Transversity distribution
Collinear case
Interference Fragmentation
left-right asymmetry from correlations between
quark transverse spin
and
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collins Fragmentation
17

42. Francesca Giordano
Transversity distribution
Collinear case
outgoing hadron direction
Interference Fragmentation
left-right asymmetry from correlations between
quark transverse spin
and
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collins Fragmentation
17

43. Francesca Giordano
Transversity distribution
Collinear case
outgoing hadron direction
relative orbital angular
momentum of the hadron pair
Interference Fragmentation
left-right asymmetry from correlations between
quark transverse spin
and
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collins Fragmentation
17

44. Francesca Giordano
Transversity distribution
Collinear case
outgoing hadron direction
relative orbital angular
momentum of the hadron pair
Interference Fragmentation
left-right asymmetry from correlations between
quark transverse spin
and
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collinear!
Collins Fragmentation
17

45. Francesca Giordano
Transversity distribution
Collinear case
outgoing hadron direction
relative orbital angular
momentum of the hadron pair
TMD!
Interference Fragmentation
left-right asymmetry from correlations between
quark transverse spin
and
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collinear!
Collins Fragmentation
17

46. Francesca Giordano
Transversity distribution
Collinear case
outgoing hadron direction
relative orbital angular
momentum of the hadron pair
TMD!
Interference Fragmentation
left-right asymmetry from correlations between
quark transverse spin
and
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collinear!
Collins Fragmentation
17
Depends on transverse
momentum!

47. Francesca Giordano
Transverse Momentum dependent PDFs
18
1D
Chapter2
2.2. The interpretation of TMD
probabilistic interpretation chiral properties
chiral-even
chiral-even
chiral-odd
transverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
entation and chiral properties of the leading-twist PDF: The notation of
bution functions uses the letters f,g,h specifying the quark polarisation
transverse longitudinal
nucleon spin
parton spin

48. Francesca Giordano
3D!
Transverse Momentum dependent PDFs
18
1D
Chapter2
2.2. The interpretation of TMD
probabilistic interpretation chiral properties
chiral-even
chiral-even
chiral-odd
transverse and longitudinal nucleon polarisation
transverse and longitudinal quark polarisation
entation and chiral properties of the leading-twist PDF: The notation of
bution functions uses the letters f,g,h specifying the quark polarisation
transverse longitudinal
nucleon spin
parton spin
TMDs - Probabilistic interpretation
f1T =
h1 =
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
parton transverse
momentum

49. Francesca Giordano
Transverse Momentum dependent PDFs
19
1D
target
polarization
beam
polarization virtual photon
polarization
Each Structure function
expanded in Ph⊥/Q serie
higher twist contributes!Ph? >> Q
higher twist suppressedPh? << Q

50. Francesca Giordano
Transverse Momentum dependent PDFs
20
1D momentum helicity Boer-Mulders
Sivers
worm-gears
transversity
pretzelosity
target
polarization
beam
polarization virtual photon
polarization
TMDs Leading Twist Table

51. Francesca Giordano
Transverse Momentum dependent PDFs
21
The observation of transverse single-spin asymmetries at the HERMES exper
nals for transverse-momentum dependent quark distribution and fragmentation f
transversity and Sivers distributions and the Collins fragmentation function. In th
analysis of transverse single-spin asymmetries for semi-inclusive electroproducti
charged K-mesons on a transversely nuclear-polarised hydrogen target is presen
Transverse single-spin asymmetries Ah
U? for some hadron type h and using an
beam (U) are defined as the difference of the transverse-target (?) spin-depen
s h
U* and s h
U+ for semi-inclusive electro-production of hadrons, normalised to th
sections:
Ah
U? =
s h
U* s h
U+
s h
U* +s h
U+
.
In an experiment, the transverse target spin orientation, denoted as“*” and “+”
dicular to the lepton beam direction. Hence, the notation Ah
U? is used for the m
single-spin asymmetries in contrast to the notation Ah
UT, applied in theoretica
transverse target spin orientation is aligned perpendicular to the direction of the
Transverse single-spin asymmetries depend on the azimuthal angle fS of the
the azimuthal angle f of the produced hadron (figure 2.4). A decomposition
components in these azimuthal angles provides signals for the various contributio
target spin-dependent cross-section, e.g., for the 2hsin(f +fS)iU? Fourier comp
mechanism and the 2hsin(f fS)iU? Fourier component of the Sivers mecha
components, in the following denoted also as single-spin asymmetries amplit
EXPERIMENT: setting the proper beam and target polarization states
(U, L, T)
ANALYSIS: fitting the cross section asymmetry for opposite spin states
and extracting the relevant Fourier components based on their peculiar
azimuthal dependences.
How can we disentangle all
these contributions ?

52. Francesca Giordano
Transversity distribution
Collinear case
TMD!
Interference Fragmentation
H1
⪦ Ph⊥
Ph⊥
q
H1
⊥ Ph⊥
q
Collinear!
Collins Fragmentation
22
Depends on transverse
momentum!
AUT∝ h1 x H1
⊥
0
∫ h1 (x,pT) H1 (x,kT) dpT dkT
⊥
(and same in the denominator for the
unpolarized pdfs and ffs)
AUT∝ h1 x H1
⪦
direct product!
(same in the denominator)

53. Francesca Giordano
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
Collins amplitudes
H?
1h1 ⇥AUT /
Non-zero transversity!
Opposite sign for favored and unfavored FF
23

54. Francesca Giordano
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
Gunar Schnell
quark pol.
U L T
nucleonpol.
U f1 h1
L g1L h1L
T f1T g1T h1, h1T
Twist-2 TMDs
significant in size and
opposite in sign for charged
pions
disfavored Collins FF large
and opposite in sign to
favored one
leads to various cancellations
in SSA observables
2
Trans
(Co
+
u
Wednesday, May 11, 2011
H?,unfav
1 ⇡ H?,fav
1
Collins amplitudes
H?
1h1 ⇥AUT /
Non-zero transversity!
Opposite sign for favored and unfavored FF
23

55. Francesca Giordano 24
H?
1h1 ⇥AUT /
𝜋𝜋 Collins moments

56. Francesca Giordano 24
H?
1h1 ⇥AUT /
𝜋𝜋 Collins moments
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
π+/−
Κ+/−
Deuterium

57. Francesca Giordano 24
H?
1h1 ⇥AUT /
𝜋𝜋 Collins moments
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
π+/−
Κ+/−
Deuterium
𝜋 Collins FF
Anselmino et al.
PRD75 (2007)
PRD87 (2013)

58. Francesca Giordano 24
H?
1h1 ⇥AUT /
Anselmino et al.
PRD75 (2007)
PRD87 (2013)
transversity
𝜋𝜋 Collins moments
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
π+/−
Κ+/−
Deuterium
𝜋 Collins FF
Anselmino et al.
PRD75 (2007)
PRD87 (2013)

59. Francesca Giordano 25
Transversity distribution
First access in SIDIS
Complementary reactions
TMD factorization assumed
FF universality assumed
AUT∝ h1 x H1
⊥
0Collins
FF
TMD M. Anselmino et al.,
PRD75:054032, 2007

60. Francesca Giordano 26
Transversity distribution
First access in SIDIS
Very different energies between
Hermes/Compass and Belle:
Is TMD evolution different from
Collinear?
Complementary reactions
Collinear evolution assumed
TMD factorization assumed
FF universality assumed
AUT∝ h1 x H1
⊥
0Collins
FF
TMD M. Anselmino et al.,
PRD75:054032, 2007

61. Francesca Giordano 27
Transversity distribution
First access in SIDIS
Very different energies between
Hermes/Compass and Belle:
Is TMD evolution different from
Collinear?
Different energies at Hermes/
Compass: how does transversity
evolve?
Complementary reactions
Collinear evolution assumed
No evolution assumed
TMD factorization assumed
FF universality assumed
AUT∝ h1 x H1
⊥
0Collins
FF
TMD M. Anselmino et al.,
PRD75:054032, 2007

62. Francesca Giordano 28
Transversity distribution
First access in SIDIS
Very different energies between
Hermes/Compass and Belle:
Is TMD evolution different from
Collinear?
Different energies at Hermes/
Compass: how does transversity
evolve?Which is the TMD transversity and the TMD
Collins pT dependence? And the unpolarized
TMD pT dependence?
Complementary reactions
Collinear evolution assumed
No evolution assumed
TMD factorization assumed
Gaussian pT dependence assumed
FF universality assumed
AUT∝ h1 x H1
⊥
0Collins
FF
TMD M. Anselmino et al.,
PRD75:054032, 2007

63. Francesca Giordano
Bacchetta, Radici, Courtoy
Phys.Rev.Lett.107:012001,2011
AUT /z1, m2
1, m2
2) ∝
1
2
sin2
θ
1 + cos2 θ
⎡
⎣
q,q
e2
q z2
1z2
2 H<) q
1 (z
×
⎡
⎣
q,q
e2
q z2
1 z2
2 Dq
1(z1, m2
1) Dq
1(z2,
h1 ⇥
IFF amplitudes
[Airapetian et al., JHEP 0806:017, 2008]
𝜋+ 𝜋-
29

64. Francesca Giordano
Bacchetta, Radici, Courtoy
Phys.Rev.Lett.107:012001,2011
AUT /z1, m2
1, m2
2) ∝
1
2
sin2
θ
1 + cos2 θ
⎡
⎣
q,q
e2
q z2
1z2
2 H<) q
1 (z
×
⎡
⎣
q,q
e2
q z2
1 z2
2 Dq
1(z1, m2
1) Dq
1(z2,
h1 ⇥
IFF amplitudes
30
Collinear evolution well known
pT dependence not needed
Universality & factorization
ok for collinear FF and PDF
Still:
collinear and TMD transversity
extracted not in conflict!

65. Francesca Giordano
Bacchetta, Radici, Courtoy
Phys.Rev.Lett.107:012001,2011
AUT /z1, m2
1, m2
2) ∝
1
2
sin2
θ
1 + cos2 θ
⎡
⎣
q,q
e2
q z2
1z2
2 H<) q
1 (z
×
⎡
⎣
q,q
e2
q z2
1 z2
2 Dq
1(z1, m2
1) Dq
1(z2,
h1 ⇥
IFF amplitudes
30
Collinear evolution well known
pT dependence not needed
Universality & factorization
ok for collinear FF and PDF
Still:
collinear and TMD transversity
extracted not in conflict!
arXiv:1505.05589
Consistent with new TMD extraction
with proper TMD evolution

66. Francesca Giordano
Collins amplitudes
Non-zero signal for K+!
K+ amplitudes larger than 𝜋+
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
31

67. Francesca Giordano
Collins amplitudes
Non-zero signal for K+!
K+ amplitudes larger than 𝜋+
[Airapetian et al., Phys. Lett. B 693 (2010) 11-16]
31
Collins FF for kaons
from Belle

68. Francesca Giordano
Transverse Momentum dependent PDFs
32
The observation of transverse single-spin asymmetries at the HERMES exper
nals for transverse-momentum dependent quark distribution and fragmentation f
transversity and Sivers distributions and the Collins fragmentation function. In th
analysis of transverse single-spin asymmetries for semi-inclusive electroproducti
charged K-mesons on a transversely nuclear-polarised hydrogen target is presen
Transverse single-spin asymmetries Ah
U? for some hadron type h and using an
beam (U) are defined as the difference of the transverse-target (?) spin-depen
s h
U* and s h
U+ for semi-inclusive electro-production of hadrons, normalised to th
sections:
Ah
U? =
s h
U* s h
U+
s h
U* +s h
U+
.
In an experiment, the transverse target spin orientation, denoted as“*” and “+”
dicular to the lepton beam direction. Hence, the notation Ah
U? is used for the m
single-spin asymmetries in contrast to the notation Ah
UT, applied in theoretica
transverse target spin orientation is aligned perpendicular to the direction of the
Transverse single-spin asymmetries depend on the azimuthal angle fS of the
the azimuthal angle f of the produced hadron (figure 2.4). A decomposition
components in these azimuthal angles provides signals for the various contributio
target spin-dependent cross-section, e.g., for the 2hsin(f +fS)iU? Fourier comp
mechanism and the 2hsin(f fS)iU? Fourier component of the Sivers mecha
components, in the following denoted also as single-spin asymmetries amplit
EXPERIMENT: setting the proper beam and target polarization states
(U, L, T)
ANALYSIS: fitting the cross section asymmetry for opposite spin states
and extracting the relevant Fourier components based on their peculiar
azimuthal dependences.
How can we disentangle all
these contributions ?

69. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
33

70. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
33

71. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
Boer-Mulders
the other naively T-odd distribution
Wednesday, May 11, 2011
the parton transverse spin
Boer-Mulders
33

72. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
Boer-Mulders
the other naively T-odd distribution
Wednesday, May 11, 2011
the parton transverse spin
Boer-Mulders
Spatial deformation due
to spin-orbit correlations
33

73. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
Boer-Mulders
the other naively T-odd distribution
Wednesday, May 11, 2011
the parton transverse spin
Boer-Mulders
Spatial deformation due
to spin-orbit correlations
u
FSI
Both are Naively T-odd
Final State Interaction
33

74. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
Boer-Mulders
the other naively T-odd distribution
Wednesday, May 11, 2011
the parton transverse spin
Boer-Mulders
u
FSI
Both are Naively T-odd
Final State Interaction
33
Special Universality!
Change of sign of Naive T-odd
function from SIDIS to Drell-Yan

75. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
34

76. Francesca Giordano
Sivers & Boer-Mulders TMDs
Azimuthal asymmetries generated by correlations between quark transverse
momentum and
DY 2011, BNL - May 11th
, 2011
listic interpretation
f1T =
h1 =
h1T =
h1L =
g1T =
n/ photon goes into the screen
the proton transverse spin
Sivers
34
Drell-Yan run just started
to observe Sivers sign!

77. Francesca Giordano
H?
1h1 ⇥
⊥
H1
⊥
q
Ph⊥
Ph⊥
Collins effect:
Spatial distortions due to
spin-orbit correlations
Boer-Mulders Naive T-odd:
Final State Interactions
u
FSI
u
Boer-Mulders-Collins effect
35
Together generate a cos2φ
signature in the cross section!

78. Francesca Giordano
Cos2ứ: Pions & Kaons
Phys.Rev.D87:012010, 2013
Pion and Kaon results are
very different:
possibly related to fragmentation that
involve the strange?
36
Gamberg, Goldstein
Phys. Rev. D77:094016, 2008
COMPASS'6LiD'(25%'of'the'2004'data)''''preliminaryCOMPASS'6LiD'(25%'of'the'2004'data) preliminary

79. Francesca Giordano
The Kaon puzzle
Phys.Rev.D87:012010, 2013
37
K+ amplitudes larger
than 𝜋+?
Transversity-Collins AsymmetriesBoer-Mulders-Collins Asymmetries
Pion and Kaon results are very different:
Kaons: Larger asymmetries, same sign for
K+ and K-
K- different from 𝜋-?

80. Francesca Giordano
The Kaon puzzle
Phys.Rev.D87:012010, 2013
Need to extract
Collins fragmentation
for Kaons in e+e- !!!
37
K+ amplitudes larger
than 𝜋+?
Transversity-Collins AsymmetriesBoer-Mulders-Collins Asymmetries
Pion and Kaon results are very different:
Kaons: Larger asymmetries, same sign for
K+ and K-
K- different from 𝜋-?
in
progress!

81. Francesca Giordano
Transverse Momentum dependent PDFs
38
The observation of transverse single-spin asymmetries at the HERMES exper
nals for transverse-momentum dependent quark distribution and fragmentation f
transversity and Sivers distributions and the Collins fragmentation function. In th
analysis of transverse single-spin asymmetries for semi-inclusive electroproducti
charged K-mesons on a transversely nuclear-polarised hydrogen target is presen
Transverse single-spin asymmetries Ah
U? for some hadron type h and using an
beam (U) are defined as the difference of the transverse-target (?) spin-depen
s h
U* and s h
U+ for semi-inclusive electro-production of hadrons, normalised to th
sections:
Ah
U? =
s h
U* s h
U+
s h
U* +s h
U+
.
In an experiment, the transverse target spin orientation, denoted as“*” and “+”
dicular to the lepton beam direction. Hence, the notation Ah
U? is used for the m
single-spin asymmetries in contrast to the notation Ah
UT, applied in theoretica
transverse target spin orientation is aligned perpendicular to the direction of the
Transverse single-spin asymmetries depend on the azimuthal angle fS of the
the azimuthal angle f of the produced hadron (figure 2.4). A decomposition
components in these azimuthal angles provides signals for the various contributio
target spin-dependent cross-section, e.g., for the 2hsin(f +fS)iU? Fourier comp
mechanism and the 2hsin(f fS)iU? Fourier component of the Sivers mecha
components, in the following denoted also as single-spin asymmetries amplit
EXPERIMENT: setting the proper beam and target polarization states
(U, L, T)
ANALYSIS: fitting the cross section asymmetry for opposite spin states
and extracting the relevant Fourier components based on their peculiar
azimuthal dependences.
How can we disentangle all
these contributions ?
worm-gears
pretzelosity

82. Francesca Giordano
Worm-gear
Pretzelosity
39
More TMDs

83. Francesca Giordano 40
TMDs open points:
- What is the pT dependence of TMD polarized and
unpolarized pdfs? And of polarized and unpolarized
fragmentation functions? .
- How do TMD pdfs and fragmentation functions evolve?
Work in progress!!
- Do naive-T-odd TMDs obey the ‘special universality’?
Compass Drell-Yan run just started
Mostly missing!!

84. Francesca Giordano
SuperStar
fsPHENIX
EIC
Jlab12
Babar
Belle/BelleII
FERMILAB
PAX?
Star
Exciting times!
41
CompassII
Phenix

85. Francesca Giordano
Thank you!
42

86. Francesca Giordano
Backup slides
43

87. Francesca Giordano 44
Hall A
Hall B

88. Francesca Giordano
SM1
SM2
MuonWall
MuonWall
E/HCAL E/HCAL
RICH
Polarised Target
SciFi
Silicon
Micromegas
GEMs
Straws
Drift Chambers
MWPC
50 m
!
+ beam
HERMES@DESY COMPASS@CERN
160 GeV beam off
6LiD/NH3 target
µ+
27.6 GeV (e+/e-) lepton
beam off D/H target
45

89. Francesca Giordano
HERMES@DESY COMPASS@CERN
Q2
> 1 GeV 2
0.023 < x < 0.27
0.3 < y < 0.85
W2
> 10 GeV 2
0.2 < z < 0.75
0.05 < Ph? < 1 GeV
Q2
> 1 GeV 2
0.003 < x < 0.13
0.2 < y < 0.9
W2
> 5 GeV 2
0.2 < z < 0.85
0.1 < Ph? < 1 GeV
160 GeV beam off
6LiD/NH3 target
µ+
27.6 GeV (e+/e-) lepton
beam off D/H target
46

90. Francesca Giordano
HERMES@DESY COMPASS@CERN
Q2
> 1 GeV 2
0.023 < x < 0.27
0.3 < y < 0.85
W2
> 10 GeV 2
0.2 < z < 0.75
0.05 < Ph? < 1 GeV
Q2
> 1 GeV 2
0.003 < x < 0.13
0.2 < y < 0.9
W2
> 5 GeV 2
0.2 < z < 0.85
0.1 < Ph? < 1 GeV
+
, , K+
, K
160 GeV beam off
6LiD/NH3 target
µ+
27.6 GeV (e+/e-) lepton
beam off D/H target
46