Selected TMD results from HERMES

hardtofindcurtainUrban and Civil

Nov 16, 2013 (3 years and 4 months ago)

93 views

Luciano L.
Pappalardo

University of Ferrara

Selected TMD
results from
HERMES

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
18 2013

The
full phase
-
space distribution of the partons
encoded in the
Wigner function


๐‘Š
(
๐‘ฅ
,


,

)

2

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The phase
-
space distribution of partons

The
full phase
-
space distribution of the partons
encoded in the
Wigner function


๐‘Š
(
๐‘ฅ
,


,

)


(
๐‘ฅ
,


)



3


TMDs

H
(
x
,
ฮพ
,

)



2



GPDs

...but
โˆ†
๐‘ฅ
โˆ†

โ‰ฅ
โ„
2

๏‚ฎ

no simultaneous knowledge of momentum and position


cannot be directly accessed experimentally
๏‚ฎ

integrated quantities

The phase
-
space distribution of partons

3

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

๐‘Š
(
๐‘ฅ
,


,

)


(
๐‘ฅ
,


)



3


TMDs

The
non
-
collinear
structure of the nucleon

P
๏ฒ
q
๏‚ฎ
T
p
P
x
p
๏ฒ
๏ฒ
๏€ฝ
โ€ข
TMDs depend on
๐‘ฅ

and



โ€ข
D
escribe
correlations
between



and
quark
or
nucleon spin

(
spin
-
orbit

correlations
)

โ€ข
Provide
a 3
-
dim picture
of the
nucleon in momentum space
(
nucleon tomography
)

Sivers

worm
-
gears

Boer
-
Mulders

pretzelosity

helicity

transversity

momentum

Sivers

worm
-
gears

H
(
x
,
ฮพ
,

)



2



GPDs

The
full phase
-
space distribution of the partons
encoded in the
Wigner function


...but
โˆ†
๐‘ฅ
โˆ†

โ‰ฅ
โ„
2

๏‚ฎ

no simultaneous knowledge of momentum and position


cannot be directly accessed experimentally
๏‚ฎ

integrated quantities

4

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The
non
-
collinear
structure of the nucleon

โ€ข
TMDs depend on
๐‘ฅ

and



โ€ข
D
escribe
correlations
between



and
quark
or
nucleon spin

(
spin
-
orbit

correlations
)

โ€ข
Provide
a 3
-
dim picture
of the
nucleon in momentum space
(
nucleon tomography
)

Sivers

worm
-
gears

Boer
-
Mulders

pretzelosity

helicity

transversity

momentum

Sivers

worm
-
gears

DF
๏ณ
FF

Mostly investigated in
SIDIS
: detection of transverse momentum of produced hadrons gives access to



1
D
๏ž
1
H
L
G
1
๏ž
L
H
1
๏ž
T
D
1
T
G
1
1
H
๏ž
T
H
1
Fragmentation Functions (FF)

h
a
d
r
o
n

Collins FF
chiral
-
odd

u
npol
. FF

chiral
-
even

5

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The SIDIS cross
-
section

}

6

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

DF
๏ณ
FF

The SIDIS cross
-
section

}

b
eam polarization

unpolarized

b
eam and target
polarization

t
arget polarization

7

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The SIDIS cross
-
section

}

8

L.L. Pappalardo
-

SPIN2012
โ€“

JINR, Dubna, Russia

โ€“

September 17
-
22 2012

18 Structure Functions

Leading
twist

Sub
-
leading
Twist

๐‘ญ

โˆ
๐‘ซ๐‘ญ
โŠ—
๐‘ญ๐‘ญ

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

๏ž
1
H
Selected
twist
-
2

and
twist
-
3

1
-
hadron SIDIS results

9

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

}

Sivers function

Describes correlation between quark
transverse momentum and nucleon
transverse polarization

10

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Sivers

amplitudes

significantly positive

slightly positive

consistent with zero

consistent with Sivers func. of
opposite sign for u and d quarks

(isospin
-
symmetry)

[
Anselmino

et
al
.,
Eur.Phys.J.A3,2009
]

1
1
D
f
T
๏ƒ„
๏‚ต
๏ž
[
Airapetian

et al
.,
Phys
. Rev.
Lett
. 103 (2009) 152002]

11

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Sivers

amplitudes

significantly positive

slightly positive

consistent with zero

(isospin
-
symmetry)

[
Anselmino

et
al
.,
Eur.Phys.J.A3,2009
]

consistent with Sivers func. of
opposite sign for u and d quarks

[
Airapetian

et al
.,
Phys
. Rev.
Lett
. 103 (2009) 152002]

12

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Similar kinematic dependence of

+

significantly positive

slightly positive

1
1
D
f
T
๏ƒ„
๏‚ต
๏ž

Sivers
kaons

amplitudes: open questions

๏ฐ
+
/K
+

production dominated by u
-
quarks, but:

13

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013


Sivers
kaons

amplitudes: open questions

๏ฐ
+
/K
+

production dominated by u
-
quarks, but:

14

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

different
role of
various sea quarks ?

๏‚ฎ
๏‚บ
๏‚บ
๏€ซ
๏€ซ
s
u
K
d
u
,
๏ฐ
?

no effect for
pions
, but hint of a systematic
shifts for
kaons


Sivers
kaons

amplitudes: open questions

different
role of
various sea quarks ?

๏‚ฎ
๏‚บ
๏‚บ
๏€ซ
๏€ซ
s
u
K
d
u
,
๏ฐ
?

๏ฐ
+
/K
+

production dominated by u
-
quarks, but:

15

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

?


Higher
-
twist
contrib. for
Kaons


only
in low
-
Q
2

region significant deviation

each x
-
bin divided into two Q
2
bins

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

}

Pretzelosity

Describes correlation between quark
transverse momentum and transverse
spin in a transversely pol. nucleon

๏ƒ˜
Sensitive to
non
-
spherical shape

of the nucleon

16

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

โ€ฆsuppressed by two powers of
P
h
๏ž

w.r.t.
Sivers

amplitudes

All amplitudes consistent with zero

๏ž
๏ž
๏ƒ„
๏‚ต
1
1
H
h
T
17

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The
sin
3
๐œ™
โˆ’
๐œ™

๐ฟ

amplitudes

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

}

Worm
-
gear

โŠฅ
๐‘ป

Describes the probability to find
longitudinally polarized quarks in a
transversely polarized nucleon!

๏ƒ˜
Can be accessed in
LT DSAs

18

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

}

19

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

S.
Boffi

et al. (2009)

Phys. Rev. D 79 094012

Light
-
cone
constituent
quark model

dashed
line:
interf
. L=0, L=1

dotted line:
interf

L=1, L=2

Worm
-
gear

โŠฅ
๐‘ป

๏ƒ˜
The only TMD that is both
chiral
-
even

and
naรฏve
-
T
-
even


๏ƒ˜
requires interference between wave
function
components that
differ by 1 unit of
OAM
๏ƒž

quark
orbital motion

inside
nucleons

๏ƒ˜
The only TMD that is both
chiral
-
even

and
naรฏve
-
T
-
even


๏ƒ˜
requires interference between wave
function
components that
differ by 1 unit of
OAM
๏ƒž

quark
orbital motion

inside
nucleons


๏ƒ˜
Accessible in LT DSAs
:

20

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

S.
Boffi

et al. (2009)

Phys. Rev. D 79 094012

Light
-
cone
constituent
quark model

dashed
line:
interf
. L=0, L=1

dotted line:
interf

L=1, L=2

Worm
-
gear

โŠฅ
๐‘ป

21

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

S.
Boffi

et al. (2009)

Phys. Rev. D 79 094012

Light
-
cone
constituent
quark model

dashed
line:
interf
. L=0, L=1

dotted line:
interf

L=1, L=2

Simplest way to probe

๏ž
T
g
1
Worm
-
gear

โŠฅ
๐‘ป

๏ƒ˜
The only TMD that is both
chiral
-
even

and
naรฏve
-
T
-
even


๏ƒ˜
requires interference between wave
function
components that
differ by 1 unit of
OAM
๏ƒž

quark
orbital motion

inside
nucleons


๏ƒ˜
Accessible in LT DSAs
:

The
cos
๐œ™
โˆ’
๐œ™

๐ฟ

amplitudes

s
imilar observations from
Hall
-
A and COMPASS

slightly
positive ?

slightly
positive ?

consistent with zero

consistent with zero

positive!!

1
1
D
g
T
๏ƒ„
๏‚ต
๏ž
22

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

23

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The
cos
๐œ™

๐ฟ

and

cos
2
๐œ™
โˆ’
๐œ™

๐ฟ

amplitudes

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

}

Worm
-
gear

โŠฅ


Describes the probability to find
transversely polarized quarks in a
longitudinally polarized nucleon

24

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

๏ƒ˜
some
models support
the simple relation

The sin(2
๐œ™
)
๐ฟ

amplitude

๏ž
๏ž
๏ƒ„
๏‚ต
1
1
H
h
L
Amplitudes
consistent with
zero for all
mesons and for both H and D targets

Deuterium target

Hydrogen target

A. Airapetian et al, Phys. Lett. B562 (2003)

A. Airapetian et al, Phys. Rev. Lett. 84 (2000)

25

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

A. Airapetian et al, Phys. Lett. B562 (2003)


+


0


โˆ’


+

26

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

sin(
๐œ™
)
๐ฟ

amplitude

Positive: Hydrogen results larger than
Deuteron (u
-
quark dominance)

Positive: Hydrogen and Deuteron of
same size

Deuteron positive, Hydrogen
๏‚ป
๏€ฝ
0
๏€ฝ

Positive and consistent with

+

(u
-
quark dominance)

Distribution Functions

}

Subleading twist

L.L. Pappalardo
โ€“

Structure of Nucleons and Nuclei
โ€“

Como
โ€“

June 10
-
14 2013

Sensitive to worm
-
gear , sivers,
transversity + higher
-
twist DF and FF

๏ž
T
g
1
27

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Subleading
-
twist
sin(
๏ฆ
S
) Fourier component

โ€ข

sensitive to
worm
-
gear

,
Sivers
function
,
Transversity
,
etc

โ€ข

significant non
-
zero
signal for
๏ฐ
-

and K
-

!

๏ž
T
g
1
Large
and
negative

negative

28

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Subleading
-
twist
sin(
๏ฆ
S
) Fourier component

โ€ข

sensitive to
worm
-
gear

,
Sivers
function
,
Transversity
,
etc

โ€ข

significant non
-
zero
signal for
๏ฐ
-

and K
-

!

๏ž
T
g
1
๏ƒ˜
low
-
Q
2

amplitude
larger

๏ƒ˜
hint
of Q
2

dependence for
๏ฐ
-

Large
and
negative

negative

29

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

2
-
hadron SIDIS results

Following formalism developed by
Steve Gliske


Find details in


Transverse
Target Moments of
Dihadron

Production in Semi
-
inclusive Deep Inelastic
Scattering
at HERMES

S.
Gliske
,

PhD thesis, University of Michigan, 2011


30

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

http://www
-
personal.umich.edu/~lorenzon/research/HERMES/PHDs/Gliske
-
PhD.pdf

A short digression on di
-
hadron fragmentation functions

In the
new formalism there
are only two di
-
hadron
FFs
. Names and symbols
are entirely associated with the quark spin, whereas the partial waves of the
produced hadrons
|

1

1

,
|

2

2


are associated with partial waves of FFs.

Standard definition
of di
-
hadron FF assume no polarization of final state hadrons (pseudo
-
scalar mesons)
or define mixtures of certain partial waves as new FFs

The cross
-
section is identical to the ones in literature, the only difference is the interpretation of the FFs:

31

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

๐œ’
=
๐œ’
โ€™

๐œ’
โ‰ 
๐œ’
โ€™

The di
-
hadron SIDIS cross
-
section



and


correspond to
|




angular momentum state of the hadron

Considering all terms (

๐œŽ

,

๐œŽ
๐ฟ

,

๐œŽ

๐ฟ
,

๐œŽ
๐ฟ๐ฟ
,

๐œŽ


,

๐œŽ
๐ฟ
) there are
144 non
-
zero structure functions
at twist
-
3 level. The most known is

w
hich for

=
1

and

=
1

reduces to the well known collinear
๐น

sin
๐œ—
sin
๐œ™

+
๐œ™


related to transversity

32

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The di
-
hadron SIDIS cross
-
section

โ€ข

independent
way to access
transversity

โ€ข

Collinear
๏‚ฎ

no convolution integral

โ€ข

significantly
positive amplitudes

โ€ข

1


evidence of non zero dihadron
FF

โ€ข

limited statistical power (v.r.t. 1 hadron
)

33

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

JHEP 06 (2008) 017

The di
-
hadron SIDIS cross
-
section

34

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

โ€ข
New tracking, new PID, use of
๐œ™


rather than

๐œ™

โŠฅ

โ€ข
Different fitting procedure and function

โ€ข
Acceptance
correction

JHEP 06 (2008) 017

โ€ข

independent
way to access
transversity

โ€ข

Collinear
๏‚ฎ

no convolution integral

โ€ข

significantly
positive amplitudes

โ€ข

1


evidence of non zero dihadron
FF

โ€ข

limited statistical power (v.r.t. 1 hadron
)

โ€ข

signs are consistent for all


species

โ€ข

statistics much more limited for

ยฑ

0

โ€ข

despite uncertainties may still help to
constrain global fits and may assist in

โˆ’


flavor
separation

Conclusions

A rich phenomenology and surprising effects
arise when parton transverse
momentum is not integrated out!


Transverse effects and orbital
motion of
partons

are
now
established as key
ingredients of the nucleon internal dynamics

35

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Conclusions

A rich phenomenology and surprising effects
arise when parton transverse
momentum is not integrated out!


Transverse effects and orbital
motion of
partons

are
now
established as
key
ingredients
of the nucleon internal dynamics


The HERMES experiment has played a pioneering role in these studies:

36

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Back
-
up

37

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

}

Describes correlation between quark
transverse momentum and transverse
spin in unpolarized nucleon

Boer
-
Mulders function

38

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The
cos2
๏ฆ

amplitudes


)
,
(
)
,
(
2
1
2
1
T
T
k
z
H
p
x
h
๏ž
๏ž
๏ƒ„
๏‚ต
negative

positive

A.
Airapetian

et al, Phys.
Rev
. D 87 (2013) 012010

-

Amplitudes are significant
๏‚ฎ
๏€ฝ
cๆฑฅl็ˆ r็™ฉๆ‘ฅๆนฃๆ” ๏‚ฎๆ˜ ไ‰โฅๆ™ฆๆ•ฃt
๏€ฝ
๏Š
๏€ฝ
็ฉๆตฉsๆ…ฒarๆ•ณ็•ฌ็‘ณโฆ๏‚ฎ็ˆ ไ  โ˜ ไ 
ๆฅฎiๆฅฃitๆ” โ€ โ€ โ€ ๏€ฝโ€ โ€ โ€ โ€ ๏€ฝโ€ โ€ 
๏€ฝ
๏Š
๏€ฝ
ไฝฐO๏‚ฎ็ฉsๆ” ็ฉๆฎsf๏‚ฎ็ˆ 

+
/

โˆ’

consistent with opposite signs
of
fav
/
unfav

Collins

39

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The
cos2
๏ฆ

amplitudes


-

Amplitudes are significant
๏‚ฎ
๏€ฝ
cๆฑฅl็ˆ r็™ฉๆ‘ฅๆนฃๆ” ๏‚ฎๆ˜ ไ‰โฅๆ™ฆๆ•ฃt
๏€ฝ
๏Š
๏€ฝ
็ฉๆตฉsๆ…ฒarๆ•ณ็•ฌ็‘ณโฆ๏‚ฎ็ˆ ไ  โ˜ ไ 
ๆฅฎiๆฅฃitๆ” โ€ โ€ โ€ ๏€ฝโ€ โ€ โ€ โ€ ๏€ฝโ€ โ€ 
๏€ฝ
๏Š
๏€ฝ
ไฝฐO๏‚ฎ็ฉsๆ” ็ฉๆฎsf๏‚ฎ็ˆ 

+
/

โˆ’

consistent with opposite signs
of
fav
/
unfav

Collins

)
,
(
)
,
(
2
1
2
1
T
T
k
z
H
p
x
h
๏ž
๏ž
๏ƒ„
๏‚ต
negative

positive

Large
and
negative

-


+
/

โˆ’

amplitudes are larger
than for pions , have different
kinematic dependencies than
pions and have same sign

-

different role of Collins FF for
pions and kaons?

-

Significant contribution from
scattering off strange quarks?

Large
and
negative

A.
Airapetian

et al, Phys.
Rev
. D 87 (2013) 012010

http://www
-
hermes.desy.de/cosnphi/

Analysis multi
-
dimensional
in x, y, z,and Pt

Create your own projections of results through:

40

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The
cos
๏ฆ

amplitudes


negative

negative

Large
and
negative

Consist.
w
ith 0

A.
Airapetian

et al, Phys.
Rev
. D 87 (2013) 012010

http://www
-
hermes.desy.de/cosnphi/

Analysis multi
-
dimensional
in x, y, z,and Pt

Create your own projections of results through:

41

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Distribution Functions

1
D
๏ž
1
H
Fragmentation Functions

h

}

Transversity

Describes probability to find
transversely polarized quarks in a
transversely polarized nucleon

42

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Consistent with
Belle/
BaBar

measurements
in
e
+
e
-


Collins
amplitudes

positive

consistent with zero

large and negative!

(isospin
-
symmetry)

significantly positive

consistent with zero

[
Airapetian

et al
., Phys.
Lett
. B 693 (2010) 11
-
16]

)
,
(
)
,
(
2
1
2
1
T
T
k
z
H
p
x
h
๏ž
๏ƒ„
๏‚ต
Soffer

bound

xh
1
(x)

d

xh
1
(x)

u

xh
1
(x, k )

T

u

xh
1
(x, k )

T

d

Anselmino et al. Phys. Rev. D
75 (2007)

43

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

}

๐น
๐ฟ
sin
๐œ™

Distribution Functions

Sensitive to

1

, Boer
-
Mulders +
higher
-
twist DF and FF

44

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

}

๐น
๐ฟ
sin
๐œ™

open circles 0.2<z<0.5

f
ull circles 0.5<z<0.8

o
pen squares: 0.8<z<1.0

A. Airapetian et al, Phys. Lett. B 648 (2007)

1996
-
2000 data


+


0


โˆ’

45

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

H target, 2000
-
2007 data 0.2<z<0.7

๐น
๐ฟ
sin
๐œ™

Released yesterday!!

46

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

๐น
๐ฟ
sin
๐œ™

Released yesterday!!

D

target, 2000
-
2007 data 0.2<z<0.7

47

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The sin(2
๏ฆ
+
๏ฆ
S
) Fourier component

โ€ข

arises solely from longitudinal (w.r.t.
virtual photon direction) component of
the target spin

โ€ข

related to <sin(2
๏ฆ
)>
UL

Fourier comp:



โ€ข

sensitive to
worm
-
gear

โ€ข

suppressed by one power of
P
h
๏ž

w.r.t. Collins and Sivers amplitudes

โ€ข


no
significant
signal observed
(except maybe for K+)

๏ž
L
h
1
h
UL
l
h
UT
S
)
2
sin(
2
)
sin(
2
1
)
2
sin(
2
*
๏ฆ
๏Š
๏ฆ
๏ฆ
๏ง
๏‚ต
๏€ซ
48

48

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The subleading
-
twist sin(2
๏ฆ
-
๏ฆ
S
) Fourier component

โ€ข

sensitive to
worm
-
gear

,
Pretzelosity

and
Sivers function
:

๏ž
T
g
1
โ€ข

suppressed by one power of
P
h
๏ž

w.r.t.
Collins and Sivers amplitudes


โ€ข

no significant non
-
zero signal
observed


49

49

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

1.
Assume u
quark and proton have (transverse) spin
alligned in the direction
๐œ™

=

2


. The model
assumes that the struck quark is initially connected
with the remnant via a gluon
-
flux tube (string)



2.
When the string breaks, a




pair is created with
vacuum quantum numbers

๐‘ƒ
=
0
+
. The positive
parity requires that the spins of


and



are aligned,
thus an OAM

=


has to compensate the spins




3.
This OAM generates a transverse momentum of the
produced pseudo
-
scalar meson (e.g.

+
) and deflects
the meson to the
left side
w.r.t.
t
he struck quark
direction, generating left
-
righ azimuthal asymmetries

(a phenomenological explanation of
the Collins effect)

In the cross
-
section the Collins FF is always paired
withy a distrib. function involving a transv.
p
ol. quark
.

A short digression on the Lund/
Artru

string fragmentation model

50

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Relative to the proton transv. spin, the fragmenting quark can have spin parallel or antiparallel to

1
2
,
ยฑ
1
2



Then combining the spins of the formed di
-
quark systems one can get:

1
2
โจ‚
1
2
=
1
โŠ•
0


โ‡’





1

 ๐‘–

0

๐‘Ž

|
0
,
0

3

 ๐‘–

1

๐‘Ž


|
1
,
0


|
1
,
ยฑ
1


1 pseudo
-
scalar meson (PSM)

1 Longitudinal VM

2 transvrse VM

Lund/Artru prediction at the amplitude level
: the asymmetry for PSM has opposite sign to
that for transversely polarized VM (left vs. right side), and the amplitude for
|
1
,
0


is 0

Lund/Artru model makes predictions for the individual di
-
hadrons, but the
Collins function includes pairs of di
-
hadrons


๏‚ฎ
t
o make predictions for the Collins function one needs to consider the
cross
-
section level, i.e.
t
he sum of contributing amplitudes times their
complex conjugate


Using the Clebsch
-
Gordan algebra one obtains:
|
1
,
ยฑ
1


|
1
,
ยฑ
1

โ‰ก

|
2
,
ยฑ
2



Lund/Artru prediction at the cross
-
section level
: the
|
2
,
ยฑ
2


partial waves of the Collins
func. for SIDIS VM production have the opposite sign as the respective PS Collins func.

A short digression on the Lund/
Artru

string fragmentation model

51

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013



โ€œgluon
radiaton

modelโ€ vs. Lund/
Artru

model

The Lund/Artru model only accounts for favored Collins fragmentation. An extension of the
model (the
gluon radiation model
), elaborated by
S. Gliske
accounts for the disfavored case

1.
Struck quark emits a gluon in such a way that most of its momentum is transferred to the gluon

2.
The struck quark then becomes part of the remnant

3.
The radiated gluon produces a




pair that eventually converts into a meson

4.
For PSM the di
-
quark must interact further with the remnant to get the PSM quantum numbers. In
case of VM the di
-
quark directly forms the meson

Lund/Artu

Gluon radiation

โ€ข
Di
-
quark has q.n. of vacuum

โ€ข
Struck quark
joins the anti
-
quark in the
final state
๏‚ฎ

favored fragment
.


โ€ข
Di
-
quark has q.n. of observed final state

โ€ข
Produced quark
joins the anti
-
quark in the
final state
๏‚ฎ

disfavored fragment.


Prediction
:
the
|
2
,
ยฑ
2


partial wave of the Collins
funct.
for SIDIS VM production
have
the opposite
sign as the respective PS Collins
function

Prediction
: the disfavored
|
2
,
ยฑ
2


Collins frag.
a
lso
is expected to have opposite sign as the respective
PS Collins function.

Models predict: fav = disfav for VM


Data say: fav
โ‰…
โˆ’

disfav for PSM (Collins

+


.



โˆ’
)

52

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

โ€ฆand now letโ€™s look at the results

Fragment. process

Fav/disfav

Deflection

Sign of amplitude

๐’–
โ†’

+

fav PSM

left
๐œ™
โ„Ž
โ†’
0

> 0 (Collins

+
)

๐’–
โ†’

โˆ’

disfav PSM

ight
๐œ™
โ„Ž
โ†’


<

0
(Collins

โˆ’
)

๐’–
โ†’

+
โ†’

+

0

fav VM

right
๐œ™
โ„Ž
โ†’


<

0

๐’–
โ†’

โˆ’
โ†’

โˆ’

0

disfav VM

right
๐œ™
โ„Ž
โ†’


< 0

๐’–
โ†’


โ†’

+

โˆ’

mixed VM

right
๐œ™
โ„Ž
โ†’


0 or < 0

f
rom
data

f
rom
models

u dominance

53

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

โ€ฆand now letโ€™s look at the results

Fragment. process

Fav/disfav

Deflection

Sign of amplitude

๐’–
โ†’

+

fav PSM

left
๐œ™
โ„Ž
โ†’
0

> 0 (Collins

+
)

๐’–
โ†’

โˆ’

disfav PSM

ight
๐œ™
โ„Ž
โ†’


<

0
(Collins

โˆ’
)

๐’–
โ†’

+
โ†’

+

0

fav VM

right
๐œ™
โ„Ž
โ†’


<

0

๐’–
โ†’

โˆ’
โ†’

โˆ’

0

disfav VM

right
๐œ™
โ„Ž
โ†’


< 0

๐’–
โ†’


โ†’

+

โˆ’

mixed VM

right
๐œ™
โ„Ž
โ†’


0 or < 0

f
rom
data

f
rom
models

|

,
โˆ’



consistent with zero for all flavors
N
ot in contraddiction with models: if the
transversity function causes the fragmenting
quark to have positive polarization than
Collins
|
2
,
โˆ’
2


must be zero as this partial
wave requires fragmenting quark with
negative polarization


|

,
+



consistent
with model expect:

โ€ข
No signal outside

-
mass bin



๏‚ฎ

no non
-
resonant pion
-
pairs in p
-
wave

โ€ข
Negative for

ยฑ

(model predictions)

โ€ข
very small for

0

(consistent with small
Collins

0
)

u dominance

54

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Aerogel n=1.03

C
4
F
10

n=1.0014

hadron separation


lepton
-
hadron > 98%

TRD, Calorimeter,

preshower, RICH:

๏ฐ

~ 98%, K ~ 88% , P ~ 85%

The HERMES experiment at HERA

55

55

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

Siver amplitudes: additional studies

No systematic shifts
observed between high
and low Q
2

amplitudes for
both
๏ฐ
+

and K
+

No indication of
important contributions
from exclusive VM




56

56

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013

The pion
-
difference asymmetry


Contribution from exclusive

r
0

largely cancels out!

โ€ข

significantly positive Sivers and Collins amplitudes are obtained

โ€ข

measured

amplitudes

are

not

generated

by

exclusive

VM

contribution


๏€ซ
๏ฐ
๏€ญ
๏ฐ
Contribution

by

decay

of

exclusively

produced

vector

mesons

(
r
0
,
๏ท
,
๏ฆ
)

is

not

negligible

(
6
-
7
%

for

pions

and

2
-
3
%

for

kaons),

though

substatially

limited

by

the

requirement

z<
0
.
7
.

๏€จ
๏€ฉ
)
(
)
(
)
(
)
(
1
,
๏€ญ
๏€ซ
๏€ญ
๏€ซ
๏€ญ
๏€ซ
๏€ญ
๏€ซ
๏€ญ
๏€ซ
๏‚ฏ
๏‚ฏ
๏‚ญ
๏‚ญ
๏‚ฏ
๏‚ฏ
๏‚ญ
๏‚ญ
๏€ญ
๏€ญ
๏€ซ
๏€ญ
๏€ญ
๏€ญ
๏€ญ
๏‚บ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ฐ
๏ณ
๏ณ
๏ณ
๏ณ
๏ณ
๏ณ
๏ณ
๏ณ
๏ฆ
๏ฆ
U
U
U
U
U
U
U
U
T
S
UT
P
A
a new
observable

57

57

L.L. Pappalardo
โ€“

Baryons 2013
โ€“

Glasgow
โ€“

June 24
-
28 2013