Parton fragmentation within spin-dependent TMD and collinear observables Daniel Pitonyak Penn State University-Berks, Reading, PA supported by TMD Topical Collaboration
22nd International Spin Physics Symposium Champaign, IL September 29, 2016
D. Pitonyak
Outline ! Motivation ! FFs in transverse momentum dependent (TMD) observables • • • •
Definitions Electron-positron annihilation: e+ e ! ha hb X Semi-inclusive deep-inelastic scattering (SIDIS): e N! e0 h X Proton-proton collisions (hadron in a jet): p p ! (h jet) X
! FFs in collinear observables • • • •
Definitions (twist-3) Proton-proton collisions (AN ): p p ! h X Definitions (di-hadron) Electron-positron/SIDIS/proton-proton:
e+ e ! (ha1 ha2 ) (hb1 hb2 ) X / e N! e0 (ha hb ) X / p p ! (ha hb ) X
! Summary and outlook
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Motivation
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Inclusive DIS
X
D. Pitonyak
Inclusive DIS
Twist-‐2 collinear PDFs (x) q pol. H pol.
U
U
f1
L
unpolarized
L
X
T
g1
helicity
T
D. Pitonyak
Inclusive DIS
Twist-‐2 collinear PDFs (x) q pol. H pol.
U
U
f1
L
T
unpolarized
L
X
T
g1
helicity
h1
transversity
allows us to calculate the tensor charge of the nucleon
D. Pitonyak
Inclusive DIS
Twist-‐2 collinear PDFs (x) q pol. H pol.
U
U
f1
L
T
unpolarized
L
X
T
g1
helicity
h1
transversity
chiral-‐odd CANNOT be accessed in inclusive DIS!
D. Pitonyak
Semi-‐Inclusive DIS (SIDIS)
Twist-‐2 collinear PDFs (x)
Need to know FFs
π(Ph) X
q pol. H pol.
U
U
f1
L
T
unpolarized
L T
g1
helicity
h1
transversity
chiral-‐odd CANNOT be accessed in inclusive DIS!
D. Pitonyak
Semi-‐Inclusive DIS (SIDIS)
Twist-‐2 collinear PDFs (x) q pol. H pol.
U
U
f1
Need to know FFs
π(Ph) X
⌃
strange quark helicity -‐> kaon FFs
See talk by Leader
L
T
unpolarized
L T
g1
helicity
h1
transversity
chiral-‐odd CANNOT be accessed in inclusive DIS!
D. Pitonyak
Semi-‐Inclusive DIS (SIDIS)
Twist-‐2 TMD PDFs (x, kT)
Need to know FFs
π(Ph) X
q pol. H pol.
U
U
f1
3-‐DIMENSIONAL structure of the nucleon
? f1T
T
h? 1 g1L
L T
L
g1T
h? 1L h1T
h? 1T
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AN in proton-‐proton collisions
1976
D. Pitonyak
AN in proton-‐proton collisions quark-‐gluon-‐quark FFs could resolve 40 year-‐old puzzle of what causes AN
1976
q pol. H pol.
U
Twist-‐3 collinear FFs ((z) or (z, z1))
Twist-‐2 TMD FFs (z, p ? )
U
L
? D1T
T H1?
D1
L T
D. Pitonyak
G1L
? H1L
G1T
H1T ? H1T
H pol.
U
^ ? D1 , G? , H , H 1 1 1
E, H
kinemaJcal
dynamical
?(1)
ˆ <,= H FU
?(1)
ˆ <,= H FL
H1
L HL , EL H1L
T (Unpolarized) Di-‐hadron FFs (DiFF) 2 (z, ⇣, R? , p? · R? , p2? )
intrinsic
?(1) D1T , DT , GT ?(1) G1T
ˆ <,= , G ˆ <,= D FT FT
fragmentaOon sector is rich in its own right – funcOons & parOcles
π0, π±, Κ0, Κ±, Λ, η, D0, D± …
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FFs in TMD Observables
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! Definitions q ij (z, p? )
Z Z 1 X = Nc X
1 1
d 2⇡
Z
d 2 z? e i z ip? ·z? h0|qi (0)|Ph Sh ; Xi 2 (2⇡) ⇥ hPh Sh ; X| q¯j ( m + z? ) |0i
Twist-‐2 TMD FFs (z, p ? ) h/q[
]
h/q[
j i ✏ij h/q ? h/q 2 2 ? p? Sh? = D1 (z, z p~? ) + D1T (z, z 2 p~?2 ) , Mh
5]
=
h/q ⇤h G1L (z, z 2 p~?2 )
~h? h/q p~? · S G1T (z, z 2 p~?2 ) , + Mh
j ✏ij ? h/q ? p? = H1 (z, z 2 p~?2 ) Mh " # i ~ p p~? · Sh? ? h/q ? h/q + ? ⇤h H1L (z, z 2 p~?2 ) + H1T (z, z 2 p~?2 ) Mh Mh
h/q[i
i
5]
i Sh?
h/q H1T (z, z 2 p~?2 )
(Boer, Jakob, Mulders (1997))
q pol. H pol.
U
U
D1
L T
? D1T
L
T H1?
G1L
? H1L
G1T
H1T ? H1T
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! Definitions q ij (z, p? )
Z Z 1 X = Nc X
1 1
d 2⇡
Z
d 2 z? e i z ip? ·z? h0|qi (0)|Ph Sh ; Xi 2 (2⇡) ⇥ hPh Sh ; X| q¯j ( m + z? ) |0i
Twist-‐2 TMD FFs (z, p ? ) h/q[
]
h/q[
j i ✏ij h/q ? h/q 2 2 ? p? Sh? = D1 (z, z p~? ) + D1T (z, z 2 p~?2 ) , Mh
5]
~h? h/q p~? · S h/q 2 2 G1T (z, z 2 p~?2 ) , = ⇤h G1L (z, z p~? ) + Mh
j ✏ij ? h/q ? p? = H1 (z, z 2 p~?2 ) Mh " # i ~ p p~? · Sh? ? h/q ? h/q + ? ⇤h H1L (z, z 2 p~?2 ) + H1T (z, z 2 p~?2 ) Mh Mh
h/q[i
i
5]
i Sh?
h/q H1T (z, z 2 p~?2 )
(Boer, Jakob, Mulders (1997))
q pol. H pol.
U L T
U
D1
? D1T
L
T
Collins funcJon
H1?
G1L
? H1L
G1T
H1T ? H1T
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! Electron-positron annihilation (Boer, Jakob, Mulders (1997); Boer (1998); DP, Metz, Schlegel (2014), …)
e+ e ! ha hb X
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! Electron-positron annihilation (Boer, Jakob, Mulders (1997); Boer (1998); DP, Metz, Schlegel (2014), …)
e+ e ! ha hb X
d d⌦ dza dzb d2 P~a?
Figures from Seidl, et al. (2008)
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! Electron-positron annihilation (Boer, Jakob, Mulders (1997); Boer (1998); DP, Metz, Schlegel (2014), …)
e+ e ! ha hb X
d d⌦ dza dzb d2 P~a?
Figures from Seidl, et al. (2008)
Collins effect
/ · · · + B(y) cos(2 cos(2 FU U
0)
"
cos(2
0 ) FU U
0)
ˆ · p~a? h ˆ · p~b? p~a? · p~b? 2h ¯ 1? =C H1? H M a Mb
#
/ · · · + B(y) cos( cos( FU U
a+ b)
=
X q
cos(
a+
b ) FU U ?(1)
e2q B(y) H1
a+ b)
¯ ?(1) (zb ) (za ) H 1
D. Pitonyak See talks by Anulli, Seidl
• Clear nonzero Collins asymmetry for ππ pairs
Belle (2008) √S = 10.52 GeV
• BaBar (2015) also measured ΚΚ and πΚ " access to kaon Collins FF • Measurements at different √S gives information on TMD evolution BESIII (2016) √S = 3.65 GeV
BaBar (2014) √S = 10.6 GeV
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! Semi-inclusive DIS (SIDIS) (Mulders, Tangerman (1996); Boer, Jakob, Mulders (2000); Bacchetta, et al. (2007), …)
e N! e0 h X
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! Semi-inclusive DIS (SIDIS) (Mulders, Tangerman (1996); Boer, Jakob, Mulders (2000); Bacchetta, et al. (2007), …)
e N! e0 h X
Figure from Boer, et al. (2011)
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! Semi-inclusive DIS (SIDIS) (Mulders, Tangerman (1996); Boer, Jakob, Mulders (2000); Bacchetta, et al. (2007), …)
e N! e0 h X
d 2 dx dy d s dz d h dPh? n h ~? | sin( h + / · · · + |S Figure from Boer, et al. (2011)
sin(
FU T
h+ S )
=C
"
Collins effect sin( S )FU T
h+ S )
ˆ · p~? h h1 H1? Mh
i
+ ... + ...
#
o
COMPASS (2015)
D. Pitonyak HERMES (preliminary)
JLab Hall A (2011, also 2014 for kaons)
See talks by Puckett, Schnell
COMPASS (2015)
D. Pitonyak HERMES (preliminary)
JLab Hall A (2011, also 2014 for kaons)
Simultaneously extract Collins & transversity from SIDIS and e+eIMPORTANT: Collins function is universal (Metz (2002); Collins, Metz (2004), …)
D. Pitonyak
Anselmino, et al. (2013)
Kang, et al. (2016)
uses full TMD evolution
See talks by Kang, Echevarria, Prokudin
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! Proton-proton collisions (hadron in a jet) (Yuan (2008); D’Alesio, Murgia, Pisano (2011, 2014))
p p ! (h jet) X
Figure from D’Alesio, Murgia, Pisano (2011) ~k?⇡ ⌘ P~hT
d d3 P~J dz d2 P~hT
/ sin(
s
H ~2 ⇡ ) h1 (xa , k?a )
2 2 ⌦ f1 (xb , ~k?b ) ⌦ H1? (z, ~k?⇡ ) ⌦ ˆpol
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! Proton-proton collisions (hadron in a jet) (Yuan (2008); D’Alesio, Murgia, Pisano (2011, 2014))
p p ! (h jet) X
Figure from D’Alesio, Murgia, Pisano (2011) ~k?⇡ ⌘ P~hT
d d3 P~J dz d2 P~hT
D’Alesio, Murgia, Pisano (2014)
/ sin(
s
H ~2 ⇡ ) h1 (xa , k?a )
2 2 ⌦ f1 (xb , ~k?b ) ⌦ H1? (z, ~k?⇡ ) ⌦ ˆpol
D. Pitonyak See talk by Drachenberg
Kang, et al., Data from STAR (preliminary)
• Clear nonzero Collins asymmetry for charged pions • Similar magnitude for √S = 200 GeV and √S = 500 GeV (cf. Belle and BaBar much smaller asymmetry than BESIII) • No evolution? or Cancellation of evolution effects in the asymmetry? or Simply a kinematical effect? • Data not yet included in a global fit (test the universality of the Collins function)
D. Pitonyak
FFs in Collinear Observables
D. Pitonyak
! Definitions (twist-3)
intrinsic Z Z X 1 q ij (z) = Nc X
1 1
dynamical
d e i z h0| qi (0) |Ph Sh ; Xi 2⇡ ⇥hPh Sh ; X| q¯j ( m) |0i
q,⇢ @,ij (z)
=
d2 p? p⇢?
Z Z 1 X = Nc X
and kinemaOcal
Z
q,⇢ F,ij (z, z1 )
q ij (z, p? )
1 1
d 2⇡
Z
1 1
dµ i z +i( z1 e 1 2⇡
1 z1
)µ
h0| igm⌘ F ⌘⇢ (µm)qi ( m) |Ph Sh ; Xi ⇥ hPh Sh ; X| q¯j (0) |0i
D. Pitonyak
! Definitions (twist-3)
Twist-‐3 collinear FFs ((z) or (z, z1)) H pol.
U
intrinsic
E, H
kinemaJcal
?(1)
ˆ <,= H FU
?(1)
ˆ <,= H FL
H1
L HL , EL H1L
T DT , GT
dynamical
?(1)
D1T , ?(1)
G1T
ˆ <,= , G ˆ <,= D FT FT
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! Proton-proton collisions (AN )
(Kang, Yuan, Zhou (2010); Metz, DP (2013); Kanazawa, Koike, Metz, DP (2014); Gamberg, Kang, Metz, DP, Prokudin (2014); Koike, DP, Takagi, Yoshida (2016), Kanazawa, Koike, Metz, DP, Schlegel (2016))
pp ! hX
Metz, DP (2013)
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Plot from Aidala, Bass, Hasch, Mallot (2013)
STAR (2012)
PHENIX (2014)
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Kanazawa, Koike, Metz, DP (2014)
?(1)
-Used Sivers function from SIDIS as input for Qiu-Sterman function f1T -Used Collins and transversity extracted from SIDIS/e+e-
(x) / TF (x, x)
-Used EOM relation for H
ˆ F=U (z, z1 ) -Extracted H See talks by Koike, Gamberg
D. Pitonyak
D. Pitonyak
EOM relation + Lorentz invariance relation (LIR) "
H(z) =
Z
1
dz1
z
?(1) (z) H1
Z
1
z1
=
2 z
dz2 2 z22
Z
z
"⇣
1
dz1
2( z21
Z
1
z1
Kanazawa, Koike, Metz, DP, Schlegel (2016)
1 z2 )
+
1 z1
⇣
⇣
dz2 ⇣ z22
⇣
1 z1
1 z1 1 z2
1 z2 ⌘2
2 z1
1 z2
1 z1
1 z2
⌘ ⇣
1 z1
1 z
⌘⌘
ˆ = (z1 , z2 ) H FU
⌘
= ˆ H ⌘2 F U (z1 , z2 )
ˆ = (z, z1 ) could be the main cause of AN quark-gluon-quark FF H FU
#
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! Definitions (di-hadron)
(Unpolarized) DiFFs 2 (z, ⇣, R? , p ? · R? , p2? ) ^ ? D1 , G? , H , H 1 1 1
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! Definitions (di-hadron)
Integrated (Unpolarized) DiFFs
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! Electron-positron/SIDIS (Artru, Collins (1996); Bianconi, Boffi, Jakob, Radici (1999); Boer, Jakob, Radici (2003); de Florian, Vanni (2004); Bacchetta, Courtoy, Radici (2013); Radici, Courtoy, Bacchetta, Guagnelli (2015); Pisano, Radici (2016))
Figure from Metz, Vossen (2016)
Figure from Pisano, Radici (2016)
D. Pitonyak
! Electron-positron/SIDIS (Artru, Collins (1996); Bianconi, Boffi, Jakob, Radici (1999); Boer, Jakob, Radici (2003); de Florian, Vanni (2004); Bacchetta, Courtoy, Radici (2013); Radici, Courtoy, Bacchetta, Guagnelli (2015); Pisano, Radici (2016))
Figure from Metz, Vossen (2016)
Figure from Pisano, Radici (2016)
Extract transversity in a collinear framework* *evolution of DiFFs different than single-hadron FFs (Konishi, Ukawa, Veneziano (1979); Sukhatme, Lassila (1980); de Florian, Vanni (2004))
D. Pitonyak
! Electron-positron/SIDIS (Artru, Collins (1996); Bianconi, Boffi, Jakob, Radici (1999); Boer, Jakob, Radici (2003); de Florian, Vanni (2004); Bacchetta, Courtoy, Radici (2013); Radici, Courtoy, Bacchetta, Guagnelli (2015); Pisano, Radici (2016))
Belle (2011)
HERMES (2008)
COMPASS (2014)
D. Pitonyak
Radici, et al. (2015)
See talk by Radici
D. Pitonyak
! Proton-proton collisions (Bacchetta, Radici (2004); Radici, Ricci, Bacchetta, Mukherjee (2016))
d
UT
/ sin(
R
Sa ) h1 (xa )
p p ! (ha hb ) X
⌦ f1 (xb ) ⌦ H1^ (z, Mh2 ) ⌦ ˆpol
D. Pitonyak
! Proton-proton collisions (Bacchetta, Radici (2004); Radici, Ricci, Bacchetta, Mukherjee (2016))
d
UT
/ sin(
R
Sa ) h1 (xa )
STAR (preliminary)
p p ! (ha hb ) X
⌦ f1 (xb ) ⌦ H1^ (z, Mh2 ) ⌦ ˆpol
See talks by Drachenberg, Skoby
D. Pitonyak
! Proton-proton collisions (Bacchetta, Radici (2004); Radici, Ricci, Bacchetta, Mukherjee (2016))
d
UT
/ sin(
R
Sa ) h1 (xa )
p p ! (ha hb ) X
⌦ f1 (xb ) ⌦ H1^ (z, Mh2 ) ⌦ ˆpol
Radici, et al. (2016), Data from STAR (2015, blue is preliminary)
• Another probe of transversity • Possible issues in describing AUT vs. η and AUT vs. PT in the forward region • In general, no knowledge of D1 for DiFFs • Need global fit with SIDIS/e+e-
See talks by Drachenberg, Radici, Skoby
D. Pitonyak
! Other topics of importance • Extraction of unpolarized FF D1 (z) , D1 (z, z 2 p~?2 )
See talks by Gonzalez, Leader, Nocera, Seidl
• Other SIDIS azimuthal modulations involve Collins - access to Boer-Mulders, pretzelocity •
e+ e ! ha hb X with lepton and/or hadron (Lambda) polarization and EW effects
See talk by Kaibao for VπX final state
• Model calculations of FFs (CANNOT compute FFs
See talk by Guan on lattice) See talks by Kerbizi, Schweitzer
• Sum rules (or lack there-of) providing constraints on FFs • Twist-3 TMD FFs • AN for Lambda production
See talk by Yabe
• Measurement of TMD DiFFs
#$ # # See recent review by Metz and Vossen -‐ arXiv:1607.02521
D. Pitonyak
! Other topics of importance • Extraction of unpolarized FF D1 (z) , D1 (z, z 2 p~?2 )
See talks by Gonzalez, Leader, Nocera, Seidl
• Other SIDIS azimuthal modulations involve Collins - access to Boer-Mulders, pretzelocity + • e e
! ha hb X with lepton and/or hadron (Lambda) polarization and EW effects
See talk by Kaibao for VπX final state
• Model calculations of FFs (CANNOT compute
See talk by Guan FFs on lattice) See talks by Kerbizi, Schweitzer
• Sum rules (or lack there-of) providing constraints on FFs • Twist-3 TMD FFs • AN for Lambda production See talk by Yabe • Measurement of TMD DiFFs
#$ # # See recent review by Metz and Vossen -‐ arXiv:1607.02521
Belle (preliminary)
D. Pitonyak See talk by Guan
e+ e ! ⇤" ⇡ ± X
D. Pitonyak
Belle (preliminary)
e+ e ! ⇤" ⇤" X H1(z1) x H1(z2)
e+ e ! ⇤" ⇡ ± X
+
/ p" p ! ⇤" X e p" ! e0 ⇤" X h1(x) x H1(z)
extract transversity in “true” collinear factorizaOon
See talk by Mei
D. Pitonyak
! Summary and outlook • Knowledge of fragmentation functions are crucial to understand nucleon structure, and, moreover, provide their own rich source of measurements and phenomenology
• Much progress has been made in understanding FFs in spin-dependent observables (Collins effect, AN in pp, AUT di-hadron, …), yet many open questions remain
• More precise measurements (Belle II, COMPASS, EIC, JLab12, RHIC, SuperKEKB, …) and phenomenological extractions (NLO, NNLO, proper TMD evolution, …) will be needed in order to fully grasp the 3D structure of hadrons
