Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Collinear Parton Distributions and
Front-Form Meson-Cloud Model
Stefan Kofler and Barbara Pasquini
Karl-Franzens-Universität Graz
Institut für Physik
January 13, 2016
1
University of Pavia
Collinear Parton Distributions and Front-Form Meson-Cloud Model
1
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
The Outline
Part 1: Collinear Parton Distributions (PDFs) in general
1 A convenient way to introduce PDFs is: Deep Inelastic Scattering (DIS).
• PDFs in the naive parton model
• PDFs in the QCD improved parton model
⇒ factorization
2 Front-Form
3 Field-theoretical definition of PDFs for nucleons
Part 2: Meson-Cloud Model
1 Basics
2 PDFs in a meson-cloud model
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Inclusive deep inelastic scattering (DIS)
e
e
γ*:q
p:p
,spin
X
unpolarised
scattering amplitude
inclusive: no final hadronic state detected
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Inclusive deep inelastic scattering (DIS)
e
e
Bjorken variable
γ*:q
p:p
,spin
X
unpolarised
scattering amplitude
inclusive: no final hadronic state detected
Collinear Parton Distributions and Front-Form Meson-Cloud Model
photon momentum
squared
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Inclusive deep inelastic scattering (DIS)
e
e
Bjorken variable
γ*:q
p:p
,spin
X
unpolarised
scattering amplitude
photon momentum
squared
inclusive: no final hadronic state detected
leptonic Tensor...can be calculated in QED
hadronic Tensor... describes the internal structure of the proton
p
p
depends on the strong non-perturbative
interaction dynamics
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Inclusive deep inelastic scattering (DIS)
e
e
Bjorken variable
γ*:q
p:p
,spin
X
unpolarised
scattering amplitude
photon momentum
squared
inclusive: no final hadronic state detected
leptonic Tensor...can be calculated in QED
hadronic Tensor... describes the internal structure of the proton
parameterized by structure functions
p
p
depends on the strong non-perturbative
interaction dynamics
-Lorentz invariance
-gauge invariance of QED
-parity conservation of QED
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Inclusive deep inelastic scattering (DIS)
e
e
Bjorken variable
γ*:q
p:p
,spin
X
unpolarised
scattering amplitude
photon momentum
squared
inclusive: no final hadronic state detected
leptonic Tensor...can be calculated in QED
hadronic Tensor... describes the internal structure of the proton
parameterized by structure functions
p
p
depends on the strong non-perturbative
interaction dynamics
-Lorentz invariance
-gauge invariance of QED
-parity conservation of QED
in the limit
for fixed
structure functions exhibit scaling: independent of
depend only on
--> naive parton model
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
DIS:Naive parton model
when the photon probes the proton:
made of massless, pointlike, collinear moving
and non-interacting constituents (quarks)
γ
quark carries a
momentum fraction x
of the proton momentum
(in the infinite momentum frame)
*
e-
e-
xp
γ*
p:p
(1-x)p
Collinear Parton Distributions and Front-Form Meson-Cloud Model
q:xp
q
can be calculated using QED
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
DIS:Naive parton model
when the photon probes the proton:
made of massless, pointlike, collinear moving
and non-interacting constituents (quarks)
γ
quark carries a
momentum fraction x
of the proton momentum
(in the infinite momentum frame)
*
e-
e-
xp
γ*
p:p
(1-x)p
q:xp
can be calculated using QED
q
Introduce parton distribution function (PDF) q(x) for a quark flavor q.
Probability to find a quark with momentum fraction x in the proton.
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
DIS:Naive parton model
when the photon probes the proton:
made of massless, pointlike, collinear moving
and non-interacting constituents (quarks)
γ
quark carries a
momentum fraction x
of the proton momentum
(in the infinite momentum frame)
*
e-
e-
xp
γ*
p:p
(1-x)p
q:xp
can be calculated using QED
q
Introduce parton distribution function (PDF) q(x) for a quark flavor q.
Probability to find a quark with momentum fraction x in the proton.
contributions from different quarks add incoherently in cross section
similar expressions
for other structure functions
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
F2 :Scaling violations
In the naive parton model, the structure functions scale, i.e. independent of Q 2 .
However:
significant rise at small x
approximate scaling around x~0.15
decrease at high x
pdg.lbl.gov/2014/reviews/rpp2014-rev-structure-function-figs.pdf
the scaling violation can be explained with QCD
-> QCD improved parton model
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
QCD improved parton model
Next-To-Leading order (NLO)
Leading Order
virtual gluon
correction
real gluon
emission
γ*
q
q
q
q
p
g
final state
gluon radiation
p
g
p
q
q
p
Collinear Parton Distributions and Front-Form Meson-Cloud Model
g
initial state
gluon radiation
p
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
QCD improved parton model
Next-To-Leading order (NLO)
Leading Order
virtual gluon
correction
real gluon
emission
γ*
q
q
q
q
p
p
g
p
q
massless quarks and gluons
-> infrared singularities
(related to long-distance)
UV-singularities (related to short-distance)
(already taken care of)
g
final state
gluon radiation
q
p
Collinear Parton Distributions and Front-Form Meson-Cloud Model
g
initial state
gluon radiation
p
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
QCD improved parton model
Next-To-Leading order (NLO)
Leading Order
virtual gluon
correction
real gluon
emission
γ*
q
q
q
q
p
p
g
p
q
massless quarks and gluons
-> infrared singularities
(related to long-distance)
UV-singularities (related to short-distance)
(already taken care of)
g
final state
gluon radiation
q
p
Collinear Parton Distributions and Front-Form Meson-Cloud Model
g
initial state
gluon radiation
p
Deep inelastic scattering
Front-form
PDFs
QCD improved parton model:Factorization
we encounter two different
IR-singularities (
)
- gluon and quark become collinear
- soft gluon: canceled by virtual gluon corrections
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
QCD improved parton model:Factorization
introduce IR-regulator
we encounter two different
IR-singularities (
)
- gluon and quark become collinear
- soft gluon: canceled by virtual gluon corrections
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
QCD improved parton model:Factorization
introduce IR-regulator
we find a term like this in the
partonic cross section
We have isolated the singularity.
we encounter two different
Can we control it?
IR-singularities (
)
- gluon and quark become collinear
- soft gluon: canceled by virtual gluon corrections
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
QCD improved parton model:Factorization
introduce IR-regulator
we find a term like this in the
partonic cross section
We have isolated the singularity.
we encounter two different
Can we control it?
IR-singularities (
)
- gluon and quark become collinear
- soft gluon: canceled by virtual gluon corrections
short-distance fluctuation
belongs to the partonic cross section
~ 300 MeV
long-distance fluctuation
corresponds to a fluctuation within the
proton -> belongs to the PDF q(x)
Feldmann T., Eur. Phys. J. Special Topics 140 (2007)
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
QCD improved parton model:Factorization
introduce IR-regulator
we find a term like this in the
partonic cross section
We have isolated the singularity.
we encounter two different
Can we control it?
IR-singularities (
)
- gluon and quark become collinear
- soft gluon: canceled by virtual gluon corrections
short-distance fluctuation
belongs to the partonic cross section
~ 300 MeV
long-distance fluctuation
corresponds to a fluctuation within the
proton -> belongs to the PDF q(x)
Feldmann T., Eur. Phys. J. Special Topics 140 (2007)
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
QCD improved parton model:Factorization
introduce IR-regulator
we find a term like this in the
partonic cross section
We have isolated the singularity.
we encounter two different
Can we control it?
IR-singularities (
)
- gluon and quark become collinear
- soft gluon: canceled by virtual gluon corrections
short-distance fluctuation
belongs to the partonic cross section
~ 300 MeV
long-distance fluctuation
corresponds to a fluctuation within the
proton -> belongs to the PDF q(x)
Feldmann T., Eur. Phys. J. Special Topics 140 (2007)
free of IR-singularities
sensitive to the IR-sector of QCD
absorbed into PDF
contribution to the cross section of the form
- Schwartz M.D., Quantum Field Theory and the Standard Model
- Yorikiyo Nagashima, Elementary Particle Physics v2
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
QCD improved parton model:Factorization
hadronic cross section
factorization can be proved in DIS
->factorization theorem
all uncanceled IR-singularties
free of IR-singularities (IR-safe)
are absorbed into PDF
to all orders in
universal
Collinear Parton Distributions and Front-Form Meson-Cloud Model
factorization property holds
up to terms of this order
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
QCD improved parton model:Factorization
hadronic cross section
factorization can be proved in DIS
->factorization theorem
all uncanceled IR-singularties
free of IR-singularities (IR-safe)
are absorbed into PDF
to all orders in
universal
factorization property holds
up to terms of this order
cross section independent
of fac. sclale
-dependence of
by DGLAP eqs.
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
QCD improved parton model:Factorization
QCD
high energy/short distance
hard part
low energy/long distance
ASYMPTOTIC
FREEDOM
CONFINEMENT
soft part
pQCD
Feynman Diagrams
IR-safe
phenomenological functions
PDFs
(modeling, non-perturbative QCD methods)
sensitive to IR-sector
factorization theorem: process is divided into hard part and soft part
"QCD nowadays has a split personality.
It embodies 'hard' and 'soft' physics, both being hard subjects
and the softer the harder." Yuri Dokshitzer
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Front-form
a convenient set of variables for high-energy scattering processes are light-cone variables
a0
a+
-
a
a
a3
show nicely the dominant components
simple transformation property under boosts
DIS is dominated by space-time region close to the light-cone.
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Front-form
a convenient set of variables for high-energy scattering processes are light-cone variables
a0
a+
-
a
a3
a
show nicely the dominant components
simple transformation property under boosts
DIS is dominated by space-time region close to the light-cone.
Associated with this choice of coordinates: Front-form.
quantize on light-front at x = 0
Time
Space
Energy
Momentum
,
,
Brodsky S.J., Pauli H.C., Pinsky S.S., Phys. Rept. 301 (1998)
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Front-form
a convenient set of variables for high-energy scattering processes are light-cone variables
a0
a+
-
a
a3
a
show nicely the dominant components
simple transformation property under boosts
DIS is dominated by space-time region close to the light-cone.
Associated with this choice of coordinates: Front-form.
quantize on light-front at x = 0
We use this approach to model PDFs in
terms of light-cone wavefunctions.
Time
Space
Energy
Momentum
,
,
Brodsky S.J., Pauli H.C., Pinsky S.S., Phys. Rept. 301 (1998)
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Definition of (collinear) PDFs
proton PDFs are defined by a Fourier transform (FT) of a bilocal product of
quark field operators sandwiched between two proton states
this matrix element is the hadronic
matrix element of the appropriate number
operator for finding a quark
working in LC-gauge, i.e.
otherwise there would be a Wilson line
between the two quark field operators
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Definition of (collinear) PDFs
proton PDFs are defined by a Fourier transform (FT) of a bilocal product of
quark field operators sandwiched between two proton states
proton momentum aligned
along + direction
quark momentum = x p+
->collinear PDFs
proton with with mom. p
and helicity μ
p:p,μ
creates a quark at 0
y-
0
q:x,λ
q(x)
annihilates a quark at y
with flavor q, mom fraction x and helicity λ
q:x,λ
...depends on the quark polarization
(combination of Dirac matrices)
p:p,μ
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Definition of (collinear) PDFs
proton PDFs are defined by a Fourier transform (FT) of a bilocal product of
quark field operators sandwiched between two proton states
proton momentum aligned
along + direction
quark momentum = x p+
->collinear PDFs
proton with with mom. p
and helicity μ
p:p,μ
creates a quark at 0
y-
0
q:x,λ
q(x)
annihilates a quark at y
with flavor q, mom fraction x and helicity λ
q:x,λ
...depends on the quark polarization
(combination of Dirac matrices)
p:p,μ
number density of quarks with mom. frac. x in an unpolarised proton
unpolarised PDF
(momentum distribution)
polarised PDF
number density of quarks with helicity + minus the number density
of quarks with helicity - and proton helicity +
(helicity distribution)
number density of quarks with transverse pol. minus the number
density of quarks with transverse pol. and proton has transverse pol.
transversity PDF
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Semi-inclusive DIS
In DIS only chiral even-quantities can be exp. accessed.
Semi-inclusive-DIS gives us experimentally access
to the transversity distribution.
E.g. one particle in the final state is detected.
e
e
γ*:q
π
X
Collinear Parton Distributions and Front-Form Meson-Cloud Model
h 1 x FF
}
p:p
fragmentation function FF
chiral even
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Modeling of PDFs: Meson-cloud model
for unpolarised proton PDFs, it is exp. established that
perturbative sea
flavor asymmetry in the sea
which is of non-perturbative nature
q
g
q
meson-cloud model can describe this asymmetry reasonable well
Every realistic model of unpolarised proton PDF must
incorporate this asymmetry.
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Modeling of PDFs: Meson-cloud model
for unpolarised proton PDFs, it is exp. established that
perturbative sea
flavor asymmetry in the sea
which is of non-perturbative nature
q
g
q
meson-cloud model can describe this asymmetry reasonable well
Every realistic model of unpolarised proton PDF must
incorporate this asymmetry.
It allows to go beyond the valence quark picture and take into account
higher Fock states in the nucleons.
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Modeling of PDFs: Meson-cloud model
for unpolarised proton PDFs, it is exp. established that
perturbative sea
flavor asymmetry in the sea
which is of non-perturbative nature
q
g
q
meson-cloud model can describe this asymmetry reasonable well
Every realistic model of unpolarised proton PDF must
incorporate this asymmetry.
It allows to go beyond the valence quark picture and take into account
higher Fock states in the nucleons.
Meson cloud plays a role
e.g. in the description of electric
form factor of the neutron.
taken from
Pasquini B. and Boffi S.
Phys. Rev. D 76 (2007)
valence contribution
meson cloud contribution
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Motivation of our project
- calculate for the first time the non pert. sea quark contribution
to the transversity of the proton (h1 PDF)
we expect it to be very small but nobody has quantified it yet
- compare valence contribution of h1 to other groups
valence contribution to the transversity
Radici M. et al, JHEP 05 (2015)
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Meson-cloud model for the proton
in the one-meson approximation, the physical proton state
is written as
bare proton
meson-baryon-fluctuation
q
q
q
B:q,q,q
valence quarks
M:q,q
3-valence quarks
...renormalization factor
determined by normalization
of proton state
...splitting function
probability amp. for a proton to
fluctuate into a virtual BM-system
Collinear Parton Distributions and Front-Form Meson-Cloud Model
we consider
assume:
different contributions add incoherently
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Meson-cloud model for the proton
in the one-meson approximation, the physical proton state
is written as
bare proton
meson-baryon-fluctuation
q
q
q
B:q,q,q
valence quarks
M:q,q
3-valence quarks
we consider
...renormalization factor
determined by normalization
of proton state
...splitting function
probability amp. for a proton to
fluctuate into a virtual BM-system
assume:
different contributions add incoherently
general structure of the vertex function
p
depends on B-M interaction Lagrangian
Collinear Parton Distributions and Front-Form Meson-Cloud Model
B
M
field operators
of the meson and baryon
Deep inelastic scattering
Front-form
PDFs
PDFs in the meson-cloud model
the photon can either hit the bare proton
when the photon couples
to the anti-quark in the meson
Collinear Parton Distributions and Front-Form Meson-Cloud Model
or
the meson/baryon
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
PDFs in the meson-cloud model
the photon can either hit the bare proton
or
the meson/baryon
when the photon couples
to the anti-quark in the meson
the combination of the splitting functions
depend on the PDF in question
Collinear Parton Distributions and Front-Form Meson-Cloud Model
B
M
M
B
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
PDFs in the meson-cloud model
the photon can either hit the bare proton
or
the meson/baryon
when the photon couples
to the anti-quark in the meson
the contribution from the
baryon-meson fluctuations
the combination of the splitting functions
depend on the PDF in question
Collinear Parton Distributions and Front-Form Meson-Cloud Model
B
M
M
B
Deep inelastic scattering
Front-form
PDFs
Light-cone wave function overlap
light-front helicity amplitude
...hadron helicity
...quark helicity
PDFs can be expressed through linear combination
of helicity amplitudes
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Light-cone wave function overlap
light-front helicity amplitude
...hadron helicity
...quark helicity
PDFs can be expressed through linear combination
of helicity amplitudes
in front-form a hadron state can we written as
light-cone wave function:
prob. amp. to find N particle Fock state in a hadron H
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Light-cone wave function overlap
light-front helicity amplitude
...hadron helicity
...quark helicity
PDFs can be expressed through linear combination
of helicity amplitudes
in front-form a hadron state can we written as
light-cone wave function:
prob. amp. to find N particle Fock state in a hadron H
representation of the helicity amplitudes as
an overlap of light-cone wave functions
Diehl M., Feldmann T., Jakob R. and Kroll P., Nucl. Phys. B596 (2001)
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Status of the project
- implemented all bare PDFs
- implemented all meson/baryon fluctuations in the PDFs
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Meson-cloud model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Status of the project
- implemented all bare PDFs
- implemented all meson/baryon fluctuations in the PDFs
missing
- find the initial scale Q02
- evolve in the scale Q 2
code already there (provided by Barbara)
⇒ results and more details will follow in the PhD-Seminar in the summer term
Collinear Parton Distributions and Front-Form Meson-Cloud Model
Deep inelastic scattering
Front-form
PDFs
Meson-cloud model
Summary
- naive parton model gets modified by QCD
- factorization: key concept in high-energy processes
allows us to use a parton model to describe high-energy scattering
processes
”QCD nowadays has a split personality. It embodies ’hard’ and ’soft’
physics, both being hard subjects and the softer the harder.”
Yuri Dokshitzer
- PDFs defined as hadronic matrix elements: number densities
- basics of the meson-cloud model
- PDFs in the meson-cloud model, in particular h1 (x)
Outlook
Finish the calculations.
Thank you for your attention.
Collinear Parton Distributions and Front-Form Meson-Cloud Model