Access to the Parton Model through Unpolarized Semi-Inclusive Pion

ElectroproductionE00-108 experiment in Hall C, 10 (!) days of beam timePAC-30 Proposal E12-06-104, approved for 40 days with A- per

PAC-36PAC-34 Proposal PR12-09-017, conditionally approvedRolf Ent, Hall C Summer Workshop, August 27, 2010

• Semi-Inclusive Deep Inelastic Scattering & the Parton Model

• E00-108 Results: The Onset of the Parton Model• General Pion Electro-production Formalism

- Bridging the Formalism and the High-Energy “Factorized”

Viewpoint• 12 GeV Examples: R in SIDIS &

transverse momentum dependence

SIDIS

SIDIS – Flavor Decomposition

(e,e’)

(e,e’m)

Mx2 = W2 = M2 + Q2 (1/x – 1)

Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z)

z = Em/

(For Mm small, pm collinear with , and Q2/2 << 1)

(M,0)

Solution: Detect a final state hadron in addition to scattered electron Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

DIS probes only the sum of quarks and anti-quarks requires assumptions on the role of sea quarks

zMx

2 = W’2

Solution: Detect a final state hadron in addition to scattered electron Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

DIS probes only the sum of quarks and anti-quarks requires assumptions on the role of sea quarks

Measure inclusive (e,e’) at same time as (e,e’h)

SIDIS

SIDIS – Flavor Decomposition

• Leading-Order (LO) QCD • after integration over pT and • NLO: gluon radiation mixes x and z dependences

qqq

q

hqqq

(e,e') (x)(x)fe

(z)(x)DfehX)(ep

dzdσ

σ 2

2

1

: parton distribution function : fragmentation function)(xfq)(zDh

q

How Can We Verify Factorization?Neglect sea quarks and assume no pt dependence to parton distribution functions

Fragmentation function dependence drops out in Leading Order

[p(+) + p(-)]/[d(+) + d(-)]= [4u(x) + d(x)]/[5(u(x) + d(x))]~ p/d independent of z and pt

[p(+) - p(-)]/[d(+) - d(-)]= [4u(x) - d(x)]/[3(u(x) + d(x))]

independent of z and pt,but more sensitive to assumptions

Closed (open) symbols reflect data after (before) events from coherent production are subtracted

GRV & CTEQ,@ LO or NLO

(Note: z = 0.65 ~ Mx

2 = 2.5 GeV2)

E00-108: Onset of the Parton Model

Good description for p and d targets for 0.4 < z < 0.65

E00-108: Onset of the Parton Model

1R*4R4

DD

π

π

NN

R

(Resonances cancel (in SU(6)) in D-/D+ ratio extracted from deuterium data)

(Deuterium data)

quark

Collinear Fragmentation

factorization

eq2q(x) Dq

(z)

E00-108: Onset of the Parton Model

x = 0.4

x = 0.4

Solid (open) symbols are after (before) subtraction of diffractive eventsSolid curve is a naïve parton model calculation assuming CTEQ5M parton distribution functions at NLO and BKK fragmentation functions

Overall, one finds good agreement, but there are detailed differences in the cross section measurements (also for the deuterium target)

E00-108: Onset of the Parton ModelSolid (open) symbols are after (before) subtraction of diffractive events. Blue symbols are old Cornell measurements.Solid curve is a naïve parton model calculation assuming CTEQ5M parton distribution functions at NLO and BKK fragmentation functions

Agreement with the naïve parton model expectation is always far better for ratios, also for D/H, Al/D, or ratios versus z or Q2.

General formalism for (e,e’h) coincidence reaction w. polarized beam:SIDIS Formalism

( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

If beam is unpolarized, and the (e,e’h) measurements are fully integrated over , only the FUU,T and FUU,L responses, or the usual transverse (T) and longitudinal (L) cross section pieces, survive.

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

yxyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

R = L/T in DIS• RDIS is in the naïve parton model related to the parton’s transverse momentum: R = 4(M2x2 + <kT

2>)/(Q2 + 2<kT

2>).

• RDIS 0 at Q2 ∞ is a consequence of scattering from free spin-½ constituents • Of course, beyond this, at finite Q2, RDIS sensitive to gluon and higher-twist effects • No distinction made up to now between diffractive and non-diffractive contributions in RDIS

• RDISH = RDIS

D, to very good approximation (experimentally)

- from formal point of view they should differ! (u not equal to d at large x +

evolution in Q2, H = spin-1/2 and D = spin-1, at low Q2)

R = L/T in (e,e’) SIDIS

quark

Knowledge on R = L/T in SIDIS is essentially non-existing! • If integrated over z (and pT, , hadrons), RSIDIS = RDIS

• RSIDIS may vary with z• At large z, there are known contributions from exclusive and diffractive channels: e.g., pions from and +-

• RSIDIS may vary with transverse momentum pT

• Is RSIDIS+ = RSIDIS

- ? Is RSIDISH = RSIDIS

D ?• Is RSIDIS

K+ = RSIDIS+ ? Is RSIDIS

K+ = RSIDISK- ? We

measure kaons too! (with about 10% of pion statistics)

• RSIDIS = RDIS test of dominance of quark fragmentation

eq2q(x) Dq

(z)

“A skeleton

in our closet”

RDIS

RDIS (Q2 = 2 GeV2)

Cornell data of 70’sR = L/T in SIDIS (ep e’X)

Conclusion: “data both consistent with R = 0 and R = RDIS”

Some hint of large R at large z in Cornell data?

So what about R = L/T for pion electroproduction?

quark

“Semi-inclusive DIS”

RSIDIS RDIS disappears with Q2!

“Deep exclusive scattering” is the z 1 limit of this “semi-inclusive DIS” processHere, R = L/T ~ Q2 (at fixed x)

Have no idea at all how R will behave at large pT

Example of 12-GeV

projected data

assuming RSIDIS =

RDIS

Not including a comparable systematic uncertainty: ~1.6%

Planned scans in z at Q2 = 2.0 (x = 0.2) and 4.0 GeV2 (x = 0.4) should settle the behavior of L/T for large z.Planned data cover range Q2 = 1.5 – 5.0 GeV2, with data for both H and D at Q2 = 2 GeV2

eq2q(x) Dq

(z)

Planned data cover range in PT up to ~ 1 GeV. The coverage in is excellent (o.k.) up to PT = 0.2 (0.4) GeV.

Transverse Momentum Dependence of Semi-Inclusive Pion Production• Not much is known about the orbital motion of partons• Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks

Pt = pt + z kt

+ O(kt2/Q2)

Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt.

z = E/

pT ~ < 0.5 GeV optimal for studies as theoretical framework for Semi-Inclusive Deep Inelastic Scattering has been well developed at small transverse momentum [A. Bacchetta et al., JHEP 0702 (2007) 093].

TMDq(x,kT)

p

m

XTMD

Transverse momentum dependence of SIDISLinked to framework of Transverse Momentum Dependent Parton Distributions

Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions q and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width Emerging new area of study

Unpolarized targetLongitudinally pol.

targetTransversely pol.

target

N q U L T

U f1 h1

L g1 h1 L

T f1T g1T h1 h1T

I. Integrated over pT and

II. PT and dependence

Hall C: PRL 98:022001 (2007) Hall B: arXiv:0809.1153

Hall B: arXiv:0809.1153Hall C: PL B665 (2008) 20

Possibility to constrain kT dependence of up and down quarks separately by combination of + and

- final states, proton and deuteron targets III. Transverse polarized target: E06-010 transversity experiment in Hall A

Transverse momentum dependence of SIDISGeneral formalism for (e,e’h) coincidence reaction w. polarized beam:

( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

Azimuthal h dependence crucial to separate out kinematic effects (Cahn effect) from twist-2 correlations and higher twist effects.data fit on EMC (1987) and Fermilab (1993) data assuming

Cahn effect → <02> = 0.25

GeV2

(assuming 0,u = 0,d)

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

yxyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

General formalism for (e,e’h) coincidence reaction:

Factorized formalism for SIDIS (e,e’h):

In general, A and B are functions of (x,Q2,z,pT,).

e.g., “Cahn

effect”:

Transverse momentum dependence of SIDIS

PR12-09-017: PT coverage

• Excellent coverage up to pT = 0.2 GeV• Sufficient coverage up to pT = 0.4 GeV (compared to the E00-108 case below, now also good coverage at ~ 0o)• Limited coverage up to pT = 0.5 GeV

PT ~ 0.5 GeV: use dependencies measured in CLAS12 experiments (E12-06-112, LOI12-09-005)

= 0o

= 90o

= 180o

= 270o

pT = 0.4

pT = 0.6

Can do meaningful measurements at low pT (down to 0.05 GeV) due to excellent momentum and angle resolutions!

E00-108

Model PT dependence of SIDISGaussian distributions for PT dependence, no sea quarks, and leading order in (kT/q)

Inverse of total width for each combination of quark flavor and fragmentation function given by:

And take Cahn effect into account, with e.g. (similar for c2, c3, and c4):

Unpolarized SIDIS – JLab data (cont.)Constrain kT dependence of up and down quarks separately

1) Probe + and - final states2) Use both proton and neutron (d) targets3) Combination allows, in principle, separation of quark width from fragmentation widths

(if sea quark contributions small)1st example: Hall C, PL B665 (2008) 20

Simple model, host of assumptions (factorization valid, fragmentation functions do not depend on quark flavor, transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature, sea quarks are negligible, assume Cahn effect, etc.)

Example

Unpolarized SIDIS – JLab data (cont.)Constrain kT dependence of up and down quarks separately

1) Probe + and - final states2) Use both proton and neutron (d) targets3) Combination allows, in principle, separation of quark width from fragmentation widths

(if sea quark contributions small)1st example: Hall C, PL B665 (2008) 20

<pt2 >

(fav

ored

)

<kt2> (up)

Numbers are close to expectations! But, far too early to claim success: simple model only, not a complete coverage, uncertainties in exclusive event & diffractive contributions, SIDIS partonic framework valid?

Example

Examplex = 0.32z = 0.55

PR12-09-017 Projected Results - I

III

II

I

IV

VI

V

Kaon IdentificationParticle identification in SHMS:0) TOF at low momentum (~1.5 GeV)1)Heavy (C4F8O) Gas Cherenkov

to select + (> 3 GeV)2)60 cm of empty space could be

used for two aerogel detectors:- n = 1.015 to select + (> 1 GeV)

select K+ (> 3 GeV)- n = 1.055 to select K+ (>1.5 GeV)

Heavy Gas Cherenkov and 60 cm of empty space

Spin-off: study x-z Factorization for kaonsP.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000)

At large z-values easier to separate current and target fragmentation region for fast hadrons factorization (Berger Criterion) “works” at lower energies At W = 2.5 GeV: z > 0.6If same arguments as validated for apply to K: (but, z < 0.65 limit may not apply for kaons!)

PR12-09-017 Projected Results - Kaons

III

II

I

IV

VI

V

Summary• Access to the parton model through semi-inclusive DIS data was established with 6-GeV data• Still many questions about the exact interpretation of SIDIS experiments and the validity of such access in cross section measurements• In ratios (or similar, asymmetries) life seems to become simpler, and access seems verified• Many outstanding questions remain:

- Is R in SIDIS the same as R in DIS, as anticipated from the high-energy factorized Ansatz?- To what extent is factorization truly valid? (especially at high pT, at small pT it should be valid at tree-level) - Experimentally, where does it work for kaons?- Does fragmentation depend on quark flavor?- What are the transverse momentum distributions of the various quark and fragmentation functions?

HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering

For semi-inclusive, less Q2 phase space at fixed x due to:i) MX

2 > 2.5 GeV2; and ii) need to measure at both sides of

Choice of Kinematics (here for PR12-09-017)

6 GeV phase space

11 GeV phase space

E00-108

PR12-09-017Scan in (x,z,pT)+ scan in Q2

at fixed x

Kinematic FactorizationBoth Current and Target Fragmentation Processes Possible. At Leading Order:

Berger Criterion > 2 Rapidity gap for factorization

Separates Current and Target Fragmentation Region in Rapidity

eq2q(x) Dq

(z)(after integration over pT and )

Low-Energy x-z FactorizationP.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000)

At large z-values easier to separate current and target fragmentation region for fast hadrons factorization (Berger Criterion) “works” at lower energies

At W = 2.5 GeV: z > 0.4 At W = 5 GeV: z > 0.2(Typical JLab-6 GeV) (Typical HERMES)

(after integration over pT and )eq

2q(x) Dq(z)

Radiation contributions, including from exclusive

Contributions from

Non-trivial contributions to (e,e’) Cross Section

Further data from CLAS12 () and Hall C (F -12, CT-12) will constrain!

Estimate of Contribution of to R = L/T

Conclusion: If contribution is as simulated andknown to 10% 5% relative error in R (worst case) (CLAS12 data important to constrain contributions!)• Above uncertainty assumed RSIDIS = RDIS (small!)• Essentially same uncertainty at Q2 = 2.0 and 4.0 GeV2

High

Low

General formalism for (e,e’h) coincidence reaction w. polarized beam:SIDIS Formalism

( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions fq and (one or more) fragmentation functions Dq

h, each with own characteristic (Gaussian) width.

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

yxyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

Transverse momentum dependence of SIDIS

Pt dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller?

E00-108

Pt dependence very similar for proton and deuterium targets

Transverse Momentum Dependence: E00-108 SummaryE00-108 results can only be considered suggestive at best:• limited kinematic coverage

- assume (PT,) dependency ~ Cahn effect • very simple model assumptions

but PT dependence off D seems shallower than Hand intriguing explanation in terms of flavor/kT

deconvolutionMany limitations could be removed with 12 GeV:• wider range in Q2

• improved/full coverage in (at low pT)• larger range in PT• wider range in x and z (to separate quark from fragmentation widths)• possibility to check various model assumptions

- Power of (1-z) for D-/D+

- quantitative contribution of Cahn term- Du

+ = Dd-

- Higher-twist contributions- consistency of various kinematics (global fit vs. single-point fits)

PR12-09-017 Projected Results - IISimulated data use (u)2 = (d)2 = 0.2, and then fit using statistical errors.Step 1: Kinematics I-VI fitted separately, (pT,) dependency ~ Cahn

Step 2: Add eight parameters to mimic possible HT, but assume Cahn uncertainties grow with about factor of two

Step 3: Simulate with and without Cahn term results remain similar as in step 2

Step 1: Kinematics I-VI fitted separately, (pT,) dependency ~ Cahn(if all six fitted together, diameter < 0.01 GeV2)

Step 2: Add eight parameters to mimic possible HT, but assume Cahn uncertainties grow with about factor of two(if all six fitted together, diameter remains < 0.01 GeV2)

Step 3: Simulate with and without Cahn term results remain similar as in step 2(if all six fitted together, diameter grows to < 0.02 GeV2)

PR12-09-017 Projected Results - II

Step 1: Kinematics I-VI fitted separately, (pT,) dependency ~ Cahn

Step 2: Add eight parameters to mimic possible HT, but assume Cahn uncertainties grow with about factor of two

Step 3: Simulate with and without Cahn term results remain similar as in step 2

Simulated data use (u)2 = (d)2 = 0.2, and then fit using statistical errors.

Non-trivial contributions to (e,e’) Cross SectionRadiative Corrections - Typical corrections are <10% for z < 0.7.

- Checked with SIMC and POLRAD 2.0. - Good agreement between both methods.

Exclusive Pions - Interpolated low-W2, low-Q2 of MAID with high-W2, high-Q2 of Brauel/Bebek. - Introduces large uncertainty at low z, but contributions there are small. - Tail agreed to 10-15% with “HARPRAD”. - Further constraints with F-12 and CT-12.

Pions from Diffractive - Used PYTHIA with modifications as implemented by HERMES (Liebing,Tytgat). - Used this to guide cross section in SIMC. - simulated results agree to 10-15% with CLAS data (Harut Avagian). - In all cases, quote results with/without diffractive subtraction.