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Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction

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Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction

E00-108 experiment in Hall C, 10 (!) days of beam time

PAC-30 Proposal E12-06-104, approved for 40 days with A- per PAC-36

PAC-34 Proposal PR12-09-017, conditionally approved

Rolf 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 – Flavor Decomposition

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

Solution: Detect a final state hadron in addition to scattered electron

SIDIS

Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

(M,0)

(e,e’)

Mx2 = W2 = M2 + Q2 (1/x – 1)

(For Mm small, pm collinear with g, and Q2/n2 << 1)

(e,e’m)

Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z)

z

z = Em/n

Mx2 = W’2

SIDIS – Flavor Decomposition

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

Solution: Detect a final state hadron in addition to scattered electron

SIDIS

Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

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

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

: parton distribution function

: fragmentation function

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

[sp(p+) + sp(p-)]/[sd(p+) + sd(p-)]

= [4u(x) + d(x)]/[5(u(x) + d(x))]

~ sp/sd independent of z and pt

[sp(p+) - sp(p-)]/[sd(p+) - sd(p-)]

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

independent of z and pt,

but more sensitive to assumptions

E00-108: Onset of the Parton Model

GRV & CTEQ,

@ LO or NLO

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

(Note: z = 0.65 ~

Mx2 = 2.5 GeV2)

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

quark

E00-108: Onset of the Parton Model

Collinear Fragmentation

Seq2q(x) Dqp(z)

(Deuterium data)

factorization

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

E00-108: Onset of the Parton Model

Solid (open) symbols are after (before) subtraction of diffractive r events

Solid 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)

x = 0.4

x = 0.4

E00-108: Onset of the Parton Model

Solid (open) symbols are after (before) subtraction of diffractive r 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:

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

(Y = 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 f, only the FUU,T and FUU,L responses, or the usual transverse (sT) and longitudinal (sL) cross section pieces, survive.

- RDIS is in the naïve parton model related to the parton’s
- transverse momentum: R = 4(M2x2 + <kT2>)/(Q2 + 2<kT2>).
- 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 = RDISD, 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)

quark

R = sL/sTin (e,e’p) SIDIS

Knowledge on R = sL/sT in SIDIS is essentially non-existing!

- If integrated over z (and pT, f, hadrons), RSIDIS = RDIS
- RSIDIS may vary with z
- At large z, there are known contributions from exclusive
- and diffractive channels: e.g., pions from D and r p+p-
- RSIDIS may vary with transverse momentum pT
- Is RSIDISp+ = RSIDISp- ? Is RSIDISH = RSIDISD ?
- Is RSIDISK+ = RSIDISp+ ? Is RSIDISK+ = RSIDISK- ? We measure kaons too! (with about 10% of pion statistics)
- RSIDIS = RDIS test of dominance of quark fragmentation

“A skeleton in our closet”

Seq2q(x) Dqp(z)

R = sL/sT in SIDIS (ep e’pX)

Cornell data of 70’s

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

RDIS

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

RDIS (Q2 = 2 GeV2)

quark

So what about R = sL/sT for pion electroproduction?

“Deep exclusive scattering” is the z 1 limit of this “semi-inclusive DIS” process

“Semi-inclusive DIS”

Seq2q(x) Dqp(z)

Here, R = sL/sT ~ Q2(at fixed x)

RSIDIS RDIS disappears with Q2!

Planned scans in z at Q2 = 2.0 (x = 0.2) and 4.0 GeV2 (x = 0.4) should settle the behavior of sL/sT for large z.

Not including a comparable systematic uncertainty:

~1.6%

Example of 12-GeV projected data assuming RSIDIS = RDIS

Planned data cover range Q2 = 1.5 – 5.0 GeV2, with data for both H and D at Q2 = 2 GeV2

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

Planned data cover range in PT up to ~ 1 GeV. The coverage in f 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

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.

Pt= pt +zkt+ O(kt2/Q2)

z = Ep/n

pT ~ L < 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].

p

X

TMD

Transverse momentum dependence of SIDIS

Linked to framework of Transverse Momentum Dependent Parton Distributions

s

Unpolarized target

Longitudinally pol. target

TMDq(x,kT)

Transversely pol. target

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

I. Integrated over pT and f

Hall C: PRL 98:022001 (2007)

Hall B: arXiv:0809.1153

II. PT and f dependence

Possibility to constrain kT dependence of up and down quarks separately by combination of p+ and p- final states, proton and deuteron targets

Hall B: arXiv:0809.1153

Hall C: PL B665 (2008) 20

III. Transverse polarized target: E06-010 transversity experiment in Hall A

Transverse momentum dependence of SIDIS

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

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

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

Azimuthal fh 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→ <m02> = 0.25 GeV2

(assuming m0,u =m0,d)

Transverse momentum dependence of SIDIS

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,f).

e.g., “Cahn effect”:

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

f= 90o

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

pT = 0.6

pT = 0.4

f= 0o

f= 180o

E00-108

f= 270o

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

Gaussian 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 p+ and p- final states

2) Use both proton and neutron (d) targets

3) Combination allows, in principle, separation of quark width from fragmentation widths

(if sea quark contributions small)

Example

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.)

Unpolarized SIDIS – JLab data (cont.)

Constrain kT dependence of up and down quarks separately

1) Probe p+ and p- final states

2) Use both proton and neutron (d) targets

3) Combination allows, in principle, separation of quark width from fragmentation widths

(if sea quark contributions small)

Example

1st example: Hall C, PL B665 (2008) 20

x = 0.32

z = 0.55

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

Example

<pt2> (favored)

<kt2> (up)

- Particle identification in SHMS:
- 0) TOF at low momentum (~1.5 GeV)
- Heavy (C4F8O) Gas Cherenkov
- to select p+ (> 3 GeV)
- 60 cm of empty space could be
- used for two aerogel detectors:
- - n = 1.015 to select p+ (> 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 kaons

P.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

If same arguments as validated for p apply to K:

At W = 2.5 GeV: z > 0.6

(but, z < 0.65 limit may not apply for kaons!)

- 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?

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

HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering

11 GeV phase space

6 GeV phase space

E00-108

PR12-09-017

Scan in (x,z,pT)

+ scan in Q2

at fixed x

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

i) MX2 > 2.5 GeV2; and ii) need to measure at both sides of Qg

Kinematic Factorization

(after integration over pT and f)

Both Current and Target Fragmentation Processes Possible. At Leading Order:

Berger Criterion

Dh > 2 Rapidity gap for

factorization

Separates Current and Target Fragmentation Region in Rapidity

Seq2q(x) Dqp(z)

(after integration over pT and f)

P.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

p

At W = 2.5 GeV: z > 0.4 At W = 5 GeV: z > 0.2

(Typical JLab-6 GeV) (Typical HERMES)

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

Radiation contributions, including from exclusive

Contributions from r

Further data from CLAS12 (r) and Hall C (Fp-12, pCT-12) will constrain!

Estimate of Contribution of r to R = sL/sT

High e

Low e

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

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

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

(Y = 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 Dqh, each with own characteristic (Gaussian) width.

Transverse momentum dependence of SIDIS

E00-108

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

Pt dependence very similar for proton and deuterium targets

Transverse Momentum Dependence: E00-108 Summary

- E00-108 results can only be considered suggestive at best:
- limited kinematic coverage
- - assume (PT,f) dependency ~ Cahn effect
- very simple model assumptions
- but PT dependence off D seems shallower than H
- and intriguing explanation in terms of flavor/kT deconvolution

- Many limitations could be removed with 12 GeV:
- wider range in Q2
- improved/full coverage in f (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
- Dup+ = Ddp-
- Higher-twist contributions
- consistency of various kinematics (global fit vs. single-point fits)

PR12-09-017 Projected Results - II

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

Step 1: Kinematics I-VI fitted separately, (pT,f) 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

PR12-09-017 Projected Results - II

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

Step 1: Kinematics I-VI fitted separately, (pT,f) 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)

Step 1: Kinematics I-VI fitted separately, (pT,f) 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

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

Radiative 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 Fp-12 and pCT-12.

Pions from Diffractive r - Used PYTHIA with modifications as

implemented by HERMES (Liebing,Tytgat).

- Used this to guide r cross section in SIMC.

- simulated results agree to 10-15% with

CLAS data (Harut Avagian).

- In all cases, quote results with/without

diffractive r subtraction.

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