# Presentation: 035179

## Transverse Momentum Dependence of Semi-Inclusive Pion Production

*PAC-34 Proposal PR12-09-017*
*Spokespersons Peter Bosted, Rolf Ent, and Hamlet Mkrtchyan*

- PR12-09-017: Map the pT dependence (pT ~  < 0.5 GeV) of + and - production off proton and deuteron targets to study the kT dependence of (unpolarized) up and down quarks.

-  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 ~  <0.5 GeV chosen 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].

## PR12-09-017 Collaboration

## Semi-Inclusive Deep-Inelastic Scattering

- Potentially rich physics arena for flavor decomposition, kT-dependent parton distribution functions, fragmentation, etc., but also many potential issues...
- Multi-hall approach seems best, combining the large acceptance potential of CLAS12:
**E12-06-112**	   Azimuthal distributions of final-state particles
**E12-06-109**	   Flavor decomposition at large-x **(SIDIS part)**
**E12-07-107**	   Spin-Orbit Correlations w. Long. Pol. Target
**E12-09-0xx**	   3 similar experiments emphasizing kaons
- and the precision of the Hall C magnetic-spectrometer setup:
**E12-06-104**    Measurement of **R** = ******L**/******T** in SIDIS
-     (PAC-34)	Precision ******+****/********-** ratios in SIDIS:
**E12-09-002**		I.   Charge-Symmetry Violating PDFs
**E12-09-004**		II. Flavor Dependence of the EMC Effect
**E12-09-017**   Transverse Momentum Dependence of 						Semi-Inclusive Pion production
*	**(third advantage: reaching important ****corners of phase space****, is not well enough established yet)*

## SIDIS – Flavor Decomposition

****** ****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

*         *: parton distribution function
-          : fragmentation function

## E00-108: Applicability of Parton Model

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

- GRV & CTEQ,
- @ LO or NLO

*(Note: z = 0.65 ~*
*    **M**x**2** = 2.5 GeV**2**)*

**E00-108: Applicability of Parton Model**

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

**PR12-09-017:**
**2.9 < M****x****2**** < 7.8 GeV****2**

## SIDIS – kT Dependence

- Final transverse momentum of the detected pion  **P**t arises from convolution of the struck quark transverse momentum **k**t with the transverse momentum generated during the fragmentation **p**t.

**Linked to framework of Transverse Momentum Dependent Parton Distributions**

**SIDIS – k****T**** Dependence**

## Transverse momentum dependence of SIDIS

**Transverse momentum dependence of SIDIS**

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

- _Unpolarized k__T__-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.

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

## Transverse momentum dependence of SIDIS

*General 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]

## Transverse momentum dependence of SIDIS

- Constrain kT dependence of up and down quarks *separately*

- 1) Probe ******+** and ******-** final states
- 2) Use both **proton** and neutron (**deuteron**) targets
- 3) Combination allows, in principle, separation of
- 	quark width from fragmentation widths
*	**(if sea quark contributions small)*

- Spectrometers a _must_ for such %-type (!) measurements:
- acceptance is a common factor to all measurements
- (and can use identical H and D cells)

- First example from JLab at 6 GeV on next slide
- (E00-108 experiment in Hall C,
- 		H. Mkrtchyan, P. Bosted et al.,
- 		Phys. Lett. B665 (2008) 20)

## 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 of SIDIS

**Transverse momentum dependence of SIDIS**

*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.) ***

- (+)2 ~ width of D+(z,pt),  ()2 ~ width of D-(z,pt), (u)2 ~ width of  u(x,kt),   (d)2 ~ width of  d(x,kt)

**Many authors believe these widths to be of order 0.25 GeV****2**** ******** these numbers are close! But ... is (********u****)****2**** < (********d****)****2****?? Expected from diquark models... Or, is there something wrong in our simple model or the used SIDIS framework?**

## - assume (PT,) dependency ~ Cahn effect 

- E00-108 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 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  (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)

## Choice of E12-09-017 Kinematics

- HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering

- 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 

**Choice of E12-09-017 Kinematics**

- 6 GeV phase space

- 11 GeV phase space

- E00-108

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

- + scan in Q2
-    at fixed x

## Choice of Kinematics – cont.

| Kin | x | Q2 (GeV2) | z | P    (GeV) |      (deg) |
| --- | --- | --- | --- | --- | --- |
| I | 0.2 | 2.0 | 0.3 -0.6 | 1.7 – 3.3 | 8.0 – 23.0 |
| II | 0.3 | 3.0 | 0.3 -0.6 | 1.7 – 3.4 | 5.5 – 25.5 |
| III | 0.4 | 4.0 | 0.3 -0.6 | 1.7 – 3.4 | 5.5 – 25.5 |
| IV | 0.5 | 5.0 | 0.3 -0.6 | 1.7 – 3.5 | 8.0 – 28.0 |
| V | 0.3 | 1.8 | 0.3 -0.6 | 1.1 – 2.1 | 8.0 – 30.5 |
| VI | 0.3 | 4.5 | 0.3 -0.6 | 2.5 – 5.0 | 5.5 – 20.5 |

- Kinematics I, II, III, and IV are identical to those where this collaboration also plans to map R (= L/T) in SIDIS in E12-06-104. This saves a total of five days, as follows:
- 	1) three days of data taking
- 	2) one day of dedicated checkout
- 	3) one day for pass/kinematics changes and beam energy meas.

- Map of pT dependence in x and z,
-         in Q2 to check (pT/Q) and (pT2/Q2) behavior

## 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 **** ~ 0**o**)*
-  Limited  coverage
-          up to pT = 0.5 GeV

*P**T **~ 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 p**T** (*_*down to 0.05 GeV*_*) due to excellent momentum and angle resolutions!*

- E00-108

## Choice of Kinematics – cont.

| Kin | E (GeV) | E’ (GeV) | e’ (deg) | W2 (GeV2) |  (deg) | q (GeV) |
| --- | --- | --- | --- | --- | --- | --- |
| I | 11.0 | 5.67 | 10.27 | 8.88 | 10.57 | 5.51 |
| II | 11.0 | 5.67 | 12.59 | 7.88 | 12.75 | 5.60 |
| III | 11.0 | 5.67 | 14.55 | 6.88 | 14.49 | 5.69 |
| IV | 11.0 | 5.67 | 16.28 | 5.88 | 15.96 | 5.78 |
| V | 8.8 | 5.60 | 10.96 | 5.08 | 17.90 | 3.47 |
| VI | 11.0 | 5.67 | 21.26 | 11.38 | 7.57 | 8.27 |

-  Keep HMS momentum (~E’) constant for all kinematics
-  Dedicated measurements (within requested beam time) 	will be added with E’ increased by 25% and possibly
- 	50% for radiative correction modeling.
- 	*(HMS goes to 7.3 GeV momentum **** need to swap HMS-SHMS roles for 50%)*
-  E12-06-104 includes beam time at E = 6.6 GeV.
- 	We plan to dedicate part of that time also for
- 			radiative correction modeling.

## Systematic Uncertainties in +/- Ratios

| Project Source | HMS(*) | SHMS |
| --- | --- | --- |
| Spectrometer Acceptance(**) | 0.1% | 0.4% |
| Tracking Efficiency(**) | 0.1% | 0.4% |
| Detection Efficiency(**) | 0.1% | 0.4% |
| Pion Absorption Correction |  | 0.1% |
| Radiative Corrections(***) |  | 0.5% |
| Added in Quadrature |  | 0.9% |

- Anticipated systematic uncertainties in ratios of transverse momentum dependences. The combined use of the CLAS12 experiments is assumed to fully constrain the (pT,) dependency.

- (*) HMS is kept at constant momentum of 5.67 GeV, at forward scattering angles (<22 degrees, hence viewing a 3.7 cm effective target length), at singles rates < 100 kHz, and at /e ratios < 13.

- (**) The main uncertainties are due to spectrometer polarity changes.
- The SHMS total rate is kept <700 kHz to constrain the tracking eff.

- (***) Assuming dedicated measurements to constrain the
- 			required radiative correction model input.

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

- 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!*

## Non-trivial contributions to (e,e’) 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 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.

## PR12-09-017 Projected Results - I

**III**

**II**

**I**

**IV**

**VI**

**V**

## Kaon Identification

- Particle identification in SHMS:
- 0)   TOF at low momentum (~1.5 GeV)
- Heavy (C4F8O) Gas Cherenkov
- 	to select + (> 3 GeV)
- 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*

## PR12-09-017 Projected Results - Kaons

**PR12-09-017 Projected Results - Kaons**

**III**

**II**

**I**

**IV**

**VI**

**V**

## Transverse Momentum Dependence of Semi-Inclusive Pion Production

- PR12-09-017: Map the pT dependence (pT ~  < 0.5 GeV) of + and - production off proton and deuteron targets to measure the kT dependence of up and down quarks

-  Not much is known about the orbital motion of partons
-  Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks

*Can only be done using spectrometer setup capable of %-type measurements ** (an essential ingredient of the global SIDIS program!)*

- Beam time request: 32 days of beam time in Hall C

- Spin-off:	Radiative correction modeling for (e,e’)
- 		Single-spin asymmetries at low pT (< 0.2 GeV)
- 		Low-energy (x,z) factorization for kaons

## Appendix

## PR12-09-017: Beam Time Request

-  Map yields as function of z and pT at x = 0.2 and Q2 = 2.0 GeV2
- 				**4.5 Days*** (incl. overhead)*
-  Map yields as function of z and pT at x = 0.3 and Q2 = 3.0 GeV2
- 				**5.8 Days**
-  Map yields as function of z and pT at x = 0.4 and Q2 = 4.0 GeV2
- 				**5.3 Days**
-  Map yields as function of z and pT at x = 0.5 and Q2 = 5.0 GeV2
- 				**5.3 Days**
-  Map yields as function of z and pT at x = 0.3 and Q2 = 1.8 GeV2
- 				**6.9 Days**
-  Map yields as function of z and pT at x = 0.3 and Q2 = 4.5 GeV2
- 				**4.0 Days**
**	****	****Total:****	****        32 Days*** **(incl. overhead)*

- * Overhead consists of spectrometer polarity, momentum, and angle, and target changes

## PR12-09-017 Projected Results - II

**PR12-09-017 Projected Results - II**

- Simulated 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

## PR12-09-017 Projected Results - II

- 		(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.

## Choice of PR12-09-017 Kinematics

-  W2 = 5.08 GeV2 and larger (up to 11.38 GeV2)
-  Use SHMS angle down to 5.5 degrees (for  detection)
-             HMS angle down to 10.5 degrees (e- detection)
-           separation HMS-SHMS > 17.5 degrees
-  MX2 = Mp2 + Q2(1/x – 1)(1 – z) > 2.9 GeV2 *(up to 7.8 GeV**2**)*
-  Choice to keep Q2/x fixed  q ~ constant
-  *exception are data scanning Q**2** at fixed x*
-  All kinematics both for + (and K+) and - (and K-),			     both for LH2 and LD2 (and Al dummy)
-  Choose z > 0.3 (p > 1.7 GeV) to be able to neglect
-                             differences in (+N) and (-N)
-  *not possible for x = 0.3, Q**2** = 1.80: p**** > 1.1 GeV*

## Experimental Details

-  Beam current is varied to keep the total SHMS rate below 700 kHz
* **10-80 ****A beam currents (with 10 cm LH2/LD2)*
* **rate limitation to guarantee precision ****+**/****-** ratios*
* **Anticipated syst. uncertainty in *_*ratio*_* 0.9%*
* **Real : Accidental ratio typically ~ 2 : 1*

**Experimental Details and ****Spin-Off**

-  Syst. uncertainty has four roughly equal ingredients: spectrometer
-      acceptance,  tracking + detector efficiencies, radiative corrections
* **to **model latter, include dedicated runs at lower E and E’*
* **Collaboration did similar (published) modeling efforts on *
*            **JLab inclusive  **1**H(e,e’) and **2**H(e,e’) scattering results*

-  While this measurement is not ideally suited to measurement of Single-Spin Asymmetries (lack of full  coverage), we expect to map such SSA’s well up to pT ~ 0.2 GeV (with errors of typ. 0.003-0.008), further facilitating kT-dependence model checking
* **Hence, we request 80% long. polarized beam*

-  Kaon identification would be facilitated by the addition of an
-          aerogel detector to the SHMS base detector package
-  study the low-energy (x,z) factorization for charged kaons
* **Collaboration built HMS aerogel detector (NIM A548, 364) *

## PR12-09-017 TAC Report

- The proposal assumes that the experiment will be scheduled so that its run plan can be combined with E12-06-104. Therefore, the time request does not include time for checkout, pass changes and beam energy measurements.
-     This is correct. Including this time would require an additional five (three DAQ and two overhead) days. In the proposal we stated eight days, which is incorrect: E12-06-104 required higher statistics runs.
- In the early years of 12 GeV operation, the practical limit on beam current for 11 GeV running will be 75 A.
-     In about half of the kinematics beam currents of 75 A or less are used to limit the hadron singles rates in SHMS to less than 700 kHz. The impact from Table IX is then ((80-75)/75*260) = 17.5 hours.
- Comments on measurements of SIDIS observables:
-      The adequate  coverage at small (!) pT is shown in the proposal. This experiment only addresses the pT dependence of + and - off LH2 and LD2. Pions from diffractively produced  mesons are simulated taking into account HERMES input and checked vs. CLAS data.
- 4. Comments on measurements involving kaons/strange quarks:
-      PR12-09-017 kaon measurements affect factorization tests only.

## Backup Slides (not printed)

## Systematic Uncertainties – the (e,e’) Case

**Total point-to-point systematic uncertainty for E94-110 is 1.6%.**

- Compare with SLAC E140X (DIS)
- 1 x 10-3		0.3%
- 1 x 10-3   	0.2%
- 0.1 mr		0.3%
- 0.3%		0.3%
- 0.2%		0.2%
- 0.3%		0.3%
- 0.1%		0.1%
- 0.2%		0.2%
- 0.5%		0.5%
- _1.0%__	__	__1.0%_
- 		1.3%

**Systematic Uncertainties – the (e,e’) Case**

## Systematic Uncertainties – the z  1 Limit

| Projected Systematic
Uncertainty
Source | Pt-Pt
ε-random
t-random | ε-uncorrelated
common to all t-bins | Scale
ε-global
t-global |
| --- | --- | --- | --- |
| Spectrometer Acceptance | 0.4% | 0.4% | 1.0% |
| Target Thickness |  | 0.2% | 0.8% |
| Beam Charge | - | 0.2% | 0.5% |
| HMS+SHMS Tracking | 0.1% | 0.4% | 1.5% |
| Coincidence Blocking |  | 0.2% |  |
| PID |  | 0.4% |  |
| Pion Decay Correction | 0.03% | - | 0.5% |
| Pion Absorption Correction | - | 0.1% | 1.5% |
| MC Model Dependence | 0.2% | 1.0% | 0.5% |
| Radiative Corrections | 0.1% | 0.4% | 2.0% |
| Kinematic Offsets | 0.4% | 1.0% | - |

**Added in quadrature: 1.8%**

**Systematic Uncertainties – the z ******** 1 Limit**

*From: G. Huber’s presentation on PR12-06-101 “Measurement of the Charged Pion Form Factor to High Q**2**”*

## SHMS Tracking Efficiency Considerations

- Several approved experiments **(E12-06-101, E12-06-104, E12-07-105)** require good tracking efficiency knowledge at ~1 MHz rate.
- HMS tracking efficiency is robust, but we typically still restrict rates to < 0.5 MHz:

- Rate dependence well understood on basis of Poisson statistics:
-  DC TDC’s have wider window than hodoscope TDC’s (difference fit with 77 ns)
-  varying width of DC TDC window  find same corrected yield!
-  2 electron tracks  tracking efficiency 70 +/- 3% (can’t find track for two electrons close-by): agrees well with number found from TDC window study
-  Important to have device with well-defined rates and aperture

**SHMS Design incorporates well-shielded detector hut, well-defined apertures, 3X and 3Y measurements per chamber, and multi-hit TDCs ******** Good knowledge @ 1 MHz probable (but lot of work)**

## Example of 12-GeV projected data assuming RSIDIS = RDIS

- “Semi-inclusive DIS”

- RSIDIS  RDIS disappears with Q2!

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

- Here, R = L/T ~ Q2

- Not clear what R will behave like at large pT

- Example of 12-GeV projected data assuming RSIDIS = RDIS

## 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 p**t*

- [p(+) - p(-)]/[d(+) - d(-)]
- 		= [4u(x) - d(x)]/[3(u(x) + d(x))]
- 			    	*independent of z and p**t**,*
*	**	**	**	**but more sensitive to assumptions*

## E00-108: Leading-Order x-z factorization

**E00-108: Leading-Order x-z factorization**

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

-  region

- (Deuterium data)

*Should not depend on x*

*But should depend on z*

- Solid lines: simple Quark Parton Model prescription assuming factorization

- Collinear Fragmentation

- factorization

## E00-108 (6 GeV): PT coverage

**E00-108 (6 GeV): P****T**** coverage**

- E00-108 measured up to PT2 ~ 0.2 GeV2, but  coverage was not complete  needed to make assumptions on (PT,) dependencies: ~ Cahn effect

## 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,).

***e.g., “Cahn effect”:***

**Transverse momentum dependence of SIDIS**

## Model PT dependence of SIDIS

**Model P****T**** dependence of SIDIS**

*Gaussian distributions for P**T** dependence, no sea quarks, and leading order in  (k**T**/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 c**2**, c**3**, and c**4**):*

## Duality in Meson Electroproduction

- hadronic description		quark-gluon description

-  Transition
- Form Factor

-    Decay
- Amplitude

- Fragmentation
-      Function

- Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is questionable

**Duality and factorization possible for Q****2****,W****2 ******** 3 GeV****2 ****(Close and Isgur, Phys. Lett. B509, 81 (2001))**

## kT-dependent SIDIS

- p┴ = PT – z k┴  + O(k┴2/Q2)

**k****T****-dependent SIDIS**

- data fit assuming Cahn effect → <02> = 0.25 GeV2

- EMC (1987) and Fermilab (1993) data
- (assuming ******0****u**** **=** ********0****d**)

**Anselmino et al**

-  Factorization of kT-dependent PDFs proven at low PT of hadrons (Ji et al)
-  Universality of kT-dependent distribution and fragmentation functions
- 						proven (Collins,Metz, ...)

## Transverse Momentum Dependence of Semi-Inclusive Pion Production

- _Outline:_
-  SIDIS: framework and general remarks
-  Results from E00-108
- - Low-energy (x,z) factorization for charged pions
- - Transverse momentum dependence of charged pions
-  PR12-09-017
-  Choice of kinematics
-  Experimental details
-  Spin-off relevant for the general SIDIS program
-  Radiative correction modeling: linking to z = 1
-  Single-spin asymmetries
-  Low-energy (x,z) factorization for charged kaons
-  PR12-09-07 Beam Time Request and Projected Results

*PAC-34 Proposal PR12-09-017*

## SIDIS – Flavor Decomposition

****** ****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

**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 M**m** small, p**m** collinear with ****, and Q**2**/****2** << 1)*

- (M,0)

## Low-Energy x-z Factorization

**Low-Energy x-z Factorization**

- 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

- 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 )

## SIDIS – kT Dependence

- Final transverse momentum of the detected pion  **P**t arises from convolution of the struck quark transverse momentum **k**t with the transverse momentum generated during the fragmentation **p**t.

**SIDIS – k****T**** Dependence**

- PR12-09-017: Map the pT dependence (pT ~  < 0.5 GeV) of + and - production off proton and deuteron targets to study the kT dependence of (unpolarized) up and down quarks

- Pt = pt + z kt  + O(kt2/Q2)

## Spin-off: study x-z Factorization for kaons

**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

- At W = 2.5 GeV: z > 0.6

- If same arguments as validated for  apply to K:

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