Studies of Hadronization Mechanisms Using Pion Electroproduction in Deep Inelastic Scattering from Nuclei

Studies of Hadronization Mechanisms using Pion Electroproduction in Deep Inelastic Scattering from Nuclei

Will Brooks, Hayk Hakobyan, Cristian Peña, Miguel Arratia Universidad Técnica Federico Santa María Valparaíso, Chile for the CLAS collaboration related posters: π0, T. Mineeva; Σ-, G. & I. Niculescu • Goal: study space-time properties of parton propagation and fragmentation in QCD: • Characteristic timescales • Hadronization mechanisms • Partonic energy loss • Use nuclei as spatial ﬁlters with known properties: • size, density, interactions • Unique kinematic window at low energies Comparison of Parton Propagation in Three Processes

DIS D-Y RHI Collisions

Accardi, Arleo, Brooks, d'Enterria, Muccifora Riv.Nuovo Cim.032:439553,2010 [arXiv:0907.3534] Majumder, van Leuween, Prog. Part. Nucl. Phys. A66:41, 2011, arXiv:1002.2206 [hep- ph] Deep Inelastic Scattering - Vacuum

h tf

production time tp - propagating quark

h formation time tf - dipole grows to hadron partonic energy loss - dE/dx via gluon radiation in vacuum Low-Energy DIS in Cold Nuclear Medium

Partonic multiple scattering: medium-stimulated gluon emission, broadened pT Low-Energy DIS in Cold Nuclear Medium

Partonic multiple scattering: medium-stimulated gluon emission, broadened pT

Hadron forms outside the medium; or.... Low-Energy DIS in Cold Nuclear Medium

Hadron can form inside the medium; then also have prehadron/hadron interaction Low-Energy DIS in Cold Nuclear Medium

Hadron can form inside the medium; then also have prehadron/hadron interaction

Amplitudes for hadronization inside and outside the medium can interfere Comparison of pT broadening data - Drell-Yan and DIS

) 0.22 2 + - + 0.2 HERMES ! , ! , K CLAS/JLab preliminary !+ 0.18 E772 0.16 E866 0.14 0.12 0.1 0.08 0.06 0.04 0.02 Transverse Momentum Broadening (GeV 0 0 50 100 150 200 250 Mass number (JLab/HERMES data shifted for better view) • New, high-precision data with identiﬁed hadrons! + 2 • CLAS π : 81 four-dimensional bins in Q , ν, z h, and A New: dependence of pT broadening on Feynman x

z Pb

xF CLAS preliminary • xF and zh are partially correlated

π π • Feynman x is the fraction pL/max{ pL} in the γ*-N CM system • Separate current (xF>0) and target (xF<0) fragmentation • First observation that pT broadening originates in both regimes New: dependence of pT broadening on φpq

lead

iron

carbon CLAS preliminary

curves shown contain terms in cos(φpq) and cos(2φpq) only statistical uncertainties shown • Expectation within classical picture: any distribution seen in carbon will become more ‘washed out’ in heavier nuclei • Not seen! ﬁrst observation of quantum effect in pT broadening - persistent effect in all bins; more study needed to quantify uncertainties New: dependence of pT broadening on W

h Entries 9 Mean 2.43 3.4< <4.0 0.5

! CLAS preliminary 0.05

0.04 lead 0.03 iron 0.02 carbon 0.01

0 2 2.2 2.4 2.6 2.8 3 W • Some variations, but no systematic evidence for inﬂuence of resonance region Production Time Extraction - Geometrical Effects

Lp5 1/3Entries 10 Mean 4.759 Quark Path Length * Nuclear Density vs. A RMS 1.253

Lp=20 fm 0.6

0.5

0.4 Lp=5 fm

0.3

Lp=3 fm 0.2 Lp=2 fm Quark Path Length * Nuclear Density 0.1 Lp=1 fm Lp=0.5 fm 0 0 1 2 3 4 5 6 7 8 9 10 Mass number to the 1/3 power (A1/3) Production Time Extraction - Geometrical Effects

Lp5 1/3Entries 10 Mean 4.759 Quark Path Length * Nuclear Density vs. A RMS 1.253

Lp=20 fm 0.6

0.5

0.4 Lp=5 fm

0.3

Lp=3 fm 0.2 Lp=2 fm Quark Path Length * Nuclear Density 0.1 Lp=1 fm Lp=0.5 fm 0 0 1 2 3 4 5 6 7 8 9 10 Mass number to the 1/3 power (A1/3) Production Time Extraction - Geometrical Effects

Lp5 1/3Entries 10 Mean 4.759 Quark Path Length * Nuclear Density vs. A RMS 1.253

Lp=20 fm 0.6

0.5

0.4 Lp=5 fm

0.3

Lp=3 fm 0.2 Lp=2 fm Quark Path Length * Nuclear Density 0.1 Lp=1 fm Lp=0.5 fm 0 0 1 2 3 4 5 6 7 8 9 10 Mass number to the 1/3 power (A1/3) Production Time Extraction - Geometrical Effects

Lp5 1/3Entries 10 Mean 4.759 Quark Path Length * Nuclear Density vs. A RMS 1.253

Lp=20 fm 0.6

0.5

0.4 Lp=5 fm

0.3

Lp=3 fm 0.2 Lp=2 fm Quark Path Length * Nuclear Density 0.1 Lp=1 fm Lp=0.5 fm 0 0 1 2 3 4 5 6 7 8 9 10 Mass number to the 1/3 power (A1/3) Production Time Extraction - Geometrical Effects

Fits of Z-Scaled Broadening vs. A1/3 0.35 Q2=3 GeV2, =3.5 GeV, Z =0.45 i / Q2=3 GeV2, =3.5 GeV, Z =0.55 0.3 i / 2 2 )

2 Q =3 GeV , =3.5 GeV, Z =0.65 i / 0.25

0.2

0.15

Lp5 1/3Entries 10 Mean 4.759 Quark Path Length * Nuclear Density vs. A RMS 1.253 0.1 -Scaled Broadening (GeV Lp=20 / fm 0.6 Z 0.05 JLab/CLAS preliminary 0.5 0 2 2.5 3 3.5 4 4.5 5 5.5 6 Mass Number to the 1/3 power (A1/3) 0.4 Lp=5 fm

0.3

Lp=3 fm 0.2 Lp=2 fm Quark Path Length * Nuclear Density 0.1 Lp=1 fm Lp=0.5 fm 0 0 1 2 3 4 5 6 7 8 9 10 Mass number to the 1/3 power (A1/3) Geometrical model Geometrical model • Three-parameter model: • scale factor (~proportional to transport coefficient) • production time (distributed exponentially) • effective absorption cross section Geometrical model • Three-parameter model: • scale factor (~proportional to transport coefficient) • production time (distributed exponentially) • effective absorption cross section • Fourth parameter: quark dE/dx, recently explored Geometrical model • Three-parameter model: • scale factor (~proportional to transport coefficient) • production time (distributed exponentially) • effective absorption cross section • Fourth parameter: quark dE/dx, recently explored • Simultaneous fit of pT broadening and multiplicity ratio in the same 3-fold kinematic bin in Q2, ν, and z Geometrical model • Three-parameter model: • scale factor (~proportional to transport coefficient) • production time (distributed exponentially) • effective absorption cross section • Fourth parameter: quark dE/dx, recently explored • Simultaneous fit of pT broadening and multiplicity ratio in the same 3-fold kinematic bin in Q2, ν, and z • Realistic nuclear densities • Path begins at point with probability proportional to density • Part of path is quark, part of path is (pre-) hadron Results from combined fit 3 or 4 parameter geometric model various bins in Q2, ν, and z

ﬁts are consistent with τp=1.6 - 2 fm/c (

C Fe Pb

2 1/3 π+ 1/3 ∆kT vs. A RM vs. A

2 1/3 π+ 1/3 ∆kT vs. A RM vs. A New: exploring a direct measurement of quark energy loss using π+ energy spectrum

• Order of magnitude can be estimated from theory as ~100 MeV/fm, although factors of up to 10 are disputed • Measurements of energy loss in cold nuclear matter have been attempted with 800 GeV protons • 6 fm * 100 MeV/fm = 600 MeV ...not easy to see with Drell-Yan muon pairs from 800 GeV protons on tungsten; but should be ‘easy’ to see with 2 GeV pions produced in DIS How to directly measure quark energy loss?

• Energy loss is predicted on very solid grounds to be independent of energy for a medium that is thin enough. • “Thin enough” depends on energy, see next slide; if medium is thicker than “thin enough” it still loses energy • If the energy loss is independent of energy, it will produce a shift of the energy spectrum, for higher energies. • We can look for a shift of the Pb energy spectrum compared to that of the deuterium energy spectrum

shift

Pion energy Energy Loss in pQCD (BDMPS version)

dE ΔE L L < Critical Lqˆ − dx ∝

dE L L > Critical Eqˆ − dx ∝ L LCritical

Eq at L = LCritical, Lˆq Eq ˆq ; L Critical ∝ · ∝ ˆq E ν few GeV, ˆq 0.02 0.1GeV2/fm, q ≈ ≈ ≈ − E q (multiplied by an Rlead Rcarbon −→ ˆq ≈ − unknown prefactor) Full lineshapes, deuterium and Pb (CLAS EG2 data) with and without cut on xFeynman (normalized to area 1.0)

Nu*Zh+0. {Nu*Zh>0.&&Nu*Zh<2.5-0.&&TargType==2} pb1pbd1d Entries 318125833457619043321 744673 Mean 0.67490.8025 1.3021.325 RMS 0.52940.47230.50120.5032 0.05

shift 0.04 Pion energy

0.03

with cut on xFeynman 0.02

0.01

0 0 0.5 1 1.5 2 2.5 Epion (GeV) Minimize RMS of shifted ﬁtted spectra CLAS Preliminary

Minimum RMS Pb = 0.42 MeV at ΔE~575 MeV

Pb D CLAS Preliminary

Fe Minimum RMS = 0.52 MeV at ΔE~405 MeV CLAS Preliminary

CLAS Preliminary

C Minimum RMS Resulting ΔE consistent with independently = 0.98 MeV at determined values of pT broadening! ΔE~120 MeV Conclusions Conclusions

• systematic features of π+ pT broadening have been explored, such as xF dependence and W dependence. The xF dependence indicates broadening comes from both current and target fragmentation for z<0.5 • the 'production time' (virtual quark lifetime) has been extracted from pT broadening data and found to be in the range 1.6-2 fm/c within a geometric model prototype Conclusions

• ﬁrst observation of a φpq dependence of pT broadening, which increases with target size, suggesting a quantum description is necessary Conclusions

• ﬁrst observation of a φpq dependence of pT broadening, which increases with target size, suggesting a quantum description is necessary • a promising method for directly extracting quark energy loss is being explored, giving results consistent with observed pT broadening and production time analysis Backup Slides Exploring a direct measurement of quark energy loss using π+ energy spectrum - next steps

• Continue studies with GENIE event generator to evaluate effect of hadronic cascades, etc., and try other cascade models • Radiative corrections • Acceptance corrections • Explore more restrictive cuts? • Believe the results if: - robust, not sensitive to cuts - works over a wide energy range - the match in shape is extremely accurate - can’t ﬁnd any other explanation for the shift CLAS Preliminary

CLAS Preliminary CLAS Preliminary

CLAS Preliminary

CLAS Preliminary CLAS Preliminary

CLAS Preliminary

CLAS Preliminary CLAS Preliminary Genie simulations for Pb

E {E>2.111 && E<2.5 && Xf>0.1}

0.09 Ed Entries 17060 0.08 EMean {E>2.111 2.289 && E<2.5 && Xf>0.1} RMS 0.1108 0.09 0.07 Ed Entries 17060 0.08 EMean {E>2.111 2.289 && E<2.5 && Xf>0.1} 0.06 RMS 0.1108 0.07 0.05 0.09 Ed Entries 17060 0.06 0.04 0.08 Mean 2.289 RMSE {E>2.111 0.1108 && E<2.5 && Xf>0.1} 0.05 0.07 0.03 0.09 Ed 0.04 Entries 17060 0.02 0.06 0.08 Mean 2.289 RMSE {E>2.111 0.1108 && E<2.5 && Xf>0.1} 0.03 0.01 0.05 0.07 0.09 Ed 0.02 0 0.04 0.06 Entries 17060 1 1.2 1.4 1.6 1.8 2 2.2 2.4 0.08 Mean 2.289 0.01 E {E>2.111 && E<2.5 && Xf>0.1} 0.03 0.05 RMS 0.1108 0.07 0 0.09 Ed 1 1.2 1.4 0.021.6 1.8 2 2.20.04 2.4 0.06 Entries 17060 0.08 Mean 2.289 0.01 0.03 0.05 RMS 0.1108 0.07 0 0.02 1 1.2 1.4 1.6 1.8 2 2.20.04 2.4 0.06 0.01 0.03 0.05 0 1 1.2 1.4 0.021.6 1.8 2 2.2 2.4 0.04 0.01 0.03 0 1 1.2 1.4 0.021.6 1.8 2 2.2 2.4

0.01

0 1 1.2 1.4 1.6 1.8 2 2.2 2.4 398 41. Plots of cross sections and related quantities

Hadronic broadening or partonic broadening? 10 2 pT broadening for Pb does not show any π+ p ⇓ strong trendtotal with pion energy, while hadronic

!"#$$%$&'()#*%+,-. elastic scattering cross section changes by 10 more than an order of magnitude

+ π p elastic

Plab GeV/c

-1 2 10 1 10 10 1.2 2 3 4 5 6 7 8 9 10 20 30 40 πp √s GeV πd 2.2 3 4 5 6 7 8 9 10 20 30 40 50 60

10 2 CLAS preliminary ⇓ π∓ d total

⇓ π− p total

!"#$$%$&'()#*%+,-. 10

π− p elastic

Plab GeV/c

-1 2 10 1 10 10

Figure 41.13: Total and elastic cross sections for π±p and π±d (total only) collisions as a function of laboratory beam momentum and total center-of-mass energy. Corresponding computer-readable data ﬁles may be found at http://pdg.lbl.gov/current/xsect/.(Courtesyofthe COMPAS Group, IHEP, Protvino, August 2005) Quark kT broadening vs. hadron pT broadening

The transverse momentum broadening experienced by a quark is diluted by the time it is part of a hadron

pπ Quark kT broadening vs. hadron pT broadening

The transverse momentum broadening experienced by a quark is diluted by the time it is part of a hadron

p (pion) zk (quark) T ≈ T pq

pπ Quark kT broadening vs. hadron pT broadening

The transverse momentum broadening experienced by a quark is diluted by the time it is part of a hadron

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2 + 0.4 # #- + [GeV

" K 2 t p !

0.2 D

] 0.05 2 [GeV " 2 t

Hermes pT p

$! 0 broadening data He

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World’s ﬁrst comparison between p + $! 0 pion and K pT broadening Ne

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t !ν"[GeV] !Q "[GeV ] !x" !z"

Xe p 0.04 2 + $! ∆!pt " vs. A $ 0 - He 13.7 2.4 0.101 0.42 [GeV $ Kr # + 2 t K Ne 13.8 2.4 0.101 0.42 ] p 0.05 Kr 2 Kr 14.0 2.4 0.100 0.41 !" Xe 14.0 2.4 0.099 0.41

[GeV 2 " pt ν

2 ∆! " vs.

0.02 t p ν-bin# 1 8.0 2.1 0.141 0.49 $! 0 Ne ν-bin# 2 11.9 2.5 0.111 0.43 Xeν-bin# 3 14.7 2.6 0.096 0.40 He ] 0.05 ν-bin# 4 18.5 2.4 0.073 0.37 2 2 2 ∆!pt " vs. Q 0 2 [GeV

" Q -bin# 1 13.7 1.4 0.063 0.42 2 t 2 p Q -bin# 2 14.0 2.5 0.105 0.41

$! 0 2 Q -bin# 3 14.4 3.9 0.153 0.40 0 20 40 60 80 100 120 140 QXe2-bin# 4 14.6 6.5 0.248 0.39 2 ∆!p10t " vs. x 20 2 5 0.2 0.4 0.5 1 A % [GeV] Q2 [GeV2] xx zz x − -bin# 1 15.2 1.6 0.059 0.40 + + 2 2 FIG. 1: The pt-broadening for π , π ,andK mesonsFIG. 2: Fromas left to right,x the ν, Q , x,andz dependence of !pt " for D (top row) and pt-broadening (remaining rows) for + − -bin# 2 12.3 + 3.0 0.131 0.42 a function of atomic mass number A. The inner errorπ and barsπ produced on He,x-bin# Ne, Kr, 3 and Xe targets11.5 and for K 5.5produced on0.254 a Xe target0.42 (bottom row). The inner error bars represent the statistical uncertainties; the total error bars represent the total uncertainty, evaluated as the sum in quadrature represent the statistical uncertainties; the total barsof statistical repre- and systematicx-bin# uncertainties. 4 10.1 8.1 0.422 0.41 sent the total uncertainty, obtained by adding statistical and 2 pt z systematic uncertainties in quadrature. ∆! " vs. z-bin# 1 14.5 2.4 0.097 0.32 z-bin# 2 13.1 2.4 0.106 0.53 z-bin# 3 12.4 2.4 0.107 0.75 z-bin# 4 10.8 2.3 0.115 0.94 pt-broadening at large atomic mass numbers, support- ing models which treat its origin in the partonic stage. + TABLE II: Average kinematics for the (π ) pt-broadening Within such models, this behavior suggests that the color 2 results. The ν,Q,andz kinematics are for the Xe target. neutralization happens near the surface of the nucleus or outside for the average kinematics of this measurement [22]. The panels presented in Fig. 2 show !p2" for D (top t data presented here do not allow the study of the Q2 row) and the pt-broadening (remaining rows) as a func- − and x dependence separately, or any other two kinematic tion of either ν, Q2, x, and z for π+ or π for the various observables. nuclear targets. Since the uncertainties of the K+ sam- ple are rather large, only the results for the Xe target The pt-broadening is seen to vanish as z approaches 2 unity while the !p2" for D is 0.2 or higher in the high- are presented in the bottom row. The values of !pt " for t 2 D are between 0.2 and 0.4 GeV while the pt-broadening est z-bin. Due to energy conservation the struck quark shows values from 0 up to 0.05 GeV2. This means that cannot have lost energy when z = 1, leaving no room 2 for broadening apart from a possible modification of the pt-broadening adds between 0 to 10% to !pt ". The data do not reveal a significant dependence on ν in the kine- primordial quark transverse momentum. The observed 2 h matic range covered. vanishing of the ∆!pt "A at high values of z indicates that Since models that describe hadron formation in nuclei there is no or little dependence of the primordial trans- commonly connect formation length with ν, the basically verse momentum on the size of the nucleus. It also indi- flat behavior in ν supports again the picture that color cates that pt-broadening is not due to elastic scattering neutralization mainly happens at the surface (or outside) of pre-hadrons or hadrons already produced within the of the nucleus for the Hermes kinematics [22]. The effect nuclear volume, as this would lead to substantial broad- slightly increases with Q2 in contrast to the model cal- ening even for values of z very close to unity. culation in Ref. [23], where a decrease of the broadening In summary, the first direct determination of pt- with Q2 is predicted, and in agreement with the model broadening in semi-inclusive deep-inelastic scattering for calculation in Ref. [24]. The behavior as a function of x charged pions and positively-charged kaons was per- is very similar to the Q2 behavior, due to a strong cor- formed on He, Ne, Kr, and Xe targets. The broadening relation between x and Q2 in the Hermes kinematics, was measured as a function of the atomic number A and hence it can not be excluded that the Q2 dependence ob- the kinematic variables ν, Q2, x or z. The broadening served is actually an underlying x dependen ce or both increases with A and remains constant with ν, suggest- a Q2 and x dependence. The statistical precision of the ing that the effect is due to the “partonic” stage and that 2 1.0

1.4 1.4

1.2 1.2

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2 CLAS Preliminary 0.2 CLAS Preliminary 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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ν z (1 z) τ · · − p ∝ dE dx |vacuum+medium

with z z =E /ν ≡ hadron hadron

This form explicitly demonstrates the connection between the production length and the vacuum energy loss process Consistency between measured ΔE and the energy loss estimated from pT broadening Pb: ΔE = 575 MeV (uncorrected for acceptance and radiation)

2 Pb pT broadening ~0.04 GeV for z=0.5 production length found is 1.6 fm

dE α N = s c ∆p2 − dx 4 T

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