Hadron Physics

Hadron Physics

NNPSS 2009 1E. Beise, U Maryland

Lecture #1: The quark model, QCD, and hadron spectroscopy

Lecture #2: Internal structure of hadrons: momentum and spin

Lecture #3: Internal structure of hadrons: charge, magnetism, polarizability

Lecture #4: Hadrons as laboratories (and other miscellaneous topics)

Properties of hadrons: momentum and spin

Structure functions and Deep Inelastic Electron Scattering

spin and flavor structure

Other processes:Semi-inclusive scattering, transversityDeeply Virtual Compton Scattering & Generalized

Parton Distributions

04/19/20232

E. Beise, U Maryland

“quark model” vs “partons”

references for this sectionHalzen & Martin: Quarks and LeptonsF.E. Close: An Introduction to Quarks and PartonsPerkins: Introduction to High Energy PhysicsCahn and Goldhaber: The Experimental Foundations of Particle Physics

Xiangdong Ji: Graduate nuclear physics lecture noteshttp://www.physics.umd.edu/courses/Phys741/xji/lecture_notes.htm

Lectures from the Hampton University Graduate School (HUGS), particularly 2007 (Reno), 2008 (Elouadhriri) and 2009 (Burkardt)

http://www.jlab.org/hugs/archive/

Special thanks toZein-Eddine Meziani, Temple UniversityNaomi Makins, University of Illinois

04/19/2023 3E. Beise, U Maryland

http://www.jlab.org/hugs/archive/

1930’s:

(Chadwick NP 1935)(Stern NP 1943)

1950’s:

proton charge radius from (e,e’) (Hofstadter NP 1961)

1970’s:

partons in proton via inelastic (e,e’) (Friedman,Taylor,Kendall, NP 1990)asymptotic freedom QCD(Gross, Politzer, Wilcek, NP 2004)

1990’s:

polarized targetsIntense CW electron beamsimprovement in polarized e sources

mp ~ 3 mN

rp ~ 1 fm

2000’s:

lattice QCDGeneralized Parton Distributionstransversity, DVCS, moments, ….

1980’s: exploration of phenomenavarious scaling phenomena“the spin crisis”“the EMC effect”


Deep Inelastic Electron ScatteringM. Briedenbach et al, Phys Rev Lett 23, 935 (1969)

from J. Friedman Nobel lecture, 199004/19/2023 5E. Beise, U Maryland

Kinematics of electron scattering

p

k’k

p’

qm

A common reference frame to work in is the LAB frame with a stationary target:

'),(

cos'ˆˆ

)','('),(

)',(')0,(

kkqq

kk

kEkkEk

pEpMp R

)0(2222 Qqq

It is common to assume the electron is massless (extreme relativistic limit). In this case, if one conserves 4-momentum:

EMMkMEWs 2)( 2222

and can easily show:

222 sin'4 EEQ

case 1: elastic scattering

'EE 04/19/2023 6E. Beise, U Maryland

Inelastic electron scattering

Wl

E

E

QdEd

d '4

2

Using Fermi’s Golden rule, we integrate over the recoiling target quantities, average over initial spin states, sum over final spin states. For elastic scattering, we integrate over an energy-conserving delta function. For inelastic scattering we skip the last step.

p

k’k

p’

qminteraction strength and photon propagation

lepton current '

21 )','(),(),()','(

s

skuskuskuskul

'2 43

21 pqpPJXXJPW

X

hadron current

)(]?)['( pupuJ

outgoing may no longer be a proton


the hadronic current)(]?)['( pupuJ

Elastic scattering: the target is left intact and we measure its net response to the EM current as a function of momentum transferred to it by the photon.

qiQFM

QF )(2

)(]?[ 22

21

Inelastic scattering: target might to into an excited state, or break up

2222

21

'

q

qpqp

q

qpqp

M

W

q

qqgW

XJPXJPW

where in principle W1 and W2 depend on both Q2 and energy loss ( ). n These

encode all of the strong interaction dynamics between the partons.


Unpolarized electron scattering, cont’d

after some manipulation, the cross section becomes

222

12

22

42

2

2

2

tan,2,sin

cos

4

QWQWEdEd

d

This is the famous “Rosenbluth” formula. Often this is also expressed in terms of helicity of the photon being exchanged.

... LTdEd

d

sMott

,0,0,1

0

0,,1,02

11

2

2

QQ

i

photon polarization, wrt q

virtual photon “flux” photoabsorptioncross sections


Deep Inelastic Electron Scattering

222

12

2 tan,2, QWQW

d

d

Edd

d

Mott

2

22

hhtgtbeam EEEEWs

energy available to produce particles in final state

Experimentally, W2 and W1 seem to depend on only one variable

“scaling” (anticipated by Bjorken, 1967)

from Nobel lectures, 1990

)(2)(

)(,

)(,

12

22

2

12

1

xxFxF

xFQWM

xFQW

1,10,

2

2

partonstgt

xxM

Qx

scaling good when (Q2,n) →, and if the partons have no transverse momentum .


DIS and quark momentum distributionsx = fraction of proton’s momentum carried by individual quark(in reference frame where proton moving ~ speed of light…)

)()()()(9

1)()(

9

4)(

)()()()(2)(

2

212

xsxsxdxdxuxuxxF

xfexPxxPxxFxF

p

quarksii

parton distribution functions

proton:

The scaling behavior is good when (Q2,n) →, and holds in the limit that the quark transverse momentum is 0.

)()()()(

9

1)()(

9

4)(2 xsxsxuxuxdxdxxF n

If isospin symmetry is good, which says that u in the neutron is just like d in the proton:


interpretation of parton distributionsx = fraction of the proton’s momentum carried by the struck quark, in the “infinite momentum”frame

i

i xxfdx 1)(

p

xp

(1-x)p

q

limits:1

02

2 xp

n

F

F

4

11

2

2 xp

n

F

F

at very low x, the sea quarksshould dominate

here the valence quarks should dominate and uv >> dv .


parton distribution functions

The parton distribution functions are a property of the target, not of the process.

partons pointlike quarks

Phys. Rev. Lett. 23, 1415 - 1417 (1969)


quark distribution functionsF2(x) “scaling” is violatedwhen the strong interaction is “strong” (low x or small Q2)

1

0

5.0)( dxxPquarks


parton flavors

from http://pdg.lbl.gov


Deep Inelastic nucleon scattering

xxFy

yxxFy

xFyEMG

dxdy

d NF

31

2

2

22

2

12

21

beamtgt E

vy

M

Qx ,

2

2

F1,2,3 are weak interaction equivalents of those measured in electron

scattering. Experimentally, they seem again to only depend on x (to lowest order) and are combinations of quark momentum distributions.

/

hadronsnucleon

quarks

ixPxPxxPxF )()()()(2

Experimentally, for target w/equal numbers of neutrons and protons:

)(5

18)( 22

xFxF e(if ignore s-quarks...)


NuTeV: deep inelastic scattering

http://home.fnal.gov/~bugel/tour.html

SSQT: series of magnets selects charge state of p,K

p

ee 2


neutrino scattering: F3(x)

M. Tzanov, et al., Phys. Rev. D 74 (2006) 012008

)()(2

)()(2

)()(2

)()(2

3

2

3

2

xdxuF

xdxuxF

xuxdF

xuxdxF


NuTeV s-quark momentum distributions

RR WCCCC

NCNC

2sin

2

1

)s(

9

4s

3

71 2

212

Ws

W

vvvv

vv

dxdux

dxssx

dxdux

dxduxNR

see also http:// home.fnal.gov/~gzeller/nutev.html

0013.00013.0

dxssxS

NuTeV fit (NLO)

0 0.1 0.2 0.3 0.4 0.5

x

0.01

0

-0.01

-0.02

-0.03

-0.04

x[s(

x)-s

(x)]

CTEQ6M, NLONuTeV D. Mason et al, hep-ex/0405037

from this they extract sin2qW


The Drell-Yan process: antiquarks

1 2 1 2

1 2 1 2

4 1( ) ( ) ( ) ( )

9 94 1

( ) ( ) ( ) ( )9 9

pp

pn

u x u x d x d x

u x d x d x u x

FNAL E866: E. Hawker, etal, PRL 80 (1998) 3715

FNAL E906: scheduled for 2010

future program at J-PARC


sum rules

counts the net excess of quarks over anti-quarks of each type

Gross-Llewellyn-Smith sum rule: counts the excess quarks over anti-quarks, as seen by neutrinos

2)()( 22

1

0

xFxFx

dx pn Adler sum rule (neutrinos)

3

1)()( 22

1

0

xFxFx

dx enep Gottfried sum rule (electrons)

V

Aenenepep

g

gxFxAxFxA

x

dx

3

1)()()()( 22

1

0

Bjorken sum rule (axial charge)


The hadronic tensor with spin-dependencehttp://pdg.lbl.gov


Spin Structure Functions

Unpolarized structure functions F1(x,Q2)

and F2(x,Q2)

Polarized structure functions

g1(x,Q2) and g2(x,Q2)

Q2 :Four-momentum transferx : Bjorken variable : Energy transferM : Nucleon massW : Final state hadrons mass

L

T

U

(slide from Z. Meziani)

iiiii

ii xqexqxqexg )()()()( 2

212

21

1


Polarized Deep Inelastic Scattering

Semi-inclusive asymmetry

q(x) = q(x)+ – q(x)–

q(x) = q(x)+ + q(x)–

+ quark nucleon

– quark nucleon

q~

q~

)Q,x(F

)Q,x(g

)Q,x(q e

)Q,x(q e)Q,x(A

21

21

2

q

2q

2

q

2q2

1

)Q,z(D)Q,x(q e

)Q,z(D)Q,x(q e)Q,z,x(A

2hq

2

q

2q

2hq

2

q

2q

hh

hh2h

1

Inclusive asymmetry

04/19/2023

fragmentation function

25E. Beise, U Maryland


Many experiments…..

SLAC:E80, E130,E142, E154,and others…

CERN:EMC,SMC, COMPASS

Brookhaven:RHIC-Spin program gluon spin

DESY:HERMES

JLAB:Hall A, Hall B


A relatively simple magnetic spectrometer

drift chambers

plastic scintillator arrays

aerogel Cerenkov

electromagneticshower detector

High MomentumSpectrometer,Hall C,Jefferson Lab


Example of a standard setup (in Hall A at JLab)

Polarized beamEnergy: 0.86-5.1 GeVPolarization: > 70%Average Current: 5 to 15 µA

Hall A polarized 3He targetPressure ~ 10 atmPolarization average: 35%Length: 40 cm with 100 µm thickness

Measurement of helicity dependent 3He cross sections Extract g1 and g2 spin structure functions of 3He Extract moments of spin structure functions of 3He and Neutron

Highest polarized luminosity: ~1036cm-2s-1

L

Spectrometersset at 15.5º

Electron beam

R

Hall A polarized 3He target

(slide from Z. Meziani)


COMPASS NIM A 577(2007) 455

160 GeV m

SciFiveto

6LiD target

Si Micromegas

Drift Chambers

GEMs

Straws

SM1

RICH

ECALs & HCALs

m Filters/ Walls

Trigger Hodoscopes

MWPCs

50 mSM2

O. Kouznetsov, CIPANP 2009


HERMES detector at DESY (Hamburg)


Polarized Electrons

Reverse pol’n of beam at rate of 30 Hz

Feedback on laser intensity and position at high rate

Electron retains circular polarization of laser beam: Pe ~ 85%

See also Physics Today, Dec 2007

D.T. Pierce et al., Phys. Lett. 51A (1975) 465.


( In CLAS detector in Hall B at JLab,slide from K. Griffeon, DIS2007)


Polarized 3He

p p

n

Spin –dependent scattering

eHe 3

ne

looks like

photo from G. Cates, CIPANP 2009used in Hall A at JLab


spin structure of the neutron and proton

04/19/2023

from http://pdg.lbl.gov


spin structure of the proton

04/19/2023

example: HERMES

A. Airapetian, et al. PRD 71 (2005) 012003

Uses semi-inclusive scattering aswell to disentangle u,d,s and valence/sea

009.0033.0028.0

011.0033.0054.0

050.0039.0226.0

029.0036.0002.0

049.0039.0601.0

s

d

d

u

u


a twist-2 term (Wandzura & Wilczek, 1977):

a twist-3 term with a suppressed twist-2 piece (Cortes, Pire & Ralston, 1992):

Twist -2 Twist -3

Transversityq-g correlations

g2 and Quark-Gluon Correlationsg2 and Quark-Gluon Correlations

(QCD & Hadron Physics Town meeting, Rutgers)

coming in the future….


Measurement of the gluon polarization DG at RHIC

Courtesy of G. Bunce, S. Vigdor

Dominates at high pT

Dominates at low pT


Structure of the nucleon – valence region

Courtesy of Z.-E. Meziani, K. Griffioen, S. Kuhn, G. Petratos

Helicity conservationd/u = 1/5

Scalar diquarkdominanced/u=0

SU(6)d/u=1/2

proposed to be done at JLAB with 11 GeV beam

coming in the future….


quark angular momentum

04/19/2023

lattice QCD (LHPC, QCDSF)Lu + Ld small, but individual parts large

gq JL 2

1

quark spins 30%

gluon polarizationsmall but still uncertain

??






GPDs: Non-local, off-diagonal matrix elements

(x + ξ) and (x - ξ) : longitudinal momentum fractions of quarks

The structure of the nucleon can be described by 4 Generalized Parton Distributions :

Vector : H (x, ξ ,t)

Tensor : E (x, ξ ,t)

Axial-Vector : H (x, ξ ,t)

Pseudoscalar : E (x, ξ ,t)

~

~

x + ξ x - ξ

P - Δ/2 P + Δ/2GPD (x, ξ ,t)

Mueller

(1995)

slide from F. Sabatie, CIPANP 2009

, ,

g r pK,…

.


Properties, applications of GPDs

first moments : nucleon electroweak form factors

ξ-independence :

Lorentz invariance

P - Δ/2 P + Δ/2

Δ

Pauli

Dirac

axial

pseudo-scalar

forward limit : ordinary parton distributions

unpolarized quark distributions

polarized quark distributions

: do NOT appear in DIS … new information

They contain what we know already through sum rules and kinematical limits: Form Factors, parton distributions



Generalized Parton Distributions

Elastic Scatteringtransverse quark distribution in coordinate space

DISlongitudinal

quark distributionin momentum space

DES (GPDs)fully-correlated

quark distribution in both coordinate and

momentum space

GPDs yield 3-dim quark structure of the nucleon

Burkardt (2000, 2003)

Belitsky, Ji, Yuan (2003)



CHL-2

Upgrade magnets and

power supplies

Enhance equipment in existing halls

JLab at 12 GeV new Hall

plan:construction 2009-2013begin physics 2014


Overview of 12 GeV Physics Program

Hall C – precision determination of valence quark properties in nucleons and nuclei

Hall A – short range correlations, form factors, hyper-nuclear physics, future new experiments

Hall D – exploring origin of confinement by studying exotic mesons

Hall B – understanding nucleon structure via generalized parton distributions



Summary of this section

04/19/2023 E. Beise, U Maryland 52

Lepton scattering and parton distributions explicitly reveal the intracacies of hadron structure, and the inadequacy of the simple quark model

Decades of precision data now give a clear picture of flavor and spin, particularly in the regime where QCD is a perturbative theory.

Still to be understood are the “motional” dynamics (orbital motion), the full role of gluons, and how to numerically make the transition from a perturbative to a non-pertubative theory.

Documents

Hadron Physics