the curse of spin: lurching from one crisis to the …2008/02/06 · the curse of today may be the...

The Curse of Spin: Lurching from One Crisis

to the Next

Elliot Leader

Imperial College London

1

What do I mean by “CURSE” ?

The CURSE of today may be the BLESSING

of tomorrow

The curse of spin is its ability to demonstrate

the shortcomings of a theory and, in some

cases, to destroy it.

Spin dependent measurements have a scalpel

like ability to probe a theory, which may have

been able to fudge the results of ordinary e.g.

cross-section measurements.

Thus the path of spin is strewn with the wreck-

age of discarded theories. The positive aspect

is that better (hopefully) theories arise from

the debris.

2



of tomorrow











the debris.

3



of tomorrow











the debris.

4



of tomorrow











the debris.

5



of tomorrow











the debris.

6

Contents

1) The Ancient World (brief)

2) The Renaissance (the European Muon Col-

laboration experiment)

3) The Present (new problems)

7

THE ANCIENT WORLD

8

An example: Electroweak Theory

Weak interactions were supposed to involve S-

T coupling:

1 and i2[γµ, γν]

Eventually learned: V-A

γµ(1− γ5)

Role of spin in comparing rates for π → eν and

π → µν was crucial. Measurement of the Helic-

ity of the neutrino was also a vital experiment

in confirming this.

9



T coupling:



γµ(1− γ5)




in confirming this.

10



T coupling:



γµ(1− γ5)




in confirming this.

fig

11

Without this unification of Weak and Electro-

magnetic interactions would have been impos-

sible!

12

Another example: Regge Poles

Totally unexpected SHRINKING of diffraction

peaks in dσdt for elastic cross-sections

A(p1) + B(p2) → A(p3) + B(p4)

t = (p1 − p3)2

fig

13

Beautiful explanation by Theory of Complex

Angular Momentum: simplest version: Regge

Poles————–BUT

Total failure to predict POLARIZATIONS

14

Beautiful explanation by Theory of Complex

Angular Momentum: simplest version: Regge

Poles————–BUT

Total failure to predict POLARIZATIONS

15

Despite the important role played by spin-dependent

measurements, the subject has NOT attracted

a large following. WHY?

Possibly two reasons:

1) Practical: Polarization measurements are

very difficult. Sources, acceleration, depolariz-

ing resonances etc etc

2) Pedagogical-psychological

Spin had a difficult birth: fine structure of hy-

drogen (spin-orbit coupling); Stern-Gerlach ex-

periment; “mysterious effects too complicated

to explain in an undergraduate text” etc etc

16













17













18








2) Pedagogical-psychological:





19








2) Pedagogical-psychological:





slides

20

THE RENAISSANCE

21

Deep Inelastic Scattering: a reminder

slide

22

lepton

nucleon

kk’

q

s

s’

S

XP

Deep Inelastic Scattering in the parton model

fig

23

Deep Inelastic Scattering in the parton model

Q2 ≡ −q2 = −(k − k′)2 ν ≡ ELab − E′Lab

x ≡ xBjorken = Q2

2Mν

24

The cross-sections are expressed in terms of

two (unpolarized) STRUCTURE FUNCTIONS:F1,2

In simple Parton Model: F1,2(x)

Including some aspects of QCD:F1,2(x, Q2)

Slow evolution in Q2

F1(x, Q2) =1

2

∑

flav

e2j [qj(x, Q2) + qj(x, Q2)]

A key ingredient: the UNPOLARIZED parton

number density q(x)

fig

25

The cross-sections are expressed in terms of

two (unpolarized) STRUCTURE FUNCTIONS:F1,2

In simple Parton Model: F1,2(x)

Including some aspects of QCD:F1,2(x, Q2)

Slow evolution in Q2

F1(x, Q2) =1

2

∑

flav

e2j [qj(x, Q2) + qj(x, Q2)]

A key ingredient: the UNPOLARIZED parton

number density q(x)

fig

26

Quite analogously, POLARIZED cross-section

expressed in terms of two spin-dependent STRUC-

TURE FUNCTIONS: g1,2

g1(x, Q2) =1

2

∑

flav

e2j [∆qj(x, Q2) + ∆qj(x, Q2)]

The key ingredient here is the polarized quark

density

fig

27

Quite analogously, POLARIZED cross-section

expressed in terms of two spin-dependent STRUC-

TURE FUNCTIONS: g1,2

g1(x, Q2) =1

2

∑

flav

e2j [∆qj(x, Q2) + ∆qj(x, Q2)]

The key ingredient here is the polarized quark

density

fig

28

THE EMC EXPERIMENT OF 1988

Notation:

∆q =∫

dx∆q(x) (1)

Important flavour combinations :

a3 = ∆u + ∆u−∆d−∆d (2)

= 1.267± 0.0035

a8 = ∆u + ∆u + ∆d−∆d− 2(∆s + ∆s) (3)

= 0.585± 0.025

∆Σ =∑

f

(∆qf + ∆qf) (4)

29


Notation:

∆q =∫

dx∆q(x)


a3 = ∆u + ∆u−∆d−∆d (5)

= 1.267± 0.0035

a8 = ∆u + ∆u + ∆d + ∆d− 2(∆s + ∆s) (6)

= 0.585± 0.025

∆Σ =∑

f

(∆qf + ∆qf) (7)

30


Notation:

∆q =∫

dx∆q(x)


a3 = ∆u + ∆u−∆d−∆d

= 1.267± 0.0035

a8 = ∆u + ∆u + ∆d + ∆d− 2(∆s + ∆s)

= 0.585± 0.025

∆Σ =∑

f

(∆qf + ∆qf)

Note that ∆Σ = a8 + 3(∆s + ∆s)

31


Notation:

∆q =∫

dx∆q(x)


a3 = ∆u + ∆u−∆d−∆d

= 1.267± 0.0035

a8 = ∆u + ∆u + ∆d + ∆d− 2(∆s + ∆s)

= 0.585± 0.025

∆Σ =∑

f

(∆qf + ∆qf)

Note that ∆Σ = a8 + 3(∆s + ∆s)

32

Ellis -Jaffe Theory: safe to ignore ∆s + ∆s

=⇒∆Σ ' a8 ' 0.59

Now EMC measurement of

Γp1 =

∫dxg

p1(x)

=1

12

[a3 +

1

3(a8 + 4a0)

]

=⇒ aEMC0 ' 0

But in naive parton model a0 = ∆Σ Moreover,since

∆Σ = 2Squarksz (8)

EMC seems to imply Squarksz = 0

and there appears to be a crisis in the partonmodel: where, oh where, is the proton’s spin?[Anselmino and L, Z.Phys. C41,(1988) 239 ]

33


=⇒∆Σ ' a8 ' 0.59


Γp1 =

∫dxg

p1(x)

=1

12

[a3 +

1

3(a8 + 4a0)

]

=⇒ aEMC0 ' 0

But in naive parton model a0 = ∆Σ Moreover,

since



and there appears to be a crisis in the parton

model: where, oh where, is the proton’s spin?

[Anselmino and L, Z.Phys. C41,(1988) 239 ]

34


=⇒∆Σ ' a8 ' 0.59


Γp1 =

∫dxg

p1(x)

=1

12

[a3 +

1

3(a8 + 4a0)

]

=⇒ aEMC0 ' 0

But in naive parton model a0 = ∆Σ

∴ Gross contradiction with Ellis-Jaffe Theory

Moreover, since



and there appears to be a crisis in the partonmodel: where, oh where, is the proton’s spin?[Anselmino and L, Z.Phys. C41,(1988) 239 ]

35


=⇒∆Σ ' a8 ' 0.59


Γp1 =

∫dxg

p1(x)

=1

12

[a3 +

1

3(a8 + 4a0)

]

=⇒ aEMC0 ' 0

But in naive parton model a0 = ∆Σ

∴ Gross contradiction with Ellis-Jaffe Theory

Moreover, since

∆Σ = 2Squarksz


and there appears to be ’A crisis in the partonmodel: where, oh where, is the proton’s spin?’[Anselmino and L, Z.Phys. C41,(1988) 239]

36

Resolution (??)of the crisis : The Anomalous

Gluon Contribution

The Operator Product Expansion has no gluon

operator contributing to the first moment of

g1, but Feynman diagram approach yields re-

sult:

a0 = ∆Σ− ?αs(Q2)

2π∆G(Q2) (1)

1

Resolution (??)of the crisis : The Anomalous

Gluon Contribution

The Operator Product Expansion has no gluon

operator contributing to the first moment of

g1, but Feynman diagram approach yields re-

sult:

a0 = ∆Σ− 3αs(Q2)

2π∆G(Q2) (2)

2

a0 = ∆Σ− 3αs(Q2)

2π∆G(Q2)

It was thus hoped that one could have a rea-

sonable ∆Σ ' 0.6 and still obtain a very small

a0.

But even with present day estimates a0 ≈ 0.2

this requires

∆G ' 1.7 at Q2 = 1GeV 2

Is this acceptable? What do we know about

∆G?

39

a0 = ∆Σ− 3αs(Q2)

2π∆G(Q2)



a0.


this requires

∆G ' 1.7 at Q2 = 1GeV 2


∆G?

40

a0 = ∆Σ− 3αs(Q2)

2π∆G(Q2)



a0.


this requires

∆G ' 1.7 at Q2 = 1GeV 2


∆G?

41

THE PRESENT

ATTEMPTS TO MEASURE ∆G

There are three ways to access ∆G(x) :

(1) Polarized Deep Inelastic Scattering (DIS)—

parametrize polarized quark and gluon densi-

ties and fit data on g1(x, Q2).

Main role of gluon is in EVOLUTION with Q2,

but range of Q2 is very limited so determination

of ∆G(x) is imprecise.

Figure 3 shows world results on ∆G(x)

42

THE PRESENT










43

THE PRESENT










44

THE PRESENT









fig world results on ∆G(x)

45

0.01 0.1 10.0

0.2

0.4

0.6

0.8 x G BB2 AAC03 GRSV LSS'05 (Set 1)

Q2 = 4 GeV2

X

This is a test.

1

Typically one has ∆G ≈ 0.29±0.32 much smaller

than the desired 1.7 !

(2) cc production in DIS. Requires high energy

lepton beam: COMPASS at CERN.

Given that the nucleon has no INTRINSIC charm,

the cc are produced via ’gluon-photon fusion’.

Figure 4.

46







Figure 4.

47







fig

48

Detecting BOTH charmed particles would be

an absolutely clean signal for the mechanism!

But the intensity is too low—-factor of 30 in

rate lost in detecting second charmed meson—

- so rely on single charm production. Also on

back-to-back jets—much less clean.

Figure shows some of the COMPASS results

49

Suggests very small ∆G compatible with result

quoted above

(3) ALL with polarized protons: uniquely at

RHIC.

Several reactions:

~p + ~p −→ π0 + X

~p + ~p −→ Jet + X

Dominant partonic reactions:

~g + ~g −→ g + g : dominates at smaller p2T

~g + ~q −→ g + q: dominates at larger p2T

Nice test: PQCD describes cross-sections quite

well.Figure 6

50


quoted above


RHIC.

Several reactions:

~p + ~p −→ π0 + X (needs Fragmentation Func-

tions)

~p + ~p −→ Jet + X





well.Figure 6

51


quoted above


RHIC.

Several reactions:


tions)

~p + ~p −→ Jet + X





well.Figure 6

52


quoted above


RHIC.

Several reactions:


tions)

~p + ~p −→ Jet + X





well. Fig

53

Results: ALL is SMALL!

Fig

54

¨

45.0

7.2 1

≈

=∫ −

P

pbLdt

Consistent with ZERO gluon polarization

THE SPIN CRISIS

IS STILL WITH US !

55

Consistent with ZERO gluon polarization

THE SPIN CRISIS

IS STILL WITH US !

56

Expect more definite statement on ALL very

soon: much improved accuracy

fig

57

TRANSVERSE SINGLE-SPIN

ASYMMETRIES

Hadronic reactions like

p↑ + p → π + X

p↑ : transversely polarized proton

Asymmetry under reversal of direction of po-

larisation

AN ≡ dσ↑ − dσ↓

dσ↑ + dσ↓

Partonic mechanism:

fig

58


ASYMMETRIES


p↑ + p → π + X



larisation


dσ↑ + dσ↓

Partonic mechanism:

fig

59


ASYMMETRIES


p↑ + p → π + X



larisation


dσ↑ + dσ↓

Partonic mechanism:

fig

60

In collinear Parton Model AN ≈ 0

To get an idea of the size, at the parton level

aN = αsmq√

sf(θ∗)

where f(θ∗) is of order 1

Gives asymmetries of a fraction of a percent

The data strogly contradicts this!

fig

1


To get an idea of the size, at parton level

aN = αsmq√

sf(θ∗)



The data strogly contradicts this!

fig

2



aN = αsmq√

sf(θ∗)



The data strongly contradicts this!

fig

3



aN = αsmq√

sf(θ∗)



THE DATA STRONGLY CONTRADICT THIS!

fig

4

How to extricate QCD from this mess???

1) Include intrinsic transverse momentum kT

of partons.

Conceptually no problem; but makes serious

calculations horrendous

2) Invent new SOFT mechanisms—-beyond

the parton model

SIVERS: Number density of quarks with mo-

mentum xP +kT depends on polarization P of

parent hadron

A + B P · (xP × kT

65



of partons.


calculations horrendous.


the parton model



parent hadron

A + B P · (xP × kT

66



of partons.




the parton model



parent hadron

A + B P · (xP × kT

67



of partons.




the parton model

a) SIVERS: Number density of quarks with mo-

mentum xP + kT depends on polarization P

of parent hadron:

A + B P · (xP × kT

68



of partons.




the parton model

a) SIVERS: Number density of quarks with mo-


parent hadron:

q(x, kT ) = A + BS P ·(xP × kT )

69

BUT can show this violates Parity and Time

Reversal invariance IF

hadron → quark + X

is treated as an independent reaction——-as

it is in the parton model.

To avoid this need INITIAL or FINAL state

interactions, thereby spoiling UNIVERSALITY

of parton model.

b) COLLINS: In fragmentation of quark of mo-

mentum p into hadron allow hadron to have

intrinsic transverse momentum kT relative to

quark.

Number density of hadrons with momentum1zp + kT depends on polarization P of frag-

menting quark.

70








of parton model.




quark.


menting quark.

71








of parton model.




quark.


menting quark.

72








of parton model.




quark.

Number density of hadrons with momentum

Ph = 1zp + kT depends on polarization P of

fragmenting quark.

73

D(z, Ph) = A + BC P·(p× Ph)

Again, vanishes if fragmentation q → hadron+

X is treated as an independent reaction, as it

is in the parton model.

So again lose universality.

Can’t calculate BS or BC so need to introduce

new functions phenomenologically. Ugly!

74


Again, vanishes if fragmentation

q → hadron + X

is treated as an independent reaction, as it is

in the parton model.


Can’t calculate BS or BC so need to introduce

new functions phenomenologically. Ugly!

75



q → hadron + X




Moreover, can’t calculate BS or BC so need to

introduce new functions phenomenologically,

for each flavour of quark and antiquark. Ugly!

76



q → hadron + X




Moreover, can’t calculate BS or BC so need to

introduce new functions phenomenologically,

for each flavour of quark and antiquark. Ugly!

77

THE LATEST PROBLEM

1

One of the oldest and supposedly best under-

stood reactions:

electron + proton(p) → electron + proton(p′)

Measurement of the ELECTROMAGNETIC FORM

FACTORS OF THE PROTON

As always, assume ONE PHOTON Exchange

fig

78

One of the oldest and supposedly best under-

stood reactions:

electron + proton(p) → electron + proton(p′)

Measurement of the ELECTROMAGNETIC FORM

FACTORS OF THE PROTON

As always, assume ONE PHOTON Exchange

fig

79

proton

electron

The photon-proton vertex is given by:

u(p′)[γµF em1 (q2) +

iσµνqν

2MκF em

2 (q2)]u(p)

q = p′ − p κ = anomalous magnetic mo-

ment

F1,2 Dirac em form factors. Sachs more con-

venient: GE = F1+ κq2

4M2F2 GM = F1+κF2

80

The photon-proton vertex is given by:

u(p′)[γµF em1 (Q2) +

iσµνqν

2MκF em

2 (Q2)]u(p)

q = p′− p κ = anomalous magnetic moment

Q2 = −q2

F1,2 Dirac em form factors. Sachs more con-

venient: GE = F1 − κτF2 GM = F1 + κF2

τ = Q2

4M2

GE(0) = 1

GM(0) = total magnetic moment(µ) = 2.79

81

Diff. cross-section in the LAB: ROSENBLUTH

dσ

dΩ=

( dσ

dΩ

)′Mott

[G2

E + τG2M

1 + τ

+ 2τG2M tan2(θ/2)

]

Both GE and GM drop with increasing Q2

Long standing experimental assertion that

GM(Q2) ≈ µGE(Q2)

82

Diff. cross-section in the LAB: ROSENBLUTH

dσ

dΩ=

( dσ

dΩ

)′Mott

[G2

E + τG2M

1 + τ

+ 2τG2M tan2(θ/2)

]

Both GE and GM drop with increasing Q2

Long standing experimental assertion that

GM(Q2) ≈ µGE(Q2)

fig

83

New cross-section measurements are consis-

tent with this:

fig

84

HOWEVER

A totally new kind of measurement: Polariza-tion transfer to the proton from a longitudi-nally polarized electron colliding with an unpo-larized target:

LONGITUDINAL polarization of the recoil pro-ton:

PL ∝[E + E′

M

] √τ(1 + τ)G2

M tan2(θ/2)

TRANSVERSE (in scattering plane) polariza-tion of the recoil proton:

P ∝ −2√

τ(1 + τ)GE GM tan(θ/2)

fig

85

HOWEVER



PL ∝[E + E′

M

] √τ(1 + τ)G2

M tan2(θ/2)


P ∝ −2√


fig

86

HOWEVER



PL ∝[E + E′

M

] √τ(1 + τ)G2

M tan2(θ/2)


PT ∝ −2√


fig

87

What’s wrong?!? Possibly two-photon exchange.

But expected to be negligible: extra factor of

α = 1/137 i.e. ≤ 1 % effect

Size consistent with comparison of electron-

proton with positron-proton

Exact calculation would require evaluation of

Feynman graph:

fig

88



α = 1/137 i.e. ≤ 1 % effect




Feynman graph:

fig

89



α = 1/137 i.e. ≤ 1 % effect




Feynman graph:

fig

90

Not possible. Can do approximate calculation

of simplest two photon graph:

fig

91

Surprisingly, seems to help!

Mainly affects Rosenbluth extraction and sug-

gests polarization results for GE/GM are cor-

rect!

i.e. GE/GM decreasing fairly rapidly with in-

creasing Q2

What about famous prediction of perturbative

QCD:

GE/GM → constant as Q2 →∞ ?????

92




rect!


creasing Q2


QCD:


93




rect!


creasing Q2


QCD:


94




rect!


creasing Q2


QCD:


95

SUMMARY

1) I have tried to give you an idea of the dra-matic role spin-dependent measurements haveplayed, both historically and in the present, inexposing weaknesses in theories and inspiringnew theories

2) Regarding the present we are still left withthree puzzles:

(a) We don’t know how the spin of the nucleonis built up from the angular momentum of itsconstituents

(b) We don’t know how to explain the hugetransverse single-spin asymmetries at a funda-mental level i.e. not relying on additional phe-nomenologically determined functions

(c) We are facing the realization that what isarguably the best-understood of all reactionsi.e. electron-proton elastic scattering, has, infact, been significantly misunderstood

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