Generalized Parton Distributions of the Photon

[Pages:41]Generalized Parton Distributions of the Photon

Sreeraj Nair In collaboration with Prof.Asmita Mukherjee,Vikash.K.Ojha

Sreeraj Nair (IIT Bombay)

IIT Bombay

October 10, 2013

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Outline

1 Introduction to Proton GPDs 2 How and Why GPDs 3 Photon GPDs 4 Helicity Flip Photon GPDs 5 Conclusion

Defination of Proton GPDs

They are defined as off-forward matrix elements of well defined field operators in between proton states having different momenta.

F, =

dy- eixP+y-/2 P, | ? (0) +(y) |P,

8

y+ =0,y =0

=

1 2P?+

U?

(P,

)

H(x, , t) + + E(x, , t) i+(-) 2M

U(P, )

F~, =

dy- 8

eixP+ y- /2

P, | ? (0) +5(y) |P,

y+ =0,y =0

=

1 2P?+

U?

(P,

)

H~ (x,

,

t)

+ 5

+

E~(x,

,

t)

5(-+) 2M

U(P, )

x fractional momentum carried by the active quark. = Q2 skewness variable.

2P.q = P - P Momentum transfer from intial target state to final state (t = 2)

Sreeraj Nair (IIT Bombay)

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Basic properties of GPDs

In the forward limit (p = p, t = 0) :

Hq(x, 0, 0) = q(x), Hq(x, 0, 0) = -?q(-x),

H~ q(x, 0, 0) = q(x) H~ q(x, 0, 0) = ?q(-x)

for x > 0, for x < 0.

Connection to elastic FFs :

where,

1

dxHq(x, , t) = F1q(t),

-1

1

dxH~ q(x, , t) = gqA(t),

-1

1

dxEq(x, , t) = F2q(t),

-1

1

dxE~q(x, , t) = gqP(t)

-1

F1q(t) and F2q(t) are the Dirac and Pauli FFs respectively. gqA(t) and gqP(t) are the axial and psedoscalar FFs respectively.

=

2 1+

Sreeraj Nair (IIT Bombay)

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Outline

1 Introduction to Proton GPDs 2 How and Why GPDs 3 Photon GPDs 4 Helicity Flip Photon GPDs 5 Conclusion

Deeply Virtual Compton Scattering(DVCS) on a Proton target

e-

Exclusive Process All final states are known.

The final and intial state momenta are different: e-

P=

P+,

- 0 ,

M2 P+

P =

(1

-

)P+ ,

-,

M2 + 2 (1 - )P+

GPD

momentum transfer = P - P LC co-ordinates V? = V0 ? Vz

p ep ep p

V2 = V+V- - (V)2

Final state has a real photon (q) + p(P) (q) + p(P)

Factorization of DVCS amplitude hard part perturbative soft part generalised parton distributions(GPD) X. Ji, PRL, 1997

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GPDs and Nucleon Spin Crisis

before the EMC experiment at CERN in 1988: quarks carry all of the nucleon spin After EMC experiment: only around 30% is carried by the quarks what about the remaining 70% ? How does the spin add up?

Candidates for the remaining 70% are:

Quark Orbital Angular Momentum (OAM) Gluon spin( likely to be small) Gluon OAM

Sreeraj Nair (IIT Bombay)

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GPDs and spin sum rule

Second moment of the GPDs gives the fraction of the nucleon spin carried by the quarks

Jq is accessible through GPDs:

1

1

dx x Hq(x, 0, 0) + Eq(x, 0, 0) = Jq(Q2)

20

Jq + Jg = 1 2

q

X.Ji, 1997

DVCS to probe Jq = Sq + Lq

but no further decomposotion of Jg

Sreeraj Nair (IIT Bombay)

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