16/08/06 CERN Students Sessions

Stefano Di Vita 1

About mSUGO with Extra Vogon

Dimensions in a Cubic Hyperspace in d=42

spontaneously broken by Boredons

Stefano Di Vita Summer Students Sessions Talk

16/08/06 CERN Students Sessions

Stefano Di Vita 2

Slide number Zero Hello! I’m Stèfano (not Stefàno, the accent goes on the

‘e’!!) I’m a wanna-be theorist, I’m a Summer student, I’m studying SUperSYmmetry here @ CERN

And I’m having a

great time!

DO YOU EXPECT ME TO TALK ABOUT

THAT? NO!

16/08/06 CERN Students Sessions

Stefano Di Vita 3

Between the static quark model and QCD:

basic facts about THE PARTON MODEL

(A theorist hanging out @ CERN)

STEFANO DI VITA (Universita’ degli Studi Roma Tre)

16/08/06 CERN Students Sessions

Stefano Di Vita 4

Schedule “Drive out” the quarks from their

hadronic “nest” Scare you all with some formulae Spot some of the properties of

partons Prove that theoretical physics can

be enormously boring… especially at 9.15 in the morning!That’s why I

always wake up at 11!!

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Stefano Di Vita 5

DEEP INELASTIC SCATTERING (1)

Kinematics1960s SLAC-MIT experiments

q¹ = (º;~q)

p0 = p+ q

ep! eXW2 = p02 = M + q2 + 2p¢qp¢q= (M ;~0) ¢(v;~q) = M º

Note the elastic limit

Q2 = 2M º + M 2 ¡ W2

W = M ) Q2 = 2M º

Q , v are INDEPENDENT!!

Define the useful

quantityx = Q2

2M º

Q2 := ¡ q2 = ¡ 4E E 0 sin2(µ2)

16/08/06 CERN Students Sessions

Stefano Di Vita 6

DEEP INELASTIC SCATTERING (2)

e-He analogy: spotting the CONSTITUENTS

1 x0,2 0,4Elastic e-He

X=1Elastic e-p

X=0.25

INELASTIC e-He

Around x=0.25

Q2 = 2mº

If inelastic scattering is due to INCOHERENT ELASTIC SCATTERING from the N=4 constituents (nucleons) Then the

inelastic peak should

be at

M ¼4m

x = Q2

2M º ¼ 14 = 0:25

After Hofstadter ( 1956)

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Stefano Di Vita 7

After Hofstadter ( 1956)

DEEP INELASTIC SCATTERING (2)

e-He analogy: POINTLIKE constituents

1 x0,1

0,2 0,4REDUCED

Elastic e-p

X=0.25

UNAFFECTED

INELASTIC e-He

Around x=0.25

REDUCED Elastic

e-HeX=1

Suppressed by a

factor 6-7

This behaviour is called SCALING and reveals the existence of POINTLIKE

CONSTITUENTS of the target

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Stefano Di Vita 8

DEEP INELASTIC SCATTERING (4)

electrons scattering on a proton

0.145

0.293

0.484

1

Elastic peak

Resonances

Broad continuum (quasi-elastic constituent scattering)

AT HIGHER Q2 the cross section SCALES,indicating scattering fromPOINTLIKE CONSTITUENTS!

Are they Gell-Mann’s quarks?

After Bartel et al. ( 1968)

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Stefano Di Vita 9

Some UNAVOIDABLE Formulae: Structure

Functions

Sep! eX = W2(Q2;º) cos2(µ2) + 2W1(Q2;º) sin2(µ

2)Se¹ ! e¹ = [cos2(µ

2) + Q2

2M 2 sin2(µ2)]±(º ¡ Q2

2M )

W2 = ±(º ¡ Q2

2m ) ) ºW2(Q2;º) = ±(1¡ Q2

2mº )2W1 = Q2

2m2 ±(º ¡ Q2

2m ) ) 2mW1(Q2;º) = Q2

2mº ±(1¡ Q2

2mº )

If the inelastic scattering is due to ELASTIC scattering from the constituents (mass m)

d2¾d dE 0 = 4®2E 02

Q4 S

16/08/06 CERN Students Sessions

Stefano Di Vita 10

Bjorken Scaling Hypothesis

In the DIS

regime

Q2;º ! 1x = Q2

2M º fixed

M W1(Q2;º) ! F1(x)

ºW2(Q2;º) ! F2(x)It MEANS that the photon scatters against something POINTLIKE:

It’s GOOD because you can EXPERIMENTALLY TEST it!!!

Summarizing, we can formulate the scaling hypothesis:

1=x

F2(x)

Q2

F2(x) IT WORKS!!

After Miller et al.( 1972)

After Friedman and Kendall ( 1972)

Bjorken

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Stefano Di Vita 11

The Parton Model (1)

LET PARTONS

BE!!•Pointlike particles•Different kinds (different quarks?)•Carry a fraction x of the proton momentum P•Have a mass roughly a fraction x of the proton mass M

The scaling variable

x = Q2

2M º

R.P. Feynman

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Stefano Di Vita 12

The Parton Model (2):

DIS at the parton levelHypotheses: The proton is made up of POINTLIKE

PARTONS Inelastic scattering is a SUPERPOSITION of

ELASTIC scattering e-parton

Sum over parton types Part

on charge

Cross section

“structure” for

parton i

Integral over

momentum

fractions

Parton Density Function(Prob. of having a fraction

x)

ºW2(Q2;º) ! F2(x) = Pi e2

i xf i (x)M W1(Q2;º) ! F1(x) = P

ie2

i2 f i (x)

d2¾d dE 0 = 4®2E 02

Q4P

iRdx f i (x) ei Sepi ! eX (x)

Redefine the GLOBAL proton structure

functions+ “bonus” Callan-Gross relation

2xF1(x) = F2(x)

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Stefano Di Vita 13

pairs have OPPOSITE quantum numbers

The Parton Model (3)implications: e.g. SEA QUARKS

PARTONS HAVE SPIN ½ (related to the Callan-Gross relation)

Q ¹Q

THE QUARKS!!

A proton (uud) remains a proton even if it contains an ARBITRARY NUMBER OF

SEA QUARKS

Q ¹Q

A PROTON Only the NET BALANCE matters!!

R10 [u(x) ¡ ¹u(x)]dx = 2

R10 [d(x) ¡ ¹d(x)]dx = 1

R10 [s(x) ¡ ¹s(x)]dx = 0

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Stefano Di Vita 14

I’m having FUN @ CERN DIS (ep>eX) evidences SCALING

behaviour Scaling is due to the existence of

POINTLIKE CONSTITUENTS of p (partons) Inelastic scattering is due to the

INCOHERENT SUPERPOSITION of elastic scattering on partons

Parton model doesn’t forbid the presence of SEA QUARKS

What did I tell you?

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Stefano Di Vita 15

The end…Thanks to You all! I can’t believe you’ve been listening (?)

to my delirium The Summer Student Staff! You have arranged

everything for us in such a brilliant way My supervisors G. Altarelli and M. Seymour! I

swear I’ll go back to my SUSY book after this talk All my friends here! Thanx for the great time I’m

having this summer… I owe you all another party : )

Myself! Thanx for reminding me I want to be a physicst

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Stefano Di Vita 16

What is missing?This is just the beginning.

In fact: I didn’t explain why quarks have SPIN ½ I didn’t mention neither neutrino-nucleon

nor electron neutron DIS, so I couldn’t tell you that experiments support the hypotheses that

I didn’t tell you about the valence/sea quarks ratio

I didn’t tell you that there are VIOLATIONS to Bjorken scaling (see QCD!)

Quarks have FRACTIONARY charge the existence of GLUONS