16/08/06 CERN Students SessionsStefano Di Vita1 About mSUGO with Extra Vogon Dimensions in a Cubic...
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Transcript of 16/08/06 CERN Students SessionsStefano Di Vita1 About mSUGO with Extra Vogon Dimensions in a Cubic...
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!!
16/08/06 CERN Students Sessions
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)
16/08/06 CERN Students Sessions
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
16/08/06 CERN Students Sessions
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)
16/08/06 CERN Students Sessions
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
16/08/06 CERN Students Sessions
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
16/08/06 CERN Students Sessions
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)
16/08/06 CERN Students Sessions
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
16/08/06 CERN Students Sessions
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?
16/08/06 CERN Students Sessions
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
16/08/06 CERN Students Sessions
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