KIT – Universität des Landes Baden-Württemberg und
nationales Forschungszentrum in der Helmholtz-Gemeinschaft
KIT-Centrum Elementarteilchen- und Astroteilchenphysik KCETA
www.kit.edu
KIT – Universität des Landes Baden-Württemberg und
nationales Forschungszentrum in der Helmholtz-Gemeinschaft
KIT-Centrum Elementarteilchen- und Astroteilchenphysik KCETA
www.kit.edu
Kern- und Teilchenphysik SS2012
Johannes Blümer
Vorlesung-Website
IKP in KCETA KT2012 Johannes Blümer
v14 12. Juni 2012 Quarkstruktur der Hadronen
Von Nukleonen zu den Quarks
Elastische, inelastische Streuung
Formfaktoren des Nukleons Quasielastische Streuung Tiefinelastische Streuung
Nukleonanregungen Strukturfunktionen
Partonen, Breit-System EMC-Effekt
Quarkstruktur der Hadronen
Quarkmodell, additive QZ, Ladungsbetrachtungen Vergleich von eN mit νN-Streuung
Charakteristika von F
2, neue Messungen an HERA, Skalenbrechung Aufbau von Hadronen aus Quarks
R-Wert aus e
+e
–-Streuung, “Color”
farbige Quarks und qg-Wechselwirkung
!2
√ v13
KT2012 Johannes Blümer IKP in KCETA
SLAC-Spektrometer
!3
KT2012 Johannes Blümer IKP in KCETA
Hinweise auf punktförmige Spin-1/2 Streuzentren im Nukleon
!4
Formfaktor/Strukturfunktion hängt nicht von Q
2ab: Punktstreuung!
Callan-Gross-Relation: 2x F
1= F
2ist erfüllt, d.h. die punktförmigen
Streuzentren haben Spin 1/2
Breit - System
■ Breit – System = "brick wall frame"
- Energieübertrag des virtuellen Photons = 0
- Parton wird zurückgestreut wie an fester Wand
p -p
Nukleon Parton Elektron
Nukleonrest
ɣ ɣ
-x·P x·P
2x·P Parton
P
KIT-IEKP 15 00.00.0000
anschaulich: x = Bruchteil des Viererimpulses des
Nukleons, der vom Proton getragen wird
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 7
Labor – System virtuelles ɣ, überträgt nur
Impuls, keine Energie
M ν
x Q
2 2
=
=
= q x P
q r 2 r
0
~ 0
Nukleon Parton Nukleonrest
Nukleonrest (1-x)·P
Nukleon
P
Breit – System:
KT2012 Johannes Blümer IKP in KCETA
!5
Breit-System, Partonen, SF im Quarkbild
Strukturfunktionen im Partonmodell
- Nukleon sei aus Quarktypen f aufgebaut. elektr. Ladung z f · e , WQ für e.m.-Streuung ∝ z f 2
- Proton : uud , Neutron : udd ; Quantenzahlen durch "Valenzquarks" geg.
- Quarks haben Impulsanteile x
Verteilungsfunktion: q f (x) = E (Zahl der Quarks mit Flavour f im Impulsintervall [x, x+dx] )
- Neben Valenzquarks sind auch "Seequarks" (virtuelle qq-Paare) im Nukleon
KIT-IEKP 16 00.00.0000
vorhanden:
- Neutrale Konstituenten : Gluonen: g(x)
F 2 (x) = Σ der mit x und z f 2 gewichteten Impulsverteilungen (pro Nukleon)
Exp. Bestimmung aus Streuexp. an H-, D-Kernen
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 7
q f (x) = Verteilungsfunktion von f-Antiquarks
Auswirkungen des Kernverbands EMC-Effekt (unverstanden)
mit e, µ oder ν (koppelt an schwache Ladung)
∑ ⋅ +
⋅
=
f
f f
f q x q x
z x
x
F 2 ( ) 2 ( ( ) ( ) )
F
2p(x) F
2D(x) = (F
2p(x)+F
2n(x)) /2 = F
2N(x)
[F
2← W
2← elektrischer Anteil der WW]
Quarktypen f, Impulsanteile x, Verteilungsfunktion q f (x)
Seequarks aus virtuellen Quark-Antiquark-Paaren
Von Partonen zu Quarks
KT2012 Johannes Blümer IKP in KCETA
F2-Vergleich in e, ν-Streuung
!7
[Perkins]
GGM: Gargamelle,
berühmte Blasenkammer
am CERN
KT2012 Johannes Blümer IKP in KCETA
Gargamelle-Blasenkammer am CERN
!8
KT2012 Johannes Blümer IKP in KCETA
F2-Vergleich in e, ν-Streuung
!9
alle Quarks
Valenzquarks = Quarks – Antiquarks
Anti-/Seequarks
KT2012 Johannes Blümer IKP in KCETA
Grenzfälle...
!10
Strukturfunktionen
■ Bilde F
2n/ F
2pund untersuche Grenzfälle:
x → 0 : Seequarks dominieren
sind gleich in p und n
x → 1 : , nicht
Quarks spielen nicht die gleiche Rolle im Nukleon; das , das
2
1
2n
F
p= F
2 2
2
2
4 1
u d
p
n
F z z
F = =
2 22 2
2 2
3 2
u d
u d
z z
z z
+
= +
=
u d
p n
KIT-IEKP 5 00.00.0000
Quarks spielen nicht die gleiche Rolle im Nukleon; das , das unterscheidet, hat eine Sonderrolle (mehr Impuls).
Die Zusammenhänge sind noch nicht sehr gut verstanden.
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 8
d n
?
KT2012 Johannes Blümer IKP in KCETA
noch unverstanden: “EMC-Effekt”
!11
< Erwartung
F 2 eN (x) = 5
18 (u + ¯ u + d + ¯ d) + 1
9 (s + ¯ s) F 2 ν, ν ¯ N ≈ 18
5 F 2 eN (x)
KT2012 Johannes Blümer IKP in KCETA
Quarks und Strukturfunktionen
!12
Strukturfunktionen im Partonmodell
- Nukleon sei aus Quarktypen f aufgebaut. elektr. Ladung z f ·e , WQ für e.m.-Streuung ∝ z f 2
- Proton : uud , Neutron : udd ; Quantenzahlen durch "Valenzquarks" geg.
- Quarks haben Impulsanteile x
Verteilungsfunktion: q f (x) = E (Zahl der Quarks mit Flavour f im Impulsintervall [x, x+dx] )
- Neben Valenzquarks sind auch "Seequarks" (virtuelle qq-Paare) im Nukleon
KIT-IEKP 16 00.00.0000
vorhanden:
- Neutrale Konstituenten : Gluonen: g(x)
F 2 (x) = Σ der mit x und z f 2 gewichteten Impulsverteilungen (pro Nukleon)
Exp. Bestimmung aus Streuexp. an H-, D-Kernen
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 7
q f (x) = Verteilungsfunktion von f-Antiquarks
Auswirkungen des Kernverbands EMC-Effekt (unverstanden)
mit e, µ oder ν (koppelt an schwache Ladung)
∑ ⋅ +
⋅
=
f
f f
f q x q x
z x
x
F 2 ( ) 2 ( ( ) ( ) )
F
2p(x) F
2D(x) = (F
2p(x)+F
2n(x)) /2 = F
2N(x)
[F 2 ← W 2 ← elektrischer Anteil der WW]
Strukturfunktionen
■ s-Quarks vernachlässigen F
2eN(x) = 5/18 x Σ (q(x)+q(x))
■ vgl. Neutrino-Streuung + Antineutrino-Streuung:
( ) ( )
(
3 2)
2 1 3 2 2 2 1 2 2 2 1
)
( + = +
= u d
f z z
z mit f = u,d
) ( )
(
185 2,
2
x F x
F
ν ν N≈ ⋅
eNW+
ν
µ-d u
W-
ν
µ+u d
KIT-IEKP 4 00.00.0000
■ q
v(x) hat Maximum bei x ≈ 0.17
mittlerer Impulsanteil eines Valenzquarks: <x
v> ≈ 0.12 mittlerer Impulsanteil eines Seequarks: <x
s> ≈ 0.04
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 8
5 . 0 )
5 ( ) 18
(
1
0 2 1
0
2
≈ ∫ ≈
∫ F
νNx dx F
eNx dx
d u
u
d d
u u
schwache Ladung d
=1 schwache Ladung
=1 siehe später : schwache WW
d.h. weitere 50% des Nukleonimpulses wird von Teilchen getragen, die keine elektrische und
keine schwache Ladung tragen.
Gluonen tragen die Hälfte des Nukleonimpulses
Strukturfunktionen
■ s-Quarks vernachlässigen F 2 eN (x) = 5/18 x Σ (q(x)+q(x))
■ vgl. Neutrino-Streuung + Antineutrino-Streuung:
( ) ( )
(
32 2 13 2)
2 2 1
2 2
2 1
)
( + = +
=
u df
z z
z mit f = u,d
) (
)
( 18 5 2
,
2 x F x
F ν ν N ≈ ⋅ eN
W +
ν µ -
d u
W -
ν µ +
u d
KIT-IEKP 4 00.00.0000
■ q v (x) hat Maximum bei x ≈ 0.17
mittlerer Impulsanteil eines Valenzquarks: <x v > ≈ 0.12 mittlerer Impulsanteil eines Seequarks: <x s > ≈ 0.04
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 8
5 . 0 )
5 ( ) 18
(
1
0
2 1
0
2
≈ ∫ ≈
∫ F ν
Nx dx F
eNx dx
d u
u
d d
u u
schwache Ladung d
=1 schwache Ladung
=1 siehe später : schwache WW
d.h. weitere 50% des Nukleonimpulses wird von Teilchen getragen, die keine elektrische und
keine schwache Ladung tragen.
Gluonen tragen die Hälfte des Nukleonimpulses
untersuche Grenzfälle: x ! 0, x ! 1
0 0.2 0.4 0.6 0.8 1 1.2
10 -4 10 -3 10 -2 10 -1
x
x f( x)
0 0.2 0.4 0.6 0.8 1 1.2
10 -4 10 -3 10 -2 10 -1
x
x f( x)
KT2012 Johannes Blümer IKP in KCETA
Strukturfunktionen front-line
!13
[rpp2010]
10 -1 1 10 10 2 10 3 10 4 10 5 10 6
10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1
x
Q
2( G eV
2)
KT2012 Johannes Blümer IKP in KCETA
Strukturfunktionen front-line
!14
[rpp2010]
22 | Particle Physics
INNER
STRUCTUREª
Insights into the depths of the proton
Anyone wishing to understand how the strong force works has to first understand the structure of the proton. That’s because protons are made up of quarks and gluons which are subject to the strong force. What’s more, the energy contained in the field of these particles determines the proton’s mass. That makes protons ideal laboratories for studying the strong force.
HERA did a terrific job in performing its main task of creating high resolution “images” of the proton’s interior. The HERA ex- periments H1 and ZEUS already provided totally new insights into the workings of the proton during HERA’s first phase of operation. When HERA started up in 1992, scientists only had vague notions of what they expected to find in the depths of the proton. It was known that the quarks in the proton emit gluons – the particles that stick the quarks together – and that these gluons in turn create other gluons or pairs of quarks and antiquarks. However, it was generally assumed that apart from the three valence quarks that are responsible for the charge of the proton, there were only very few quark-antiquark pairs and gluons in the proton. With the help of HERA’s extremely high energy, the H1 and ZEUS experiments pushed forward to in- creasingly shorter distances and smaller momentum fractions and measured the structure function F2 over a range that spans four orders of magnitude of the kinematic parameters x and Q2 – two to three orders of magnitude more than were ac- cessible to earlier experiments (see box). What the physicists discovered during these tests came as a great surprise: the HERA measurements show that the interior of the proton is like a thick, bubbling soup in which gluons and quark-antiquark pairs are continuously emitted and annihilated again. The smaller the momentum fractions x are to which the HERA microscope is set, the more quark-antiquark pairs and gluons are seen in the proton. This high density of gluons and quarks in the proton, which increases at small momentum fractions x, represented a completely new and until then uninvestigated state of the strong force.
Valence quarks, sea quarks and gluons
The super electron microscope HERA makes the proton’s detailed struc- ture visible. There are three valence quarks inside the proton, which are bound together by the exchange of gluons. Quantum theory allows the gluons to transform into quark-antiquark pairs for an extremely short time.
Alongside the valence quarks, the proton therefore also contains a whole
“sea” of gluons and short-lived quark-antiquark pairs.
The kinematic variables
x
andQ
2º Momentum fraction x: the fraction of the proton’s momentum carried by the quark with which the electron collides.
º The momentum transfer Q2, also called the resolution parameter, is the square of the momentum transferred in the collision between the collision partners. It is a measure of the resolution of the HERA microscope (Q2 = 1 GeV2 corresponds to a resolution equal to one-fifth of the proton radius).
Bem. zu HERA
POINTING THE WAYª
How HERA
is helping to shape the future of physics
For 15 years, electrons and protons collided inside the HERA particle accelerator, which lies deep in the earth beneath Hamburg. Data taking at HERA ended in the summer of 2007. This is thus a perfect occasion to take a backward look at Germany’s largest research instrument, which has written physics history, and look ahead at what HERA still has to offer.
After all, the evaluation of the recorded measurement data, which will be completed sometime in the next decade, will give us a comprehensive overall picture of the proton and the forces acting within it – with a precision that won’t be matched by any other particle accelerator in the world for years to come.
Accelerators | Photon Science | Particle Physics
Deutsches Elektronen-Synchrotron Member of the Helmholtz Association
NS60CH05-Wagner ARI 16 September 2010 20:5
H1 and ZEUS
x F 2(x,Q2 )
10–5 10–4 10–3 10–2 10–1 100
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Q2 = 3.5 GeV2
HERA-I NC e+p HERAPDF1.0
Q2 = 15 GeV2
Q2 = 650 GeV2
Figure 2
Structure function xF2 of the proton measured by the H1 and ZEUS Collaborations at HERA in three bins of Q2 as a function of x. Abbreviation: NC, neutral-current.
radiated gluon will split into a quark–antiquark pair, which would increase the low-xquark density.
This figure demonstrates the size of the kinematic region covered as well as the good agreement with previous results.
These HERA data are the only precise source of information on the structure of the proton at values of x smaller than 10−3 and at values of Q2 larger than a few hundred gigaelectronvolts squared. They are of particular interest at the Large Hadron Collider (LHC).
4.1.3. Electroweak effects at high Q2. The center-of-mass energy of HERA was sufficiently large to access the region of phase space in which weak and electromagnetic effects are of com- parable magnitude. This is clearly demonstrated in Figure 4, which shows the NC and CC e±p scattering cross sections as a function of Q2 (19–21). At small values of Q2, the NC process domi- nates because only electromagnetic effects contribute. When Q2 is comparable to the mass squared of the Z0 and W± bosons, the two cross sections are of similar magnitude. Figure 4 also demon- strates that the CC cross section is much larger in e−p than in e+p scattering. In the former cross section, the exchanged W− couples mostly to theu-valence quarks, which are approximately twice as abundant in the proton than the d-valence quarks.
A similar but smaller effect can be observed in the NC cross section, where the difference between the e+p and e−p cross sections is due to interference between photon and Z0 exchange.
From the difference one obtains the structure function xF3 (Equation 1), which provides informa- tion about the valence quark distributions. These measurements currently also provide the most stringent constraint on the weak couplings of the u and d quarks.
www.annualreviews.org • Physics Accomplishments of HERA 107
Annu. Rev. Nucl. Part. Sci. 2010.60:101-128. Downloaded from www.annualreviews.org by University Karlsruhe on 01/24/11. For personal use only.
KT2012 Johannes Blümer IKP in KCETA
HERA
!15
Physics Accomplishments of HERA
C. Diaconu,T. Haas, M. Medinnis, K. Rith, and A.Wagner Annu. Rev. Nucl. Part. Sci. 2010. 60:101–28
http://www.desy.de/sites2009/site_www-desy/content/e421/e55042/
e3003/e68431/e10845/e69406/HERA_Pointing_the_way_eng.pdf
HERA: Hadron-Elektron- Ring-Anlage Betrieb 1991 - 2007
Länge 6,3 km, Endenergie der e± 30 GeV, der Protonen 820 GeV.
4 Wechselwirkungszonen: Experimente H1, ZEUS, HERA-B und HERMES.
Vorab: deutet der drastische Anstieg von F
2☛
bei hohen Q
2auf eine Substruktur der Quarks o. ä.?
Nein, die höhere Auflösung “bringt immer mehr gg-
Paare zum Vorschein”
Particle Physics | 23
y!>!7/43F.6 y!>!1/111213
y!>!1/111272 y!>!1/111364
y!>!1/1115 y!>!1/1116
y!>!1/111743 y!>!1/1119
y!>!1/1124 y!>!1/1132
y!>!1/1143 y!>!1/116
y!>!1/119
y!>!1/124 y!>!1/132
y!>!1/143 y!>!1/16
y!>!1/19 y!>!1/24
y!>!1/29 y!>!1/36
y!>!1/5 y!>!1/76
2 21
1 2 3 4 5 6
OND F776 CDENT [FVT!:70:8 I2!)qsfm/*!::011 I2!:5.11 I2!QEG!3111!gju [FVT!OMP!RDE!gju
2 3 6 21 31 61 211 311
1/13 1/14 1/15 1/16 1/18 1/2 1/3 1/4 1/5 1/6 1/8 2/1
f!.!E!TMBD
n!.!E!CDENT
n!.!E!OND!:1!HfW
n!.!E!OND!391!HfW
n!.!D!CDENT
o!.!Gf!DDGS
Qspupo!tusvduvsf!gvodujpo!G
Npnfouvn!usbotgfs!R!!!)HfW!!*
Qspupo!tusvduvsf!gvodujpo!G
Npnfouvn!usbotgfs!R!!!)HfW!!*
The structure function F2(x,Q2) of the proton as a function of the resolution Q2 for various momentum fractions x. Particularly noticeable is the rapid increase of F2 with Q2 at decreasing values of x. A comparison of the HERA measurements (right) with the data from 1992 (left) shows the considerable increase in precision and the accessible kinematic range.
ª
Nobel Prize Laureate Frank Wilczek on the HERA measurements
“The most dramatic of these specific experimental tests, that protons viewed at ever higher resolution would appear more and more as field energy (soft glue), was only clearly verified at HERA twenty years later.”
KT2012 Johannes Blümer IKP in KCETA
F 2 Vergleich von HERA mit früheren Messungen
!16
KT2012 Johannes Blümer IKP in KCETA
Skalenbrechung
!17
Skalenbrechung
F
2hängt bei hohen Q
2doch von Q
2ab (für große und kleine x)
doch endl. Ausdehnung der Quarks?
NEIN: Auflösung von virtuellen Substrukturen im Quarkverbund: ein Quark "besteht" aus Quarks und Gluonen, ein Gluon "besteht"
aus Quarks und Antiquarks.
F
2Q
2x klein
mittleres x x groß
KIT-IEKP 14 00.00.0000
Je höher Q
2, desto häufiger können Aufspaltungsprozesse stattfinden.
Entwicklung in der QCD vorhersagbar.
Altarelli – Parisi – Gleichungen (gekoppelte Differential-/Integralgleichungen)
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 8
"normal" Quark mit Impuls y·P strahlt Gluon ab und trägt danach Impuls x·P (kleiner!)
Gluon "zerfällt" in qq, von
denen eines vom Photon
getroffen wird.
KT2012 Johannes Blümer IKP in KCETA
Q 2 -Entwicklung von xq und xg
!18
Q 2 -Evolution von Quark- und Gluon-Verteilungen
hohes Q
2:
weniger Valenzanteil mehr See-Anteil
viele Quarks bei kleinem x
Quark-Verteilung Gluon-Verteilung
KIT-IEKP 16 00.00.0000 Michael Feindt, Moderne Experimentalphysik III, Vorlesung 8
( )
df
f
f
x q x F
q x x
q
x
25 ) 18
( )
( )
( = ⋅ + ≈
⋅ ∑ G ( x , Q
2) = x ⋅ g ( x )
KT2012 Johannes Blümer IKP in KCETA
Viele Teilchen – einfache Erklärung?
!19
Elektron Positron Myon
Kerne Neutron Pion Kaon ... J/Psi ...
Proton; Nukleon
Leptonen
Hadronen
KT2012 Johannes Blümer IKP in KCETA
!20
The left-hand image shows the decay of a neutral kaon, captured the previous year, 1946. Being uncharged the neutral kaon leaves no track, but a
"V" of tracks appears when it decays into two lighter charged particles, each of which is a pion (just below the central bar towards right of the chamber).
The right-hand image shows the decay of a charged kaon into a muon and a neutrino. The kaon has come in at the top right of the chamber and the decay occurs where the track appears to bend to the left abruptly.
The track beyond this kink is due to the muon, which penetrates the bar across the chamber. The neutrino has no charge and so remains invisible in the detector - its presence is inferred from the imbalance in
momentum where the kink occurs.
http://www.particlephysics.ac.uk/news/picture-of-the-week/picture-archive/the-kaon-s-50th-anniversary.html
KT2012 Johannes Blümer IKP in KCETA
Hadronen
!21
Quarks in Hadronen
Hadronen = stark wechselwirkende Teilchen
Baryonen
"schwere"
qqq
halbzahliger Spin Fermionen
Mesonen
"leichte"
ganzzahliger Spin Bosonen
KIT-IEKP 6 00.00.0000
■ Experimenteller Befund: Anzahl der Baryonen - Anzahl der Antibaryonen ist bei jeder Reaktion konstant.
■ Def. Baryonenzahl: B = +1 für Baryonen B = -1 für Antibaryonen Baryonenzahlerhaltung: Σ B = konstant
Michael Feindt, Moderne Experimentalphysik III, Vorlesung 8
konstant
=
−
BB