Basics of QCD Lecture 1: the core ingredients - ICTP … · Basics of QCD Lecture 1: the core...
Transcript of Basics of QCD Lecture 1: the core ingredients - ICTP … · Basics of QCD Lecture 1: the core...
Basics of QCDLecture 1: the core ingredients
Gavin Salam
CERN Theory Unit
ICTP–SAIFR school on QCD and LHC physicsJuly 2015, Sao Paulo, Brazil
QCD[What is QCD]
QUANTUM CHROMODYNAMICS
The theory of quarks, gluons and their interactions
It’s central to allmodern colliders.
(And QCD is whatwe’re made of)
Gavin Salam (CERN) QCD Basics 1 2 / 24
QCD predictions v. data for many processes[What is QCD]
∫L dt
[fb−1] Reference
ts−chantotal
95% CL upper limit 0.7 ATLAS-CONF-2011-11895% CL upper limit 20.3 arXiv:1410.0647 [hep-ex]
W±W±jj EWKfiducial
20.3 PRL 113, 141803 (2014)
Wγγfiducial, njet=0 20.3 arXiv:1503.03243 [hep-ex]
H→γγfiducial
20.3 Preliminary
Zjj EWKfiducial
20.3 JHEP 04, 031 (2014)
ttγfiducial
4.6 arXiv:1502.00586 [hep-ex]
ttZtotal
95% CL upper limit 4.7 ATLAS-CONF-2012-126
20.3 ATLAS-CONF-2014-038
ttWtotal
20.3 ATLAS-CONF-2014-038
Zγfiducial
4.6 PRD 87, 112003 (2013)arXiv:1407.1618 [hep-ph]
WW+WZfiducial
4.6 JHEP 01, 049 (2015)
Wγfiducial
4.6 PRD 87, 112003 (2013)arXiv:1407.1618 [hep-ph]
ZZtotal
4.6 JHEP 03, 128 (2013)
20.3 ATLAS-CONF-2013-020
WZtotal
4.6 EPJC 72, 2173 (2012)
13.0 ATLAS-CONF-2013-021
Wttotal
2.0 PLB 716, 142-159 (2012)
20.3 ATLAS-CONF-2013-100
γγfiducial
4.9 JHEP 01, 086 (2013)
WWtotal
4.6 PRD 87, 112001 (2013)
20.3 ATLAS-CONF-2014-033
tt−chantotal
4.6 PRD 90, 112006 (2014)
20.3 ATLAS-CONF-2014-007
ttfiducial
4.6 Eur. Phys. J. C 74: 3109 (2014)
20.3 Eur. Phys. J. C 74: 3109 (2014)
Ztotal
0.035 PRD 85, 072004 (2012)
Wtotal
0.035 PRD 85, 072004 (2012)
Dijets R=0.4|y |<3.0, y∗<3.0 4.5 JHEP 05, 059 (2014)0.3 < mjj < 5 TeV
Jets R=0.4|y |<3.0 4.5 arXiv:1410.8857 [hep-ex]0.1 < pT < 2 TeV
pptotal 8×10−8 Nucl. Phys. B, 486-548 (2014)
σ [pb]10−3 10−2 10−1 1 101 102 103 104 105 106 1011
observed/theory0.5 1 1.5 2
LHC pp√s = 7 TeV
TheoryObservedstatstat+syst
LHC pp√s = 8 TeV
Theory
Observedstatstat+syst
Standard Model Production Cross Section Measurements Status: March 2015
ATLAS Preliminary
Run 1√s = 7, 8 TeV
Gavin Salam (CERN) QCD Basics 1 3 / 24
QCD for Higgs physics[What is QCD]
QCD is especially relevant inorder to deduce information
about the Higgs boson.
[cf. lectures by Andre Sznajder& Claude Duhr]
Gavin Salam (CERN) QCD Basics 1 4 / 24
QCD for Higgs physics[What is QCD]
QCD is especially relevant inorder to deduce information
about the Higgs boson.
[cf. lectures by Andre Sznajder& Claude Duhr]
) µSignal strength (
2− 0 2 4
ATLASIndividual analysis
-1 = 7 TeV, 4.5-4.7 fbs
-1 = 8 TeV, 20.3 fbs
0.27-
0.27+ = 1.17µOverall:
0.38-
0.38+ = 1.32µggF:
0.7-
0.7+ = 0.8µVBF:
1.6-
1.6+ = 1.0µWH:
0.1-
3.7+ = 0.1µZH:
γγ →H 125.4
125.4
125.4
125.4
125.4
0.33-
0.40+ = 1.44µOverall:
0.4-
0.5+ = 1.7µggF+ttH:
0.9-
1.6+ = 0.3µVBF+VH:
ZZ*→H 125.36
125.36
125.36
0.21-
0.24+ = 1.16µOverall:
0.26-
0.29+ = 0.98µggF:
0.47-
0.55+ = 1.28µVBF:
1.3-
1.6+ = 3.0µVH:
WW*→H 125.36
125.36
125.36
125.36
0.37-
0.43+ = 1.43µOverall:
1.2-
1.5+ = 2.0µggF:
0.54-
0.59+ = 1.24µVBF+VH:
ττ →H 125.36
125.36
125.36
0.40-
0.40+ = 0.52µOverall:
0.61-
0.65+ = 1.11µWH:
0.49-
0.52+ = 0.05µZH:
b Vb→VH 125.36
125
125
3.7-
3.7+ = -0.7µOverall: µµ →H 125.5
4.3-
4.5+ = 2.7µOverall: γ Z→H 125.5
1.1-
1.1+ = 1.5µ: bb
1.2-
1.4+ = 2.1µMultilepton:
1.75-
2.62+ = 1.3µ: γγ
ttH125
125
125.4
(GeV)Hm
Input measurements
µ on σ 1±
Gavin Salam (CERN) QCD Basics 1 4 / 24
QCD and searches for new physics[What is QCD]
Identification and/or exclusion ofpotential new physics relies indiverse ways on a QCD-basedunderstanding of signals and
backgrounds.
Search for stop squarks
[GeV]missT
pE
vent
s / 5
0 G
eV0
20
40
60
80
100
120
140Data
+Xhadrτ →/Wtt+Xµ e,→/Wtt
νν→Z (500, 100)0χ∼ t→t~
(650, 50)0χ∼ t→t~
CMS
(8 TeV)-119.4 fb
[GeV]missT
p200 250 300 350 400 450 500D
ata
Dat
a -
MC
-2-1012
Gavin Salam (CERN) QCD Basics 1 5 / 24
QCD and searches for new physics[What is QCD]
Mass scales [GeV]0 200 400 600 800 1000 1200 1400 1600 1800
233'λ µ tbt→
Rt~
233λt ντµ →
Rt~ 123
λt ντµ → R
t~
122λt νeµ →
Rt~
112''λ qqqq →
Rq~ 233
'λ µ qbt→ q~
231'λ µ qbt→ q
~ 233λ ν qll→ q
~123
λ ν qll→ q~
122λ ν qll→ q
~ 112''λ qqqq → g
~323
''λ tbs → g~ 112
''λ qqq → g~
113/223''λ qqb → g
~ 233'λ µ qbt→ g
~231'λ µ qbt→ g
~233
λ ν qll→ g~ 123
λ ν qll→ g~
122λ ν qll→ g
~
0χ∼ l → l~
0
χ∼ 0
χ∼ν τττ → ±χ∼ 2
0χ∼
0
χ∼ 0
χ∼ν τ ll→ ±χ∼ 2
0χ∼
0χ∼
0χ∼ H W →
2
0χ∼ ±χ∼
0χ∼
0χ∼ H Z →
2
0χ∼
2
0χ∼
0χ∼
0χ∼ W Z →
2
0χ∼ ±χ∼
0χ∼
0χ∼ Z Z →
2
0χ∼
2
0χ∼
0χ∼
0χ∼νν-l
+ l→
-χ∼
+χ∼
0
χ∼ 0
χ∼ν lll → ±χ∼ 2
0χ∼
0χ∼ bZ → b
~
0χ∼ tW → b
~
0χ∼ b → b
~
) H 1
0χ∼ t →
1t~
(→ 2
t~
) Z 1
0χ∼ t →
1t~
(→ 2
t~
H G)→ 0
χ∼(0
χ∼ t b → t~
)0
χ∼ W→ +
χ∼ b(→ t~
0χ∼ t → t
~
0χ∼ q → q
~
))0
χ∼ W→ ±
χ∼ t(→ b~
b(→ g~
)0
χ∼ W→±
χ∼ qq(→ g~
)0
χ∼ t→ t~
t(→ g~
0χ∼ tt → g
~
0χ∼ bb → g
~
0χ∼ qq → g
~
SUS-13-006 L=19.5 /fb
SUS-13-008 SUS-13-013 L=19.5 /fb
SUS-13-011 L=19.5 /fbx = 0.25 x = 0.50
x = 0.75
SUS-14-002 L=19.5 /fb
SUS-13-006 L=19.5 /fbx = 0.05
x = 0.50x = 0.95
SUS-13-006 L=19.5 /fb
SUS-12-027 L=9.2 /fb
SUS-13-007 SUS-13-013 L=19.4 19.5 /fb
SUS-12-027 L=9.2 /fb
SUS 13-019 L=19.5 /fb
SUS-14-002 L=19.5 /fb
SUS-12-027 L=9.2 /fbSUS-13-003 L=19.5 9.2 /fb
SUS-13-006 L=19.5 /fb
SUS-12-027 L=9.2 /fb
EXO-12-049 L=19.5 /fb
SUS-14-011 L=19.5 /fb
SUS-12-027 L=9.2 /fb
SUS-13-008 L=19.5 /fb
SUS-12-027 L=9.2 /fb
EXO-12-049 L=19.5 /fb
SUS-12-027 L=9.2 /fb
SUS-12-027 L=9.2 /fb
SUS-13-024 SUS-13-004 L=19.5 /fb
SUS-13-003 L=19.5 /fb
SUS-12-027 L=9.2 /fb
SUS-13-019 L=19.5 /fb
SUS-13-018 L=19.4 /fb
SUS-13-014 L=19.5 /fb
SUS-14-011 SUS-13-019 L=19.3 19.5 /fb
SUS-13-008 SUS-13-013 L=19.5 /fb
SUS-13-024 SUS-13-004 L=19.5 /fb
SUS-13-013 L=19.5 /fb x = 0.20x = 0.50
SUS-12-027 L=9.2 /fb
SUS-13-003 L=19.5 9.2 /fb
SUS-12-027 L=9.2 /fb
SUS-13-008 SUS-13-013 L=19.5 /fb
SUS-12-027 L=9.2 /fb
SUS-14-002 L=19.5 /fb
SUS-12-027 L=9.2 /fb
SUS-13-013 L=19.5 /fb
SUS-13-006 L=19.5 /fb x = 0.05x = 0.50x = 0.95
SUS-13-006 L=19.5 /fb
RP
Vgl
uino
pro
duct
ion
squa
rkst
opsb
otto
mE
WK
gau
gino
ssl
epto
n
Summary of CMS SUSY Results* in SMS framework
CMS Preliminary
m(mother)-m(LSP)=200 GeV m(LSP)=0 GeV
ICHEP 2014
lspm⋅+(1-x)
motherm⋅ = xintermediatem
For decays with intermediate mass,
Only a selection of available mass limits*Observed limits, theory uncertainties not included
Probe *up to* the quoted mass limit
Gavin Salam (CERN) QCD Basics 1 6 / 24
Aims of the course[What is QCD]
The school will cover many aspects of QCD, from theadvanced calculation techniques to the experimental
consequences.
This course:
A reminder of what QCD is
A few core equations & concepts(running coupling, collider cross sectionsinfrared divergences and infrared safety)
More depth on topics not covered in other lectures(parton distribution functions, jets)
Gavin Salam (CERN) QCD Basics 1 7 / 24
The ingredients of QCD[What is QCD]
I Quarks (and anti-quarks): they come in 3 colours
I Gluons: a bit like photons in QEDBut there are 8 of them, and they’re colour charged
I And a coupling, αs, that’s not so small and runs fastAt LHC, in the range 0.08(@ 5 TeV) to O (1)(@ 0.5 GeV)
Gavin Salam (CERN) QCD Basics 1 8 / 24
Lagrangian + colour[What is QCD]
Quarks — 3 colours: ψa =
ψ1
ψ2
ψ3
Quark part of Lagrangian:
Lq = ψa(iγµ∂µδab − gsγµtCabAC
µ −m)ψb
SU(3) local gauge symmetry ↔ 8 (= 32 − 1) generators t1ab . . . t
8ab
corresponding to 8 gluons A1µ . . .A8
µ.
A representation is: tA = 12λ
A,
λ1 =
0 1 01 0 00 0 0
, λ2 =
0 −i 0i 0 00 0 0
, λ3 =
1 0 00 −1 00 0 0
, λ4 =
0 0 10 0 01 0 0
,
λ5 =
0 0 −i0 0 0i 0 0
, λ6 =
0 0 00 0 10 1 0
, λ7 =
0 0 00 0 −i0 i 0
, λ8 =
1√3
0 0
0 1√3
0
0 0 −2√3
,
Gavin Salam (CERN) QCD Basics 1 9 / 24
Let’s write down QCD in full detail
(There’s a lot to absorb here — but it should become morepalatable as we return to individual elements later)
Lagrangian + colour[What is QCD]
Quarks — 3 colours: ψa =
ψ1
ψ2
ψ3
Quark part of Lagrangian:
Lq = ψa(iγµ∂µδab − gsγµtCabAC
µ −m)ψb
SU(3) local gauge symmetry ↔ 8 (= 32 − 1) generators t1ab . . . t
8ab
corresponding to 8 gluons A1µ . . .A8
µ.
A representation is: tA = 12λ
A,
λ1 =
0 1 01 0 00 0 0
, λ2 =
0 −i 0i 0 00 0 0
, λ3 =
1 0 00 −1 00 0 0
, λ4 =
0 0 10 0 01 0 0
,
λ5 =
0 0 −i0 0 0i 0 0
, λ6 =
0 0 00 0 10 1 0
, λ7 =
0 0 00 0 −i0 i 0
, λ8 =
1√3
0 0
0 1√3
0
0 0 −2√3
,
Gavin Salam (CERN) QCD Basics 1 9 / 24
Lagrangian + colour[What is QCD]
Quarks — 3 colours: ψa =
ψ1
ψ2
ψ3
Quark part of Lagrangian:
Lq = ψa(iγµ∂µδab − gsγµtCabAC
µ −m)ψb
SU(3) local gauge symmetry ↔ 8 (= 32 − 1) generators t1ab . . . t
8ab
corresponding to 8 gluons A1µ . . .A8
µ.
A representation is: tA = 12λ
A,
λ1 =
0 1 01 0 00 0 0
, λ2 =
0 −i 0i 0 00 0 0
, λ3 =
1 0 00 −1 00 0 0
, λ4 =
0 0 10 0 01 0 0
,
λ5 =
0 0 −i0 0 0i 0 0
, λ6 =
0 0 00 0 10 1 0
, λ7 =
0 0 00 0 −i0 i 0
, λ8 =
1√3
0 0
0 1√3
0
0 0 −2√3
,
Gavin Salam (CERN) QCD Basics 1 9 / 24
Lagrangian: gluonic part[What is QCD]
Field tensor: FAµν = ∂µAA
ν − ∂νAAν − gs fABCAB
µACν [tA, tB ] = ifABC t
C
fABC are structure constants of SU(3) (antisymmetric in all indices —SU(2) equivalent was εABC ). Needed for gauge invariance of gluon part ofLagrangian:
LG = −1
4FµνA FAµν
Exercise
Consider gauge transformations
ψ → U(x)ψ , U(x) = e iuA(x)tA
How should the gluon field ACµ transform in order for Lq to be gague
invariant. Show that with the same transformations, LG is gague invariant.
Gavin Salam (CERN) QCD Basics 1 10 / 24
Lagrangian: gluonic part[What is QCD]
Field tensor: FAµν = ∂µAA
ν − ∂νAAν − gs fABCAB
µACν [tA, tB ] = ifABC t
C
fABC are structure constants of SU(3) (antisymmetric in all indices —SU(2) equivalent was εABC ). Needed for gauge invariance of gluon part ofLagrangian:
LG = −1
4FµνA FAµν
Exercise
Consider gauge transformations
ψ → U(x)ψ , U(x) = e iuA(x)tA
How should the gluon field ACµ transform in order for Lq to be gague
invariant. Show that with the same transformations, LG is gague invariant.
Gavin Salam (CERN) QCD Basics 1 10 / 24
Lagrangian: gluonic part[What is QCD]
Field tensor: FAµν = ∂µAA
ν − ∂νAAν − gs fABCAB
µACν [tA, tB ] = ifABC t
C
fABC are structure constants of SU(3) (antisymmetric in all indices —SU(2) equivalent was εABC ). Needed for gauge invariance of gluon part ofLagrangian:
LG = −1
4FµνA FAµν
Exercise
Consider gauge transformations
ψ → U(x)ψ , U(x) = e iuA(x)tA
How should the gluon field ACµ transform in order for Lq to be gague
invariant. Show that with the same transformations, LG is gague invariant.
Gavin Salam (CERN) QCD Basics 1 10 / 24
Perturbation theory[What is QCD]
[Perturbation theory]
Relies on idea of order-by-order expansion small coupling, αs � 1
αs + α2s︸︷︷︸
small
+ α3s︸︷︷︸
smaller
+ . . .︸︷︷︸negligible?
Interaction vertices of Feynman rules:A, µ
ba
−igstAbaγµ
A, µ
B, ν
C, ρ
p
q
r
−gs f ABC [(p − q)ρgµν
+(q − r)µgνρ
+(r − p)νgρµ]
B, ν
D, σ
C, ρ
A, µ
−ig2s f
XAC f XBD [gµνgρσ −gµσgνγ ] + (C , γ)↔
(D, ρ) + (B, ν)↔ (C , γ)
These expressions are fairly complex, so you reallydon’t want to have to deal with too many orders ofthem! i.e. αs had better be small. . .
[Zvi Bern will show you how to do things more easily!]
Gavin Salam (CERN) QCD Basics 1 11 / 24
What do Feynman rules mean physically?[What is QCD]
[Perturbation theory]
A, µ
b a
ψb(−igstAbaγµ)ψa
A, µ
b a
( 0 1 0 )
︸ ︷︷ ︸ψb
0 1 01 0 00 0 0
︸ ︷︷ ︸
t1ab
100
︸ ︷︷ ︸
ψa
A gluon emission repaints the quark colour.A gluon itself carries colour and anti-colour.
Gavin Salam (CERN) QCD Basics 1 12 / 24
What does “ggg” Feynman rule mean?[What is QCD]
[Perturbation theory]
A, µ
B, ν
C, ρ
p
q
r
−gs f ABC [(p − q)ρgµν
+(q − r)µgνρ
+(r − p)νgρµ]
A, µ
B, ν
C, ρ
p
q
r
A gluon emission also repaints the gluon colours.
Because a gluon carries colour + anti-colour, it emits ∼twice as strongly as a quark (just has colour)
Gavin Salam (CERN) QCD Basics 1 13 / 24
Quick guide to colour algebra[What is QCD]
[Perturbation theory]
Tr(tAtB) = TRδAB , TR = 1
2
A B
∑A tAabt
Abc = CF δac , CF =
N2c − 1
2Nc=
4
3a c
∑C ,D f ACD f BCD = CAδ
AB , CA = Nc = 3A B
tAabtAcd =
1
2δbcδad −
1
2Ncδabδcd (Fierz)
1
2 2N
−1
b a
c d
=
Nc ≡ number of colours = 3 for QCD
Gavin Salam (CERN) QCD Basics 1 14 / 24
Quick guide to colour algebra[What is QCD]
[Perturbation theory]
Tr(tAtB) = TRδAB , TR = 1
2
A B
∑A tAabt
Abc = CF δac , CF =
N2c − 1
2Nc=
4
3a c
∑C ,D f ACD f BCD = CAδ
AB , CA = Nc = 3A B
tAabtAcd =
1
2δbcδad −
1
2Ncδabδcd (Fierz)
1
2 2N
−1
b a
c d
=
Nc ≡ number of colours = 3 for QCD
Gavin Salam (CERN) QCD Basics 1 14 / 24
Quick guide to colour algebra[What is QCD]
[Perturbation theory]
Tr(tAtB) = TRδAB , TR = 1
2
A B
∑A tAabt
Abc = CF δac , CF =
N2c − 1
2Nc=
4
3a c
∑C ,D f ACD f BCD = CAδ
AB , CA = Nc = 3A B
tAabtAcd =
1
2δbcδad −
1
2Ncδabδcd (Fierz)
1
2 2N
−1
b a
c d
=
Nc ≡ number of colours = 3 for QCD
Gavin Salam (CERN) QCD Basics 1 14 / 24
Quick guide to colour algebra[What is QCD]
[Perturbation theory]
Tr(tAtB) = TRδAB , TR = 1
2
A B
∑A tAabt
Abc = CF δac , CF =
N2c − 1
2Nc=
4
3a c
∑C ,D f ACD f BCD = CAδ
AB , CA = Nc = 3A B
tAabtAcd =
1
2δbcδad −
1
2Ncδabδcd (Fierz)
1
2 2N
−1
b a
c d
=
Nc ≡ number of colours = 3 for QCD
Gavin Salam (CERN) QCD Basics 1 14 / 24
Exercise[What is QCD]
[Perturbation theory]
Use the Fierz identity (fourth line of previous slide) to derive the secondline.
Gavin Salam (CERN) QCD Basics 1 15 / 24
The running coupling[What is QCD]
[Running coupling]
All couplings run (QED, QCD, EW), i.e. they depend on the momentumscale (Q2) of your process.
The evolution equation for the QCD coupling, αs(Q2), is:
Q2 ∂αs
∂Q2= β(αs) , β(αs) = −α2
s (b0 + b1αs + b2α2s + . . .) ,
b0 =11CA − 2nf
12π, b1 =
17C 2A − 5CAnf − 3CFnf
24π2=
153− 19nf24π2
Note sign: Asymptotic Freedom, due to gluon to self-interaction
I At high scales Q, coupling becomes smallåquarks and gluons are almost free, interactions are weak
I At low scales, coupling becomes strongåquarks and gluons interact strongly — confined into hadrons
Perturbation theory fails.
Gavin Salam (CERN) QCD Basics 1 16 / 24
The running coupling[What is QCD]
[Running coupling]
All couplings run (QED, QCD, EW), i.e. they depend on the momentumscale (Q2) of your process.
The evolution equation for the QCD coupling, αs(Q2), is:
Q2 ∂αs
∂Q2= β(αs) , β(αs) = −α2
s (b0 + b1αs + b2α2s + . . .) ,
b0 =11CA − 2nf
12π, b1 =
17C 2A − 5CAnf − 3CFnf
24π2=
153− 19nf24π2
Note sign: Asymptotic Freedom, due to gluon to self-interaction
I At high scales Q, coupling becomes smallåquarks and gluons are almost free, interactions are weak
I At low scales, coupling becomes strongåquarks and gluons interact strongly — confined into hadrons
Perturbation theory fails.
Gavin Salam (CERN) QCD Basics 1 16 / 24
Running coupling (cont.)[What is QCD]
[Running coupling]
Solve Q2 ∂αs
∂Q2= −b0α
2s ⇒ αs(Q
2) =αs(Q
20 )
1 + b0αs(Q20 ) ln Q2
Q20
=1
b0 ln Q2
Λ2
Λ ' 0.2 GeV (aka ΛQCD) isthe fundamental scale of QCD,at which coupling blows up.
I Λ sets the scale for hadronmasses(NB: Λ not unambiguouslydefined wrt higher orders)
I Perturbative calculations validfor scales Q � Λ.
QCD αs(Mz) = 0.1185 ± 0.0006
Z pole fit
0.1
0.2
0.3
αs (Q)
1 10 100Q [GeV]
Heavy Quarkonia (NLO)
e+e– jets & shapes (res. NNLO)
DIS jets (NLO)
Sept. 2013
Lattice QCD (NNLO)
(N3LO)
τ decays (N3LO)
1000
pp –> jets (NLO)(–)
Gavin Salam (CERN) QCD Basics 1 17 / 24
Running coupling (cont.)[What is QCD]
[Running coupling]
Solve Q2 ∂αs
∂Q2= −b0α
2s ⇒ αs(Q
2) =αs(Q
20 )
1 + b0αs(Q20 ) ln Q2
Q20
=1
b0 ln Q2
Λ2
Λ ' 0.2 GeV (aka ΛQCD) isthe fundamental scale of QCD,at which coupling blows up.
I Λ sets the scale for hadronmasses(NB: Λ not unambiguouslydefined wrt higher orders)
I Perturbative calculations validfor scales Q � Λ.
QCD αs(Mz) = 0.1185 ± 0.0006
Z pole fit
0.1
0.2
0.3
αs (Q)
1 10 100Q [GeV]
Heavy Quarkonia (NLO)
e+e– jets & shapes (res. NNLO)
DIS jets (NLO)
Sept. 2013
Lattice QCD (NNLO)
(N3LO)
τ decays (N3LO)
1000
pp –> jets (NLO)(–)
Gavin Salam (CERN) QCD Basics 1 17 / 24
Nobel prize citation (annotated by Skands)[What is QCD]
[Running coupling]
Gavin Salam (CERN) QCD Basics 1 18 / 24
Exercise
There is a freedom in defining the “scheme” for αs. E.g.
αscheme-Bs = αscheme-A
s + cB(αscheme-As )2
where cB is some scheme-conversion coefficient.
The β-function coefficients, usually given in the so-calledMS renormalisation scheme, are known up to b3.
Which of the b0, b1, b2, etc. coefficients is modified if thescheme is changed?
Gavin Salam (CERN) QCD Basics 1 19 / 24
A dilemna[Basic methods]
QCD αs(Mz) = 0.1185 ± 0.0006
Z pole fit
0.1
0.2
0.3
αs (Q)
1 10 100Q [GeV]
Heavy Quarkonia (NLO)
e+e– jets & shapes (res. NNLO)
DIS jets (NLO)
Sept. 2013
Lattice QCD (NNLO)
(N3LO)
τ decays (N3LO)
1000
pp –> jets (NLO)(–)
I We want to investigate collisions athigh energies (∼ 100 GeV to fewTeV), where the coupling is small→ perturbative methods are thenatural choice
I But the LHC collides protons,m ' 0.94 GeV, which definitelyinvolve strong coupling physics
There is no escape from non-perturbative physics
Gavin Salam (CERN) QCD Basics 1 20 / 24
Lattice QCD[Basic methods]
[Lattice]
I Put all the quark and gluon fieldsof QCD on a 4D-lattice
NB: with imaginary time
I Figure out which fieldconfigurations are most likely (byMonte Carlo sampling).
I You’ve solved QCD
image credits: fdecomite [Flickr]
Gavin Salam (CERN) QCD Basics 1 21 / 24
Lattice hadron masses[Basic methods]
[Lattice]
Lattice QCD is great at cal-culation static properties of asingle hadron.
E.g. the hadron mass spec-trum
Durr et al ’08
Gavin Salam (CERN) QCD Basics 1 22 / 24
Lattice for LHC?[Basic methods]
[Lattice]
How big a lattice do you need for an LHC collision @ 14 TeV?
Lattice spacing:1
14 TeV∼ 10−5 fm
Lattice extent:
I non-perturbative dynamics for quark/hadron near rest takes place on
timescale t ∼ 1
0.5 GeV∼ 0.4 fm/c
I But quarks at LHC have effective boost factor ∼ 104
I So lattice extent should be ∼ 4000 fm
Total: need ∼ 4× 108 lattice units in each direction, or 3× 1034 nodes total.Plus clever tricks to deal with high particle multiplicity,
imaginary v. real time, etc.
Gavin Salam (CERN) QCD Basics 1 23 / 24
Neither lattice QCD nor perturbative QCD can offera full solution to using QCD at colliders
What the community has settled on is
1) factorisation of initial state non-perturbative problem
from
2) the “hard process,” calculated perturbatively
supplemented with
3) non-perturbative modelling of final-state hadronic-scale processes(“hadronisation”).
Gavin Salam (CERN) QCD Basics 1 24 / 24