particle physics phenomenology 9. total cross sections and...
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Particle Physics Phenomenology9. Total Cross Sections and Generator Physics
Torbjorn Sjostrand
Department of Astronomy and Theoretical PhysicsLund University
Solvegatan 14A, SE-223 62 Lund, Sweden
Lund, 24 March 2015
Units and naive cross sections
Natural size : length 1 fm = 10−15 m⇒ area 1 fm2 = 10−30 m2
Historically: 1 barn = 1 b = 10−24 cm2 = 10−28 m2
⇒ 1 mb = 10−3 b = 10−31 m2 = 0.1 fm2
Outdated, but recall that [L] = cm−2s−1.
Proton radius rp ≈ 0.7 fm⇒ area Ap ≈ πr2
p ≈ 1.5 fm2 → 1 fm2 since 2 of 3 dimensions.
Total hadronic cross section ≈ when two protons overlap ?
⇒ σpp ≈ π(2rp)2 ≈ 4 fm2 = 40 mb .
σQEDpp = ∞ since protons are charged,
but for pp → pp elastic scattering in θ → 0 limit ⇒ unmeasurable
Conventionally: σtotpp = σQCD
pp
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 2/63
Total cross section
13. Discussion
The result for the total hadronic cross section presented here, σtot = 95.35 ± 1.36 mb, can be com-pared to the value measured by TOTEM in the same LHC fill using a luminosity-dependent analysis,σtot = 98.6 ± 2.2 mb [11]. Assuming the uncertainties are uncorrelated, the difference between the AT-LAS and TOTEM values corresponds to 1.3σ. The uncertainty on the TOTEM result is dominated bythe luminosity uncertainty of ±4%, while the measurement reported here profits from a smaller luminosityuncertainty of only ±2.3%. In subsequent publications [16, 54] TOTEM has used the same data to performa luminosity-independent measurement of the total cross section using a simultaneous determination of elas-tic and inelastic event yields. In addition, TOTEM made a ρ-independent measurement without using theoptical theorem by summing directly the elastic and inelastic cross sections [16]. The three TOTEM resultsare consistent with one another.
The results presented here are compared in Fig. 19 to the result of TOTEM and are also compared withresults of experiments at lower energy [29] and with cosmic ray experiments [55–58]. The measured totalcross section is furthermore compared to the best fit to the energy evolution of the total cross section fromthe COMPETE Collaboration [26] assuming an energy dependence of ln2 s. The elastic measurement isin turn compared to a second order polynomial fit in ln s of the elastic cross sections. The value of σtot
reported here is two standard deviations below the COMPETE parameterization. Some other models prefera somewhat slower increase of the total cross section with energy, predicting values below 95 mb, and thusagree slightly better with the result reported here [59–61].
[GeV]s10 210 310 410
[mb]
σ
0
20
40
60
80
100
120
140
totσ
elσ
ATLASTOTEM
ppLower energy ppLower energy and cosmic ray
Cosmic raysCOMPETE RRpl2u
)s(2) + 1.42lns13.1 - 1.88ln(
Figure 19: Comparison of total and elastic cross-section measurements presented here with other published measurements [11,29, 55–58] and model predictions as function of the centre-of-mass energy.
33
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 3/63
Impact-parameter MPI unitarization
Here naive model — more sophisticated later
Assume Poissonian distribution of〈n(b)〉, i.e. average number of MPIat impact parameter b:
Pi (b) =〈n(b)〉
i !exp(−〈n(b)〉)
P0(b) = exp(−〈n(b)〉)P≥1(b) = 1− exp(−〈n(b)〉)
σMPI =
∫d2b (1− exp(−〈n(b)〉))
Increasing energy ⇒ more MPI:• Bigger: non-negligible to larger b• Blacker: P≥1(b) → 1 for small b• Edgier?: rim P≥1(b) ≈ 0.5 thinner
b
⟨n(b)⟩1− exp(−⟨n(b)⟩)
1
2
3
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 4/63
The optical theorem – 1
|ψout〉 = S |ψin〉 = (1 + iM) |ψin〉
Unitarity: conservation of probability:
S†S = 1 ⇒ (1− iM†)(1 + iM) = 1
⇒ i(M−M†) +M†M = 0 ⇒ 2 ImM = M†M
1− a a
y
ℓ
|ψin⟩ ∼ (1,0)
|ψout⟩ ∼ (x, y)
iM|ψin⟩ ∼ (−a, y)
x = 1− a
y =√
1− x2
=√
1− (1− a)2
=√
2a− a2
ℓ2 = (−a)2 + y2
= a2 + 2a− a2 = 2a
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 5/63
The optical theorem – 2
Introduce 2-body in-state |ab〉,and complete set of possible final states |n〉:
∑n |n〉〈n| = 1
2 Im〈ab|M|ab〉 = 〈ab|M†M|ab〉=
∑n
〈ab|M†|n〉〈n|M|ab〉
=∑n
|〈n|M|ab〉|2
Im 〈ab|M|ab〉 ∼ amplitude for forward (t = 0) elastic scattering,∑n |〈n|M|ab〉|2 ∼ total cross section to all possible final states,
⇒ dσel(s, t = 0)
dt∝ σ2
tot(s)
If you understand the elastic cross section you get the total for free.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 6/63
The optical theorem and unitarization
Eikonal function χ(b, s), for now real, gives scattering amplitude
σtot(s) ∼ Im f (s, 0) = 2
∫d2b
(1− e−χ(b,s)
)σel(s) ∼ |f (s, t)|2 =
∫d2b
(1− e−χ(b,s)
)2
σinel(s) = σtot(s)− σel(s) =
∫d2b
(1− e−2χ(b,s)
)Associate σMPI(s) = σinel(s) ⇒ 2χ(b, s) = 〈n(b)〉 or
χ(b, s) =1
2σMPI(s) A(b)
A(b) =
∫d2b′ G (b′) G (b− b′)∫
d2b A(b) =
∫d2(b− b′) G (b− b′)
∫d2b′ G (b′) = 1
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 7/63
The Pomeron
Amplitude for (forward) elastic scattering from total cross section:
p
p
p
p
=⇒
p
p
p
p
=⇒
p p
p p
IP
p
p
p
p
IP IP
introducing the Pomeron IP as shorthandfor the effective 2-gluon exchange.
Since p → p IP the Pomeron must havethe quantum numbers of the vacuum:0+ colour singlet.
Recall: elastic cross section requiressquaring one more time:
p
p
p
p
=⇒
p
p
p
p
=⇒
p p
p p
IP
p
p
p
p
IP IP
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 8/63
Field theory
Historically, the Pomeron precedes QCD and established quarks.Instead based on general properties of field theory;
Unitarity: optical theorem.
Crossing: if M(s, t, u) describes 1 + 2 → 3 + 4then M(t, s, u) describes 1 + 3 → 2 + 4and M(u, t, s) describes 1 + 4 → 3 + 2.
p
π−
∆0
n
π0
p
n
∆0
π+
π0
p
π0
∆0
π+
n
Analyticity: M analytic function of s, t, u⇒ poles, branch cuts, dispersion relations, . . .
Regge theory.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 9/63
Regge theory – 1
Start with elastic-scattering partial-wave series in s channel:
M(s, t) =∞∑
J=0
(2J + 1)MJ(s) PJ(cos θ)
where J is s-channel angular momentum,PJ Legendre polynomials, and
cos θ = 1 +2t
s − 4m2if m2
1 = m22 = m2
3 = m24 = 0 .
Cross to t-channel
M(s, t) =∞∑
J=0
(2J+1)MJ(t) PJ(cos θt) with cos θt = 1+2s
t − 4m2.
For s →∞, t fixed: cos θt → −∞:
PJ(cos θt) ∼ (cos θt)J ∼ sJ
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 10/63
Regge theory – 2
Gives divergent series
M(s, t) =∞∑
J=0
(2J + 1) sJ fJ(t)
so resum with analytic continuation,using J → α as complex variable.
Simple example: 1 + x + x2 + x3 + . . . badly divergent for x > 1,but resums to 1/(1− x), which is finite except in pole x = 1.
Result: if there exists a “trajectory” of particles α(t),i.e. straight line of poles corresponding to integer or half-integer α,
then M(s, t) ∼ f (t) sα(t)
and σtot ∼M(s, 0)/s ∼ sα(0)−1.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 11/63
Regge trajectories
Linear trajectories α(t) = α(0) + α′tboth in meson and baryon sector:
Most important is ρ trajectory with intercept α(0) ≈ 0.5.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 12/63
Why linear trajectory?
View a meson at rest as a stiffly rotating stringwith endpoint quarks moving at the speed of light
0 ≤ r ≤ d , v(r) = r/d , γ(r) = 1/√
1− r2/d2
m = 2
∫ d
0dr κγ(r) = 2κd
∫ 1
0
dy√1− y2
= πκd
L = 2
∫ d
0dr r κv(r)γ(r) = 2κd2
∫ 1
0
y2 dy√1− y2
=π
2κd2 =
m2
2πκ
α′ =dαdt
=dL
dm2=
1
2πκ
Data α′ ≈ 0.9 GeV−2 gives κ ≈ 0.9 GeV/fm.
Linear Regge trajectories and linear confinement are closely related!
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 13/63
The Reggeon(s)
The ρ trajectory hasα(0) ≈ 0.5⇒ σtot ≈ s−0.5:required for low energiesbut not enough.
σpptot ≈ 21.7 s0.08 + 98.4 s−0.45
σpptot ≈ 21.7 s0.08 + 56.1 s−0.45
Pomeron term “universal”,while Reggeon contributionsare process-dependent:pp only ρ0 exchange pp → ppwhile pp has pp → ppand pp → nn.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 14/63
The Pomeron trajectory
α(t) = α(0) + α′ t = 1 + ε+ α′ t.Critical Pomeron (original): ε = 0 ⇒ σtot constant.Supercritical Pomeron: ε > 0 ⇒ σtot rises.
Need a trajectory withintercept α(0) ≈ 1.08.
Consistent with spin-2glueball around m = 2 GeV,but mixing gg ↔ qqg ↔ qqleaves no clear glueball.
Excess number of neutralstates consistent with it,however.
Purist’s view: the Pomeron is not a physical state,only a field theoretical construction.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 15/63
Trajectories and PDFs
The Regge limit, t fixed and s →∞ corresponds to x → 0.
p
π−
∆0
n
π0
p
n
∆0
π+
π0
p
π0
∆0
π+
n
p
p
ρ0
p
p
p
p
p
p
IP
related to exchange ofvalence quarks
σtot,Reggeon ∝ 1/√
s
⇒ qval ∝ 1/√
x
or more properly
q(x) = Nq(1− x)nq
√x
p
π−
∆0
n
π0
p
n
∆0
π+
π0
p
π0
∆0
π+
n
p
p
ρ0
p
p
p
p
p
p
IP
related to exchange ofgluons (and sea quarks)
σtot,Pomeron ∝ 1/s1.08
⇒ g ∝ 1/x1.08
or more properly
g(x) = Ng(1− x)ng
x1.08
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 16/63
Elastic scattering
Recall M(s, t) ≈ C f (t) sα(t), with α(t) ≈ α(0) + α′t.Here f (t) form factor, amplitude that hadrons do not break up.Simple ansatz f (t) ≈ exp(bAt) exp(bBt) for A + B → A + B.Dimensional consistency s → s/s0 = s;e.g. with s0 = 1/α′ = 4 GeV2.
M(s, t) ≈ i C exp(bAt) exp(bBt) sα(0)+α′t
= i C sα(0) exp((bA + bB + α′ ln s )t
)Bel = 2 (bA + bB + α′ ln s)
σtot =ImM(s, 0)
s= C sα(0)
dσel =|M(s, t)|2
2s
dt
8πs=|M(s, 0)|2 exp(Bel t)
s2
dt
16π
= σ2tot exp(Bel t)
dt
16π
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 17/63
The ρ parameter
What if M not purely imaginary? Introduce
ρ(s) =ReM(s, 0)
ImM(s, 0)⇒ |M(s, 0)|2 = (1 + ρ2(s)) ImM(s, 0)
101 102 103 104
2
5
102
2Σ!tot!s" #mb$
s GeV
101 102 103 104
"0.3
"0.2
"0.1
0.0
0.1
0.2
0.3Ρ!!s,0"
pp
pp
s GeV
ρ2(s) ≈ 0.04 at LHC⇒ often neglected
dσel(s)
dt= (1 + ρ2(s))
σ2tot(s)
16πexp(Bel(s) t)
σel(s) = (1 + ρ2(s))σ2
tot(s)
16π Bel(s)Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 18/63
The differential elastic cross section – 1
]2 [GeV-t
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
]2 [m
b/G
eVtd/
elσd
1
10
210
310
ATLAS
TOTEM
=7 TeVs
Nice exponentialat intermediate |t| values.
ISR:
More complicated structureat large |t| values:interference between contributingamplitudes, e.g. Reggeons.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 19/63
The differential elastic cross section – 2
[1] G. B. West and D. R. Yennie, Phys. Rev. 172 (1968) 1413.
dV/dt v |FC+H|2 = Coulomb + hadronic + “interference”
from QED
constrained by measured eB(t)
B(t) = b1t + b2t2 + … Nb = # parameters in exp.
Simplified West-Yennie (SWY) [1]: often used “standard”, only compatible with pure exponential amplitude & constant phase
Exclude Coulomb-hadronic interference with constant phase & constant exponential slope for hadronic amplitude (Nb= 1) at >7V using same data ruling out SWY approach
Evidence for non-exponential elastic proton-proton differential cross-section at low |t| and s = 8 TeV
Coulomb dominatesat small |t|:perfect luminometerif measurable.However: unknownrelative phase toordinary “nuclear”(=”QCD”)
Further: “perfect”exponential is model,not theory.Could haveB(t) = b1t+b2t
2+· · · .TOTEM observes∼ 1% deviations.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 20/63
The elastic slope
Bel = 2 (bA + bB + α′ ln s) = 9.2 + 0.5 ln(s/4) [GeV−2]undershoots at 7 TeV: 17.4 vs. data 19.8.
[GeV]s
210 310 410
]-2
[GeV
B
10
12
14
16
18
20
22ATLAS
TOTEM
TevatronSppS
RHICISR
)0
ss(2) + 0.037 ln
0ss)=12 - 0.22 ln(s(B
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 21/63
Parametrization comments
Common with c0 + c1 ln s + c2 ln2 s parametrizationsfor σtot(s), σel(s) and Bel(s), inspired by
Froissart−Martin bound : σtot(s) ≤π
m2π
ln2 s
but nowhere near saturation at LHC, so s0.08 also OK.
• Several Pomerons? Two-Pomeron models common!Higher intercept = “perturbative Pomeron” = QCD jets.
• Odderon: odd-parity exchange, could give σpptot(s) > σpp
tot(s).• Multiple Reggeon trajectories.
⇒ Quite complicated fits to data, see e.g.Review of Particle Physics, pp. 537 – 544 in 2014 edition.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 22/63
Cut Pomerons
Naively 1 IP ≈ 1 MPI interaction, but in p⊥ → 0 limit⇒ longitudinal hadronization, multiparticle productionso multiple exchanges possible just like several MPIs
p p
p p
=⇒
p p
p p
IP IP
Physical cut: final state in squared Feynman graph.
Only one physical cut, duplicated for easier drawings.Cut Pomeron: only one gluon line exchanged in physical finalstate, so coloured beam remnants and multiparticle production.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 23/63
Uncut Pomerons
Also need virtual corrections to compensate real Pomerons:
p p
p p
=⇒
p p
p p
IP IP
p p
p p
=⇒
p p
p p
IP IP
Uncut Pomeron: a Pomeron exchange that leaves no explicit tracein final state, just like loops in standard perturbation theory.Restores unitarity: Pcut + Puncut = 1;just like real and virtual singularities cancel for matrix elements:
Minor issue: p⊥ = 0, so not ordering variable, but rapidity OK.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 24/63
The triple Pomeron vertex
Gluon chains can split or fuse, giving diffraction:
p p
p p
=⇒
p p
p p
IP
IP IP
Develops into a whole “Feynman diagram” framework:
Pomeron propagator GIP(s, t) = i sα(t)−1.
βA(t) = βA(0) exp(bAt), A = p,n, π, . . .,strength of AAIP vertex and A form factor.
g3IP triple-Pomeron vertex.
(GIR(s, t) and gIRIRIP for Reggeons.)
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 25/63
Differential cross section expressions
totalA
B
elasticA
B
single diffractiveA
B
double diffractiveA
B
central diffractiveA
B
p
p
p
pIP IP
IP
σABtot = βA(0)βB(0) Im GIP(s/s0, 0)
dσABel
dt=
1
16πβ2
A(t)β2B(t) |GIP(s/s0, t)|2
dσAB→AXsd
dt dM2=
1
16πM2g3IP β
2A(t)βB(0)|GIP(s/M2, t)|2 Im G (M2/s0, 0)
dσAB→X1X2
dd
dt dM21 dM2
2
=1
16πM21 M2
2
g23IP βA(0)βB(0) |GIP(ss0/(M
21M2
2 ), t)|2
× Im G (M21/s0, 0) Im G (M2
2/s0, 0)
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 26/63
Event-type properties
Phase space for diffractivemasses and rapidity gapsroughly like dM2/M2 = dy ,i.e. flat in rapidity.
Extra divergence∫ ss0
dM2/M2 = log(s/s0)means σsd grow faster thatσtot, and σdd even faster.
Plausibly sequence ofincreasingly complicatedtopologies.
Bel(s) > Bsd(s,M2) >
Bdd(s,M21 ,M
22 )
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 27/63
Single diffractive kinematics
ξ =M2
X
s⇒ xp =
2Ep
Ecm= 1− ξ
d(log M2X ) =
dM2X
M2X
=dξξ
= d(log ξ)
∆ytot ≈ 2 log
((E + pz)p
mp
)= log
s
m2p
∆yX ≈ logM2
X
m2p
∆ygap ≈ ∆ytot −∆yX ≈ logs
M2X
= log1
ξ= − log ξ
Experimentally: spurious “false” gaps if ∆ygap ≤ 3 ⇒ ξ ≥ 0.05.Bsd ∼ 10 GeV−2 ⇒ 〈p2
⊥〉 ≈ 〈|t|〉 ≈ 0.1 GeV2.Ecm = 7 TeV⇒ 〈θ〉 ≈ 0.35/3500 = 10−4 so need Roman pots.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 28/63
Rise of diffractive cross section
Naive steep rise of all diffractive topologies problematic.Goulianos: rescale Pomeron flux by hand:
Aspen 13-20 Feb 2005 Diffraction @ Tevatron / LHC K. Goulianos 10
Unitarity problem:With factorizationand std pomeron fluxσSD exceeds σT at
Renormalization:normalize the pomeronflux to unity
Renormalization )(Mσξ)(t,f
dtdξσd 2
XpIPIP/pSD
2
−•=
KG, PLB 358 (1995) 379
TeV.2s ≈
1dtdξξ)(t,f0.1
ξIP/p
0
tmin
=∫ ∫−∞=
~10
εσ 2~ sSD
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 29/63
Cross section fractions
Schuler&Sjostrand 1993: patch up for finite asymptotic ratios:σpp [mb]
Ecm [GeV]
elastic
single diffractive (pX)
single diffractive (Xp)
double diffractive
non-diffractive
Fig. 1
σi/σtot
Ecm [GeV]
elastic
single diffractive
double diffractive
single+double diffractive
all diffractive (assumed)
non-diffractive
Fig. 2
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 30/63
Total unitarization
DTUJET/DPMJET/PHOJET: eikonalization of four components:i = s: soft Pomerons ⇔ normal nondiffractive exchangei = h: hard cross section ⇔ QCD jetsi = t: triple-Pomeron processes ⇔ single diffractioni = c : cut loops ⇔ double diffraction
χi (b, s) =σi (s)
8πBi (s)exp
(− b2
4Bi (s)
)with
∫2χi (b, s) d2b = σi (s)
σ(ns , nh, nt , nc , b, s) =(2χs)
ns
ns !
(2χh)nh
nh!
(2χt)nt
nt !
(2χc)nc
nc !
× exp
(−2∑
i
χi (b, s)
)Soft+hard interactions may overlay single/double diffractionand fill up rapidity gaps. ⇒ Diffraction killed for central collisionsbut survives for peripheral ones.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 31/63
Measured gap size
0 1 2 3 4 5 6 7 8
[mb]
F η∆/dσd
1
10
210 -1bµData L = 7.1 PYTHIA 6 ATLAS AMBT2BPYTHIA 8 4CPHOJET
ATLAS = 7 TeVs > 200 MeV
Tp
Fη∆0 1 2 3 4 5 6 7 8
MC
/Dat
a
1
1.5
PYTHIA 8 tune 4C has reduced diffraction, but not enough.Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 32/63
Gaps by subprocess
0 1 2 3 4 5 6 7 8
[mb]
F η∆/dσd
1
10
210 -1bµData L = 7.1 PYTHIA 8 4CNon-DiffractiveSingle DiffractiveDouble Diffractive
ATLAS = 7 TeVs > 200 MeV
Tp
Fη∆0 1 2 3 4 5 6 7 8
MC
/Dat
a
1
1.5
Non-diffractive fine, but wrong gap spectrum for diffraction.Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 33/63
Diffractive mass dependence
Cutξ
-810 -710 -610 -510 -410 -310
[mb]
Xξ d
Xξdσd
1 Cut
ξ∫
40
45
50
55
60
65
70
75
ATLAS = 7 TeVs
-1bµATLAS L = 7.1 -1bµATLAS L = 20
-1bµTOTEM L = 1.7 PYTHIA 6 ATLAS AMBT2B PYTHIA 8 4CPHOJET RMK
-1bµATLAS L = 7.1 -1bµATLAS L = 20
-1bµTOTEM L = 1.7 PYTHIA 6 ATLAS AMBT2B PYTHIA 8 4CPHOJET RMK
Need more low-mass enhancement than already in PYTHIA.Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 34/63
The Ingelman–Schlein model
Regge theory predicts/parametrizes rate of diffractive interactions,but does not tell what diffractive events look like.
Ingelman-Schlein (1984): Pomeron as hadron with partonic contentDiffractive event = (Pomeron flux) × (IPp collision)
pp → pX
IPp subcollision just like a pp one,with (semi)hard interaction, MPIs, ISR, FSR, beam remnants,only with a different IP PDF.
IP PDF mainly determined from HERA data.IP flux and IP PDF not separately determined.IP not real particle so not normalized to unit momentum sum (!?).
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 35/63
Multiplicity in diffractive events
0 5 10 15 20 25 30 35 40
Eve
nts
10
210
310
410
510
610
710
ATLAS
< 6Fη ∆ 4 < = 7 TeVs > 200 MeV
Tp
DataMC PYTHIA 6MC PYTHIA 8MC PHOJET
CN0 5 10 15 20 25 30 35 40
MC
/Dat
a
1
2
3
PYTHIA 6 lacks MPI, ISR, FSR in diffraction, so undershoots.Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 36/63
Hard diffraction
Diffractive events can contain high-p⊥ jets:
σ =
∫dxIP fIP/p(xIP, t)
∫dxi fi/IP(x ′i ,Q
2) dxj
∫fj/p(xj ,Q
2)
∫dσij(s)
with M2X = xIPs = ξs and s = x ′i xjM
2X = βxjM
2X ,
i.e. xi = xIPx ′i = ξβ.
fIP(xIP, t) ∼1
xIP⇒ dσ
dM2X
∼ 1
M2X
⇒ dσdygap
∼ constant
Many issues, e.g.:
1 imperfect factorizationfi/p(xIP, t, xi ,Q
2) = fIP/p(xIP, t) fi/IP(xi ,Q2)
2 poor knowledge of fIP/p(xIP, t) and fi/IP(xi ,Q2)
3 parameters of multiple interactions framework
4 multipomeron topologies, . . .
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 37/63
Non-universalityDiffractive dijets in Run I
H1 CDF
~8 ~8
~20
All hard-diffraction processes in Run I at √s=1.8 TeV are suppressed by factor ~8 relative to predictions based on HERA-measured PDFs.
8 EDS2013, Saariselca Hard Diffraction at CDF K. Goulianos
Diffractive dijetproduction.
HERA diffraction(flux and PDF)overpredictsTevatron oneby factor ∼ 8.
Could be explainedby MPI filling upand killing gaps(MPI not presentin DIS at HERA).
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 38/63
Central diffraction
Can apply Ingelman-Schleinalso to double diffractionor central diffraction:
Extreme case is exclusivecentral diffraction: noPomeron beam remnants.
pp
IP
p
pp→ pX
pp
IP
pp
IPpp→ pXp
Observed e.g. as exclusive χc or exclusive (?) jets:
27
EXCLUSIVE DijetÆ Excl. Higgs THEORY CALIBRATION
p
p _
JJ
Exclusive dijets
PRD 77, 052004 (2008)
EDS2013, Saariselca Hard Diffraction at CDF K. Goulianos Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 39/63
Central Higgs production (Mike Albrow)
Mike Albrow Diffraction in High Energy Collisions CERN June09 44
Central Exclusive Production of Higgs ?
Higgs has vacuum quantum numbers, vacuum has Higgs field. So pp ! p+H+p is possible in principle. Allowed states: Process is gg ! H through t-loop as usual with another g-exchange to cancel color and even leave ps in ground state. If we measure ps (4-vectors):
H
2CEN 1 2 3 4M ( )p p p p= + − −
+ - ±Even for H W W l νJJ → → !
Aim: to be limited by incoming beam momentum spread Realistic; ~ 2 GeV
p -4σ10 0.7 GeV
p≈ =
PC ++I J =0 evenJ >= 2 strongly suppressed at small |t|
t
( ) 2 GeV per eventHMσ ≈
Cross section calculations a topic of some debate.Exclusive bb production non-negligible background to H → bb.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 40/63
Generator physics
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 41/63
The generator landscape
specialized often best at given task, but need General-Purpose core
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 42/63
The bigger picture
Need standardized interfaces: see next!
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 43/63
PDG Particle Codes – 1
A. Fundamental objects
1 d 11 e− 21 g
2 u 12 νe 22 γ 32 Z′0
3 s 13 µ− 23 Z0 33 Z′′0
4 c 14 νµ 24 W+ 34 W′+
5 b 15 τ− 25 h0 35 H0 37 H+
6 t 16 ντ 36 A0 39 Graviton
add − sign for antiparticle, where appropriate
+ a wide range of exotica, e.g.SUSY 1000021 gTechnicolor 3000113 ρTC
compositeness 4000005 b∗
extra dimensions 5100039 G∗raviton
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 44/63
PDG Particle Codes – 2
B. Mesons100 |q1|+ 10 |q2|+ (2s + 1) with |q1| ≥ |q2|particle if “heaviest” quark u, s, c, b; else antiparticle
111 π0 311 K0 130 K0L 421 D0
211 π+ 321 K+ 310 K0S 431 D+
s
221 η0 331 η′0 411 D+ 443 J/ψ
C. Baryons1000 q1 + 100 q2 + 10 q3 + (2s + 1)with q1 ≥ q2 ≥ q3, or Λ-like q1 ≥ q3 ≥ q2
2112 n 3122 Λ0 2224 ∆++ 3214 Σ∗0
2212 p 3212 Σ0 1114 ∆− 3334 Ω−
D. Diquarks1000 q1 + 100 q2 + (2s + 1) with q1 ≥ q2
1103 uu1 2101 ud0 2103 ud3 2203 dd3
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 45/63
Les Houches Accord
Context: ME generator → PS/UE/hadronization
Transfer info on processes, cross sections, parton-leven events, . . .
LHA: Les Houches Accord (2001)formulated in terms of two Fortran commonblocks1) overall run information for initialization2) parton configuration one event at a time
LHEF: Les Houches Event File(s) (2006)same information, but stored as a single plaintext file.+ language-independent, cleaner separation, reuse same file− large files if many events
LHEF3: Les Houches Event File(s) (2014)backwards compatible, but adds further information,notably for matching/merging: event weights, event groups,. . .
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 46/63
Other interfaces
SLHA — SUSU Les Houches Accord: file with infoon SUSY or other BSM model (+top, Higgs, W/Z):parameters, masses, mixing matrices, branching ratios, . . . .Output from spectrum calculator, input to event generator.
LHAPDF: uniform interface to PDF parametrizations.LHAPDF5 drawback: in Fortran; bloated!LHAPDF6: in C++, still rather new
HepMC: output of complete generated events(intermediate stages and final state with hundreds of particles)for subsequent detector simulation or analysis
Binoth LHA: provide one-loop virtual corrections
FeynRules: input of Lagrangian and output of Feynman rules,to be used by matrix element generators
ProMC: event record in highly compressed format
. . .
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 47/63
MCnet
? “Trade Union” of (QCD) Event Generator developers ?Main projects: HERWIG, SHERPA, PYTHIA and MadGraph.
Also smaller ones: ARIADNE, DIPSY, HEJ, VINCIA, . . . ,RIVET generator validation and PROFESSOR tuning.
(Manchester, CERN, Durham, Gottingen, Karlsruhe, Louvain,Lund, UC London, + associated).
? Funded as EU Marie Curie training network ?2007–2010 and 2013–2016
Money for postdocs, graduate students, short-term visits.
? Annual Monte Carlo school: 30 Aug – 4 Sep, Spa, Belgium ?+ Lectures on QCD & Generators at many other schools +
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 48/63
The workhorses: what are the differences?
HERWIG, PYTHIA and SHERPA offer convenient frameworksfor LHC physics studies, but with slightly different emphasis:
PYTHIA (successor to JETSET, begun in 1978):• originated in hadronization studies: the Lund string• leading in development of MPI for MB/UE• pragmatic attitude to showers & matching
HERWIG (successor to EARWIG, begun in 1984):• originated in coherent-shower studies (angular ordering)• cluster hadronization & underlying event pragmatic add-on• spin correlations in decays; MatchBox match&merge
SHERPA (APACIC++/AMEGIC++, begun in 2000):• own matrix-element calculator/generator• extensive machinery for matching and merging• hadronization & min-bias physics lower priority
PYTHIA & HERWIG originally in Fortran, now all C++
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 49/63
Other special-purpose programs – examples
ARIADNE: dipole shower.
DIPSY: dipole-based picture of pp, pA and AA collisions.
HEJ: BFKL-inspired approximate multijet matrix elements.
VINCIA: antenna shower.
EVTGEN: B decays, with detailed handling of interference,polarization and CP-violation effects.
TAUOLA, τ decays, with polarization effects (correlated inpairs).
PHOTOS: photon emission in decays of (electroweak)resonances or hadrons.
. . .
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 50/63
Matrix element generators – examples (Frank Krauss)
Now: MadGraph5 aMC@NLO first truly general-purpose NLO.Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 51/63
RIVET (Hendrik Hoeth)
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 52/63
PROFESSOR – 1 (Hendrik Hoeth)
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 53/63
PROFESSOR – 2 (Hendrik Hoeth)
Requires O(n2) points at random inside allowed parameter volume
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 54/63
PROFESSOR – 3 (Hendrik Hoeth)
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 55/63
MCPLOTS
Repository of comparisons between various tunes and data,mainly based on RIVET for data analysis,see http://mcplots.cern.ch/.Part of the LHC@home 2.0 platform for home computerparticipation.
η-2 0 2
η/d
ch
dNev
1/N
2
3
4
5
6
7
8ATLASPythia 8Pythia 8 (Tune 2C)Pythia 8 (Tune 2M)Pythia 8 (Tune 4C)
7000 GeV pp Minimum Bias
mcp
lots
.cer
n.ch
Pythia 8.153
ATLAS_2010_S8918562
> 0.1 GeV/c)T
> 2, pch
Distribution (NηCharged Particle
-2 0 20.5
1
1.5Ratio to ATLAS
η-2 0 2
η/d
ch
dNev
1/N
1
1.5
2
2.5
3
3.5
ATLASPythia 8Pythia 8 (Tune 2C)Pythia 8 (Tune 2M)Pythia 8 (Tune 4C)
7000 GeV pp Minimum Bias
mcp
lots
.cer
n.ch
Pythia 8.153
ATLAS_2010_S8918562
> 0.5 GeV/c)T
> 1, pch
Distribution (NηCharged Particle
-2 0 20.5
1
1.5Ratio to ATLAS
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 56/63
Tuning (Peter Skands)
3 Kinds of Tuning
1. Fragmentation TuningNon-perturbative: hadronization modeling & parametersPerturbative: jet radiation, jet broadening, jet structure
2. Initial-State TuningNon-perturbative: PDFs, primordial kT
Perturbative: initial-state radiation, initial-nal interference
3. Underlying-Event & Min-Bias TuningNon-perturbative: Multi-parton PDFs, Color (re)connections, collective effects, impact parameter dependence, … Perturbative: Multi-parton interactions, rescattering
43
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 57/63
PYTHIA 8 tuning – 1
Tuning to e+e− closely related to p⊥-ordered PYTHIA 6.4;done by Rivet+Professor (H. Hoeth).Tunes 2C and 2M done “by hand” (using Rivet, but not Professor)to Tevatron MB+UE data (R. Corke):
with comparably good description as old PYTHIA 6 tunes.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 58/63
PYTHIA 8 tuning – 2
Tune 2C applied to LHC data does not do so good:
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 59/63
PYTHIA 8 tuning – 3
Tune 4C dampens diffractive cross section and uses LHC data:
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 60/63
PYTHIA 8 tuning – 4
. . . but at the expense of Tevatron agreement:
so problem to get energy dependence right with p⊥0 ∝ sε.
(Possibly also some systematics offset Tevatron vs. LHC?)
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 61/63
PYTHIA 8 tuning – 5
Current default: Monash 2013 (Skands et al.):complete retune from e+e− up.Typically minor but consistent improvements relative to 4C,but sometimes more significant:
0 50 100
)Ch
Prob
(n-710
-610
-510
-410
-310
-210
-110
1|<2.5)η>0.5, |
T 1, p≥
ChChg. Mult. (n
Pythia 8.185Data from New J.Phys. 13 (2011) 053033
ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)
bins/N25%χ
0.0±2.7 0.0±2.7 0.0±9.6
V I N
C I
A R
O O
T
pp 7000 GeV
Chn0 50 100
Theo
ry/D
ata
0.60.8
11.21.4
0 5 10 15 20
T/d
pCh
dn
T)/pπ
/(2Ch
1/n
-810
-710
-610
-510
-410
-310
-210
-110
1
10|<2.5)η>0.5, |
T 1, p≥
Ch (n
Tp
Pythia 8.185Data from New J.Phys. 13 (2011) 053033
ATLAS PY8 (Monash 13)PY8 (4C)PY8 (2C)
bins/N25%χ
0.0±1.5 0.0±0.8 0.1±5.8
V I N
C I
A R
O O
T
pp 7000 GeV
[GeV]T
p0 5 10 15 20
Theo
ry/D
ata
0.60.8
11.21.4
0 50 100 150 200
)Ch
Prob
(n
-610
-510
-410
-310
-210
-110
1|<2.5)η>0.1, |
T 2, p≥
ChSoft Chg. Mult. (n
Pythia 8.185Data from New J.Phys. 13 (2011) 053033
ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)
bins/N25%χ
0.0±4.5 0.0±4.9 0.1±19.7
V I N
C I
A R
O O
T
pp 7000 GeV
Chn0 50 100 150 200
Theo
ry/D
ata
0.60.8
11.21.4
0 5 10 15 20
T/d
pCh
dn
T)/pπ
/(2Ch
1/n
-910
-710
-510
-310
-110
10|<2.5)η>0.1, |
T 2, p≥
Ch (n
Tp
Pythia 8.185Data from New J.Phys. 13 (2011) 053033
ATLASPY8 (Monash 13)PY8 (4C)PY8 (2C)
bins/N25%
χ
0.0±4.3 0.1±7.3
0.2±15.5
V I N
C I
A R
O O
T
pp 7000 GeV
[GeV]T
p0 5 10 15 20
Theo
ry/D
ata
0.60.8
11.21.4
Figure 18: Min-bias pp collisions at 7 TeV. Charged-multiplicity and p? distributions, with standard(top row) and soft (bottom row) fiducial cuts, compared to ATLAS data [91].
28
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 62/63
PYTHIA 8 tuning – 6
Currently 32 tunes available:
6 internal MB+UE tunes, leading up to 4C and 4Cx.
8 ATLAS MB or UE tunes, based on 4C or 4Cx.
2 CMS UE tunes based on 4C.
1 Monash 2013 tune.
14 ATLAS A14 UE tunes based on Monash 2013,whereof 4 central with different PDF sets,and 2× 5 eigentune variations up/down.
1 CMS UE tune based on Monash 2013.
To note:
Even ambitious tunes, like ATLAS A14, with ∼ 10 parametersin Professor approach, start from “by hand” tunes.
Split into UE and MB tunes mainly by user community;physics conflict beyond reasonable levels not established.
Torbjorn Sjostrand PPP 9: Total Cross Sections and Generator Physics slide 63/63