particle physics phenomenology 9. total cross sections and...

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Outdated, but recall that [L] = cm−2s−1.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


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


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


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.


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


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


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.


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


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.


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.


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!


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.


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.


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


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


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.


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.


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


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.


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.


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.


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.)


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)


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 )


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.


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


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


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.


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 (!?).


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, . . .


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).


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.


Generator physics


The generator landscape

specialized often best at given task, but need General-Purpose core


The bigger picture

Need standardized interfaces: see next!


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


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


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,. . .


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

. . .


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 +


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++


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.

. . .


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)


PROFESSOR – 1 (Hendrik Hoeth)



Requires O(n2) points at random inside allowed parameter volume


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


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


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.



Tune 2C applied to LHC data does not do so good:



Tune 4C dampens diffractive cross section and uses LHC data:



. . . 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?)



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

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pp 7000 GeV

Chn0 50 100

Theo

ry/D

ata

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11.21.4

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pCh

dn

T)/pπ

/(2Ch

1/n

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-710

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1

10|<2.5)η>0.5, |

T 1, p≥

Ch (n

Tp


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

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pp 7000 GeV

[GeV]T

p0 5 10 15 20

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ata

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0 50 100 150 200

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Prob

(n

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-510

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T 2, p≥

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bins/N25%χ

0.0±4.5 0.0±4.9 0.1±19.7

V I N

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pp 7000 GeV

Chn0 50 100 150 200

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ry/D

ata

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T)/pπ

/(2Ch

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-510

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Ch (n

Tp



bins/N25%

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0.0±4.3 0.1±7.3

0.2±15.5

V I N

C I

A R

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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



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.


particle physics phenomenology 9. total cross sections and...

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