Cross sections and diffraction in PYTHIA 8 - Lunds universitethome.thep.lu.se/~torbjorn/talks/RasmussenMCnet16.pdf · lund university dept. of astronomy and theoretical physics Cross

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lund un i v er s i ty dept . o f a stronomy and theoret i ca l phy s i c s

Cross sections and di↵raction in PYTHIA 8

Christine O. Rasmussen

• Goals

• Regge theory intro

• Total and elastic cross sections

• Di↵raction cross sections

• Conclusion and outlookApril 2016

Slide 1/19


Goals

• Better description of the total and elastic cross sectionsat LHC energies(Pythia currently is too low)

• Better description of elastic di↵erential cross section(Pythia currently only exponential)

• Better description of di↵ractive (di↵erential) crosssections(none of the models available in Pythia currentlydescribes all aspects of data)

• Include possibility for producing truly hard QCD andelectroweak particles in di↵ractive events(only soft with small tail of hard QCD available inPythia before).See arXiv:1512.05525 [hep-ph].

Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016

Slide 2/19


Regge theory intro

Old-school scattering theory describing particle collisions,eg. pp elastic scattering.Can be described in a diagrammatic way, similar toFeynman diagrams in QFT.

pp pp

pp pp

,

p p

R

p p

pp pp

pp pp

,

p p

P

p p

We can construct propagators for X andvertex rules for Xp, XXX etc. (X = R,P).


Slide 3/19


Regge theory introNeglecting Couloumb scattering, amplitude forelastic scattering at lowest order is

p p

X

tp p

Ael = ⇠ F 2(t) · GX(ss0, t)

And the cross section

p p

X X

p p

�el ⇠ ⇠ F 4(t) · |GX(ss0, t)|2


Slide 4/19


Regge theory introThe amplitude for pp!anything is

p

p

A(pp ! X ) = X

p p

p p

�tot ⇠ ⇠

p p

X

p p

⇠ F 2(0)GX(ss0, 0)

Amplitudes and cross sections for various processes,eg. elastic, total and di↵ractive processes, can be constructedwith these form factors, propagators and vertices fromRegge theory, to various degrees of complexity.Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016

Slide 5/19


Total and elastic cross sections

• Old Donnachie-Landsho↵ parametrization does notdescribe measured cross sections at the LHC.

�DL, oldtot = X s↵P(0)�1 + Y s↵R(0)�1

• Pythia currently only includes simple exponential fallofin d�el

dt , and do not fully describe LHC data.

d�el

dt=

�2tot

16⇡exp(Belt)

• Various parametrizations of di↵erential elastic crosssection available from di↵erent authors.

• Two chosen: COMPETE parametrization from PDGsReview of particle physics 2014 (RPP), DL-basedparametrization from Appleby et.al. (ABMST).


Slide 6/19



AABMSTpp =

4X

i=1

Ai (s, t) + Aggg ARPPpp =

6X

i=1

F i+ + F i

�

• Hard P.• Soft P.• f2, a2 trajectory.

• ⇢,! trajectory.

• Triple-gluon.

• Froissaron (FH+ ).

• Maximal O (FMO� ).

• P, O poles (FP+ , FO

+ ).

• f2, a2 and ⇢,! trajectories(FR

+ ,FR� ).

• PP, RP, OP cuts(FPP

+ , FRP± , FOP

� ).

• Triple-gluon exchanges(N+, N�).


Slide 7/19



101 102 103 104 105ps (GeV)

0

50

100

150

200

�to

t(m

b)RPP pp

ABMST pp

DL pp

PDG pp data


Slide 8/19



101 102 103 104 105ps (GeV)

0

10

20

30

40

50

�el

(mb)

RPP pp

ABMST pp

SaS pp

PDG pp data


Slide 9/19



0 1 2 3 4 5

�t (GeV2)10�6

10�5

10�4

10�3

10�2

10�1

100

101

102

103d�

el/d

t(m

b/G

eV2 )

RPP pp

ABMST pp

SaS pp

pp data

ps = 23.5 GeV


Slide 10/19



0 1 2 3 4 5

�t (GeV2)10�6

10�5

10�4

10�3

10�2

10�1

100

101

102

103d�

el/d

t(m

b/G

eV2 )

RPP pp

ABMST pp

SaS pp

ps = 13 TeV


Slide 11/19


Di↵ractive cross sections

The single di↵ractive amplitude can be constucted similarly

p p

t

X

pX

ASD = �SD ⇠

p pX X

Xp p

and obtain

�SD ⇠ F 2(0)|GX(M2

X

s0, 0)|2 · g2

XXX · F 4(t)|GX(s

M2X

, t)|4

The fractional momentum loss of the proton is ⇠ =M2

Xs .


Slide 12/19



Default in Pythia: Schuler-Sjostrand parametrization (SaS)

d�2SD

dtd⇠=gPPP16⇡

�3pP⇠

exp(BSDt)FSD

where

�2pP =Xpp s

✏Pref

BSD(s) =2bp � 2↵0Pln(⇠)

FSD =(1 � ⇠)(1 +cresM2

res

M2res + ⇠ s

)

andpsref = 20 GeV, gPPP ' 0.318mb

1/2, bp = 2.3,cres = 2 and Mres = 2 GeV.Additional options available.


Slide 13/19



8− 6− 4−

) [m

b]cu

tξ(

σ

40

50

60

70

80

90 )cutξ(σ

Pythia 8.212Data from EPJC72(2012)1926, NatComm2(2011)463, EPL101(2013)21003

ATLAS (+TOTEM)MonashMonash DL

QCDMonash CR4CA14 NNPDF

bins/N25%χ

0.0±2.1 0.0±0.1 0.0±1.8 0.0±2.3 0.0±2.1

V I N

C I

A R

O O

T

pp 7000 GeV

)cut

(xi10

log8− 6− 4−

Theo

ry/D

ata

0.60.8

11.21.4


Slide 14/19



DataSaSDLMBRH1 Fit B

10�1

1

10 1

10 2

Rapidity gap size in h starting from h = ±4.9, pT > 200 MeV

ds

/d

Dh

F[m

b]

0 1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

DhF

MC

/Dat

a


Slide 14/19



New implementation: ABMST parametrizationMX > Mcut MX < Mcut

d�2SD

dtd⇠=gPPPs

✏P⇠↵P(0)�2↵P(t)

+gPPRs✏R⇠↵R(0)�2↵P(t)

+gRRPs✏P⇠↵P(0)�2↵R(t)

+gRRRs✏R⇠↵R(0)�2↵R(t)

+g2⇡⇡p

16⇡2

|t|(t � m2

⇡)2F 2(t)

· ⇠1�↵⇡(t)�⇡0p(s⇠)

d�2SD

dtd⇠=a(t, s)(⇠ � ⇠t)

2

+b(s, t)(⇠ � ⇠t)

�d�2HM(⇠c, t, s)

dtd⇠

⇠ � ⇠t⇠c � ⇠t

+exp(13.5(t + 0.05))

⇠·

4X

l=1

clml�l(s⇠ � m2

l )2 + (ml�l)2


Slide 15/19



10�8 10�7 10�6 10�5 10�4 10�3 10�2 10�1 100

�

101

102

103

104

105

106

107

108d�

SD/d

�(m

b)TotalLow massHigh massResonances

ps = 7 TeV


Slide 16/19



10�6 10�5 10�4 10�3 10�2 10�1 100

�

10�5

10�4

10�3

10�2

10�1

100

101

102

103

104

105

106d�

SD/d

�(m

b)TotalPPP

PPRRRP

RRRPion

ps = 7 TeV


Slide 17/19



101 102 103 104ps (GeV)

101

�SD

(mb)

ABMSTSaS

SD integrated cross section for � < 0.05


Slide 18/19


Conclusion and outlook

• Implemented two new parametrizations of the total andelastic cross sections in Pythia 8.

• Implemented new parametrization of SD cross sections.

• Compare the new SD parametrization to LHC data.

• Invent description for double- and central di↵ractionclose to ABMST description.

• Implement alternative scenario, keeping ABMST goodpoints, but with di↵erent high-energy behavior.


Slide 19/19

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Cross sections and diffraction in PYTHIA 8 - Lunds universitethome.thep.lu.se/~torbjorn/talks/RasmussenMCnet16.pdf · lund university dept. of astronomy and theoretical physics Cross