cross sections and diffraction in pythia 8 - lunds...
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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
lund un i v er s i ty dept . o f a stronomy and theoret i ca l phy s i c s
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
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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
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).
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
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
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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
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).
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Total and elastic cross sections
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�).
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Total and elastic cross sections
101 102 103 104 105ps (GeV)
0
50
100
150
200
�to
t(m
b)RPP pp
ABMST pp
DL pp
PDG pp data
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Total and elastic cross sections
101 102 103 104 105ps (GeV)
0
10
20
30
40
50
�el
(mb)
RPP pp
ABMST pp
SaS pp
PDG pp data
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Total and elastic cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Total and elastic cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
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 .
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Di↵ractive cross sections
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.
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Di↵ractive cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Di↵ractive cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
Slide 14/19
lund un i v er s i ty dept . o f a stronomy and theoret i ca l phy s i c s
Di↵ractive cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Di↵ractive cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Di↵ractive cross sections
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
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
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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
Di↵ractive cross sections
101 102 103 104ps (GeV)
101
�SD
(mb)
ABMSTSaS
SD integrated cross section for � < 0.05
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
Slide 18/19
lund un i v er s i ty dept . o f a stronomy and theoret i ca l phy s i c s
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.
Christine O. Rasmussen — Cross sections and di↵raction in PYTHIA 8 — April 2016
Slide 19/19
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