Forward Physics in PYTHIA 8

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Forward Physics in PYTHIA 8

Torbj¨ orn Sj¨ ostrand

Department of Astronomy and Theoretical Physics Lund University

S¨olvegatan 14A, SE-223 62 Lund, Sweden

Forward Physics Facility Kickoff Meeting, 9-10 November 2020

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Forward data - 1

1000 2000 3000 4000 5000 6000

]-1 dN/dE [GeVine1/N

−10

10

−9

10

−8

10

−7

10

−6

10

−5

10

=13TeV photon s

LHCf

° φ=180

∆ > 10.94, η

Ldt=0.191nb-1

∫

Data QGSJET II-04 EPOS-LHC DPMJET 3.06 SIBYLL 2.3 PYTHIA 8.212

Energy [GeV]

1000 2000 3000 4000 5000 6000

MC/Data

0 1 2 3

4 1000 2000 3000 4000 5000 6000

]-1 dN/dE [GeVine1/N

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−6

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−5

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=13TeV photon s

LHCf

° φ=20

∆

<8.99, η 8.81<

Ldt=0.191nb-1

∫

Energy [GeV]

1000 2000 3000 4000 5000 6000

MC/Data

0 1 2 3 4

Figure 4: Comparison of the photon spectra obtained from the experimental data and MC predictions. The top panels show the energy spectra, and the bottom panels show the ratio of MC predictions to the data. The hatched areas indicate the total uncertainties of experimental data including the statistical and the systematic uncertainties.

Acknowledgments

We thank the CERN staff and the ATLAS Collaboration for their essen- tial contributions to the successful operation of LHCf. This work was partly

290

supported by JSPS KAKENHI Grant Numbers JP26247037, JP23340076 and the joint research program of the Institute for Cosmic Ray Research (ICRR), University of Tokyo. This work was also supported by Istituto Nazionale di Fisica Nucleare (INFN) in Italy. Parts of this work were performed using the computer resource provided by ICRR (University of Tokyo), CERN and CNAF

295

(INFN).

References

[1] A. Aab et al. (Pierre Auger Collaboration), Nucl. Instrum. Methods Phys.

Res., Sect. A 798 (2015) 172.

14

V. Kireyeu et al.: Hadron production in elementary nucleon-nucleon reactions from low to ultra-relativistic energies 9

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

a) -

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

b) +

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

c) -

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

d) +

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

e) p

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

f) p

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

g) s0

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06

10² 10³

h) + ⁰

FSIon / FSIo

s_NN, GeV

p+pp+n n+n

Fig. 6. Ratios of total multiplicities with FSI (’FSIon’) and without FSI (’FSIo↵’) of ⇡^±, K^±, p , ¯p, Ks⁰and ⇤ + ⌃⁰produced in N + N collisions: the red lines correspond to p + p, blue lines – to p + n and green lines – to n + n reactions.

0 0.2 0.4 0.6 0.8 1

xF 0.2

0.4 0.6 0.8 1 1.2 1.4 1.6

FdN/dx

= 17.3 GeV sNN

p, PHSD PYTHIA NA49 data

0 0.2 0.4 0.6 0.8 1

xF 0.2

0.3 0.4 0.5 0.6 0.7 0.8

> (GeV/c)T<p

= 17.3 GeV sNN

p, PHSD PYTHIA NA49 data

0 0.2 0.4 0.6 0.8 1

xF 0.2

0.3 0.4 0.5 0.6 0.7 0.8

> (GeV/c)T<p

= 17.3 GeV sNN +, π

PHSD PYTHIA NA49 data

Fig. 7. Proton xF distribution (left plot) in p + p collisions atpsN N = 17.3 GeV. Mean transverse momentum < pT > of protons (middle plot) and ⇡⁺(right plot) as a function of xF in p + p collisions atpsN N= 17.3 GeV. The experimental data are taken from the NA49 Collaboration [40, 38].

V. Kireyeu et al., arXiv:2006.14739 LHCf, PLB 78, 233

Need mechanism for protons to take more energy (from pions)?

Diffractive-related or not?

Forward region also important for cosmic-ray physics.

Torbj¨orn Sj¨ostrand Forward Physics in PYTHIA 8 slide 2/30

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Forward data - 2

Cleanest environment may be DIS:

JHEP06(2009)074

ZEUS

0 0.05 0.1 0.15 0.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x_L 1/σinc ⋅ dσLB/dxL

ZEUS 12.8 pb^-1 e⁺p → e⁺Xp p_T²<0.04 GeV² Q²>3 GeV² 45<W<225 GeV

ZEUS 40 pb^-1 e⁺p → e⁺Xn p_T²<0.04 GeV² Q²>2 GeV² 45<W<225 GeV

Figure 16. The rate 1/σinc· dσLB/dxLfor leading proton (dots) and leading neutron production (circles). The bands show the systematic uncertainties.

proton production rate 1/σinc· dσLP/dxLand to the p²Tslopes. In both MC models, the QCD radiation was performed either by the parton shower [40] or colour dipole (CDM) [48]

models. None of the DIS Monte Carlo models can reproduce the flat dependence of xL below the diffractive peak. The MC generator Djangoh, with SCI and MEPS, reproduces quite well the dependence of b on xL, although the mean values of the slope are lower than those measured. In the other MC models, the value of the slope is consistent with the measurements only at high xL.

11 Summary

The cross section of leading proton production for xL> 0.32 and p²T< 0.5 GeV²and its ratio to the inclusive DIS cross section have been measured in the range Q²> 3 GeV²

– 48 –

ZEUS, JHEP 06 (2009) 074

xF 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 F/dxσ dDISσ1/

0 0.05 0.1 0.15

0.2 H1 Data

× 0.6 1.4 + RAPGAP-π CDM ×

CDM π RAPGAP-

Forward Neutrons 70 < W < 130 GeV

H1

xF 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 F/dxσ dDISσ1/

0 0.05 0.1 0.15

0.2 H1 Data

× 0.6 1.4 + RAPGAP-π CDM ×

H1

xF 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 F/dxσ dDISσ1/

0 0.05 0.1 0.15

0.2 H1 Data

× 0.6 1.4 + RAPGAP-π CDM ×

H1

Figure 6: Normalised cross sections of forward neutron production in DIS as a function of xF in three W intervals in the kinematic region given in Table 1. The inner error bars show the statistical uncertainty, while the outer error bars show the total experimental uncertainty, calculated using the quadratic sum of the statistical and systematic uncertainties. Also shown are the predictions of CDM (dotted line), RAPGAP-π (dashed line) and a linear combination of CDM and RAPGAP-π predictions (solid line).

25 H1, EPJC 74 (2014) 2915

Data exists, but need RIVET analyses to facilitate comparisons.

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Simple remnants

Assume one parton kicked out of proton, in pp (or DIS):

1 Kick outvalence quark: colour triplet diquark left,

⇒ single stringstretched out from beam remnant.

2 Kick outgluon: colour octet q1q2q3 remnant left

⇒ split momentum between two strings, one to q₁q₂ antitriplet and one to q₃ triplet.

3 Kick outsea antiquark q₄: colour triplet q₁q₂q₃q₄ remains,

⇒ split momentum between B = q₁q₂q₄ singlet andstring to q3 triplet.

4 Kick outsea quarkq₄: colour antitriplet q₁q₂q₃q₄ remains,

⇒ split momentum between M = q1q₄ singlet andstring to q₂q₃ antitriplet.

13 TeV pp nondiffractive collisions:

∼85% gluons, ∼5% each for others;

(but no gluons for DIS to LO)

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The Lund Model

Combine yo-yo-style string motion with string breakings!

space time

quark antiquark pair creation

Aqfrom one string break combines with aqfrom an adjacent one.

String tensionκ≈ 1 GeV/fm relates (t, x) and (E , p).

Gives simple but powerful picture of hadron production.

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The popcorn model for baryon production

B M

B

M M B B

M

- z

6 t

SU(6) (flavour×spin) Clebsch-Gordans needed.

Expected strong suppression of multistrange and spin 3/2 baryons damped by effective parameters.

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Fragmentation and beam remnants

Recursive fragmentation from one end:

f (z)∝ 1

z (1− z)^a exp

−bm_⊥² z

, z = (E + pz)_hadron (E + p_z)left in string

By defaulta = 0.68and b = 0.98 GeV⁻² from LEP tune.

To be continued . . .

Split momentum between remnant parts:

1 for each valence quark pick x_i according to (1− xi)^p/√x_i, with p = 3.5 for u and p = 2.0 for d

2 for diquark form x_ij = 2(x_i + x_j) from above

3 for sea (anti)quark use kicked-out sister x (in hard process) as if pair comes a fromg→ q4q₄ perturbative splitting

4 rescale sum to remaining beam momentum

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Simple results

0 2 4 6 8 10

y 0.0

0.1 0.2 0.3 0.4 0.5

dnp/dy

Proton rapidity distribution valence quark

gluon sea antiquark sea quark

0.2 0.4 0.6 0.8 1.0

xF

0.0 0.5 1.0 1.5

dnp/dxF

Proton Feynman-x distribution valence quark gluon sea antiquark sea quark

0 2 4 6 8 10

y 0.0

0.5 1.0 1.5 2.0 2.5

dnπ/dy

π^± rapidity distribution

valence quark gluon sea antiquark sea quark

0.2 0.4 0.6 0.8 1.0

xF

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution valence quark gluon sea antiquark sea quark

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The structure of an event

An event consists of many different physics steps to be modelled:

PDF ME ISR FSR M&M MPI BBR CR

Fragmentation Decays Rescattering BE

σ_tot= · · · Unknown?

Fragmentation can include clusters, strings, ropes, QGP, shove, . . .

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Junctions and the baryon number

A proton can be visualized as a Y-shaped topology, with a valence quark at the end of each leg and a junction in the middle.

Two valence quarks can be kicked out if two or more MPIs.

Junction u

u d

r^′ g^′ b^′g^′′

g^′′

r b

g

b^′ g^′′

b^′

r bg^′′

The junction then can be shifted in towards center of event, carrying the baryon number and baryon production with it.

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Beam remnants – the general case

Parton in beam remnant

Composite object

Parton going to hard interaction qq

qv1

qv2

qv3

g1

g2

a)

B

qv1

qv2

qv3

qc

qs

g

b)

M

qv1

qv2

qv3

g qs

q_c

c)

Figure 10: Examples of the formation of composite objects in a baryon beam remnant: (a) diquark, (b) baryon and (c) meson.

2. Composite objects may be formed, but only when all partons involved in the formation are valence quarks.

3. The formation of diquarks may involve both valence and sea quarks, but the formation of colour singlet subsystems (i.e. hadrons) is still restricted to involve valence quarks only.

4. Sea quarks may also be used for colour singlet formation.

The idea is thus that (spectator) valence quarks tend to have comparable velocities, while sea quarks can be more spread out and therefore are less likely to form low-mass systems.

Whether composite systems in the beam remnant are formed or not has important consequences for the baryon number flow. For pp collisions at 1.8 TeV CM energy, we show in Fig. 11 the Feynman x (left plot) and rapidity (right plot) distributions for the baryon which ‘inherits’ the beam baryon number. We denote this baryon the ‘junction baryon’. To better illustrate what happens to each of the two initial beam baryon numbers separately, only distributions for the junction baryon, not anti baryon, are shown. Possibilities 1 and 2 above are compared with the old multiple interactions model (Tune A). One immediately observes that the beam baryon number migrates in a radically different way when diquark formation is allowed or not (compare the dashed and dotted sets of curves). In fact, in the new model it is not possible to reproduce the old distribution (compare the solid curve).

This comes about since, even when all possible diquark formation is allowed in the new model, it is not certain that the beam remnant actually contains the necessary quark content, hence in some fraction of the events the formation of a beam remnant diquark is simply not possible. Here is thus an example where the introduction of more physics into the model has given rise to a qualitatively different expectation: the beam baryon number appears to be stopped to a larger extent than would previously have been expected.

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Need to model:

Flavour content of remnant; also valence vs. sea/companion Colour structure of partons; including junctions and CR Longitudinal sharing of momenta

Transverse sharing of momenta — primordial k_⊥ (nontrivially relates to low-p_⊥ ISR handling)

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Results for full model

0 2 4 6 8 10

y 0.00

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

dnp/dy

Proton rapidity distribution no MPI/ISR/FSR no MPI no ISR/FSR all on

0.2 0.4 0.6 0.8 1.0

xF

0.0 0.5 1.0 1.5 2.0 2.5 3.0

dnp/dxF

Proton Feynman-x distribution no MPI/ISR/FSR no MPI no ISR/FSR all on

0 2 4 6 8 10

y 0

1 2 3 4 5 6 7 8

dnπ/dy

π^± rapidity distribution

no MPI/ISR/FSR no MPI no ISR/FSR all on

0.2 0.4 0.6 0.8 1.0

x_F 10^-5

10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution no MPI/ISR/FSR no MPI no ISR/FSR all on

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Diffraction

Ingelman-Schlein: Pomeron as hadron with partonic content Diffractive event = (Pomeron flux)× (IPp collision)

Diffraction

Ingelman-Schlein: Pomeron as hadron with partonic content Diffractive event = (Pomeron flux)× (IPp collision)

p p

IP p

Used e.g. in POMPYT POMWIG PHOJET

1) σ_SDand σ_DDtaken from existing parametrization or set by user.

2) Shape of Pomeron distribution inside a proton, f_IP/p(x_IP, t) gives diffractive mass spectrum and scattering p_⊥of proton.

3) At low masses retain old framework, with longitudinal string(s).

Above 10 GeV begin smooth transition to IPp handled with full pp machinery: multiple interactions, parton showers, beam remnants, . . . . 4) Choice between 5 Pomeron PDFs.

Free parameter σ_IPp needed to fix#ninteractions$ = σjet/σ_IPp. 5) Framework needs testing and tuning, e.g. of σ_IPp.

Differential cross sections set by Reggeon theory,∼ dMX²/M_X². Smooth transition from low-mass simple model

to high-mass IPp with full pp machinery: MPIs, showers, etc.

High-mass diffractive system ≈ like nondiffractive proton end, but recoling proton in single diffraction∼ dxF/(1− xF).

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Multiplicity in diffractive events

0 5 10 15 20 25 30 35 40

Events

10 102

103

104

105

106

107

ATLAS < 6 ηF

∆ 4 <

= 7 TeV s

> 200 MeV pT

Data

MC PYTHIA 6 MC PYTHIA 8 MC PHOJET

NC

0 5 10 15 20 25 30 35 40

MC/Data 1

2 3

PYTHIA 6 lacks MPI, ISR, FSR in diffraction, so undershoots.

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Results with diffraction

Excluding“elastically scattered” proton of single diffraction

0 2 4 6 8 10

y 0.00

0.05 0.10 0.15 0.20 0.25 0.30

dnp/dy

Proton rapidity distribution

nondiffractive single diffractive double diffractive inelastic

0.2 0.4 0.6 0.8 1.0

xF

0.0 0.5 1.0 1.5 2.0 2.5 3.0

dnp/dxF

Proton Feynman-x distribution nondiffractive single diffractive double diffractive inelastic

0 2 4 6 8 10

y 0

1 2 3 4 5 6 7 8

dnπ/dy

π^± rapidity distribution nondiffractive single diffractive double diffractive inelastic

0.2 0.4 0.6 0.8 1.0

xF

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution nondiffractive single diffractive double diffractive inelastic

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More on fragmentation functions

f (z)∝ 1

z (1− z)^a exp

−bm²_⊥ z

⇔ P(Γ) ∝Γ^a exp(−bΓ) where Γ = (κτ )²,

κ≈ 1 GeV/fm.

What if diquark takes longer to produce?

Favoured by LEP data:

aq= 0.68,aqq = 1.65.

Schematic illustration of three cases

space quarks time

diquarks pair creation

i →j : f (z)∝ 1

z z^aⁱ 1− z z

aj

exp

−bm²_⊥ z

You do not escape from(1− z)^a suppression for z → 1!

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Results for varied fragmentation function

0 2 4 6 8 10

y 0.00

0.05 0.10 0.15 0.20 0.25 0.30 0.35

dnp/dy

default aqq=a=0.68 aqq=a=0, b=0.50 ditto, no popcorn

0.2 0.4 0.6 0.8 1.0

xF

0.0 0.5 1.0 1.5 2.0 2.5 3.0

dnp/dxF

Proton Feynman-x distribution default aqq=a=0.68 aqq=a=0, b=0.50 ditto, no popcorn

0 2 4 6 8 10

y 0

1 2 3 4 5 6 7 8

dnπ/dy

π^± rapidity distribution default aqq=a =0.68 aqq=a =0, b =0.50 ditto, no popcorn

0.2 0.4 0.6 0.8 1.0

x_F 10^-5

10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution default aqq=a=0.68 aqq=a=0, b=0.50 ditto, no popcorn

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Transverse momentum in the forward direction

0 2 4 6 8 10

y 0.0

0.2 0.4 0.6 0.8

p®(y)

Average transverse momentum as function of rapidity all charged proton π^± γ

0.2 0.4 0.6 0.8 1.0

xF

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

p®(xF)

Average transverse momentum as function of Feynman x all charged proton π^± γ

0 2 4 6 8 10

η 0.0

0.2 0.4 0.6 0.8 1.0

p®(η)

Average transverse momentum as function of pseudorapidity all charged proton π^± γ

Is hp⊥i increasing or decreasing in forward region?

Depends on what it is plotted as a function of!

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Transverse momentum for hard process

Consider e.g. inclusiveZ⁰ production, with known p_⊥. How is this compensated by the other particles in the event?

0 2 4 6 8 10

y 0.0

0.2 0.4 0.6 0.8 1.0

p®(y) (GeV)

Average transverse momentum as function of rapidity pZ<20 GeV pZ>40 GeV pZ<20 GeV, no kT pZ>40 GeV, no kT

0 2 4 6 8 10

y 0

2 4 6 8 10 12 14

dpx/dy (GeV)

Transverse momentum compensation for Z⁰ pZ<20 GeV pZ>40 GeV pZ<20 GeV, no kT pZ>40 GeV, no kT

(Z⁰ along−x axis in transverse plane; π⁰ set stable)

Conclusion 1: Primordial k_⊥ kicks are imposed on beam remnants, and does give higherhp⊥i for |y| > 5.

Conclusion 2: hard p_⊥ kick does not influence|y| > 5 region.

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Impact of central activity on forward one

Classify nondiffractive events by charged multiplicity in|η| < 2.5:

0 2 4 6 8 10

y 0.0

0.2 0.4 0.6 0.8

dnp/dy

Proton rapidity distribution nch 12 13 nch40 41 nch100 nch>100

0.2 0.4 0.6 0.8 1.0

xF

10^-2 10^-1 10⁰ 10¹

dnp/dxF

Proton Feynman-x distribution nch 12 13nch40 41nch100 nch>100

0 2 4 6 8 10

y 0

5 10 15 20

dnπ/dy

π^± rapidity distribution nch 12 13 nch 40 41 nch 100 nch>100

0.2 0.4 0.6 0.8 1.0

xF

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution nch 12 13nch40 41nch100 nch>100

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Forward muons and neutrinos

Capability to trace full history of particle production and decay, including space–time evolution from fm to km scales.

Example: flux of muons and neutrinos 100 m from interaction, for total cross section (elastic/diffractive/nondiffractive):

0 2 4 6 8 10

y 10^-6

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹

dnµ±/dy

muon rapidity distribution all muons from π/η/ρ/ω from K/φ from charm from beauty from hyperons from `/γ^∗/

0 2 4 6 8 10

y 10^-6

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹

dnν/dy

neutrino rapidity distribution all neutrinos from π/η/ρ/ω from K/φ from charm from beauty from hyperons from `/γ^∗/

(note: secondary decaysD→ π → µ count as π, not charm)

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Summary

Forward physics is extensively modelled in PYTHIA . . . . . . but little tested, and rather constrained,

e.g. central MPI activity⇒ possible remnant structures.

Action list:

Gather existing data, implement in RIVET analyses Compare DIS and pp forward spectra

Find way that gives more forward protons?

(P. Ed´en, G. Gustafson, Z.Phys.C75 (1997) 41, “curtain quarks”?) Compare rate of different forward baryons (p, n, Λ, . . . ) and mesons (π⁺,π⁻,K⁰_S, . . . )

Correlate flavour, y/x_F and p_⊥ for leading vs. second-leading particle. Consistent with single or multiple strings?

Correlate central and forward activity

Develop and implement new physics mechanisms?

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Backup: How does the string break?

String breaking modelled by tunneling:

P ∝ exp −πm²_⊥q κ

!

= exp −πp_⊥q² κ

!

exp −πm_q² κ

!

• Common Gaussian p⊥ spectrum, hp⊥i ≈ 0.4 GeV.

• Suppression of heavy quarks,

uu : dd : ss : cc≈ 1 : 1 : 0.3 : 10⁻¹¹.

• Diquark ∼ antiquark ⇒ simple model for baryon production.

Extended by popcorn model: consecutive qq pair production

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Backup: MPIs in PYTHIA

MPIs are gererated in a falling sequence of p_⊥ values;

recall Sudakov factor approach to parton showers.

Core process QCD 2→ 2, but also onia,γ’s, Z⁰, W^±. Energy, momentum and flavour conservedstep by step:

subtracted from proton by all “previous” collisions.

Protons modelled as extended objects, allowing both central and peripheral collisions, with more or less activity.

Colour screening increases with energy, i.e. p_⊥0 = p_⊥0(E_cm), as more and more partons can interact.

Colour connections: each interaction hooks up with colours from beam remnants, but also correlations inside remnants.

Colour reconnections: many interaction “on top of” each other ⇒ tightly packed partons ⇒ colour memory loss?

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Backup: Interleaved evolution in PYTHIA

• Transverse-momentum-ordered parton showers for ISR and FSR

• MPI also ordered in p⊥

⇒ Allows interleaved evolution for ISR, FSR and MPI:

dP dp_⊥ =

dPMPI

dp_⊥ +XdPISR

dp_⊥ +XdPFSR

dp_⊥

× exp

−

Z p_⊥max p_⊥

dPMPI

dp⁰_⊥ +XdPISR

dp⁰_⊥ +XdPFSR

dp⁰_⊥

dp_⊥⁰

Ordered in decreasing p_⊥ using “Sudakov” trick.

Corresponds to increasing “resolution”:

smaller p_⊥ fill in details of basic picture set at larger p_⊥. Start from fixed hard interaction ⇒ underlying event No separate hard interaction ⇒ minbias events Possible to choose two hard interactions, e.g. W⁻W⁻

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Backup: ZEUS comparison

JHEP06(2009)074

ZEUS

10^-1 1 10

0.3 0.4 0.5 0.6 0.7 0.8 0.9 x1_L

1/σinc ⋅ dσLP/dxL

(a)

0 2 4 6 8 10

0.3 0.4 0.5 0.6 0.7 0.8 0.9 x1_L

b (GeV-2 )

(b) ZEUS 12.8 pb^-1

p_T²<0.5 GeV² Q²>3 GeV² 45<W<225 GeV

Djangoh+SCI+MEPS Djangoh+SCI+CDM Rapgap+MEPS Rapgap+CDM

Figure 19. Expectations of various Monte Carlo models of DIS, as described in the figure, compared to (a) the leading proton production rate, 1/σinc· dσLP/dxL, and (b) the p²_T-slope, b.

The bands show the systematic uncertainties.

Acknowledgments

We thank the DESY Directorate for their encouragement, and gratefully acknowledge the support of the DESY computing and network services. We are specially grateful to the HERA machine group: collaboration with them was crucial for the successful installation and operation of the leading proton spectrometer. The design, construction and installation

– 51 –

ZEUS,

JHEP 06 (2009) 074

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Backup: Results with diffraction

Including“elastically scattered” proton of single diffraction

0 2 4 6 8 10

y 0.0

0.5 1.0 1.5 2.0

dnp/dy

Proton rapidity distribution nondiffractive

single diffractive double diffractive inelastic

0.2 0.4 0.6 0.8 1.0

xF

10^-2 10^-1 10⁰ 10¹ 10²

dnp/dxF

Proton Feynman-x distribution nondiffractive single diffractive double diffractive inelastic

0 2 4 6 8 10

y 0

1 2 3 4 5 6 7 8

dnπ/dy

π^± rapidity distribution nondiffractive single diffractive double diffractive inelastic

0.2 0.4 0.6 0.8 1.0

xF

10^-5 10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution nondiffractive single diffractive double diffractive inelastic

(28)

Backup: Results for flat f (z) for primary diquark

0 2 4 6 8 10

y 0.00

0.05 0.10 0.15 0.20 0.25 0.30

dnp/dy

default

f(z) =1 primary diquark ditto, no popcorn

0.2 0.4 0.6 0.8 1.0

xF

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

dnp/dxF

Proton Feynman-x distribution default

0 2 4 6 8 10

y 0

1 2 3 4 5 6 7 8

dnπ/dy

π^± rapidity distribution default

0.2 0.4 0.6 0.8 1.0

x_F 10^-5

10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

dnγ/dxF

Photon Feynman-x distribution default

(29)

Backup: space–time evolution

PYTHIA can calculate production vertex of each particle, e.g. number of hadrons as a function of time for pp at 13 TeV:

time(fm/c) 1 10 10² 10³ 10⁴ 10⁵ 10⁶ 10⁷ 10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹² 10¹³ 10¹⁴ 10¹⁵

hadn

0 20 40 60 80 100 120 140 160

180 Total number of hadrons

Primary hadrons Secondary hadrons Total number of final hadrons

S. Ferreres-Sol´e, TS, EPJC 78, 983

(30)

Forward Physics in PYTHIA 8