1

Charm Production/Decay Models In Atmosphere

(Part I)for Prompt Lepton Study

UW IceCube Group meeting 5/20/2005

Aya Ishihara, Teresa Montaruli and Sean Grullon

2

Considered as dominant source of very high energy neutrino background

Why so?Short life times, order of cs and it decays before reaching on the Earth (produce neutrino)Do not loose energy by colliding the nucleon in the atmosphere (prompt high energy neutrino)

- Want to set an upper limit on theoretical uncertainty of atmospheric neutrino models, for physics interest of itself (energy region can not be studied by accelerators) and for the studies of higher energy cosmic neutrino!

ProblemDetails of production mechanism unknown – cc cross-section uncertainty

Atmospheric neutrino estimation vary by orders in magnitude Shifts the energy prompt exceeds conventional

New experimental data available from CDF-II, STAR at the energy of interest over last 2 years (beam energy 20 – 2000 TeV)

many models calculated before the data came, need review of models used & update!

Atmospheric Neutrino from Charmed Mesons

E3(E) sample

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Also Neutrino Yield includes: Atmospheric depth p-A collisions occur Extrapolation from p-N to p-A

In this presentation, I only consider the largest uncertainty from charmed meson production cross-section

Atmospheric Neutrino

Models considered in part-1 are, from following papers only from pQCD:

Thunman, Ingelman and Gondolo (TIG1996)

improved version Gelmini, Gondolo, Varieschi (GGV1999)

using different parton distribution function (GGV1999GGV2000),

Pasquali, Reno, Sarcevic (PRS1998)

Martin, Ryskin, Stasto (MRS2003)

Following will be Added in part-2 (phenomenological models, any suggestion?)

Fiorentini Naumov Villante (FNV2002)

Bugaev, Misaki, Naumov, Sinegovskaya, Sinegovsky, Takahashi (BMNSST1998)

Volkova, Fulgione, Galeotti, Saavedra (VFGS1987) etc. …

eldneutrinoYitEarthEffectAtmosEffecxprimaryFlucFluxatmospheri )(

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Reference catalog athttp://www.icecube.wisc.edu/~aya/simulation/prompt/index.html

=Review=ref/review * prompt

"Prompt Lepton Cookbook"hep-ph0010306-Costa-PromptLeptonCookbook.pdf "Atmospheric Muon Flux at Sea Level, Underground and Underwater"hep-ph9803488-BMNSST.pdf

* conventionalastro-ph0502380-Gaisser-AtmosphericNeutrino.pdf

* for amanda/icecubehep-ph0104039-CostaHalzenSalles-PromptAtmosphericNeutrinoWindow.pdf

=pQCD=ref/pqcd-models * GGV

hep-ph0209111-GelminiGondoloVarieschi-MeasuringPromptAtmosphericNeutrino.pdfhep-ph9905377-GelminiGondoloVarieschi-DependenceOnGluonDistributionFunction.pdfhep-ph9904457-GelminiGondoloVarieschi-PromptNeutrinoMuonNLO-LOQCDPredictions.pdf

"MEASUREMENT OF THE GLUON PDF AT SMALL X WITH NEUTRINO TELESCOPES"By Graciela Gelmini, Paolo Gondolo, Gabriele VarieschiPhys.Rev.D63:036006,2001 e-Print Archive: hep-ph/0003307

0003307.pdf

* PRShep-ph9806428-PasqualiRenoSarcevic-LeptonFluxesFromAtmosphricCharm.pdf

* MRShep-ph0302140-MartinRyskinStasto-PromptNeutrinosFromccbbSmallGluonX.pdf

* TIG-PYTHIA(MC)hep-ph9505417-ThunmanIngelmanGondolo-CharmProductionHighEnergyAtmosphericMuonAndNeutrino.pdf

ref/pqcd-theory (tutorial)

IntroPqcd-long.pdfp-qcd-lecture.pdfcdf4113_qcd_in_hadron_coll..psSoper.pdfLHC-QCD1.ps

=non-pQCD=ref/pheno-models * FNV + QGSM/RQPM

hep0106014-FiorentiniNaumovVillante.pdf hep0201310-FiorentiniNaumovVillante.pdf

* QGSM and RQPM discussed Atmospheric Muon Flux at Sea Level, Underground and Underwater (BMNSST)

9803488.pdf

ref/pheno-theory

NuclPhysB405-80.pdf

=experimental result=ref/charm-production *pQCDPredictionCharmBottomAtRHIC_hepex-0502203.pdfhep-ph/9702287Title: Heavy-Quark ProductionAuthors: S. Frixione, M.L. Mangano, P. Nason, G. Ridolfi"Heavy Flavours II", eds. A.J. Buras and M. Lindner, Advanced Series on Directions in High Energy Physics, World Scientific Publishing Co., Singapore.Journal-ref: Adv.Ser.Direct.High Energy Phys. 15 (1998) 609-706charm-production/9702287.pdf

* experimental result in p+p and d+Au collisions at \sqrt{s}=200GeV

0407006-star-charm.pdf * CDF p+pbar collisions at \sqrt{s}=1.96TeV

RecentCharmFromCDF2004-Dec.ps.gz hepex0307080_CDFII_2TeV_charm.pdf CharmPhysicsAtTevatronII_Presen.pdf

* UA2 (p+pbar@sqrt(s)=630 Gev:Elab~180TeV) physLettB236-448-UA2Charm.pdf

* pqcd prediction(for RHIC Elab~20Tev and LHC Elab~12000TeV energy)

pQCDPredictionCharmBottomAtRHIC_hepex-0502203.pdf hep-ph0203151-Vogt-HeavyQuarkProduction.pdf

hep-ph9411438-HeavyQuarkProductionInPP.pdf … and more!

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Before stepping into deep --- The basic QCD properties

QCD special features relevant to charmed hadron production Strong in large distance (small momentum transfer), coupling constant

exponentially increases ⇒ quark confinement, infrared singularities, factorization and non-perturbative QCD

Weak in small distance (large momentum transfer), nearly free inside hadron radius ⇒ asymptotic freedom and perturbative QCD

Parton and gluon distribution functions as a function of x - F(x,Q), g(x,Q) small-x QCD

Nucleon

Quark

Gluon parton

s (Q,nf)=12(33-2nf)log(Q2 /QCD2)

nf :number of quark flavor of which masses less than ~ QCD

The Strong Coupling Constant s

xq

xgmomentumfraction x =Q2/2 ~ Q2/s

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Quick view of the hadron production models quark pair production and hadronization

Non-Perturbative phenomenological QCD (dominant for light hadrons and describe it well, historically preferred model for heavy quark production but is partially because of poor agreement of pQCD models) typically Q < 1~2GeV

String Fragmentation Quark Parton Recombination (Intrinsic Charm) (Lattice QCD?)

Perturbative QCD – cross-sections in terms of s (Q) - leading O(s2) / next-to-

reading O(s3), preferred model for heavy quarks due to its large masses ~

large momentum transferred Q : applicable for charm quark mass of the order of 1.3 GeV? (still argument compared to b-quark mass 4.5-5.6 GeV)

Models describe interaction with large momentum transfer, i.e. Jet Productions very well

Uncertainty in x (fraction of momentum carried by parton, considered to be the ‘momentum resolution’ of the partons) dependences of parton distribution function F2(x,Q2) – at small x, only gluon distribution is relevant … active area of DIS study

Uncertainty in fragmentation function

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How does it look like?? non-pQCD exampleString Fragmentation (QGSM or the Lund Model)

Charge-Dependent (CD) = Like-sign – Unlike-sign

beam axis

ΔΔ η~θColor-field string fragments along beam

axis(the Lund model of soft-particle production,

QM Tunnelling pre-QCD Regge-based approach, fragmentation function)

proton-proton collisions at 200 GeV (c.m.)consequence in particle correlations as well as the success in predicting low

energy hadron yield

Negative Gaussian on (independent of )

Local momentum, charge, flavor conservation

q

q

q

q

qq

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How does it look like?? pQCD exampleParton fragmentation (hard-particle productions)

p-p collision

mini-jet(back-to-back)

strong correlationbetween

jet thrust axis and

secondary particles

Two-particle correlationproton+proton at 200 GeV (c.m.)

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Light hadron production (e.g. ): two-component model soft

Produced

and thermali

zedby

inelastic scatteri

ngs

hardelastic process(Jet, mini-jet)

10%

(Phys. Rev. Lett. 89, 202301 (2002) )

p+p

like

Main two differences for

charmed meson production a) large quark masses b) quark doesn’t exists in

projectile/target hadron

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pQCD models for atmospheric charm

Some notes: pQCD claims soft charm production is negledgeble in the

Lund model which predicts quark-pari production ratio uu:dd:ss:cc ~ 1:1:0.3:10-11

pQCD can study x, Q dependences in principle but NOT absolute normalization. Usually parameter set to some experimental data at lower energy region

Our interest is of energy region 104<E<1012 GeV

pQCD – considered to be applicable only for a large momentum transfer interaction

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Important factors for pQCD

• Heavy quark mass mc

• QCD renormalization parameter QCD • Renormalization scale parameter for perturbative calculation r :Factor needed for the expansion of the observable in power of the strong coupling constant which is truncated at a certain order pQCD• Factorization scale parameter f :defines the separation between short-distance QCD processes and long-distance, non-perturbative processes, which are absorbed in the parton distribution

• Parton distribution function (PDF) in proton F(x, Q) or gluon distribution function g(x, Q) which depends on both x and Q• Perturbation Order: Leading-Order (LO) to Next-to-Leading-Order (NLO)

Flavor Creation (annihilation)

q b

q b

Flavor Creation (gluon fusion)

bg

g b

Flavor Excitationq q

b

g

b

Gluon Splitting

bg

g g

bLONLO

Q

Q

Q

Q

Q

QQ

Q

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pQCD Model differences TIG (starting point of pQCD calculation for atmospheric prompt leptons, 1996)

Model PDF Comments on PDF

Small-x behavior

QCD

[GeV]

mc

[GeV/c2]

Trend: The larger mass the smaller cross-section

r Renormalization-scale parameter

FFactorization-scale parameter

pQCD

order

TIG96-3 MRS (Martin-

Roberts-Stirling) GxF(x)~x-a

a=0.07 for sea quark

a=0.30 for gluon

0.25 1.35

K factor

K=2 is used

To match with experimental data at E2.5~3.5GeV

LO

TIG96-2 MRSD0 xF(x)~const. 0.25 1.35 LO

TIG96-1

Main result

MC xF(x)~x-a

a=0.08

Considering connection between non-p (Regge) to pQCD

0.25 1.35 LO

pythia (Lund) + LO pQCD

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TIG Results Summary (initial pQCD study)

Small cross section at high energy region which indicates small fluxes of prompt leptons

For Log10(convprompt

At lower energy it agrees with experimental results as it is normalized by experimental data

Fig. 10

Fig. 7

Charm production cross section

muon and neutrino distributions

Problem on PDF

(extrapolation to small x) and

K factor (the higher order p correction)

→need to be fixed

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Perturbation series 1

GGV 1: LO to NLO comparison with MNR routines (charm quark production) + PYTHIA 6.115 (charm quark fragmentation, charm interaction and decay)

Model PDFAvailable

x > 10-5

Q2>1.25-2.56GeV

Comments on PDF

Simplified extrapolation to x < 10-5

Between Regge and BFKL calculation

QCD

[GeV]mc

[GeV/c2]

r Renormalization-scale parameter

FFactorization-scale parameter

pQCD

order

GGV-1

Main results

MRS R1 Differs from R2 only the strong coupling constant sat the Z boson mass

s(mz)=0.113

Small-x behavior

xFi(x,Q2)~Aix-Q2

i: u,d quark, sea quark(S), gluon(g)

SQ02gQ0

2

Quark and gluon density differs!

ln g(x)= (gQ2 +1)ln x + ln Ag, where gQ2was taken at x=10-5

0.25 1.185

r=mT

F=2mT

Fit to Exp. E769

Elab=250 GeV

PRL77-2388(1996)

NLO

GGV-2 MRS R2Differs from R1 only the strong coupling constant sat the Z boson mass

s(mz)=0.120The same as 1

0.25 1.31 NLO

GGV-3 CTEQ 3M

Old for comparison with PRS98

Small-x behaviorxFi(x,Q2)~Aix-

Q2

SQ02gQ0

2

Quark and gluon density are the same!

0.25 1.24 NLO

GGV-4 CTEQ 4MMost up-to-date at 1999 from CTEQ collaboration

s(mz)=0.116

The same as 1 0.25 1.27

competitive

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Perturbation series 2 (BFKL)

GGV2: the main difference from GGV1 in the extrapolation to x<10-5 Model PDF

Available

x > 10-5

Q2>1.25-2.56GeV2

Comments on PDF QCD

[GeV]

mc

[GeV/c2]

r Renormalization-scale parameter

FFactorization-scale parameter

pQCD order

GGV-1 MRS R1 Differs from R2 only the strong coupling constant sat the Z boson mass

s(mz)=0.113

Small-x behaviorxFi(x,Q2)~Aix-

Q2

i: u,d quark, sea quark(S), gluon(g)

SQ02gQ0

2

Quark and gluon density differs

xg(x,Q2)~Ax-Q2

(i)g(Q2)forx > 10-5

(ii) ln g(x)= (gQ2 +1)ln x + ln Ag,

where gQ2was taken at x=10-5

(iii) xg(x,Q2)~Ax-Q2 with

g(Q2)forx > 10-5

0.25 1.185 r=mT

F=2mT

Fit to Exp. E769

Elab=250GeV

PRL77-2388(1996)

NLO

GGV-2 MRS R2Differs from R1 only the strong coupling constant sat the Z boson mass

s(mz)=0.120

0.25 1.31 NLO

GGV-4 CTEQ 4MMost up-to-date at 1999 from CTEQ collab.

s(mz)=0.116

0.25 1.27 NLO

GGV-5

Main results

New! MRS T (the latest at the time)

s(mz)=0.1175

Small-x behavior

xFi(x,Q2)~Aix-Q2

Extrapolation with different lambda

gQ2

forx > 10-5

0.25 1.25 NLO

...lnln nss

ns ss

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GGV Results Summary

Al l matched at low energies due to fixed parameter at the same energy at 250 GeV

Similar glow up to 106~7 but different from TIG above 104

CTEQ3M > otherTIG the lowest due to NLO effect, small-x

extrapolationVery similar distribution for leptons , , eand e are almost equalK factor (NLO/LO ratio) 2.1 ~ 2.5difference is mainly due to Small-x from (TIG) to –

Charm production cross-section is very much gluon distribution dependent ! which is a parameter to describe gluon distribution function contribution from small x region The spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon and distribution function at very small x a suggests prompt lepton to study small-x physics

Fig. 5Dependence on different extrapolation

Dependence on different PDF

Charm production cross section

Fig. 3

Dependence on different PDF

Dependence on different extrapolation

K factor (ratio: NLO/LO)

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PRS98: small-x behavior, factorization and renormalization scale dependence

Model PDFAvailable

x > 10-5

Q2>1.25-2.56GeV2

Extrapolated for the smaller region

Comments on PDF QCD

[GeV]

mc

[GeV/c2]

r Renormalization-scale parameter

FFactorization-scale parameter

pQCD

Order

PRS-1

Main result

(middle of 2 and 3)

CTEQ3M xFi(x,Q2)~Aix-Q2

SQ02gQ0

2

Quark and gluon density are the same!

0.239 1.3

(1.5)r=2mc F=mc

NLO

PRS-2 CTEQ3M 0.239 1.3

1.5r=mc F=mc

NLO

PRS-3 MRS D Small-x behavior suggested by BFKL theory

xg(x,Q02)~x-

Q02

note: large value effectively set an upper limit on the cross section

0.239 1.3 r=2mc F=mcNLO

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PRS98 summary

Cross section

Steeper small-x behavior by 0.2 of the parton distribution function enhance cross section by a factor of 2.6 at 108GeV

Decreasing renormalization scale from 2mc to mc decreases cross section by 2.1 at 108GeV

Flux reflects the differences

MRS D- (=0.5, r=2mc, F=mc) PRS-3

CTEQ3 (~0.3, r=2mc, F=mc) PRS-1

CTEQ3 (~0.3, r=mc, F=mc) PRS-2

TIG prompt

TIG conventional

flux

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MRS03: idea of gluon saturation

• We have seen that current problem is uncertainty associated with small-x of region which is not accessible by experiments• Gluon distribution behavior at small-x is hot topic in physics, how it saturate, CGC? • This paper study the extrapolation methods from the last known points of x … • New – inclusion of prompt (Ds decay), contribution from beauty hadrons which is small but it’s semileptonic decay channel

may be important

Model PDFAvailable

x > 10-5, Q2>1.25-2.56GeV2

Comments on PDFSmall-x behavior

QCD

GeV

mc

GeV/c2

r Renormalization-scale parameter

FFactorization-scale parameter

pQCD

Order

MRS-1

Doesn’t work for lower energy ~103GeV

MRST2001 0.220

Nf =4r=2mc F=mT

NLO

MRS-2 MRST2001 BFKL extrapolation

xg(x,Q02)~x-

Q02

0.220 F=mTNLO

MRS-3

Main result

MRST2001 Included saturation effect according to GBW model which is similar to Glauber parameterization of number of nucleon collisions in nucleus-nucleus collision, with r distance between quark pair

0.220 F=<1/r> NLO

4,325

ln)(

)(ln

16exp)Q,g(xx )Qxg(x,

00

2000

2

c

s

sc

Nb

x

x

Q

Q

b

N

Suggested by DGLAP formalism

0,1,28.0,1

)(

)(4exp1),(ˆ

0

2/

00

20

20

2

0

cGeVQx

xc

QxR

xR

rrx

Non zero c (~0.05-0.2) for triple-Pomeron effect (?)

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MRS03 summary

∙ e are essentially equal to , thus is e more visible over its conventional∙ electrons are negligible, muon 10% less than at the surface∙ contribution from beauty decay (~40%) included, still 10 times less than , e∙ Gluon saturation effect need to be included as MRS-3 which is minimum saturation thus

considered to be upper limit of cross section

FluxAlthough MRS-3 is smaller than the other models MRS-1,2 for example, authors claim that considering

saturation effect the MRS-3 would set the upper limits

MRS-3

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Charm (heavy quark) Productions at accelerators

Hints:

•Recent experiments total c-cbar cross section from

•CDF-II (PRL2003) @ Tevatron p-pbar at sqrt(s) = 1.96 TeV Elab ~ s/2mp ~ 2000 TeV

•STAR (PRL2004) @ RHIC p-p, d-Au sqrt(s) = 200GeV Elab ~ 20 TeV

• D0 (preliminary) @ Tevatron

note: direct comparison require additional information

STAR

20 TeV(lab)

In favor of NLO pQCD with

PDF: MRST HO, mc=1.2GeV, Renorm. scale: mc, Fact. scale: 2mc

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Experimental results at Tevatron

Integrated cross sectionsIntegrated cross sections at CDF-II at CDF-II::

bpD

bpD

bpD

bpD

Ts

T

T

T

22.005.075.0)1|Y|GeV,8,(

7.01.03.4)1|Y|GeV,6,(

8.01.02.5)1|Y|GeV,6,*(

5.12.03.13)1|Y|5.5GeV,,( 0

Calculation from M. Cacciari and P. Nason:

Resummed perturbative QCD (FONLL)

JHEP 0309,006 (2003)

Theory prediction:

CTEQ6M PDF

Mc=1.5GeV,

Fragmentation: ALEPH measurement

Renorm. and fact. Scale: mT=(mc2+pT

2)1/2

Theory uncertainty: scale factor 0.5-2.0

CDF-II Elab ~ 2000 TeV

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Summary of part-I

Prompt Lepton Models for the IceCube• pQCD reasonably describe the cross section from experimental data over large energy range

• (at least) NLO estimation for heavy quark production is required

• Results are very sensitive to PDF especially its small-x behaviour of gluon distribution func.

• Stay tuned on small-x saturation problem and results from experiments at RHIC/Tevatron

To do --- to be continued in the part-II !!

• Non perturbative QCD review

• Comparison with experimental results * As direct comparisons of different experiments requires extra caution, in the part-II of presentation, experimental results and models described in the part-I will be compared in indirect way, i.e. study the difference between pQCD theory compared with experimental results (pdf: MRST HO and CTEQ 6M) and pQCD models studied in this presentation and consider the modification needed to it to match to the experimental results.

• Comparison of effects other than charm production cross section

• Include some reasonable models into IceTray for IceCube prompt study for all , e,

• Because models only study energy up to 108 or 109 GeV. These model need to be extrapolated to the higher energy region to study upper energy limits on atmospheric neutrino

• Heavier (beauty) quark contribution

Any suggestion/correction/question/help welcome!