Prompt Neutrino Fluxes from Charm Production in the Atmosphere

Yu Seon Jeong

Yonsei University

Work in progress with M. H. Reno, and C. S. Kim, and with A. Bhattacharya, I. Sarcevic, and R. Enberg

YongPyong-High1 2015 Joint Winter Conference High1 Resort, Korea, January 25-31, 2015

Atmospheric Neutrino

• Cosmic rays interact with air nuclei in the atmosphere and produce hadrons.

• Hadrons subsequently decay producing neutrinos.

⇒ Atmospheric neutrino

• Atmospheric neutrinos are the background to astrophysical neutrinos.

.). Xppge

)( ee

Conventional Neutrino Flux

IceCube 1311.7048

• Neutrino flux from pion and kaon decay is called the conventional flux.

• Κ, π – long-lived particles

– interact before the decay

⇒ suppress the neutrino production at high E

Prompt Neutrino Flux

IceCube 1311.7048

• Neutrino flux from the decay of the charmed hadrons is called the prompt flux.

e.g.) D-mesons

• The charmed hadrons are short-lived particles.

• The resulting neutrino flux less depends on energy.

Cascade equations

The neutrino flux is obtained by solving the coupled cascade equations for nucleon, meson and lepton fluxes.

The function S is responsible for the generation.

)( NYNASdX

d

N

NN

)()( MYMASMYNASdX

ddec

M

M

M

MM

M

l lYMSdX

d)(

fluxnucleon - )(EN

charm from fluxesprompt for

,D ,D ,D , cs

00 DM

E

j

jk

kk

kkk

dE

EEjkdn

E

EdEjkS

),;(

)(

)()(

Cascade equations

• generation function

decayfor ),(1

productionfor ),,(

)(

1),;(

j

j

k

j

jk

kkAj

jk

dE

EjYkd

dE

EEjYkAd

EdE

EEjkdn

dn/dE – the energy distribution of the final state particle.

Z-moments

j

jk

kk

jk

jk

kk

Ekkj

dE

EEjkdn

E

E

XE

XEdEZ

),;(

)(

)(

),(

),(

)(),( :Assumption XEXE kk

j

jk

kk

jk

j

k

Ekkj

dE

EEjkdn

E

E

E

EdEEZ

),;(

)(

)()(

P. Lipari, Astropart. Phys. 1 (1993) 195 P. Gondolo, G. Ingelman and M.Thunman, Astropart. Phys. 5 (1996) 309 (TIG)

Approximate Lepton Fluxes

N

NN

NMMl

low

lZ

ZZ

1

NM

MN

NM

NN

NMMl

high

lEZ

ZZ

/1

)/ln(

1

MNiZ iiii , )1/(

The lepton flux can be obtained by interpolating these two solutions.

• The essential input to the neutrino flux evaluation is the charm production cross section.

• The charm production cross section can be calculated

1) in the perturbative QCD,

2) in the dipole model,

3) with non-perturbative “intrinsic charm” production.

Charm Production Cross Section in QCD

),(),()ˆ()(

2

2

2

1

21

2

xGxGssxx

dM

dx

dccgg

cc

F

LO

F

ccF x

s

Mxx

22

2,1

4

2

1

The cross section for charm pair production

At high energies, x1xF and x2 1.

e.g.) at Ep = 1 PeV, x2 10-6 for xF 1.

x2 become smaller at higher energy.

Gluon distribution at small x

The gluon distribution increases rapidly as x becomes small. At the high density region, gluons can be overlapped and recombined. → Saturation effect

K.Golec-Biernat – conf. proceeding arXiv:0812.1523

Color Dipole Model

The virtual photon splits into a quark-antiquark pair (color dipole) before scattering on the proton.

C. Ewerz et al, JHEP03 (2011) 062

f

Nqq

N xrQrzrddzQx ),(ˆ),,(),(2

221

0

2*

targeta with dipole a ofn interactio - ),(ˆ

n fluctuatio -),,( 2

xr

Qrz

Nqq

PP collisions in the dipole model

22

2

2

11 ,,,)( QxxGxXQQppdy

d Gp

),(),(,,2

222

2 rxrzrdzdQx dG

Q

G

Gp

nucleon target ith the w

gluon a frompair qq ofn interactio - ),( rxdG

The differential cross section for heavy quark production from proton-proton collision

dipole gluon to of splitting - ),( rzQ

G

The partonic cross section in the dipole model

YSJ, C. S. Kim, M. V. Luu and M. H. Reno, JHEP 11 (2014)025

rxrzxzrxrx ddddG ,8

1)1(,,

8

9),(

PP collisions in the dipole model

1.8r0.5for 1

8.1r and 0.5rfor ),(

er d

)(

0

)(

0

cerx

xa

rx

xarx

b

r

cbr

r

d

r a b c d e

r≤0.5 5.55 -1.098 1.839

0.5<r≤1.8 2.67 1.454 0.708 -6.16 4.238

r>1.8 2.12 -0.31 3.0

1.8)(r 00224.00325.0182.00.39

1.8)(r 044.0127.011.0196.0)(32

32

rrr

rrrr

Cosmic Ray Flux for Nucleon

T.K. Gaisser, Astropart. Phys. 35 (2012) 801

Prompt Flux in Dipole Model

New dipole cross section from the recent F2 parameterization – increases the flux by ~15%.

The effect of CR spectrum – above 1 PeV, reduction in flux is by a factor of 3-4.

Intrinsic charm

Charm can be produced from non-perturbative fluctuation of nucleon and it goes into a charmed baryon-meson pair. Meson-Baryon Model (MBM)

0 e.g.) Dp c

T.J. Hobbs, J.T. Londergan and W. Melnitchouk, PRD 89 074008 (2014) (HLM)

In the MBM, is produced through and . c

cD0 cD 0*

Intrinsic charm production cross section

Mp

tot

DDM

FM

F

xfdx

dc

c

)(*,

mb 1020*

pD

tot

Dp

tot Fxy 1

T.J. Hobbs, J.T. Londergan and W. Melnitchouk, PRD 89 074008 (2014) (HLM)

function splitting - Mcf

Prompt Flux – Intrinsic charm

Conclusion

• The prompt flux with more realistic cosmic ray nucleon spectrum is reduced relative to the prompt spectrum using the broken power law. At 1 PeV, the reduction in flux is about a factor of 3.

• The dipole cross section from the F2 parameterization by Block et al increase the flux about 15%.

• Intrinsic charm contribution based on the Hobbs et al MBM results may be important. – work in progress

• More update

– with separate lepton flavors

– with bottom quark contribution

– with other models for intrinsic charm

Prompt flux : DM vs. NLO QCD