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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
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