Upper Limit on Forward Charm Contribution to Atmospheric Neutrino Flux

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by  Francis Halzen

Upper Limit on Forward Charm Contribution to Atmospheric Neutrino Flux
Francis Halzen and Logan Wille
Wisconsin IceCube Particle Astrophysics Center and Department of Physics,
University of Wisconsin, Madison, WI 53706, USA
We revisit the calculation of charm particle production in hadron collisions, focusing on the
production of charm particles that carry a large fraction of the momentum of the incident proton.
Inthecaseofstrangeparticles,suchacomponentisfamiliarfromtheabundantproductionofK+Λ
pairs. Modern collider experiments have no coverage in the very large rapidity region where the
forward pair production dominates. While forward charm particles are produced inside the LHC
beampipe, they dominate the high-energy atmospheric neutrino flux in underground experiments
because long-lived pions and kaons interact before decaying into neutrinos. The fragmentation of
6 thespectator quarkinthepartonicsubprocessesqc qcandgc gcisresponsiblefortheforward
→ →
1 component of charm production in perturbative QCD. We use this phenomenological framework
0 to construct a charm cross section that saturates available accelerator and cosmic ray data, i.e., it
2 represents an upper limit on the normalization of the charm cross section that cannot be reliably
calculated because the charm mass is much smaller than the center-of-mass energy. Where the
n
a highest energy IceCube observations are concerned, we conclude that the upper limit on the flux
J of neutrinos from forward charm production may dominate the much-studied central component.
It may therefore also represent a significant contribution to theTeV atmospheric neutrinofluxbut
2
cannot accommodate the PeV flux of high-energy cosmic neutrinos observed by IceCube, or even
2
theexcess of eventsobserved in the 30 TeV energy range.

]
h
p I Introduction a charm background.
-
p
The production of charm hadrons by cosmic rays inter- The hadronic production of charm particles has been
e
acting in the Earth’s atmosphere [1–10] is the dominant extensively studied in the context of perturbative QCD
h
[ background for the detection of cosmic neutrinos above [12–15]. These calculations often use a color dipole de-
anenergythatdependsonthecharmcrosssectionandon scriptionofthetargetproton[16–19]inordertomitigate
3
its dependence on Feynman x . Because of their short thebreakdownoftheperturbativecalculationassociated
v F
lifetime, charm hadrons decay promptly into neutrinos with large log(1/x) where x = m /√s. Here m is the
4 c c
4 in contrast with relatively long-lived high-energy pions charmquarkmassandsthecenter-of-massenergyofthe
0 and kaons that, at high energies, interact and lose en- collidinghadrons. Athighenergy,the charmquarkisno
3 ergy before decaying. Although prompt neutrinos may longer a heavy quark whose mass controls the perturba-
0 represent the dominant component of the atmospheric tiveexpansion. Moreimportantly,thesecalculationsonly
.
1 neutrino background for the identification of the cosmic describethe centralproductionofcharmparticleswitha
0 neutrinofluxatPeVenergy,theyhavenotyetbeeniden- cross section that peaks at Feynman x 0, providing
F
∼
6 tifiedassuch. IceCubeobservations[11]indicatethatthe an incomplete picture. For strange particles, the central
1 neutrino flux is dominated by conventional atmospheric component of particle production is accompanied by a
:
v neutrinos at low energy and by cosmic neutrinos at high forward component where the incident proton transfers
i energy; charm neutrinos never dominate the measured mostofitsenergytoaK+Λpairwiththesamequantum
X
spectrum. Obviously, the issue is of great interest be- numbers [20]. It dominates strange particle production
r causeapoorunderstandingofapotentialcharmneutrino atlargeFeynmanx . Inthispaper,weevaluatethe cor-
a F
backgroundinterfereswiththeprecisecharacterizationof respondingcrosssectionfor charmproductionin pertur-
the cosmicflux measuredbyIceCube. Neutrinosprovide bative QCD making no attempt to compute its normal-
the first unobstrutced view of cosmic accelerators at the ization, which is highly uncertain as it is for the central
highest energies. component. However,limits onits magnitude canbe de-
Itisimportanttorealizethattheproductionofcharm rivedusingIceCube observationsofthe atmosphericflux
intheatmospherecannotaccommodatetheobservedflux of muon and electron neutrinos and data from archival
of high energy neutrinos. We know, independent of the- experiments performed at the CERN Intersecting Stor-
ory,thatthe charmflux tracksthe energydependence of ageRing (ISR).We willthus obtaina“maximal”contri-
the cosmic ray flux incident on the atmosphere and that bution of the forward component of charm particle pro-
itisindipendentofzenithangle. Thereisnoevidencefor ductionthat,likeforstrangeparticles,contributesquali-
such a component in any of the multiple IceCube anal- tativelyatthesamelevelasthecentralcomponenttothe
yses. On the other hand there is accumulating evidence totalcharmparticle crosssection. However,while it dic-
for a steepening of the cosmic neutrino flux with lower tates the production of the highest energy atmospheric
threshold;thefluxisnotasinglepower. Alreadythefirst neutrinos inIceCube, we conclude that it cannotaccom-
attempt to lower the threshold [11] revealedan excess of modate the flux of cosmic neutrinos that dominates the
events in 30 TeV energy range raising the possibility of spectrum at the highest neutrino energies. In addition,
2
this forward charm production is unable to explain the stituent charm quarks in the interacting hadrons,
30TeVexcessoverthe best-fitpowerlawasseeninare-
centIceCubeanalysisfocusingonlowerenergyneutrinos
∂σ(pp c¯ )
[11]. → a = dxtc(xa,Q2)f(xt,Q2)σˆfc¯→fc¯,
∂x Z
It has been pointed out some time ago that a per- a Xf
turbative QCD calculation of charm produces a forward (1)
component that peaks near x 1 where it dominates where the incoming proton interacts via its charm con-
F
the central component [21]. Th∼e forward charm parti- stituents described by the parton distribution function
clesarethehadronizationproductofthespectatorquark (PDF) c(xa,Q2). Here, f(xt,Q2) is the PDF of the tar-
in the leading-order partonic subprocesses qc qc and get, xa is the active charm quark fractional momentum,
gc gc; see Fig. 1. While the active constitue→nt charm xt isthetargetpartonfractionalmomentumandσˆfc¯→fc¯
qua→rk carries a momentum fraction x 0, the specta- is the partonic cross section. We sum over the diagrams
tor quark hadronizes with the valence q∼uarks of the in- involving a charm constituent of the interacting hadrons
coming proton into a charm hadron that carries a large shown in Fig. 2. All subprocesses are explicitly given
fraction of the proton momentum. The high-momentum in the appendix. We fix the two free parameters, Q2
charm hadrons thus produced decay leptonically to en- and tˆmin, to 3 m2c and 2 m2c, respectively, to match cc¯
ergetic muons and neutrinos that penetrate into under- cross section data following references [22–26]. Whereas
ground detectors. The spectrum of these neutrinos ex- the charm structure function of the proton could at best
tends higher in energy than predicted by calculations be guessed at in reference [21], the charm partonic dis-
that have neglected the forward component. While this tribution function has now been determined by collider
promptneutrinofluxcannotexplainthehigh-energyneu- experiments. For this paper, we use the PDF set CT10
trino flux observed by IceCube, it potentially represents [27].
abackgroundtothecosmicneutrinofluxandistherefore We next focus on the contribution of the charm cross
critical to characterize. section where the spectator quark bleaches its color by
combiningwiththevalencequarksintheincidentproton,
∂σ(pp c ) ∂σ(pp c¯ )
s a
→ = dx dx dx dx →
p ∂x Z u1 u2 d a (cid:20) ∂x
s a
P(x ,x ,x )δ(1 x x x x x ) ,
u1 u2 d − s− a− u1 − u2 − d (cid:21)
Spectator c¯
c(x ) (2)
a
wherex isthespectatorcharmquarkfractionalmomen-
s
tum and xu1,xu2,xd are the valence quarks fractional
g(xt) momenta. We enforce xs =1−xa−xu1−xu2−xd such
that the spectator charm quark carries all momentum
notcarriedby the valence quarksor activecharmquark.
FIG.1. Apartonicinteraction betweentwoprotonsviaac-c¯ Finally, P(x ,x ,x ) is the probability distribution of
u1 u2 d
quark pair in one proton and a gluon in the other. We refer the valence quarks fractional momentums given by the
tothecharmquarkthatinteractswiththegluonas“active,” normalized parton distribution functions of the valence
theother as “spectator.”
quarks,
This paper is organized as follows: in section II, the
u (x )u (x )
differential cross section for production of the spectator P(x ,x ,x )= v u1 v u2 d (x ). (3)
u1 u2 d 2 2 v d
charm quark is derived within the conventional frame-
workofperturbativeQCD.InsectionIII,weevaluatethe TheresultingcharmcrosssectionisshowninFig. 3for
associatedupperlimitfluxofpromptneutrinos. Wesub- an incident proton energy E = 106 GeV. The forward
p
sequently discuss in section IV the effect of the IceCube component is shown along with the central component
veto routinely imposed in IceCube analyses. It requires dominated by the subprocess gg cc¯, Eq. (6). While
→
that candidatecosmic neutrinos arenotaccompaniedby the active charm component represents a subdominant
particles that signal the presence of an air shower. We contribution to the central production of charmed par-
finally confrontour estimates of the charm flux with the ticles, the spectator contribution dominates for x-values
data in section V. above0.2. Thespectatorcharmeffectivelybecomesava-
lence quark during this interaction, resulting in the for-
II The Forward Charm Cross Section wardproduction. NotethatperturbativeQCDgenerates
a forwardcomponent of the charmcross section without
We first perform the leading order calculation of charm resorting to intrinsic charm. The subprocess effectively
quark production including the diagrams involving con- promotes the spectator charm to a valence quark. The
3
q q g g
104
SpectatorCharmxΛc=xc/1.1
ActiveCharm
103 ISRR-422data(pp Λc)
→
102
b]
µ
[
σx
∂∂ 101
c(c¯) c(c¯) c(c¯) 100
10 1
−0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
x
FIG. 4. The Feynman xF dependence for Λc production is
compared with ISRdata [29] at √s=63 GeV.
the otherprotonconstituents intocharmhadronsreduce
its fractional momentum. We implement a hadroniza-
tion scheme inspired by reference [28] by reducing the
charmed baryon momentum, xΛc = xs/1.1. In Fig. 4,
FIG. 2. The partonic interaction diagrams that lead to the
we show that this procedure actually describes the x
F
production of a spectator charm quark in a proton-proton
dependence of the highest energy measurement avail-
interaction.
able from ISR R-422. This archival data represent the
phenomenology is therefore similar to that of intrinsic strongestconstraintonhowmuchmomentumcanbecar-
charm quarks in the proton and we do not anticipate ried by ΛcD pairs.
that an analysis modeling intrinsic charm will lead to The calculation described above leads to atmospheric
different conclusions. neutrino fluxes that exceed the data. As the normaliza-
tionofthe crosssectionis sensitive to the scalesdefining
105
the perturbative QCD expansion, we let it float and ob-
SpectatorCharm
104 Ep=106GeV AGclutiovneFusion t0a.2in14a. mInaxoimthaelrvwalouredsf,orthaerneorims aalitzeantsioionnσi(nΛnc)o/rσm(acsli)za=-
tion between the atmospheric neutrino and ISR data;
103 see also Section III. We repeat the same procedure for
b] D¯0 andD− mesonhadronizationwith a shapechangeof
µ
[ x =3x /4andcrosssectionnormalizationof0.476and
σx D s
∂∂102 0.238 respectively.
An important note, the hadronization scheme chosen
101 is maximal without exceeding measured neutrino fluxes.
Wethusobtainanupperlimitoftheforwardcharmcon-
tribution to the neutrino flux and explore its potential
100
0.0 0.2 0.4 0.6 0.8 1.0 impact on the IceCube events observed. Although it is
x straightforwardtoincludethehigherorderdiagrams,the
changesintroducedarewellwithintheuncertaintiesasso-
FIG. 3. The differential cross sections for producing charm ciated with the hadronization that is poorly constrained
quarksasafunctionoftheirlongitudinalmomentumfraction. by data.
The central gluon fusion component is shown along with the
contributionofthediagramswithanactivecharmquark. The III Prompt Neutrino Flux Upper Limit
spectator charm’s differential cross section is peaked at large
xF carryingthemajorityofthemomentumoftheprotonthat We next calculate the neutrino spectrum from the decay
produced it. ofthecharmedhadronsusingtheMCEqatmosphericin-
teraction package [30]. We use two parameterizations of
Acaveatatthispointisthatthespectatorcharmcross the incident cosmic ray flux from Gaisser and collabora-
section calculates the production of a charm quark and tors [31–33]. These fits to the cosmic ray flux assume a
not a charmedhadron. The hadronizationof the specta- very different primary composition, yet they yield very
tor charm quark with the valence quarks of the incident similarresults inthis context. We use the H3afit, which
proton results in the dominant contribution to forward assumes a heavy nuclei composition at high energies, for
scattering. The strings linking the charm quark with the rest of the paper.
4
The neutrino spectrum upper limit resulting from the spectrum of E−1.91, including a very high energy neu-
maximalcontributionofthehadronizationofthespecta- trino event with deposited energy of 2.6 PeV [37]. The
tor charm described in the previous section is compared flux ofcharmoriginshownin Fig. 6 cannotdescribe this
to the highest energy measurements [34] of the atmo- result.
sphericelectronfluxinFig.5. Itiscomparedtotheoneof
Expected Through Going Events in 2 Years
Enbergetal. referredtoasERS[1]. Notethatourfloat-
ingnormalizationspectatorcharmneutrinofluxaddedto 102 Spectator νµ+ν¯µ
the conventional pion and kaon neutrino flux [35] satu- Conventional Atmospheric ν +ν¯
µ µ
ratestheatmosphericelectronneutrinofluxmeasuredby E−2.2 Best Fit Cosmic νµ+ν¯µ
IceCube [34]. A future measurement with higher statis- Observed Events
tics will be very useful in this context. IceCube has also
performed an analysis [11] of neutrino events starting in 101
the detector that has resulted in an upper limit of the nts
e
prompt neutrino flux. We note however that the flux Ev
was modeled after the ERS flux and only the normaliza-
tion was varied. As seen in Fig. 5, the spectator charm
100
neutrinospectrumhasadifferentshape,closertoanE−2
spectrum below 100 TeV. This allows the model to par-
tially evade the current IceCube limits.
10−4 ERSνe(2008) 10-1104 105 106
Energy Proxy [GeV]
SpectatorνeH3a
1]− 10−5 SpectatorνeH4a
S Conventionalνe FIG. 6. The expected number of events in two years of Ice-
21sr−− 10−6 TAotmtaolsApthmeroicspνheericνe CcoumbpealroeotkhinegspfeocrtaνtµorevneenuttsricnoomeixnpgecttherdounguhmtbheeroEfaervthen.tsWtoe
m
thebest fit astrophysical spectrum found in [36].
c
GeV 10−7
)[
ν( IV Comparison to IceCube Observations
2φ 10−8
E
We have fixed a normalization of our maximal prompt
10−1902 103 104 105 106 107 flux that saturates the IceCube measurements of the at-
mospheric electron neutrino flux in the ten TeV energy
Eν[GeV] range as well as the muon neutrino data in the 100 TeV
energyrange;seeFig. 5andFig. 6. Atmosphericneutri-
FIG.5. Themaximalpromptneutrinospectrumforthespec- nosareproducedinairshowersandareconsequentlyac-
tatorcharmandEnbergetal. calculations. Thespectatorνe companiedundergroundbyhigh-energymuonsproduced
flux saturates the 10 TeV atmospheric νe flux measurement, in the same shower. Therefore, IceCube’s veto based
showingthenormalizationforthecharmmesonhadronization
searches for cosmic neutrinos routinely introduce a so-
cannot be larger. Note, the ERS flux is only shown down to
calledself-veto,where anatmosphericneutrino is vetoed
1 TeV.
when accompanied by atmospheric muons [38]. We use
We also calculated the expected number of ν events the technique of reference [38] to calculate the self-veto
µ
penetratingtheEarth;theresultiscomparedtothe first probability of the spectator charm neutrino flux modulo
two years of IceCube [36] in Fig. 6. It is also compared a modification that we discuss next.
to the best fit cosmic neutrino spectrum. An important For spectator charm, the charmed hadron carries a
point about the flux from the spectator charm neutrino large fraction of the incident proton energy. This re-
is the flavor and neutrino antineutrino ratio: for the as- duces the energyofthe remainingshower,whichreduces
trophysical neutrino flux the flavor ratio is assumed to the probability for producing an high-energy muon in a
be 1:1:1 for νe : νµ : ντ and equal parts neutrino and second,uncorrelatedhadron. Wecontrastcorrelatedand
antineutrino. Incontrast,for the spectator neutrino flux uncorrelatedmuons,withthe correlatedproducedin the
the flavor ratio is 1:1:0 and the neutrino to antineu- hadron decay along with the observed neutrino, and the
∼
trino ratio is 1:10. This is important when comparing uncorrelated originating from other particles in the air
∼
the spectator neutrino flux for different analyses as they shower. While negligible for central charm production,
tend to prefer specific neutrino flavors. for spectator charm this effect can be significant in cal-
Whileonemaybetemptedtoconcludethatthespecta- culatingtheuncorrelatedmuonself-vetoprobability. For
tor neutrino flux may accommodate the data, this is not the correlated muon, a muon that is produced by the
the case. The updated analysis using six years of Ice- same hadron decay as the neutrino, there is no need to
Cube livetime has revealed a high-energy astrophysical makethismodification. Theuncorrelatedmuonandcor-
5
1.0 its Feynman x distribution are concerned. Clearly an
F
0DegreesZenith additionalastrophysicalfluxisrequiredtoachieveagree-
60DegressZenith ment between the expected and observed events. Even
0.8 75DegreesZenith
afterremovingtheself-vetoofthespectatorneutrinoflux
we reach the same conclusion. The basic reason for the
te 0.6 disagreementisthesofteningoftheatmosphericneutrino
a
R
spectrum,whichisstronglysuppressedabove100TeV—
g
n
ssi 0.4 the prompt flux simply traces the atmospheric cosmic
Pa ray spectrum and cannot accommodate the highest en-
ergy events.
0.2
Solid: Uncorrelated,Dashed: Correlated V Conclusions
0.0103 104 105 106 107 Wehaveusedleading-orderperturbativeQCDtoempha-
E size the fact that one expects a central as well as a for-
ν
ward component of charm production, a fact clearly un-
derscoredbythedataforstrangeparticleproduction. We
FIG. 7. The uncorrelated and correlated self-veto passing
havecomputedthecharmcrosssectionandtheFeynman-
rateforthespectatorcharmneutrinofluxinIceCubeatthree
x distribution of the secondary charm particles includ-
differentzenithangles. Theuncorrelatedpassingrateenforces F
shower energy conservation as described in thetext. ing both components with the normalization is treated
as a parameter. It cannot be reliably predicted because
10 6 of large logartihms associated with the small value of
−
m /√s at these energies. The normalization was maxi-
c
mizedwithoutexceedingthecharmmeasurementsatcol-
1]− 10 7 liders and the high-energy atmospheric neutrino data in
S −
1− underground experiments. We subsequently calculated
r
2s− the upper limit flux of prompt neutrinos from the decay
m 10 8 of charmed particles in IceCube, which is clearly domi-
c −
V nated by a potential forward component of the flux. Fi-
e
G nally, we applied the effect of self-veto on the prompt
)[
2Eφν( 10−9 SSppeeccttaattoorrSNoourtthheerrnnSSkkyy ntieountrfoinrotwflouxyeaanrsdofshIcoewCeudbteh.eWeexpfoeucnteddtheavtentthedpisrtormibput-
HESE3YearBestFit
MESE2YearBestFit neutrino flux from a forwardcharmmay represent a sig-
10−11003 104 105 106 107 nificantbackgroundto the cosmic neutrino flux but can-
Eν[GeV] not explain the high-energy events observed by IceCube
at the highest energies.
FIG.8. Thespectatorcharmneutrinospectrumsummedover VI Acknowledgments
neutrino flavors is shown for the northern and southern sky,
with theself-veto effect added tothesouthern sky flux. Two Discussion with collaboratorsinside and outside the Ice-
IceCube veto-based-analysis best fit spectra summed over Cube Collaboration, too many to be listed, have greatly
neutrinoflavor are shown as a reference [11, 39]. shapedthispresentation. Weacknowledgethecomments
of M. Reno and M. Ahlers on an earlier version of the
related muon self-veto passing rates are shown in Fig. 7. manuscript. WealsothankA.FedynitchandJ.vanSan-
ten for assistance in modifying their programs. This re-
Using these results, we obtain Fig. 8, the maximal
searchwassupportedinpartbytheU.S.NationalScience
promptneutrino spectrumresultingfromforwardcharm
Foundation under Grants No. ANT-0937462 and PHY-
along the best fit of IceCube neutrino spectra obtained
1306958 and by the University of Wisconsin Research
in veto-imposedanalyses. We subsequently compute the
Committeewithfundsgrantedbythe WisconsinAlumni
corresponding number of events in the 2-year “MESE”
Research Foundation.
IceCube analysis [11] separately for the Southern and
Northern Hemispheres; see Fig. 9. For the Northern VII Appendix
Hemisphere, it may be tempting to conclude that the
data can be described by charm. This conclusion is Here we show the partonic cross sections used in this
helpedbythefactthatcosmicneutrinoswithPeVenergy paper with their respective threshold center of mass en-
and above are in any case absorbed by the Earth. How- ergy. These cross sections correspond to the Feynman
ever, in the southern sky, there is a significant disagree- diagrams shown in Fig.2. The cross sections follow in
mentbetweentheobservedeventsandtheexpectednum- Eqns. 4 through 6, with kinematic variables t =
min
berofeventsfortheextremespectatorneutrinofluxthat 2mc2, y0 = (sˆ2 m2)2/sˆ, tˆ0 = min(sˆ m2 tˆmin,y0),
we have constructed, both where its normalization and x0 =(1−4m2c/sˆ−)1/2 and σ0 =4πα2s(µF−)/(3sˆ−).
6
Spectator Conventional Penetrating Muons Prompt Spectator, no self-veto Observed Events
Southern Sky Northern Sky
102 102
unt101 unt101
o o
C C
nt nt
e e
Ev Ev
100 100
102 103 104 105 106 102 103 104 105 106
Desposited Energy [GeV] Desposited Energy [GeV]
FIG. 9. The expected number of events in both the northern and southern sky for two years in IceCube using a veto-based
detection scheme [11]. In the northern sky, the maximal flux from the spectator charm neutrino leaves little room for an
additional cosmic neutrino flux without exceeding the observed events. While in the southern sky, an additional cosmic
neutrino flux is needed to have agreement between the expected number of events and the observed number of events. Even
removing theself-veto effect discussed in section IV, themaximal prompt neutrinoflux cannot explain thehigh-energy events
observed in IceCube.
σˆ(qc qc)= σ0 1 tˆmin 1+ 2sˆ 2sˆln y0 ,sˆ =m2+tˆ /2+(m2tˆ +tˆ2 /4)1/2 (4)
→ 3 (cid:20)(cid:18) − y0 (cid:19)(cid:18) tˆmin(cid:19)− y0 (cid:18)tˆmin(cid:19)(cid:21) th c min c min min
σˆ(gc→gc)= 34σy00(cid:20)(cid:20)1+ 94ysˆ0(cid:18)1+ msˆ2c(cid:19)2− 29((tˆsˆ0−+mtˆm2ci)n + tˆ02tˆsˆmy0in + 9(sˆ−m2c −tˆ10)6(msˆ4c−m2c −tˆmin)(cid:21)(tˆ0−tˆmin) (5)
tˆ 4(sˆ2 6m2sˆ+6m4 sˆ m2 tˆ
+2(sˆ+m2)ln min + − c cln − c − min ,sˆ =m2+2tˆ
c tˆ0 9(sˆ−m2c) sˆ−m2−tˆ0 (cid:21) th c min
σˆ(gg cc¯)= σ0 1+ 4m2c + 4m2c ln 1+x0 x0 7+ 31m2c ,sˆ =4m2 (6)
→ 4 (cid:20)(cid:18) sˆ sˆ2 (cid:19) (cid:18)1 x0(cid:19)− 16(cid:18) sˆ (cid:19)(cid:21) th c
−
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