Atmospheric Neutrino Background
Hallsie Reno, University of Iowa PAHEN Berlin, September 27, 2019
Supported in part by a US Department of Energy grant. Collaborators: I. Sarcevic, A. Bhattacharya, R. Enberg, A. Stasto, Y. S. Jeong, C. S. Kim, Weidong Bai Neutrinos produced in the atmosphere
• background to the astrophysical flux • reflect the cosmic ray spectrum at Earth, not the spectrum at production (not the diffuse astrophysical spectrum) • depend on the cosmic Figure from https://astro.desy.de/ ray composition
2 Scaling by approximate Atmospheric neutrino flux CR energy spectrum “conventional flux” ⇡ – uncertainties in E2.7 hadronic models, ⌫ differential cross sections K
astrophysical “prompt flux” – D uncertainties in QCD charm production 2 E cartoon
E Pdecay(E)=1 exp( D/ c⌧) 1.7 1 2.7 2 EGeV cm ssrGeV D/ c⌧ = E /E ⇠ 3 ' c Atmospheric flux
IceCube, Astrophys. J. 833 (2016) 3 (1607.08006) IceCube,PRD 91, 12204 (2015) arXiv:1504.03753
4 Flavor ratios, anti/neutrinos of prompt flux
Prompt flux from charm: ⌫e : ⌫µ : µ =1:1:1 + + D ` ⌫`X (16 17%) ⌫
First opportunity to produce )*:
E⌧ 0.9ED Ds ⌧⌫⌧ (5.5%) h i' ! 5 Spectrum weighted Z-moments
1 ⇥k(E0,X) dn(k j; E0,E) S(k j)= dE0 ! ! (E ) dE ZE k 0 ⇥k(E,X) S(k j)=Zkj(E) ! k(E)
1 k(E0,X) k(E) dn(k j; E0,E) Z (E)= dE0 ! kj (E,X) (E ) dE ZE k k 0 Spectrum weights favor forward production of charm – want the largest E (charmed meson) given E’ (cosmic ray nucleon).
Spectrum weighted Z-moments are used in approximate solutions to the coupled cascade equations of cosmic ray nucleons, charm particles, leptons from their decays. 6 Analytic approximation (AA) Cosmic ray – ⇤M = M /(1 ZMM) low ZNMZM = N nucleon flux ⇡ 1 Z ✏c = 115 GeV NN ✏K = 850 GeV Z Z ln( / ) M c ⇥high = NM M M N c ⇥ 1 Z 1 / E N ✏D 108 GeV NN N M c ⇠ • Exponential atmosphere (at one T), 1D, approximate factorization of depth dependence. • Gaisser et al., PoS, ICRC2019:893: Analytic approximation compared to numerical solution (MCEq, Fedynitch et al., PoS, ICRC2015:1129) is very good. • Angular distribution: factor of 1/cos!∗, also account for curvature of the Earth. Cosmic Rays and Particle Physics, T. Gaisser, Cambridge U Press; L. V. Volkova, Sov. J. Nucl. Phys. 31 (1980); P. Lipari, Astropart. Phys. 1 (1993) 7 Perturbative charm pair production
Refs: e.g., Thunman, Ingelman, Gondolo, Astropart. Phys. (1996) at LO, Pasquali, MHR, Sarcevic, Phys. Rev. D (1999) at NLO modeled with x dependent k-factor (PRS)
LO expression for charm production: pdg.lbl.gov
(pp ccX¯ ) dx1 dx2 G(x1,µ)G(x2,µ)ˆ GG cc¯(x1x2s) ! ' ! Z x ,x : 1 2 1 2 4Mcc¯ x1,2 = xF + xF xF = x1 x2 2 s ± ! r x x = E/E0 7 6 F ' E E 10 GeV x2 10 x x 0.1,x 1 ⇠ ! ⇠ 1 ' F ⇠ 2 ⌧ 8 Charm production: three ways ln 1/' • NLO QCD evaluation of charm pair cross section and energy distribution with nuclear corrections (nCTEQ pdfs). Long history of theory of heavy flavor production. • Dipole Model: Soyez (form from approx. solution to nonlinear BK equation), Block et ln #$ al. approximation to F2 (phenomenological dipole cross section), Albacete et al. (AAMQS, From Gelis et al. rcBK). Multiple ways to include nuclear Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 corrections: Glauber-Gribov or A-dependent saturation scale. • kT factorization, low x off-shell gluon. Nuclear Nason, Dawson, Ellis, NP B303 (1988), effects through nonlinear term scaling like NP B373 (1992); Soyez, Phys. Lett. cube root of A. 655B (2007) 32, Albacete et al. Phys. Rev. D 80 (2009) 034031; Kutak and Sapeta, Phys. Rev. D 86 (2012) 094043.
9 LHCb data to “calibrate” charm
NLO perturbative for example, with a range of scale factors and dependence.
For the prompt flux from charm, need even larger rapidities (more forward production).
1 pz y = tanh E ! LHCb, Nucl. Phys. B 871 (2013) 1; JHEP 03 (2016) 159, Bhattacharya et al.,
Dipole
Uncertainty band: MF=mc – 4 mc
kT factorization
Uncertainty band: with and without saturation, kT limits LHCb, Nucl. Phys. B 871 (2013) 1; JHEP 03 (2016) 159, Bhattacharya et al., JHEP 1611(2016) 167 11 Atmospheric neutrino flux from charm
broken power law Gaisser et al. CR parameterization
Bhattacharya eta al, JHEP 1506 (2015) 110; Bhattacharya et al., JHEP 1611 (2016) 167 • Error band dictated in part by LHC experiment, in part by QCD uncertainties. • Two realistic cosmic ray spectra and composition, one simple cosmic ray parameterization (for comparison) and nuclear corrections (green). • Black: no nuclear corrections in target Nitrogen, all the rest include nuclear corrections. Nuclear corrections decrease result by 20-30%. 12 Atmospheric neutrino flux from charm
• Conventional flux: vertical muon neutrinos plus antineutrinos. • Dipole model gives larger flux than perturbative calculation. • Black line: 0.54 ERS from Radel and Schoenen for IceCube, ICRC 2015 (2015) 1079. • Short green line: approximate IceCube limit Bhattacharya et al., JHEP 1611 (2016) 167 from Astrophys. J. 833 (2016) 3. Dipole model here compared to ERS: updated cosmic ray inputs, different Zpp , updated fragmentation fractions. 13 Comparison with other recent results
Use the broken power law for comparison with recent results from other groups
GMS: Garzelli, Moch and Sigl, JHEP 10 (2015) 115 using POWHEG BOX and Pythia; GRRST: Gauld et al, JHEP 02 (2016) 130 with different assessment of PDF uncertainties. See also Benzke, Garzelli, Kniehl, Kramer, Moch, Sigl, JHEP 1712 (2017) 021.
14 Prompt atmospheric tau neutrinos plus antineutrinos Tau neutrino flux about 1/10 of the muon neutrino flux
Ds ⌧⌫⌧ ⌧ ⌫ X ! ! ⌧ Green band is from oscillation of conventional muon neutrinos, vertical to horizontal. Bhattacharya et al., JHEP 1611 (2016) 167 15 Other effects: intrinsic charm?
Laha and Brodsky, PRD 96 (2017);
See also, Halzen and Wille, arXiv: 1601.03044; PRD 94 (2016)
Cross section scales in energy like pp cross section, not perturbative charm cross section. Connect atmospheric charm to lower energy intrinsic charm.
Approximate IceCube limit (2016) Intrinsic charm would enhance forward charm production, therefore, also the prompt neutrino flux.
16 Intrinsic charm at SHiP? 400 GeV proton beam on a beam dump, designed to search for hidden sector particles. intrinsic charm: Alekhin et al, very forward Rept. Prog. Phys. 79 (2016) and has a weak Bai & Reno, JHEP02 (2019) 077 dependence on beam energy
https://ship.web.cern.ch/ship/ Also production of tau neutrinos. Beam dump facility, 2027
17 DsTau Experiment at CERN 400 GeV protons on a thin tungsten target. Look for kinks in tracks in emulsion for !" → $ + &$ (1000 events according to perturbative estimate).
intrinsic charm
perturbative
Bai & Reno, JHEP02 (2019) 077 Pilot run in 2018, runs in 2021 & 2022 18 FASER experiment at CERN ForwArd Seach ExpeRiment for light extremely weakly-interacting particles. Result: there will be (very) forward production of charm and decays to neutrinos.
arXiv:1901.04468 Approved for small detector to be installed during shutdown to be ready for Run 3. 19 Prompt atmospheric neutrino flux - perspectives
• If we had a completely reliable calculation, we wouldn’t need three different approaches. • Charm mass close to the GeV scale is a problem • And small-x extrapolations below measured regime. • Nuclear corrections for nitrogen target can suppress the flux predictions by 20-35%. . • Outlier PDFs give a much larger band of uncertainty in the prompt neutrino flux will appear, as shown by other authors. • Chances to measure forward charm: SHiP at low energy, FASER (FASER!) at the LHC could be another possibility. • Hadronic dependence – new tools to use, e.g., Dembinski et al., and Fedynitch et al., PoS (ICRC2017) 1019. MCEq: numerical solution to cascade equations, Fedynitch et al., arXiv:1503.0054; measurements of hadronic interactions in SHINE, NA61.
20 21 Flavor ratios, anti/neutrinos of conventional flux ⇡+ µ+⌫
Higher energies, muons don’t decay, but kaons contribute
E.g., Honda et al., PRD 75 (2007), using DPMJET-III, for Kamioka, calibrated to observed atmospheric muon flux, including 3-dim & geomagnetic corrections. See also Barr et al., PRD 70 (2004). Calculational method
d⇥j ⇥j ⇥j High enough = dec + S(k j) dX j j ! energies that X muons are stable . 1 ⇥k(E0) dn(k j; E0,E) S(k j)= dE0 ! ! (E ) dE ZE k 0 e.g., pA DX ! dn(k j; E ,E ) 1 d (kA jY ; E ,E ) ! k j = ! k j Production dEj kA(Ek) dEj e.g., D ⌫ X ! µ dn(k j; Ek,Ej) 1 d (k jY ; Ek,Ej) ! = ! Decay dEj K dEj Need cosmic ray flux (j=N) and energy distribution of the
final state particle. 23 Input cosmic ray spectra, composition
All particle spectrum & nucleon spectrum
Gaisser, Stanev & Tilav, 1303.3565.
Traditional to use a broken power law CR spectrum to From Table 1, Gaisser, Astropart. Phys. 35 compare flux calculations. (2012) 801
24 Comparison with more recent results
Broken power law, with CT14nlo fit and GM-VFNS, Benzke, et al., JHEP 1712 (2017) 021.
25 NLO QCD result for prompt neutrino flux
• BERSS: Bhattacharya et al., JHEP 06 (2015) 110 uses CT10 PDFs with no nuclear corrections. • Nuclear corrections via nCTEQ15 parton distribution functions reduce the flux by 20-35%, but B hadron contributions increase by ~10%. • Multi-component cosmic ray flux – two models, Gaisser & Gaisser, Stanev and Tilav. 26 Comparison with ERS
• PDFs nearly the same, but the differential energy distribution of the charm is different: dipole model vs perturbative calculation. The Z-moment emphasizes large xE, which does not have a large contribution to the cross section. The ratio of the Z-moments is approx. factor of 1.5 (ERS approximately 1.5xBERSS). • We use a different value of Zpp: in ERS, we used the Thunman et al (TIG, Astropart. Phys. 5 (1996)) PYTHIA value, ZERS(103 GeV) 0.5 pp ' ZBERSS(103 GeV) 0.27 pp ' d Here: (1 x )0.51 dx E E ⇠ 27