The LHCf data hadronic interactions and UHECR showers. Paolo Lipari LHCf meeting Catania, 6th july 2011

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1 The LHCf data hadronic interactions and UHECR showers Paolo Lipari LHCf meeting Catania, 6th july 2011

2 ~50 years of UHECR Problems of determination of: Energy Mass A Hadronic interaction Modeling Measure a single slice of the shower at the ground

3 ~50 years of UHECR hadrons Diferent components Hadronic interaction Modeling Measure a single slice of the shower at the ground

4 The Fly's Eye Detector concept Quasi-Calorimetric Energy Measurement Fluorescence Light

5 Observed Light Emitted Photons Geometry Atmospheric Absorption Shower Size Fluorescence Yields

6 Small Model dependence

7 Area Energy Shape depends on : Primary Identity Interaction Model

8

9 Longitudinal Development Longitudinal Development Shape studies

10 Fixed Target measurements COLLIDERS Nucleus targets Pion/kaon projectiles. Cover entire kinematical Phase Space [including fast particles in forward region] Fixed Target Cern Tevatron LHC

11 COMPOSITION of UHECR Very high astrophysical importance Controversial - inconsistent observations. Xmax Fluctuations of Xmax Other methods

12 AUGER

13 AUGER Shower fuctuations

14 HiRes 2009

15 HIRES 2009 Fluctuations on Xmax

16 Xmax and the Composition of Cosmic Rays

17 p He O Fe

18 p He O Fe Measurements of

19 p He O Fe Measurements of Composition evolution.

20 The theory curves <Xmax(E)> are determined by the parameters that describe hadronic interactions. (and by their energy dependence). Interaction Lengths Multiplicity Inclusive Spectra... Theoretical curves:

21 Importance of CORNERS Abrupt change in the variation of the properties of hadronic interactions with energy Abrupt change in the composition evolution.

22 Electromagnetic Showers versus Hadronic Showers Toy model discussion.

23 Electromagnetic Shower Pair production Bremsstrahlung Radiation Length (Energy independent) Vertices : theoretically understood (and scaling)

24 Electromagnetic Showers Logarithmic growth of the penetration. Energy Conservation 2 Elongation rate = 85 (g/cm )/decade

25 Heitler toy model for electromagnetic showerws Electron-photon particle Splitting length λ Critical energy ε

26 Electromagnetic showers: Fluctuations:

27 Proton Shower Vertices : theoretically not Understood (and energy dependent)

28 HADRONIC INTERACTIONS Leading nucleon 50% of energy π ο γγ Electromagnetic Shower Decay Inclusive spectra of secondary particles Interaction

29 Toy Model for hadronic shower Energy equally divided among n photons. n

30 st 1 interaction Development of photon shower of energy E/n

31 Interaction Length Equivalent to photon shower Particle production properties

32 Interaction length Softness Elongation Rate Evolution with Energy of the Interaction length Evolution with energy of the softness of the spectrum

33 Scaling model : 85 (g/cm2)/decade Increasing cross sections Softer spectra Elongation Rate for protons Log[Energy]

34 Total pp Cross Section

35 Interaction Lengths (proton, pion) π p

36 From LHCf TDR

37 Phenomenological Evidence for SCALING FERMILAB: pp Brenner et al (1982)

38 NUCLEAR efects: pp vs 12 p- C NA49

39 EXTRAPOLATION to HIGH ENERGY (Pythia pp)

40 EXTRAPOLATION to HIGH ENERGY (Pythia pp) Large scaling violation for central particles

41 EXTRAPOLATION to HIGH ENERGY (Pythia pp) Small scaling violation [?] for forward particles

42 Sibyll Montecarlo code

43 PYTHIA PROTON Spectra protons Antiprotons

44 PROTON Spectra (elasticity spectra)

45 PROTON Spectra (elasticity spectra)

46 From Cosmic Ray Data Hadronic Interactions C.R. DATA Astrophysical Information Astrophysical Composition Methods Hadronic Interactions 1 < A < 56 (very likely)

47 Astrophysical Composition Methods Energy Spectrum imprints of Energy Loss Cosmic Magnetic Spectrometer

48 IF one accepts (at least for the sake of discussion) the astrophysical hints of a proton dominated composition...

49 IF one accepts (at least for the sake of discussion) the astrophysical hints of a proton dominated composition... Proton Line!! (?)

50 If the highest energy CR are protons Models incorrect. Need to make the showers shorter! [higher cross sections, softer spectra] If the highest energy CR are mostly iron: Models incorrect. Need to make the showers longer! [smaller cross sections, harder spectra]

51 From Accelerator Data + Theory Astrophysics C.R. DATA Astrophysical Information Hadronic Interactions Energy Spectrum Composition Cross sections, Inclusive spectra Multiplicities

52 ... Let us measure the inclusive particle spectra at high energy in a laboratory!...

53 ... but the measurements have been performed...

54 LHCf data hep-ex/ [photon distributions in 2 very forward angular regions]

55

56 LARGE DISCREPANCIES!! What is the signifcance for the understanding of hadronic interactions? What is the impact on the interpretation of UHECR?

57 Pseudo-Rapidity versus angle: Very small angle production:

58

59 Directly relevant for UHECR shower development pt distribution dependence

60

61

62 Rapidity distribution [for a fxed energy] PT distribution [for a fxed energy]

63 Transverse-Momentum Distribution

64 Transverse-Momentum Distribution Tsallis parametrization Used by CMS

65 Pseudo-Rapidity Distribution (E = 1500 GeV)

66 Given a fxed Transverse-momentum distribution One obtains a pseudorapidity distribution Factorized transverse momentum distribution: Translation of the same shape for pseudo-rapidity

67

68 Fraction of events in angular acceptance windows

69 Fraction of events in angular acceptance windows

70 Ratio [High pseudo-rapidity] / [Low pseudo-rapidity]

71 LHCf data

72 Ratio [High Rapidity] / [Low Rapidity] for LHCf DATA

73 The pt distribution a sqrt[s] = 7 TeV is not a Gaussian of energy independent width. Data E (TeV)

74 Ratio [High Rapidity] / [Low Rapidity] DATA Pythia Sibyll

75 Common qualitative behaviour for ALL MC codes Curvature in the ratio With a minimum

76 Large diference between SIBYLL PYTHIA

77 Compare Pythia/Sibyll inclusive photon distribution: Remarkably similar! [pp interactions]

78 Compare Pythia/Sibyll charged pion distribution

79 Compare the Energy fow

80 Pythia (photon/charged pion energy distributions) Photon spectrum is softer

81 Average pt for photons for diferent energy regions

82

83 pt of photon determined by pt of parent pion `

84 Average pt for photons and pions for diferent energy regions SIBYLL MC code

85

86

87

88

89 Most of the large discrepancies between Data and Montecarlo codes can be attributed to an incorrect modeling of the Transverse Momentum distributions.

90 Most of the large discrepancies between Data and Montecarlo codes can be attributed to an incorrect modeling of the Transverse Momentum distributions. Without a good understanding of these Transverse Momentum distributions, it is not possible to interpret in a non-ambiguous way the LHCF published data for UHECR shower development.

91 Most of the large discrepancies between Data and Montecarlo codes can be attributed to an incorrect modeling of the Transverse Momentum distributions. Without a good understanding of these Transverse Momentum distributions, it is not possible to interpret in a non-ambiguous way the LHCF published data for UHECR shower development. Can the LHCf instrument (together with other detectors at LHC) give more information on the pseudo-rapidity distributions?

92 We are studying at the same time Gigantic Astrophysical Beasts Millions of light years away Length scale cm Microscopic Partonic constituents of matter -15 Length scale 10 cm Exciting Difcult

93 Xmax fuctuations Auger HiRes

94 Xmax fuctuations Auger Quasi monotonically Decreasing RMS Constant RMS HiRes

95 Overall comparison of Xmax data with QGSJET02 p and FE HIRES

96 FLUCTUATIONS Toy model on

97 Nuclear interaction. Several Nucleons Interact at same point.

98

99

100 Mixing Protons with Iron-nuclei

101 THEORY Construction of Hadronic Models

102 Hadronic Interactions Composite (complex) Objects Multiple interaction structure QCD

103 Cartoon of a pp interaction in the transverse plane

104 Total Cross section Properties of Particle Production Multiplicities Energy spectra...

105 Total Cross section Properties of Particle Production Multiplicities Energy spectra... Higher cross section Larger Multiplicity More complex events

106 Elastic Scattering Amplitude : PROFILE Function EIKONAL Function

107 Total, elastic, inelastic cross section Expressed in terms of the profle function

108 Total, Elastic, Difractive Cross Sections: 1 minute of 19th century physics : The OPTICAL ANALOGY. Absorption and Scattering of light from an Opaque screen

109 Black Disk Of radius R. Difraction Pattern

110 Elastic scattering distributions Larger Gray Disk smaller Black Disk

111 Absorption profles Elastic scattering

112 ISR 62.3 GeV CERN UA4 546 GeV

113 Absorption profle obtained from the elastic scattering of pp ISR, CERN SpS (UA4), CDF Failure of factorization

114 Interaction Probability Interpretation of the eikonal function Multiple interactions

115 Identifcation of Eikonal function with The average number of elementary interactions At impact parameter b. Cross section for elementary interactions

116 Identifcation of Eikonal function with The average number of elementary interactions At impact parameter b. Construction of Fluctuations of this average quantity. Explicit construction of the fnal state At the parton level.

117 Perturbative contribution to the Parton cross section Infrared Divergence!! (complete failure of perturbation theory) Attempts to resum the soft part.

118 Parton Distribution Function

119

120

121 MULTIPLE INTERACTIONS Estimate of the average number of Elementary interactions per pp scattering Spatial Distribution [proton spin] (Transverse coordinates) of the partonic constituents. Fluctuations of the parton confguration of an interactig hadron. Beyond PDF's Parton Distribution Functions

122 Good-Walker ansatz for inelastic difraction. [Extension of the optical analogy] Scattering of polarized light from a polarimeter Polarizing gray disk Incident beam: Absorption of Out scattered light In polarizations Elastic scattering inelastic difraction

123 Extension of the Good-Walker Ansatz to the scattering of Hadronic Waves. Observable states. Transmission eigenstates [ Parton Confguration states ] (Miettinen-Pumplin) 2 orthonormal basis In Hilbert space

124 One profle function for each transmission eigenstate

125

126 Description of the Underlying Event Qualitative result: Events with 1 hard scatterings Have more activity (larger multiplicity,...) Than the average event. 1. Select more central (lower b) interactions. 2. Select events where the colliding hadrons have certain parton confgurations (for example: more gluons in appropriate x interval)

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