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Estimation of charm production cross Estimation of charm production cross section in hadronic interactions section in hadronic interactions

at high energies at high energies ss > 1.8 TeV > 1.8 TeV

Yu.F. NovoseltsevYu.F. Novoseltsev11, G.M., G.M. VereshkovVereshkov1,21,2

11Institute for Nuclear Research of RASInstitute for Nuclear Research of RAS22Physics Research Institute of Rostov State UniversityPhysics Research Institute of Rostov State University

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The analysis is carried out within the frame of phenomenological model of diffractive production and quark statistics based on additive quark model (AQM)

We make use of low energy data on charm production and collider data on diffractive dissociation

At collider energies 200, 540, 900, 1800 GeV , the values of σppccX (s) were obtained by a quark statistics method

It is established, that logarithmic function with universal numerical parameters describes the whole set of low-energy and high-energy data with high accuracy

The expected values of cross section are σppccX = 250 ± 15 µb at TEVATRON energy s = 1.96 TeV and 355 ± 22 µb at LHC energy s = 14 TeV

Discussion

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The estimation of the total charm production cross section is based on The estimation of the total charm production cross section is based on processing of collider data on diffractive dissociation with use of processing of collider data on diffractive dissociation with use of phenomenological model of diffractive charm production and quark phenomenological model of diffractive charm production and quark statistics.statistics.

Cross section of diffractive dissociation in pp-interactons:Cross section of diffractive dissociation in pp-interactons: SPS --- SPS --- √s = 200 GeV, 900 GeV (Ansorge et al., 1986)√s = 200 GeV, 900 GeV (Ansorge et al., 1986) TEVATRON --- √s = 546 GeV, 1800 Gev (Abe et al., 1994)TEVATRON --- √s = 546 GeV, 1800 Gev (Abe et al., 1994)

σσDDDD(pp (pp X) = C X) = CDDDD ln(s/s ln(s/soo))

The basic assumptions consist in the following:The basic assumptions consist in the following: 1) charm production occurs in process of diffractive 1) charm production occurs in process of diffractive dissociation;dissociation; 2) charm production cross section is extracted from2) charm production cross section is extracted from total cross section by quark statistics rules:total cross section by quark statistics rules:

σσtottot( pp ( pp cc + X) ≈ k cc + X) ≈ kcccc× × σσDDDD(pp (pp X), k X), kcccc ≈ 0.025 ± 0.004 ≈ 0.025 ± 0.004 uu : dd : ss : cc = 1 : 1 : (0.38 ± 0.07) : (0.06 ± 0.01)uu : dd : ss : cc = 1 : 1 : (0.38 ± 0.07) : (0.06 ± 0.01)

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Data on total cross section of charm production Data on total cross section of charm production at at s = 20 − 40 GeVs = 20 − 40 GeV

To begin with, we clear up the opportunities of AQM and

logarithmic dependence for cross section in the description of data on charm production in pN and N interactions at low

energies:

σNcc+X(s) = ⅔ σpNcc+X(3s/2)

σpNcc+X(s) = CpN ln(s/so)

CpN = 28.84 ± 2.10 μb, √so = 18.51 ± 0.36 GeV , 2 = 0.89 (1)

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σσ(pp (pp cc +X) at collider energies cc +X) at collider energies

√√s, GeV 200 546 900 1800s, GeV 200 546 900 1800

σσDDDD, mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± 0.44, mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± 0.44

σσ(pp (pp cc +X) cc +X) = k= kcccc × × σσDD DD ,, (2)(2)

σσpp pp cc +X cc +X, , μμb 120 ± 21 197 ± 32 195 ± 32 236 ± 38b 120 ± 21 197 ± 32 195 ± 32 236 ± 38

The obtained values of charm production cross section have the statusof model dependent processing collider data

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Joint fit of low-energy and high-energy data Joint fit of low-energy and high-energy data on charm productionon charm production

The strip correspondsThe strip correspondsto 90 % CLto 90 % CL

The charm production cross section in hadronic interaction is described The charm production cross section in hadronic interaction is described by universal logarithmic dependenceby universal logarithmic dependence

Values of C and sValues of C and soo in in

(1) and (3) coincide (1) and (3) coincide within the limits of within the limits of statistical errorsstatistical errors

(3 )(3 )

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√

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Ideas of phenomenological models of diffractive production Ideas of phenomenological models of diffractive production and quark statistics were repeatedly tested at processing and quark statistics were repeatedly tested at processing

most variousmost various experimental data.experimental data.

These models give reliable quantitative predictions at theThese models give reliable quantitative predictions at the accuracy level 10 - 20 % after fixing several parameters byaccuracy level 10 - 20 % after fixing several parameters by experimental data.experimental data.

Therefore we consider possible to use the results (3) for Therefore we consider possible to use the results (3) for forecasting cross section of charm production in pp/ppforecasting cross section of charm production in pp/pp

interactions in overaccelerating energy range.interactions in overaccelerating energy range.

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Forecast of charm production cross sectionForecast of charm production cross sectionat at √s > 1.8 TeV√s > 1.8 TeV

These results mean the flux of “prompt” muons becomes equal to the flux of “conventional” (from ,K-mesons) muons of CR at Eμ = 500 − 600 TeV

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There are three possible (and alternative) variants of There are three possible (and alternative) variants of results, each of which represents the certain interest.results, each of which represents the certain interest.

The measured flux of CR muons within the limits of measurement errors The measured flux of CR muons within the limits of measurement errors coincides with calibration flux calculated according to the estimation (4).coincides with calibration flux calculated according to the estimation (4).

In this case the estimation (4) can be used for testing microscopic models.In this case the estimation (4) can be used for testing microscopic models.

The measured flux of CR muons will exceed noticeably the calibration value, The measured flux of CR muons will exceed noticeably the calibration value, but the but the σσpp pp ccX ccX at energies in the region of a break of CR energy spectrum at energies in the region of a break of CR energy spectrum will stay essentially smaller 10 mb. In this case it will be necessary to will stay essentially smaller 10 mb. In this case it will be necessary to recognize, that either quark statistics rules become incorrect in the area of recognize, that either quark statistics rules become incorrect in the area of high energies, or the new mechanism of charm production, distinct from the high energies, or the new mechanism of charm production, distinct from the diffractive one, is included at these energies.diffractive one, is included at these energies.

The measured flux of CR muons will correspond formally to The measured flux of CR muons will correspond formally to σσpp pp ccX ccX > 10 mb > 10 mb This result will mean that VHE muons carry away the energy from EAS This result will mean that VHE muons carry away the energy from EAS forming an observable break of CR spectrum. It is necessary to note, that forming an observable break of CR spectrum. It is necessary to note, that sources of such big numbers of VHE muons, most likely, are not reduced to sources of such big numbers of VHE muons, most likely, are not reduced to charmed particles charmed particles −− a New physics will required for interpretation of such a New physics will required for interpretation of such effect.effect.

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