Does the E791 experiment have measured the pion wave function. Victor Chernyak. Budker Institute of Nuclear Physics, Novosibirsk, Russia
|
|
- Lorena Harrell
- 5 years ago
- Views:
Transcription
1 Does the E791 experiment have measured the pion wave function profile? Victor Chernyak Budker Institute of Nuclear Physics, Novosibirsk, Russia Abstract The cross section of hard diffractive dissociation of the pion into two jets is calculated. It is obtained that the distribution of jets in longitudinal momenta is not simply proportional to the profile of the pion wave function, but depends on it in a complicated way. In particular, it is shown that, under the conditions of the E791 experiment, the momentum distribution of jets is similar in form for the asymptotic and CZ wave functions, and the ratio of cross sections differs from unity only within a factor of two. We argue therefore that, unfortunately, the E791-experiment have not measured yet the profile of the pion wave function. For this, the experimental accuracy has to be increased essentially. 1. The E791 experiment at Fermilab [1] has measured recently the cross section of hard diffractive dissociation of the pion into two jets. In particular, the distribution of jets in longitudinal momentum fractions y 1 and y 2, (y 1 + y 2 )=1, has been measured. The main purpose was to obtain in this way the information about the leading twist pion wave function φ π (x 1,x 2 ), which describes the distribition of quarks inside the pion in momentum fractions x 1 and x 2, (x 1 + x 2 )=1. The hope was based on the theoretical calculations of this cross section [2]. It has been obtained in these papers that the cross section is simply proportional to the pion wave function squared: dσ/dy 1 φ π (y 1 ) 2.Insuch a case, it would be sufficient to measure only the gross features of dσ/dy 1
2 x 1 p π p 1 p π φ π M x 2 p π q 1 q 2 p 2 g p ξ (u) p Figure 1: Kinematics and notations to reveal the main characteristic properties of φ π (x), and to discriminate between various available models of φ π (x). The purpose of this paper is to show that this is not the case and that, unfortunately, the real situation is much more complicated, with dσ/dy depending on φ π (x) in a highly nontrivial way. We give below (in a short form) the results of our calculation of this cross section. 2. The kinematics of the process is shown in fig. 1. The upper blob M represents the hard kernel of the amplitude which includes the hard gluon exchange. The two soft external gluons are attached in all possible ways to the hard kernel, this gives 31 Feynman diagrams on the whole. Two of them are represented explicitly in fig. 2 and fig. 3. The lower blob represents the (skewed) gluon structure function of the target, for which we take the nucleon. The hard part of the amplitude can be considered as scattering of the pion on the gluon: π + g 1 ψ 1 + ψ 2 + g 2. In the c.m.s. and to the leading twist accuracy, the initial and final gluons can be considered to be on shell, with transverse polarizations, carrying fractions (u + ξ) and(u ξ) ofthemean nucleon momentum P. 1 The nucleon can be considered as being spinless, 1 The small skewedness, ξ 1, is always implied. It is typically: ξ 10 2,inthe Fermilab experiment. 2
3 and its skewed gluon distribution g ξ (u, t) =g ξ ( u, t); 1 <u<1(see[3] and [4]) is defined as: P A a, λ (z 1) A b, ρ (z 2) P = gλρ δ ab du g ξ (u, t) (u + ξ + iɛ)(u ξ iɛ) 1 ( e i(u+ξ)(pz 1 )+i(u ξ)(pz 2 ) + e ) i(u ξ)(pz 1)+i(u+ξ)(Pz 2 ). (1) 2 This is equivalent to the standard definition: P G a µλ (z 1) G a λν (z 2) P =2P µ P ν 1 1 du g ξ (u, t) 1 ( e i(u+ξ)(pz 1 )+i(u ξ)(pz 2 ) + e ) i(u ξ)(pz 1)+i(u+ξ)(Pz 2 ). (2) 2 The kinematical variables are defined as: q 1 =(u + ξ) P, q 2 =(u ξ) P, P =(P + P )/2, =(q 1 q 2 )=2ξ P, ξ = k2 y 1 y 2 s, z 1 = u + ξ 2 ξ, z 2 = u ξ, (3) 2 ξ z 1 z 2 =1, 2(p π ) = M 2 = k2, y 1 y 2 the final quarks are on shell, carry the fractions y 1 and y 2 of the initial pion energy, and their transverse momenta are: (k +(q /2)) and ( k + (q /2)), q k,whereq is the small final transverse momentum of the nucleon, while k is large. According to the well developed approach to description of hard exclusive processes in QCD [5-8] (see [9] for a review), the hard exchanged gluon in all diagrams (see figs.2 and 3) has to be considered as a part of the hard kernel, not as a tail of the pion wave function or of the (skewed) structure function. 2 2 In [2] the authors tried to use the evolution equation for the pion wave function to obtain its tail. For instance, for the asymptotic wave function it was obtained in this way: Ψ asy π (x, k 2,µ) φasy π (x, µ)/k 2. It remains unclear for us how it is possible to obtain such result from the evolution equation for the asymptotic wave function, which looks as: dφ asy π (x, µ)/d ln µ = dy V (x, y)φ asy π (y, µ) =0. 3
4 So, the structure of the amplitude is (simbolically): T P A A P ( ψ 1 Mψ 2 ) 0 ū d π, (4) where the first matrix element introduces the skewed gluon distribution of the target, ψ 1 and ψ 2 are the free spinors of final quarks, M is the hard kernel, i.e. the product of all vertices and hard propagators, the last matrix element introduces the pion wave function, and means the appropriate convolution. As an example, let us consider the diagram in fig. 2. Proceeding in the above described way, one obtains the contribution to the amplitude (the Feynman gauge is used for the hard gluon): T 2 = 16 9 ω 1 o dx 1 φ π (x) 1 du g ξ (u) y 2 0 x 1 x 2 1 (u ξ)(u + ξ) (5) ω o = δ ij (4πα s ) 2 24 f π (ψ 1 ˆ γ5 ψ 2 ) (y 1y 2 ) 2, ˆ = µ γ µ, (6) where ψ 1 and ψ 2 are the free spinors of the final quarks, Σ spins ψ 1 ˆ γ5 ψ 2 2 = 2 k 4 /(y 1 y 2 ), ij are their colour indices, and f π 130 MeV is the pion decay constant. As it is expected that, for this process, the imaginary part of the amplitude is the main one at high energy, we have calculated only its value. For the diagram in fig. 2 this gives: ImT 2 = 16 9 πsω o y 1 k 2 k 4 1 dx 1 φ π (x) g ξ (ξ). (7) 0 x 1 x 2 As a final example, let us consider also the diagram in fig. 3, as it gives (together with the mirror diagram obtained by q 1 q 2 ) the logarithmically enhanced contribution ln(s/k 2 ): T 3 = ω o y 1 y dx 1 φ π (x) x 1 x du g ξ (u) N (u ξ)(u + ξ)[z 1 (x 1 y 1 ) x 1 y 2 ], (8) N =[ 8 z 1 z 2 ]+(8y 1 y 2 3 x 1 y 1 x 2 y 2 )+(z 1 + z 2 )(x 1 y 1 ), (9) ImT 3 = 4 πsω o k dx 1 φ π (x)g ξ (ū) Θ(ξ < ū < 1) +, (10) x 1 x 2 x 1 y 1 4
5 p π Φ π x 1 p π p 1 q 1 q 2 p 2 g p ξ (u) p Figure 2: One of the diagrams p π Φ π x 1 p π p 1 p 2 q 1 q 2 g p ξ (u) p Figure 3: The diagram giving the logarithmically enhanced contribution 5
6 ( ) x1 y 2 + x 2 y 1 ū = ξ, (11) x 1 y 1 where only the logarithmically enhanced term is shown explicitly in eq.(10), it originates from the term in square brackets in eq.(9) Proceeding in the above described way, one obtains for the cross section: dσ N = 1 1 8(2π) 5 s T dy d 2 k d 2 q, y 1 y 2 T iimt = i πsω o k 2 g ξ (ξ)ω, (12) Σ 1 = [ Ω= 1 0 dx 1 φ π (x 1 )(Σ 1 +Σ 2 +Σ 3 +Σ 4 ), (13) ] 4 g ξ (ū) Θ(ξ < ū < 1) +(y 1 y 2 ), (14) x 1 x 2 x 1 y 1 g ξ (ξ) Σ 2 = 1 x 2 1 x 2 2 y 1 y 2 { (x 1 x 2 + y 1 y 2 ) [ x 1 y 1 (x 1 y 2 ) 2 g ]} ξ(ū) g ξ (ξ) Θ(ξ < ū < 1) + (y 1 y 2 ), (15) Σ 3 = 1 { [ 9 (x 1x 2 + y 1 y 2 ) 1 x x 2 1 x 2 1 y 1 g ]} ξ(ū) 2 y 1 y 2 g ξ (ξ) Θ(ξ < ū < 1) + (y 1 y 2 ),(16) Σ 4 = ξ dg ξ(u)/du u=ξ. (17) x 1 x 2 y 1 y 2 g ξ (ξ) The expressions (12)-(17) constitute the main result of this paper. Let us note that while the separate terms in dx φ π (x)σ 2 are logarithmically divergent at x 1,2 0, it is not difficult to see that the divergences 3 It is not difficult to see that the Θ - function in eq.(10) excludes the region of x 1 too close to y 1, so that the integral is convergent and only the logarithmic enhancement ln(s/k 2 ) remains. 6
7 cancel in the sum, so that the integral is finite. And the same for Σ 3. This is an important point, as it shows that the whole approach is selfconsistent, i.e. the hard kernel remains hard and the soft end point regions x 1,2 0 give only power suppressed corrections. 4. We present in this section some numerical estimates of the cross section, based on the above expressions (12)-(17). Our main purpose here is to trace the distribution of jets in longitudinal momentum fractions, y 1,y 2, depending on the profile of the pion wave function φ π (x). a) As the calculations were performed in the leading twist approximation which becomes applicable at sufficiently large k only, we take k =2GeV for calculations, supposing that the higher twist effects are not of great importance at this value of k, and to have a possibility to compare with the E791 data. b) For the skewed gluon distribution g ξ (u, t) in the nucleon at t q 2 0 we use the simple form (as we need it at u ξ only, and because g ξ (u) g o (u) at u ξ): g ξ (u, t =0,µ k 2 GeV ) u ξ u 0.3 (1 u) 5. (18) This form agrees reasonably well (numerically) with calculated in [10] the ordinary, g o (u, µ 2 GeV ), and in [11] the skewed, g ξ (u, t =0,µ 2 GeV ), gluon distributions in the nucleon (in the typical region of the E791 experiment: u ξ 10 2 ). The detailed consideration of nuclear effects is out the scope of this paper. So, we simply assume that this results mainly in an overall factor (see [2]): dσ A (t q 2 ) dσ N(t =0) AF A (t) 2, (19) where F A (t) =exp{bt/2}, b= RA 2 /3, is the nuclear form factor. c) As for the pion leading twist wave function, φ π (x, µ), we compare two model forms: the asymptotic form, φ asy π (x, µ) =6x 1 x 2, and the CZ-model [12]. This last has the form: φ CZ π (x, µ o 0.5 GeV )=30x 1 x 2 (x 1 x 2 ) 2, at the very low normalization point. Being renormalized to the point µ k 2GeV, it looks as (see fig. 4): φ CZ π (x, µ 2 GeV )=15x 1x 2 [ (x1 x 2 ) ]. (20) The results of these numerical calculations are compared then with the E791 data, see fig. 5. 7
8 Figure 4: Profiles of the pion wave functions: a) φ CZ π (x, µ 0.5 GeV )=30x 1 x 2 (x 1 x 2 ) 2 - dotted line; b) φ CZ π (x, µ 2 GeV )= 15 x 1 x 2 [0.2+(x 1 x 2 ) 2 ] - solid line; c) φ asy π (x) =6x 1 x 2 - dashed line. 8
9 Figure 5: The y-distribution of jets calculated for k =2GeV, E π = 500 GeV and with the pion wave functions: φ CZ π (x, µ 2 GeV ) - solid line, φ asy π (x) - dashed line. The overall normalization is arbitrary, but the relative normalization of the two curves is as calculated. The data points are from the E791 experiment [1]. 9
10 It is seen that, unfortunately, while the two pion wave functions are quite different, the resulting distributions of jets in longitudinal momenta are similar and, it seems, the present experimental accuracy is insufficient to distinguish clearly between them. Moreover, even the ratio of the cross sections is not much different from unity: dσ asy /dσ CZ 1.2 aty 1 =0.5, and the same ratio is 0.7 aty 1 =0.25. In such an unhappy situation, the theoretical calculations have also to be performed with a maximal possible accuracy (higher twist corrections, hard loops corrections, the quark structure function contribution, nuclear effects, etc.). We show also in fig. 6 the same distributions with the pion energy ten times larger, E π =5TeV, k =2GeV. It is seen that even this does not help much (as the form of the distribution depends on the pion energy only logarithmically). The same ratios of the cross sections are here 1.7and 0.7 respectively. Recently the Coulomb contribution to the cross section have been calculatedin[13]. 4 Its value for Pt is: dσpt electr /dk 2 dy < 10 5 mbarn GeV 2, for E π = 500 GeV, k =2GeV. Using the above given formulae, one obtains for the strong cross section at the middle point y =0.5: dσpt CZ /dk dy mbarn GeV 2 with the same parameters, and 1 mbarn GeV 2 at E π =5TeV. It is seen that the electromagnetic contribution is small. Note added: After this work has been finished, there appeared the paper [14] on the same subject. Comparison shows that, although the qualitative conclusions are similar, the analytic expressions for the scattering amplitude differ essentially in this paper and in [14]. Acknowlegements I am grateful to V.S. Fadin for useful discussions and critical remarks. I thank also A.E. Bondar and B.I. Khazin for explaining me some details of the E791 experiment. 4 Because the electromagnetic contribution is real, while the strong one is mainly imaginary, they do not interfere. 10
11 Figure 6: The same as in Fig.5, but with E π =5TeV. 11
12 References [1] E.M. Aitala et. al. (E791 Collaboration), hep-ex/ D. Ashery, hep-ex/ ; Invited Talk at X Intern. Light-Cone Meeting, Heidelberg, June 2000: hep-ex/ [2] L. Frankfurt, G.A. Miller and M. Strikman, Phys. Lett. B304 (1993) 1; Found. of Phys. 30 (2000) 533 (hep-ph/ ); hep-ph/ [3] A.V. Radyushkin, Phys. Lett. B385 (1996) 333; Phys. Rev. D56 (1997) 5524 [4] X. Ji, Phys. Rev. Lett. 78 (1997) 610; J. Phys. G24 (1998) 1181 [5] V.L. Chernyak and A.R. Zhitnitsky, JETP Lett. 25 (1977) 510; Sov. J. Nucl. Phys. 31 (1980) 544 [6] V.L. Chernyak, V.G. Serbo and A.R. Zhitnitsky, JETP Lett. 26 (1977) 594; Sov. J. Nucl. Phys. 31 (1980) 552 [7] A.V. Efremov and A.V. Radyushkin, Phys. Lett. B94 (1980) 245; Teor. Math. Phys. 42 (1980) 97 [8] G.P. Lepage and S.J. Brodsky, Phys. Lett. B87 (1979) 359; Phys. Rev. D22 (1980) 2157 [9] V.L. Chernyak and A.R. Zhitnitsky, Phys. Rep. 112 (1984) 173 [10] M. Gluck, E. Reya and A. Vogt, Eur. Phys. J. C5 (1998) 461 [11] K.J. Golec-Biemat, A.D. Martin and M.G. Ryskin, Phys. Lett. B456 (1999) 232; hep-ph/ [12] V.L. Chernyak and A.R. Zhitnitsky, Nucl. Phys. B201 (1982) 492 [13] D. Yu. Ivanov and L. Szymanowski, hep-ph/ [14] V.M. Braun, D.Yu. Ivanov, A. Schafer and L. Szymanowski, hepph/
DIFFRACTIVE DIJET PHOTOPRODUCTION AND THE OFF-DIAGONAL GLUON DISTRIBUTION a
DIFFRACTIVE DIJET PHOTOPRODUCTION AND THE OFF-DIAGONAL GLUON DISTRIBUTION a K. GOLEC BIERNAT,,J.KWIECIŃSKI, A.D.MARTIN Department of Physics, University of Durham, Durham DH LE, England H. Niewodniczański
More informationPion Electromagnetic Form Factor in Virtuality Distribution Formalism
& s Using s Pion Electromagnetic Form Factor in Distribution Formalism A. Old Dominion University and Jefferson Lab QCD 215 Workshop Jefferson Labs, May 26, 215 Pion Distribution Amplitude & s ϕ π (x):
More informationPerturbative Pion Wave function in Coherent Pion-Nucleon. Di-Jet Production
NT@UW-99-25 Perturbative Pion Wave function in Coherent Pion-Nucleon Di-Jet Production L. Frankfurt School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv, Israel G. A. Miller Department
More informationNuclear GPDs and DVCS in Collider kinematics. Vadim Guzey. Theory Center, Jefferson Lab. Outline
Nuclear GPDs and DVCS in Collider kinematics Vadim Guzey Theory Center, Jefferson Lab Introduction Outline Nuclear PDFs Nuclear GPDs Predictions for DVCS Conclusions Introduction e(k ) Deeply Virtual Compton
More informationMEASUREMENT OF THE PROTON ELECTROMAGNETIC FORM FACTORS AT BABAR arxiv: v1 [hep-ex] 29 Nov 2013
MEASUREMENT OF THE PROTON ELECTROMAGNETIC FORM FACTORS AT BABAR arxiv:1311.7517v1 [hep-ex] 29 Nov 213 V. P. Druzhinin, on behalf of the BABAR Collaboration Budker Institute of Nuclear Physics SB RAS, Novosibirsk
More informationPoS(Baldin ISHEPP XXI)032
Prompt photon and associated heavy quark production in the k T -factorization approach A.V. Lipatov, and N.P. Zotov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University Moscow, Russia
More informationPion Transition Form Factor
First Prev Next Last Symposium on the 12% Rule and ρ π Puzzle in Vector Charmonium Decays Beijing, China, March 18-20, 2011. Pion Transition Form Factor ZE-KUN GUO In Collaboration With Qiang Zhao Institute
More informationarxiv:hep-ph/ v1 29 Oct 2005
1 Electroproduction of two light vector mesons in next-to-leading BFKL D.Yu. Ivanov 1 and A. Papa arxiv:hep-ph/0510397v1 9 Oct 005 1 Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia Dipartimento
More informationarxiv: v3 [hep-ph] 29 Sep 2017
arxiv:79.28v3 [hep-ph] 29 Sep 27 Inclusive charged light di-hadron production at 7 and 3 TeV LHC in the full NLA BFKL approach F.G. Celiberto,2, D.u. Ivanov 3,4, B. Murdaca 2 and A. Papa,2 Dipartimento
More informationDiffractive vector meson leptoproduction and spin effects
Diffractive vector meson leptoproduction and spin effects Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow region, Russia E-mail: goloskkv@theor.jinr.ru
More informationHigher Fock states and power counting in exclusive charmonium decays
Higher Fock states and power counting in exclusive charmonium decays WU B 98-15 hep-ph/9807470 P. Kroll 1 arxiv:hep-ph/9807470v1 23 Jul 1998 Fachbereich Physik, Universität Wuppertal Gaußstrasse 20, D-42097
More informationarxiv:hep-ph/ v1 22 Dec 2000
ON THE σ L /σ T RATIO IN POLARIZED VECTOR MESON PHOTOPRODUCTION S.V.Golosoov Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 980, Moscow region, Russia E-mail:
More informationM. Diehl Theory Group, Deutsches Elektronen Synchrotron DESY, Hamburg, Germany
Electroproduction of pion pairs Λ Sobolev Institute of Mathematics, 639 Novosibirsk, Russia E-mail: d-ivanov@math.nsc.ru M. Diehl Theory Group, Deutsches Elektronen Synchrotron DESY, 2263 Hamburg, Germany
More informationarxiv: v1 [nucl-th] 17 Aug 2012
Color Transparency Gerald A. Miller Physics Department, Univ. of Washington, Seattle, Wa. 98195-1560, USA arxiv:1208.3668v1 [nucl-th] 17 Aug 2012 Abstract. Color transparency is the vanishing of nuclear
More informationHADRON WAVE FUNCTIONS FROM LATTICE QCD QCD. Vladimir M. Braun. Institut für Theoretische Physik Universität Regensburg
HADRON WAVE FUNCTIONS FROM LATTICE QCD Vladimir M. Braun QCD Institut für Theoretische Physik Universität Regensburg How to transfer a large momentum to a weakly bound system? Heuristic picture: quarks
More informationStructure of Generalized Parton Distributions
=Hybrids Generalized Parton Distributions A.V. Radyushkin June 2, 201 Hadrons in Terms of Quarks and Gluons =Hybrids Situation in hadronic physics: All relevant particles established QCD Lagrangian is
More informationStudies of the hadronic component of the photon light-cone wave function using exclusive di-pion events at HERA
Submitted to the International Conference on High Energy Physics 6-22 August 2004, Beijing, China Abstract: 6-0250 Parallel Session: QCD soft interactions Studies of the hadronic component of the photon
More informationReggeon Non Factorizability and the J = 0 Fixed Pole in DVCS
Reggeon Non Factorizability and the J = Fied Pole in DVCS Stanley J. Brodsky, Felipe J. Llanes-Estrada, J. Timothy Londergan and Adam P. Szczepaniak 3 - SLAC National Laboratory, Stanford University 575
More informationPoS(DIS 2010)071. Diffractive electroproduction of ρ and φ mesons at H1. Xavier Janssen Universiteit Antwerpen
Diffractive electroproduction of ρ and φ mesons at Universiteit Antwerpen E-mail: xavier.janssen@ua.ac.be Diffractive electroproduction of ρ and φ mesons is measured at HERA with the detector in the elastic
More informationFragmentation production of Ω ccc and Ω bbb baryons
Physics Letters B 559 003 39 44 www.elsevier.com/locate/npe Fragmentation production of Ω ccc and Ω bbb baryons M.A. Gomshi Nobary a,b a Department of Physics, Faculty of Science, Razi University, Kermanshah,
More informationViolation of a simple factorized form of QCD amplitudes and Regge cuts
Violation of a simple factorized form of QCD amplitudes and Regge cuts Author affiliation Budker Institute of Nuclear Physics of SD RAS, 630090 Novosibirsk Russia Novosibirsk State University, 630090 Novosibirsk,
More informationarxiv: v1 [hep-ph] 7 Jul 2015
arxiv:1507.01916v1 [hep-ph] 7 Jul 2015 Department of Physics and Astronomy, Iowa State University, Ames, Iowa, 50011, USA E-mail: tuchin@iastate.edu An essential part of experimental program at the future
More informationProton Structure Function Measurements from HERA
Proton Structure Function Measurements from HERA Jörg Gayler DESY, Notkestrasse 85, 2263 Hamburg, Germany E-mail: gayler@mail.desy.de Abstract. Measurements of proton structure functions made in neutral
More informationarxiv: v1 [hep-ph] 14 Apr 2015
DIFFRACTIVE DISSOCIATION IN HIGH ENERGY pp COLLISIONS IN ADDITIVE QUARK MODEL Yu.M. Shabelski and A.G. Shuvaev arxiv:1504.03499v1 [hep-ph] 14 Apr 2015 Petersburg Nuclear Physics Institute, Kurchatov National
More informationarxiv:hep-ph/ v1 4 Nov 1998
Gluon- vs. Sea quark-shadowing N. Hammon, H. Stöcker, W. Greiner 1 arxiv:hep-ph/9811242v1 4 Nov 1998 Institut Für Theoretische Physik Robert-Mayer Str. 10 Johann Wolfgang Goethe-Universität 60054 Frankfurt
More informationMultiple Parton Interactions Physics
Some entertaining aspects of Multiple Parton Interactions Physics Yuri Dokshitzer LPTHE, Jussieu, Paris & PNPI, St Petersburg GGI 13.09 2011 Multi-Parton Interactions work in collaboration with B.Blok,
More informationarxiv: v1 [hep-ph] 11 Nov 2010
UHE neutrinos: higher twists, scales, saturation 1 arxiv:1011.2611v1 [hep-ph] 11 Nov 2010 R. Fiore 1 and V.R. Zoller 2 1 Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di Fisica
More informationThe flavour asymmetry and quark-antiquark asymmetry in the
The flavour asymmetry and quark-antiquark asymmetry in the Σ + -sea Fu-Guang Cao and A. I. Signal Institute of Fundamental Sciences, Massey University, Private Bag 11 222, Palmerston North, arxiv:hep-ph/9907560v2
More informationProbing nucleon structure by using a polarized proton beam
Workshop on Hadron Physics in China and Opportunities with 12 GeV Jlab July 31 August 1, 2009 Physics Department, Lanzhou University, Lanzhou, China Probing nucleon structure by using a polarized proton
More informationPhysik Department, Technische Universität München D Garching, Germany. Abstract
TUM/T39-96-19 Diffractive ρ 0 photo- and leptoproduction at high energies ) G. Niesler, G. Piller and W. Weise arxiv:hep-ph/9610302v1 9 Oct 1996 Physik Department, Technische Universität München D-85747
More informationx(1 x) b 2 dζ 2 m 2 1 x dζ 2 d dζ 2 + V (ζ) ] + k2 + m2 2 1 x k2 + m2 1 dζ 2 + m2 1 x + m2 2 LF Kinetic Energy in momentum space Holographic Variable
[ d dζ + V (ζ) ] φ(ζ) = M φ(ζ) m 1 de Teramond, sjb x ζ = x(1 x) b m b (1 x) Holographic Variable d dζ k x(1 x) LF Kinetic Energy in momentum space Assume LFWF is a dynamical function of the quark-antiquark
More informationUnitarity, Dispersion Relations, Cutkosky s Cutting Rules
Unitarity, Dispersion Relations, Cutkosky s Cutting Rules 04.06.0 For more information about unitarity, dispersion relations, and Cutkosky s cutting rules, consult Peskin& Schröder, or rather Le Bellac.
More information5 Infrared Divergences
5 Infrared Divergences We have already seen that some QED graphs have a divergence associated with the masslessness of the photon. The divergence occurs at small values of the photon momentum k. In a general
More informationV.G. Baryshevsky. Institute for Nuclear Problems, Belarusian State University, Minsk, Belarus
The phenomena of spin rotation and depolarization of highenergy particles in bent and straight crystals at Large Hadron Collider (LHC) and Future Circular Collider (FCC) energies and the possibility to
More informationAzimuthal angle decorrelation of Mueller Navelet jets at NLO
Azimuthal angle decorrelation of Mueller Navelet jets at NLO Physics Department, Theory Division, CERN, CH- Geneva 3, Switzerland E-mail: Agustin.Sabio.Vera@cern.ch F. Schwennsen II. Institut für Theoretische
More informationOmega Meson Cloud and the Proton s Light Anti-Quark Distributions
NT@UW-99-37 Omega Meson Cloud and the Proton s Light Anti-Quark Distributions Mary Alberg a,b,ernestm.henley a,c, and Gerald A. Miller a a Department of Physics, University of Washington, Seattle, WA 98195,
More informationarxiv: v1 [hep-ph] 16 Oct 2017
Angular distributions in pion-nucleon Drell-Yan process arxiv:70.05966v [hep-ph] 6 Oct 07 I V Anikin, L Szymanowski, O V Teryaev and N Volchanskiy,3 Bogoliubov Laboratory of Theoretical Physics, JINR,
More information2. HEAVY QUARK PRODUCTION
2. HEAVY QUARK PRODUCTION In this chapter a brief overview of the theoretical and experimental knowledge of heavy quark production is given. In particular the production of open beauty and J/ψ in hadronic
More informationQuasi-PDFs and Pseudo-PDFs
s and s A.V. Radyushkin Physics Department, Old Dominion University & Theory Center, Jefferson Lab 2017 May 23, 2017 Densities and Experimentally, one works with hadrons Theoretically, we work with quarks
More informationQCD and Rescattering in Nuclear Targets Lecture 2
QCD and Rescattering in Nuclear Targets Lecture Jianwei Qiu Iowa State University The 1 st Annual Hampton University Graduate Studies Program (HUGS 006) June 5-3, 006 Jefferson Lab, Newport News, Virginia
More informationFINAL-STATE INTERACTIONS AND SINGLE-SPIN ASYMMETRIES IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING
SLAC-PUB-300 FINAL-STATE INTERACTIONS AND SINGLE-SPIN ASYMMETRIES IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING STANLEY J. BRODSKY Stanford Linear Accelerator Center, Stanford University, Stanford, California
More informationRecent results at the -meson region from the CMD-3 detector at the VEPP-2000 collider
Recent results at the -meson region from the CMD-3 detector at the VEPP-2000 collider Vyacheslav Ivanov *1, Evgeny Solodov 1, Evgeny Kozyrev 1, and Georgiy Razuvaev 1 1 Budker Institute of Nuclear Physics,
More informationNovel Aspects of Hard Diffraction in QCD
SLAC-PUB-11486 September 2005 Novel Aspects of Hard Diffraction in QCD Stanley J. Brodsky Stanford Linear Accelerator Center, Stanford University Stanford, California 94309 e-mail: sjbth@slac.stanford.edu
More informationarxiv:hep-ph/ v1 24 Dec 1997
December 1997 TAUP 2471/97 arxiv:hep-ph/9712517v1 24 Dec 1997 THE F 2 SLOPE AND SHADOWING CORRECTIONS IN DIS E. G O T S M A N a),1), E. L E V I N a),b),2) and U. M A O R a),3) Abstract: a) School of Physics
More informationSeeking the Shadowing in ea Processes. M. B. Gay Ducati. V. P. Gonçalves
Seeking the Shadowing in ea Processes M. B. Gay Ducati and V. P. Gonçalves InstitutodeFísica, Univ. Federal do Rio Grande do Sul Caixa Postal 15051, 91501-970 Porto Alegre, RS, BRAZIL Abstract: We consider
More informationarxiv: v1 [hep-ph] 28 Jun 2016
BFKL effects and central rapidity dependence in Mueller-Navelet jet production at 3 TeV LHC arxiv:66.8892v [hep-ph] 28 Jun 26 Dipartimento di Fisica, Università della Calabria and Istituto Nazionale di
More informationarxiv: v2 [hep-ph] 30 Jan 2018
IPPP/17/89 January 31, 2018 Elastic proton-proton scattering at 13 TeV arxiv:1712.00325v2 [hep-ph] 30 Jan 2018 V.A. Khoze a,b, A.D. Martin a and M.G. Ryskin a,b a Institute for Particle Physics Phenomenology,
More informationarxiv:hep-ph/ v1 1 Sep 1997
WU B 97-22 hep-ph/9709203 A perturbative approach to the η c γ transition form factor arxiv:hep-ph/9709203v1 1 Sep 1997 Thorsten Feldmann 1 and Peter Kroll Department of Theoretical Physics, University
More informationFlavor Asymmetry of the Nucleon Sea and W-Boson Production*
Flavor Asymmetry of the Nucleon Sea and W-Boson Production* Department of Physics University of Illinois 7 December 2012 *R. Yang, J.C. Peng, M. Grosse-Perdekamp, Phys. Lett. B 680 (2009) 231-234 What
More informationVirtuality Distributions and γγ π 0 Transition at Handbag Level
and γγ π Transition at Handbag Level A.V. Radyushkin form hard Physics Department, Old Dominion University & Theory Center, Jefferson Lab May 16, 214, QCD Evolution 214, Santa Fe Transverse Momentum form
More informationMatching collinear and small x factorization calculations for inclusive hadron production in pa collisions
Matching collinear and small x factorization calculations for inclusive hadron production in pa collisions The Pennsylvania State University, Physics Department, University Park, PA 16802 H. Niewodniczański
More informationPolarizing Helium-3 for down quark spin enrichment. Nigel Buttimore
Polarizing Helium-3 for down quark spin enrichment Nigel Buttimore Trinity College Dublin 12 September 2012 Diffraction 2012 Polarized Helium-3 OUTLINE Introduction to the spin structure of polarized protons
More informationProduction of energetic dileptons with small invariant masses. from the quark-gluon plasma. Abstract
Production of energetic dileptons with small invariant masses from the quark-gluon plasma Markus H. Thoma and Christoph T. Traxler Institut für Theoretische Physik, Universität Giessen, 3539 Giessen, Germany
More informationarxiv: v1 [hep-ph] 4 Apr 2008
Generalized parton distributions of the pion Wojciech Broniowski, Enrique Ruiz Arriola and Krzysztof Golec-Biernat arxiv:0804.078v [hep-ph] 4 Apr 008 The H. Niewodniczański Institute of Nuclear Physics
More informationPomeron-Odderon interference in production of
LPT-ORSAY 08-86 CPHT-PC 08.1008 Pomeron-Odderon interference in production of π + π pairs in ultraperipheral collisions arxiv:08155v1 [hep-ph] 3 Nov 008 B. Pire, F. Schwennsen,, L. Szymanowski and S. Wallon
More informationGeneralized parton distributions in the context of HERA measurements
arxiv:1107.3423v1 [hep-ph] 18 Jul 2011 Generalized parton distributions in the context of HERA measurements Laurent SCHOEFFEL CEA Saclay/Irfu-SPP, 91191 Gif-sur-Yvette, France July 2, 2013 Abstract We
More informationarxiv: v1 [hep-ph] 12 May 2008
arxiv:0805.1649v1 [hep-ph] 12 May 2008 PARTON ENERGY LOSS IN COLLINEAR EXPANSION B.G. ZAKHAROV L.D. Landau Institute for Theoretical Physics, GSP-1, 117940, Kosygina Str. 2, 117334 Moscow, Russia We demonstrate
More informationMueller-Navelet jets at LHC: an observable to reveal high energy resummation effects?
Mueller-Navelet jets at LHC: an observable to reveal high energy resummation effects? LPT, Université Paris-Sud, CNRS, 945, Orsay, France E-mail: Bertrand.Ducloue@th.u-psud.fr Lech Szymanowski National
More informationarxiv:hep-ph/ v1 11 Mar 1994
An interesting charmonium state formation and decay: p p D 2 P γ M. Anselmino a, F. Caruso b,c, F. Murgia d and M.R. Negrão b arxiv:hep-ph/9403272v Mar 994 a Dipartimento di Fisica Teorica, Università
More informationTransverse Target Asymmetry in Exclusive Charged Pion Production at 12 GeV
Transverse Target Asymmetry in Exclusive Charged Pion Production at 12 GeV Dipangkar Dutta Mississippi State University (with Dave Gaskell & Garth Huber) Polarized Target Workshop: June 17-18, 2010 Outline
More informationExclusive central diffractive production of scalar, pseudoscalar and vector mesons
EPJ Web of Conferences 8, 58 (24) DOI:.5/ epjconf/ 24 858 C Owned by the authors, published by EDP Sciences, 24 Exclusive central diffractive production of scalar, pseudoscalar and vector mesons P. Lebiedowicz,a,
More informationColor dipoles: from HERA to EIC
Université de Moncton INT workshop: Gluons and the quark sea at high energies,distributions, polarisation, tomography September 29, 2010 based on work done with J. R. Forshaw, G.Shaw and B. E. Cox (Manchester
More informationWeak interactions. Chapter 7
Chapter 7 Weak interactions As already discussed, weak interactions are responsible for many processes which involve the transformation of particles from one type to another. Weak interactions cause nuclear
More informationDistribution Functions
Distribution Functions Also other distribution functions f 1 = g = 1L g 1T = h 1T = f 1T = h 1 = h 1L = h 1T = Full list of PDF at Twist-2 (Mulders et al) Dirk Ryckbosch, Feldberg, Oct.2006 p.1/33 Factorization
More information1 The pion bump in the gamma reay flux
1 The pion bump in the gamma reay flux Calculation of the gamma ray spectrum generated by an hadronic mechanism (that is by π decay). A pion of energy E π generated a flat spectrum between kinematical
More informationThe Neutron Structure Function from BoNuS
The Neutron Structure Function from BoNuS Stephen Bültmann 1 Physics Department, Old Dominion University, Norfolk, VA 359, USA Abstract. The BoNuS experiment at Jefferson Lab s Hall B measured the structure
More informationfor the production of lepton pairs and photons in collisions of relativistic nuclei
Strong-field effects for the production of lepton pairs and photons in collisions of relativistic nuclei Valery G. Serbo and Ulrich D. Jentschura Novosibirsk State University, Novosibirsk, Russia Institut
More informationarxiv:hep-ph/ v1 15 Jul 1998
The DLLA limit of BFKL in the Dipole Picture arxiv:hep-ph/9807389v1 15 Jul 1998 M. B. Gay Ducati and V. P. Gonçalves Instituto de Física, Univ. Federal do Rio Grande do Sul Caixa Postal 15051, 91501-970
More informationThe growth with energy of vector meson photo-production cross-sections and low x evolution
The growth with energy of vector meson photo-production cross-sections and low x evolution Departamento de Actuaria, Física y Matemáticas, Universidad de las Américas Puebla, Santa Catarina Martir, 78,
More informationP. Kroll. Fachbereich Physik, Universität Wuppertal Gaußstrasse 20, D Wuppertal, Germany
WU B 00-05 hep-ph/0003097 March 2000 THE b u SKEWED PARTON DISTRIBUTIONS P. Kroll Fachbereich Physik, Universität Wuppertal Gaußstrasse 20, D-42097 Wuppertal, Germany E-mail: kroll@theorie.physik.uni-wuppertal.de
More informationOpportunities with diffraction
Opportunities with diffraction Krzysztof Golec-Biernat Institute of Nuclear Physics in Kraków IWHSS17, Cortona, 2 5 April 2017 Krzysztof Golec-Biernat Opportunities with diffraction 1 / 29 Plan Diffraction
More informationPhysics at LHC. lecture one. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden
Physics at LHC lecture one Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, October 22, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1 LHC
More informationSearch for Next Generations of Quarks and Leptons at the Tevatron and LHC
UL-NTZ 03/98 Search for Next Generations of Quarks and Leptons at the Tevatron and LHC arxiv:hep-ph/9802364v1 19 Feb 1998 I.F. Ginzburg, I.P. Ivanov Institute of Mathematics, Novosibirsk, Russia, A. Schiller
More informationQCD factorization beyond leading twist in exclusive processes: ρ T -meson production
QCD factorization beyond leading twist in exclusive processes: ρ T -meson production I. V. Anikin Bogoliubov Laboratory of Theoretical Physics, JINR, 14198 Dubna, Russia E-mail: anikin@theor.jinr.ru D.
More informationProduction of e + e pairs to all orders in Zα for collisions of high-energy muons with heavy nuclei
UL NTZ 14/98 Production of e + e pairs to all orders in Zα for collisions of high-energy muons with heavy nuclei arxiv:hep-ph/9807311v1 9 Jul 1998 D. Ivanov 1,2, E.A. Kuraev 3, A. Schiller 1, and V.G.
More informationD Göttingen, Germany. Abstract
Electric polarizabilities of proton and neutron and the relativistic center-of-mass coordinate R.N. Lee a, A.I. Milstein a, M. Schumacher b a Budker Institute of Nuclear Physics, 60090 Novosibirsk, Russia
More informationPhotodisintegration of Light Nuclei
Photodisintegration of Light Nuclei Yordanka Ilieva for the CLAS Collaboration Motivation Two-body photodisintegration of deuteron Two-body photodisintegration of 3 He The 7th International Workshop on
More informationarxiv: v1 [hep-ph] 28 May 2012
Evidence for the higher twists effects in diffractive DIS at HERA M. Sadzikowski, L. Motyka, W. S lomiński Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 3-59 Kraków, Poland We
More informationProduction of charged Higgs boson pairs in the pp pph + H reaction at the LHC and FCC
Production of charged Higgs boson pairs in the pp pph + H reaction at the LHC and FCC and Antoni Szczurek The H. Niewodniczański Institute of Nuclear Physics Polish Academy of Sciences, ul. Radzikowskiego
More information2 2 ω 0 = m B m D. B D + ρ B D 0 π, B D 0 π,
.3 Massive Gauge Boson Form Factor & Rapidity Divergences MORE SCET I APPLICATIONS then we may move all usoft wilson lines into the usoft part of the operator yielding,5 (c),5 (d) Q [h Γ Y T a Y h (b)
More informationISR physics at BABAR
SLAC-PUB-499 ISR physics at BABAR S.Serednyakov, Budker Institute of Nuclear Physics, Novosibirsk, Russia Abstract A method of measuring e+e- annihilation cross sections at low energy s < 5 GeV, using
More informationAnalysis of the Isgur-Wise function of the Λ b Λ c transition with light-cone QCD sum rules
Analysis of the Isgur-Wise function of the Λ b Λ c transition with light-cone QCD sum rules Zhi-Gang Wang 1 Department of Physics, North China Electric Power University, Baoding 713, P. R. China arxiv:96.426v1
More informationarxiv: v1 [hep-ph] 10 Nov 2008
IPPP/08/83 DCPT/08/166 June 10, 2018 arxiv:0811.1481v1 [hep-ph] 10 Nov 2008 Diffractive processes at the LHC 1 A.D. Martin a,v.a. Khoze a,b and M.G. Ryskin a,b a Institute for Particle Physics Phenomenology,
More informationMeasurements of the Proton and Kaon Form Factors via ISR at BABAR
Measurements of the Proton and Kaon Form Factors via ISR at BABAR Fabio Anulli INFN Sezione di Roma on behalf of the BABAR Collaboration HADRON 015 XVI International Conference on Hadron Spectroscopy 13
More informationHigh-p T Neutral Pion Production in Heavy Ion Collisions at SPS and RHIC
High- Neutral Pion Production in Heavy Ion Collisions at SPS and RHIC K. Reygers for the WA98 and the PHENIX collaboration Institut für Kernphysik der Universität Münster Wilhelm-Klemm-Str. 9, D-4849 Münster,
More informationSt anfo rd L in ear A ccele rat o r Cent e r
SLAC-PUB-7212 July 1996 NUCLEAR EFFECTS AT HERA STANLEY J. BRODSKY St anfo rd L in ear A ccele rat o r Cent e r St anfo rd University, St anfo rd, California 94 309 To appear in the Proceedings of the
More informationTriangle diagrams in the Standard Model
Triangle diagrams in the Standard Model A. I. Davydychev and M. N. Dubinin Institute for Nuclear Physics, Moscow State University, 119899 Moscow, USSR Abstract Method of massive loop Feynman diagrams evaluation
More informationarxiv: v1 [hep-ph] 9 Jul 2013
Nuclear Physics B Proceedings Supplement Nuclear Physics B Proceedings Supplement (3) 5 Distribution of Angular Momentum in the Transverse Plane L. Adhikari and M. Burkardt Department of Physics, New Meico
More informationSpin Physics Experiments at SLAC
SLAC-PUB-9269 June, 2002 Spin Physics Experiments at SLAC P. Bosted, for the E155/E155x Collaborations 1 Stanford Linear Accelerator Center, Stanford CA 94309 and Physics Dept., University of Massachusetts,
More informationOn neutrino production of a charmed meson. Centre de Physique Théorique, École Polytechnique, CNRS, Université Paris-Saclay, Palaiseau, France
On neutrino production of a charmed meson National Centre for Nuclear Research (NCBJ), 00-681 Warsaw, Poland E-mail: jakub.wagner@ncbj.gov.pl B. Pire Centre de Physique Théorique, École Polytechnique,
More informationMueller-Navelet jets at LHC: the first complete NLL BFKL study
Mueller-Navelet jets at LHC: the first complete NLL BFKL study B. Ducloué LPT, Université Paris-Sud, CNRS, 945, Orsay, France E-mail: Bertrand.Ducloue@th.u-psud.fr L. Szymanowski National Center for Nuclear
More informationExclusive Vector Meson Production and Inclusive K 0
Exclusive Vector Meson Production and Inclusive K 0 S K0 S Final State in DIS at HERA Photon003, Frascati 07-11/04 McGill University For the H1 and Zeus Collaboration Outline: Exclusive vector meson production
More informationarxiv:hep-ph/ v1 13 Nov 2003
Unintegrated parton distributions and particle production in hadronic collisions arxiv:hep-ph/0311175v1 13 Nov 2003 Antoni Szczurek Institute of Nuclear Physics PL-31-342 Cracow, Poland Rzeszów University
More informationJet Photoproduction at THERA
DESY 0 03 ISSN 048 9833 hep ph/00309 March 200 Jet Photoproduction at THERA arxiv:hep-ph/00309v 9 Mar 200 M. Klasen II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 49, 2276
More informationImaging the Proton via Hard Exclusive Production in Diffractive pp Scattering
Exclusive Reactions at High Momentum Transfer Jefferson Lab, Newport News, VA May 21-24, 2007 Imaging the Proton via Hard Exclusive Production in Diffractive pp Scattering Charles Earl Hyde Old Dominion
More informationarxiv:hep-ph/ v1 13 Oct 2004
arxiv:hep-ph/0410184v1 13 Oct 2004 σ DIS (νn), NLO Perturbative QCD and O(1 GeV) Mass Corrections S. Kretzer a and M. H. Reno b a Physics Department and RIKEN-BNL Research Center, Bldg. 510a, Brookhaven
More informationModels of the Nucleon & Parton Distribution Functions
11th CTEQ Summer School on QCD Analysis and Phenomenology Madison, Wisconsin, June 22-30, 2004 Models of the Nucleon & Parton Distribution Functions Wally Melnitchouk Jefferson Lab Outline Introduction
More informationInvestigation of jet quenching and elliptic flow within a pqcd-based partonic transport model
Investigation of jet quenching and elliptic flow within a pqcd-based partonic transport model Oliver Fochler Z. Xu C. Greiner Institut für Theoretische Physik Goethe Universität Frankfurt Winter Workshop
More informationTransition form factors of pseudoscalar mesons: theory vs experiment
Transition form factors of pseudoscalar mesons: theory vs experiment A.E. Dorokhov JINR, Bogoliubov Laboratory of Theoretical Physics, Dubna, Russia Abstract. Recently, the BABAR collaboration reported
More informationRuben Sandapen (Acadia & Mt. A) in collaboration with M. Ahmady & F. Chishtie. September 5 th 2016
Holographic Distribution Amplitudes for mesons Ruben Sandapen (Acadia & Mt. A) in collaboration with M. Ahmady & F. Chishtie Diffraction 2016 Progress in QCD session September 5 th 2016 1 Outline Overview
More information