SELF-SIMILAR GLUON DENSITY AT SMALL x. Department of Physics, Gauhati University. Abstract

Transcription

1 SELF-SIMILAR GLUON ENSITY AT SMALL Rupjyoti Gooi and. K. Choudhury epartment of Physics, Gauhati University. Abstract Recently, the structure of the nucleon at small Bjorken variable of deep inelastic lepton nucleon scatterin is parameterized usin the concept of self-similarity to uninterated uark density. In this paper we etend the formalism to luon densities and relate them to the slope F of the structure function. st Feb 8 Workshop on Hih Enery IITG

2 OBJECTIVE We propose a parameterization of the uninterated luon distribution at low assumin self-similar pattern for it and test how far this model is consistent with the eperimental data. st Feb 8 Workshop on Hih Enery IITG

3 PLAN OF THE TALK What is self-similarity? How the idea comes to the structure of nucleon? Self-similarity in uark density inside the nucleon. Self-similarity in luon distribution inside the nucleon. st Feb 8 Workshop on Hih Enery IITG 3

4 What is self-similarity? Self-similarity is the property by virtue of which a small portion of an object can represent the compleity of the entire object. Koch curve st Feb 8 Workshop on Hih Enery IITG 4

5 IMENSION The number of self-similar objects is related to the fractal dimension and the manification factor by the power law, N ~ M () N=4, M=3 The of E. () can be epressed as, Number of self - similar objects manification factor () N=6, M=9 For Koch curve, 4 3 (6) (9) st Feb 8 Workshop on Hih Enery IITG 5

6 What is the motivation behind applyin the idea of self-similarity in the structure of nucleon? eep Inelastic ep scatterin st Feb 8 Workshop on Hih Enery IITG 6

7 eep Inelastic ep scatterin e(k) () e(k / ) Kinematic variables p( k k ) ( k k) p. X(p) P(p) proton Almost free partons st Feb 8 Workshop on Hih Enery IITG 7

8 For. i.e. below the valence uark reion, the uninterated u-uark density function ehibits a linear behavior as a function for fied of and as a function of for fied. ( st Feb 8 Workshop on Hih Enery IITG 8 (

9 u Linear behavior of vs u d d raph suests that, Similarly, u d u d d d (3) (4) Such power law behavior indicates the presence of a new physics in the structure of proton. st Feb 8 Workshop on Hih Enery IITG 9

10 Conditions of manification factors: ) positive )non-zero 3)should not have a physical dimension To meet the reuirements of manification factor, we manipulate and as, and st Feb 8 Workshop on Hih Enery IITG

11 st Feb 8 Workshop on Hih Enery IITG FRACTAL STRUCTURE OF NUCLEON We take the manification factors as, and Then the uninterated parton density can be defined as, i i f 3 ), ( (5)

12 st Feb 8 Workshop on Hih Enery IITG,, d f i i The interated parton density is iven by, Usin the definition of structure function as,,,, e F i i i ep, 3 3 F (6) (8) (7)

13 Comparison of e. (8) with standard data yields the values of the parameters as, 3.634±.4.39 ±..58±.6.435±..49 ±. (9).45 5GeV = 7.743and /dof =.357 This parameterization is an improvement over that of Lastovicka () where 3 was neative contradictory to the epectation of fractal dimension (7) T.Lastovicka, Euro Phys JC4 59() st Feb 8 Workshop on Hih Enery IITG 3

14 st Feb 8 Workshop on Hih Enery IITG 4 Self-similarity and luon distribution: The forms of uninterated and interated luon densities with selfsimilarity are identical to those of the uark distribution ecept the set of parameters will be different. Thus form of uninterated luon density (, ) will be,., 3 () ), ( 3 3 e which leads to the followin form of luon distribution, ()

15 We need four parameters,, and 3 to be determined. We choose MRST4LO[9] solutions for comparison. A comparison of e (7) and (8) with MRST4LO eact results ives the followin set of parameters, =.5597±., =.39±., =.566±.3, (), 3 =.435±., =.49±. Here too all parameters are positive consistent with fractal dimension epectation. =.634±.4, =.39±., =.58±.6, 3 =.435±., =.49±. [9] MRST: A Martin, RG Roberts, WJ Stirlin and RS Thorne Euro Phys J C 4 () 33, hep-ph/9973, Phys lett B53 6 (). st Feb 8 Workshop on Hih Enery IITG 5

16 Comparison with the results obtained with uark distribution and >, which conforms to the feature that for any, luon is steeper than uark density. We have also obtained the luon density usin the manification factor used by Lastovicka. We obtain a different set of parameters, all are positive this time. (7) T.Lastovicka, Euro Phys JC4 59() st Feb 8 Workshop on Hih Enery IITG 6

17 6 5 =5GeV =3GeV =35GeV =4GeV 4 M RST 4LO this work Ref. (7) M RST 4LO this work Ref. (7) M RST 4LO this work Ref. (7) M RST 4LO this work Ref. (7) 3 (, ) 6 5 =45GeV =5GeV =55GeV =65GeV 4 M RST 4LO this work Ref. (7) M RST 4LO this work Ref. (7) M RST 4LO this work Ref. (7) M RST 4LO this work Ref. (7) (7) T.Lastovicka, Euro Phys JC4 59() st Feb 8 Workshop on Hih Enery IITG 7

18 Gluon from the slope of the Structure Function 9 Prytz formula: G 5 S 3 df d (3) K. Bora, KC G 3 4 / 3 5 S df d (4) Gay ucati et al 7 df G (3/ ) d S (5) [5] K Prytz Phys lett B3 86 (993). [6] K Bora and K Choudhury Phys lett B354 5 (995). [7] M B Gay ucati and Victor P B Goncalves Phys lett B39 4 (997). st Feb 8 Workshop on Hih Enery IITG 8

19 Compatibility of fractal model with C evolution based euations We define ratio, MRST luon density R G(, ) 7 F S Gluon density measured from the slope of S.F. within fractal model st Feb 8 Workshop on Hih Enery IITG 9

20 R versus raph Prytz relation is modified within the fractal model. G S 3 df d A similar modification also occurs for other realtions as well. st Feb 8 Workshop on Hih Enery IITG

21 References [] B.B.Mandelbrot, Fractal Geometry of Nature (W.H.Freeman, N.Y. 983). [] Michael F.Barnsley, Fractal Everywhere (Academic Press, N.Y. 993). [3] P Carruthers and Minh uon-van, Los Alamos Report No LA-UR (unpublished). [4] I.M.remin, Mod Phys. lett. A3 333 (988) [5] R.Lipa and B.Buschbeck, Phys. lett. B3 465 (989). [6] R.C.Hwa, Phys. Rev (99). [7] W.Flokowski and R.C. Hwa, Phys. Rev (99). [8] W Yuanfu and L Lianshou Int J Mod Phys A53, 37 (3). [9] K Ghosh et al Fizika 7 (3). [] K Ghosh et al Fractals 3 35 (5). [] Y Zhan; hep-ph/9869. [] Y Zhan in proceedins of the XXVII International Symposium on Multiparticle dynamics elphi, Greece, Ed N.G. Antoniou et al (World Scientific, Sinapore, ) p 7. [3] J Ambjorn et al Nucl Phys B (995): hep-ph/9574 [4] M Bowick et al Phys lett B43 97 (997) ; hep-e/9683 [5] J Nishimura and M Oshikawa Phys lett (994). [6] S N Banerjee, A Bhattacharya, B Chakraborty and S Banerjee Int. Jour. Mod. Phys A5, 53 (), Int. Jour. Mod. Phys A6, 4939 (), Int. Jour. Mod. Phys A (). [7] T.Lastovicka, Euro Phys JC4 59();hep-ph/36; Ph. Thesis ESY-Thesis 4- (Humboldt University, Berlin)(3). st Feb 8 Workshop on Hih Enery IITG

22 [8] H: C Adloff et al, Euro Phys JC, 33(); hep-e/53. [9] ZEUS: J Brietwe et al, Phys lett B487, 53(); hep-e/58. [] K Choudhury and Rupjyoti Gooi, hep-ph/367. [] K Choudhury and Rupjyoti Gooi, hep-ph/5347; Ind J Phys 8(6) 659 (6). [] K Choudhury and Rupjyoti Gooi, Ind J Phys 8(8) 83 (6) [3] G Gustafson hep-ph/333 [4] H Jun, A V Kotikov, A V Lipatov and N P Zotor; hep-ph/693. [5] K Prytz Phys lett B3 86 (993). [6] K Bora and K Choudhury Phys lett B354 (995) 5 [7] M B Gay ucati and Victor P B Goncalves Phys lett B39 (997) 4 [8] K Choudhury and P K Sahariah Pramana J Phys () [9] MRST: A Martin, RG Roberts, WJ Stirlin and RS Thorne Euro Phys J C 4 () 33, hep-ph/9973, Phys lett B53 6 (). st Feb 8 Workshop on Hih Enery IITG

23 WORKSHOPS/SCHOOLS. School on Information Technoy oranized jointly by Indian Statistical Institute, Kolkata and North Eastern Reional Institute of Science and Technoy durin September 3.. SERC preparatory school in Theoretical Hih Enery Physics durin November 3 in University of Hyderabad. 3. SERC main school in Theoretical Hih Enery Physics durin February 4 in University of Rajasthan th Annual Technical Session of Assam Science Society durin January th Reional Conference in Physics Research in North East held in Gurucharan Collee, Silchar durin 5-6th November 4 oranized by the Physics Academy of North East (PANE) 6. AE symposium of Hih Enery Physics held at SINP, Kolkata durin ecember th International Conference on Physics & Astrophysics of uark Gluon Plasma held at VECC, Kolkata durin February 5.. Advanced School in GP held at IIT, Mumbai durin July 7.. A roadmap of uantum mechanics to Strin Theory held at IIT, Guwahati durin Sept 7. st Feb 8 Workshop on Hih Enery IITG 3

24 Conferences/Publications. On Fractal imension of Proton at Small (hep-ph/36), K Choudhury and Rupjyoti Gooi, presented at 49th Annual Technical Session of Assam Science Society.. Self-similarity in Proton Structure at small and Positive Fractal imension, K Choudhury and Rupjyoti Gooi, (Presented in 4th Reional Conference in Physics Research in North East held in Gurucharan Collee, Silchar durin 5-6th November 4 oranized by the Physics Academy of North East (PANE) ). 3. Comments on Fractality of Proton at Small (hep-ph/5347) presented in AE Symposium of Hih Enery Physics, SINP, Kolkata, An Analysis of Self-similarity of Proton at Small, K Choudhury and Rupjyoti Gooi, (Presented in 5th International Conference on Physics and Astrophysics of uark Gluon Plasma, Kolkata, 5). 5. Some Comments on Fractality of Proton at Small, K Choudhury and Rupjyoti Gooi, hep-ph/5347; Ind J Phys 8(6) 659 (6). 6. A Parameterization of Proton Structure Function at small, K Choudhury and Rupjyoti Gooi, Ind J Phys 8(8) 83 (6). 7. eep Inelastic Neutrino Nucleon Scatterin and fractal model of proton structure functions at small, Ind J Phys 8 (7). st Feb 8 Workshop on Hih Enery IITG 4

25 T H A N K Y O U st Feb 8 Workshop on Hih Enery IITG 5