Structure of the Proton CTEQ Parton Distribution Functions

Structure of the Proton CTEQ Parton Distribution Functions CTEQ 6. 6 P. M. Nadolsky, H. -L. Lai, Q. -H. Cao, J. Huston, J. Pumplin, D. Stump, W. -K. Tung, C. -P. Yuan, Implications of CTEQ global analysis for collider observables, Phys. Rev. D 78: 013004, 2008 ar. Xiv: 0802. 0007 v 3 [hep-ph] CT 10 Hung-Liang Lai, Marco Guzzi, Joey Huston, Zhao Li, Pavel M. Nadolsky, Jon Pumplin, C. -P. Yuan, New parton distributions for collider physics, Phys. Rev. D 82: 074024, 2010 ar. Xiv: 1007. 2241 v 3 [hep-ph] The results shown below are for CT 10. B 3 cteqss 11 1

CT 10 PDFs Structure of the Proton U Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) Red: u(x, Q 2) Dashed Red: ū(x, Q 2) Gray: uvalence(x, Q 2) This log-log plot shows … … for x ≳ 0. 1 the valence structure dominates … for x ≲ 0. 01 ū approaches u B 3 cteqss 11 2

CT 10 PDFs Structure of the Proton U Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) Red: x u(x, Q 2) Dashed Red: x ū(x, Q 2) Gray: x uvalence(x, Q 2) This linear plot shows the momentum fraction for Q = 3. 16 Ge. V (= area under the curve) integral ≈ 0. 32, 0. 05, 0. 27 B 3 cteqss 11 3

CT 10 PDFs Structure of the Proton U Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) Red: uvalence(x, Q 2) This linear plot demonstrates the flavor sum rule: integral = 2 B 3 cteqss 11 4

CT 10 PDFs Structure of the Proton D Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) Blue: d(x, Q 2) Dashed Blue: đ(x, Q 2) Gray: dvalence(x, Q 2) This log-log plot shows … … for x ≳ 0. 1 the valence structure dominates … for x ≲ 0. 01 đ approaches d B 3 cteqss 11 5

CT 10 PDFs Structure of the Proton D Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) Blue: d(x, Q 2) Dashed Blue: đ(x, Q 2) Gray: dvalence(x, Q 2) This linear plot shows the momentum fraction for Q = 3. 16 Ge. V (= area under the curve) integral ≈ 0. 15, 0. 06, 0. 10 B 3 cteqss 11 6

CT 10 PDFs Structure of the Proton D Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) dvalence = d – đ (x, Q 2) This linear plot demonstrates the flavor sum rule: integral = 1 B 3 cteqss 11 7

CT 10 PDFs Structure of the Proton D Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) Blue: d(x, Q 2) Dashed Blue: đ(x, Q 2) Gray: dvalence(x, Q 2) Red: u(x, Q 2) Dashed Red: ū(x, Q 2) Gray: uvalence(x, Q 2) This linear plot compares U and D -- quarks and antiquarks; naively, d = 0. 5 u, but it’s not that simple. B 3 cteqss 11 8

CT 10 PDFs Structure of the Proton D Quark (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) d(x, Q 2) / u(x, Q 2) v x d(x, Q 2) / u(x, Q 2) is interesting. Exercise: What scattering processes could provide information on this ratio? B 3 cteqss 11 9

CT 10 PDFs Structure of the Proton Gluon (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) black : g(x, Q 2) red : u(x, Q 2) The gluon dominates at small x. The valence quarks dominate at large x. B 3 cteqss 11 10

CT 10 PDFs Structure of the Proton Gluon (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) black : g(x, Q 2) purple : 2(ū + đ ) (x, Q 2) Comparing the gluon PDF and the sea quark PDFs. B 3 cteqss 11 11

CT 10 PDFs Structure of the Proton Sea Quarks and Gluon (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) sea(x, Q 2) / g(x, Q 2) v x blue: ū/g red: đ/g purple: the sum For small x, ū/g = đ/g = constant Exercise: Why? B 3 cteqss 11 12

CT 10 PDFs Structure of the Proton (Q 2 = 10 Ge. V 2; Q = 3. 16 Ge. V) All in One Plot u_valence d valence sea * 0. 05 gluon * 0. 05 B 3 cteqss 11 13

Exercise: (A) Use the Durham Parton Distribution Generator (online PDF calculator) to reproduce these graphs. (B) Show the Q 2 evolution. B 3 cteqss 11 14