Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 2

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1 Universality of Perturbative QCD Soft Radiation in ee,ep and pp Collisions Ou Zhang University of Arizona, IPN-Orsay Collabration with Christopher Lee and Deakyoung Kang, Los Alamos National Lab, U.S.A. January 13, 2015 Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 2

2 What is Happening in Accelerators? Experimental View: Jets: a cluster of hadrons moving in the same direction LEP 2 jet event CDF 4 jet top event 2 jet event at LHC Theoretical View: Field Theory (Iain Stewart 2011) Ou Zhang University of Arizona Equality of Hemisphere Soft Functions in ee, ep and pp Collisions to

3 What is Happening in Accelerators Jets-like objects are produced by particle collisions Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 2

4 Anatomy of a High Energy Collision of Two Protons (Iain Stewart 2011) Ou Zhang University of Arizona Equality of Hemisphere Soft Functions in ee, ep and pp Collisions to

5 Factorization Theorem and Effective Field Theory Energy scales are separated naturally in a collision process Different scales indicate different physics Different Effective Field Theories Different physics processes are independent from each other. (Principle of Effective Field Theories) Factorizing independent physics processes into pieces, and determining the perturbatively calculatable parts Prob(A B) = C Prob(A C)Prob(C B) (Factorization Theorem) Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 2

6 Factorization Theorem and Effective Field Theory With the separated energy scales, we construct one effective field theory for one physics process, and use factorization theorem to write the final cross section Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 3

7 Soft Radiation in ee,ep and pp collision Question: is the soft gluon radiation independent from inclusive collision processes? Motivation: The soft gluon radiation scale is well-separated from the jets scale, however can it be decoupled from the energetic jets with QCD structure and treated as universal transparent background during the hadronization process? Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, / 5

8 Factorizing Soft Radiation out by SCET Soft-Collinear Effective Theory Describing small fluctuations around light-like momentum trajectories µ s λ 4 Q p n = p k +k, K µ J Qλ 2 n p n n p 2 µh Q On light-like coordinates n = (1, z) n = (1, z) Soft modes: low energy particles without a preferred direction Collinear modes: energetic hadrons & jets E Λ QCD collimated Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 13, 2015

9 Connecting Factorization Theorem to Experimental Measurements of Jets Properties Invariant mass Effectively treating the jets much like single particles Probability Event-shape Thrust Ou Zhang University of Arizona Equality of Hemisphere Soft Functions in ee, ep and pp Collisions to

10 Factorizing probability by reorganizing large leading logs, differentiating cross-section by jets invariant mass and thrust, d 2 σ dmt 2 dm = σ 0H(Q, m, µ) t 2 Mantry, Fleming, Hoang, I.S. Qx dx dy B t s t,µ B m t s t Qy m,µ S(x, y, µ) jet function for heavy particles (calculate perturbatively in αs) probability for soft radiation (not perturbative) Soft radiation sees only direction, not energy of the original partons, but color Ou Zhang University of Arizona Equality of Hemisphere Soft Functions in ee, ep and pp Collisions to

11 Non-perturbative soft gluons need to be summed up as Wilson lines electron-positron soft radiation contributed by outgoing soft gluons to nn directions Y n [ig (x) = Pexp 0 [ Y n (x) = P exp ig 0 ] ds n A s(ns + x) ] ds n A s(n s + x) electron-proton collision. Soft radiation contributed by one incoming soft gluon jets from n B beam direction (initial states), one outgoing soft gluon jets n J final states [ 0 Y nb (x) = Pexp ig Y n J (x) = Pexp [ ig ] ds n B A s(n B s + x) ] ds n J A s(n J s + x) 0 proton-proton collision. Two incoming soft gluon jets from initial states [ 0 Y (x) = Pexp n ig 2 Y n1 (x) = P exp [ ig 0 ] ds n 2 A s(n 2s + x) ] ds n 1 A s(n 1s + x) Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 14, 2015

12 (In)Equality of Soft Radiation from ee, ep & pp Outgoing gluons become incoming ones (1) Infinite number of gluons in jets: to sum up in path order or anti-path order fashion (2) Each of them carry a color index with non-abelian properties -- bring in an extra factor when path-order --> anti-path order Ou Zhang University of Arizona Equality of Hemisphere Soft Functions in ee, ep and pp Collisions to

13 Conclusion with the (In)Equality of Soft Radiation from ee,ep & pp Perturbatively, we proved Two and three jets up to O(α 2 s ), soft radiation is universal in all inclusive collisions for ee, ep and pp Up to any perturbative order, does the equality still hold? Up to n jets does the equality still hold non-perturbatively to all orders? Non-perturbatively, If soft radiation cannot be created as universal background how does it depends on the energetic jets structure? Universality of Perturbative QCD Soft Radiation in ee, ep andjanuary pp Collisions 15, 2015