1. 11/28/20151 QCD resummation in Higgs Boson Plus Jet Production Feng Yuan Lawrence Berkeley National Laboratory Ref: Peng Sun, C.-P. Yuan, Feng Yuan, PRL 113, 232001 (2014); PRL114, 202001 (2015); arXv: 1506.06170.

2. Outlines Dijet correlation from Tevatron and LHC Soft gluon resummation  Collins-Soper-Sterman Higgs boson plus Jet production 11/28/20152

3. Dijet production at the hadron colliders Most abundant events Almost back-to-back De-correlation comes  Hard gluon jet  Soft gluon radiation 11/28/20153

4. Beautiful data from Tevatron/LHC 11/28/20154 CMS, PRL11 D0, PRL05

5. 11/28/20155 ATLAS, PRL11

6. QCD calculations Fixed order calculations divergent around π, where soft gluon radiation dominate All order resummation is needed to understand the physics around here  Two separate scales P T >>q T 11/28/20156 D0, PRL05 Leading P T Total q T ≈P T Sin(Δ ϕ )

7. 7 Sudakov Large Double Logarithms Differential cross section depends on Q 1, where Q 2 >>Q 1 2 >>  2 QCD We have to resum these large logs to make reliable predictions  Q T : Dokshitzer, Diakonov, Troian, 78; Parisi Petronzio, 79; Collins, Soper, Sterman, 85  Threshold: Sterman 87; Catani and Trentadue 89 Sudakov, 1956

8. 8 How Large of the Resummation effectsResum NLO Kulesza, Sterman, Vogelsang, 02 Z/γ *

9. 9 Collins-Soper-Sterman Resummation  (P T,Q)=H(Q) f 1 (k 1T,Q) f 2 (k 2T, Q) S( T ) Large Logs are resummed by solving the energy evolution equation of the TMDs K and G obey the renormalization group eq. ( Collins-Soper 81, Collins-Soper-Sterman 85 )

10. 10 CSS Formalism (Drell-Yan) The large logs will be resummed into the exponential form factor  A,B,C functions are perturbative calculable A: Sudakov double logs B: anomalous dimension C: hard coefficients  f 1,f 2 are integrated PDFs (Collins-Soper-Sterman 85)

11. Dijet production is different Final states carry color  Soft gluon radiation will contribute Jet algorithm will enter into the calculations as well  Only out of cone radiation contributes to the imbalance between the two jets 11/28/201511

12. Dijet (Leading Double Logs-A) Power counting: each incoming parton contributes to a half of the associated color factor 11/28/201512 Banfi-Dasgupta-Delenda, PLB 2008 Mueller-Xiao-Yuan, PRD 2013 A (1) =(C p1 +C p2 )/2

13. Next-to-leading Logs (NLL) Jet size-dependence ( Banfi-Dasgupta 2004) Matrix form ( Kidonakis-Sterman 1997) 11/28/201513 Sun,C.-P. Yuan, F. Yuan, PRL 2014 D: color-factor for the jet R: jet size

14. One-loop: Soft and collinear gluon 11/28/201514 Virtual Ellis-Sexton 86 Jet (Narrow Jet Approx.) Jager-Stratmann-Vogelsang 2004 Soft Initial state Soft Final state (out of jet cone)

15. Cross checks Divergences cancelled out between virtual, jet, sot contributions (dimension regulation applied) Final results :double logs, single logs,.. 11/28/201515 Quark channel: q i q j  q i q j

16. Compared to full calculations 11/28/201516 Leading P T Total q T ≈P T Sin(Δ ϕ ) full LO: Nagy 2002, NLOJET++ D0 kinematics Sun, Yuan, FY, PRL 113, 232001 (2014)

17. Compared to the data 11/28/201517 D0 data Full NLO: Nagy 2002, NLOJET++ NLL Resummation: Sun,C.P.Yuan, F.Yuan, PRL2014 Sun, Yuan, FY; PRL 113, 232001 (2014)

18. At the LHC 11/28/201518 Sun, Yuan, FY, 1506.06170.

19. Higgs Boson plus Jet Production 11/28/201519

21. Higgs Boson plus Jet Production One of the major channels to study Higgs boson coupling to SM particles Already data from LHC In particular, Higgs boson plus two jets with large rapidity separation to study HWW coupling As compared to dijet, it is much simpler, and a complete one-loop calculation possible

22. Jet and soft gluon radiation Virtual graphs been calculated before 11/28/201522

23. One-loop results 11/28/201523

24. Resummation 11/28/201524

25. Importance of the resummation q T : total transverse momentum of the Higgs boson and the jet 11/28/201525 Sun, Yuan, FY, PRL114, 202001 (2015)

26. Azimuthal angular correlation Φ: azimuthal angle between the Higgs boson and the jet 11/28/201526 Sun, Yuan, FY, PRL114, 202001 (2015)

27. Further applications Higgs boson PT distribution in associated with jet production 11/28/201527 Boughezal et al, 1504.07922, 1505.03893 Resummation will be important in the P cut region Work in progress

28. Higgs boson plus two jets Vector boson fusion and gluon-gluon fusion 11/28/201528

29. Competing mechanism 11/28/201529 Campbell et al, hep-ph/0608194

30. QCD resummation It’s a tough calculation However, in the most interesting channel, two jets are produced forward-backward (+y,-y), we can simplify the derivation No color-matrix needed, although there are two jets in the final state  Similar to the Mueller-Navelet dijet Mueller-Xiao-Yuan, working in progress 11/28/201530

31. Similar to W/Z and inclusive Higgs production (Collins-Soper-Sterman) 11/28/201531

32. We are working on numerics,… 11/28/201532

33. Summary Soft gluon resummation for jet production and jet plus weak boson production can be performed, and these effects are important Improvements can be made to extend the narrow jet approximation and study jet size dependence carefully Extend to W/Z and jet production, many data to test the formalism 11/28/201533

34. TMD factorization and resummation TMD evolution Soft factor 11/28/201534

35. Final results at NLL 11/28/201535

36. Factorization breaking effects In collinear calculations, it appears at α s 3 corrections, will affect A (3) coefficient 11/28/201536 Collins-Qiu 07 Factorizable, A (1)

37. Non-perturbative form factor 11/28/201537 W(b) for gluon-gluon channel for typical LHC kinematics with two different non-perturbative inputs