Resummation for Physics Beyond the Standard Model 1 University of Oslo

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1 Resummation for Physics Beyond the Standard Model 1 University of Oslo Richard Ruiz Institute for Particle Physics Phenomenology, Durham University 24 January Based on lots of work: See slides for Refs (*) = IPPP student R Ruiz - IPPP Resummation4BSM - Oslo 1 / 33

2 What this talk is about I would like to motivate the existence of new physics from a neutrino perspective breakdown of fixed order (FO) perturbation theory in collider predictions factorization and exponentiation in mass gauge theories (QED/QCD) impact of QCD resummation on BSM searches at colliders Central Idea: The property of universality of gauge interactions implies what works for SM largely works for BSM Eg, NLO+NNLL corrections for W SM and a 4 TeV W KK are identical Lots will be covered, so please ask questions! This is a BSM seminar, not a formal lecture R Ruiz - IPPP Resummation4BSM - Oslo 2 / 33

3 Where we are today The LHC is operating spectacularly! 60 fb 1 at 13 TeV ( 5x Tevatron) Higgs : Not just a hep-th problem but now also a hep-ex problem ν masses, mass hierarchy, particle nature of dark matter, origin of EWSB, etc, require more data and thought R Ruiz - IPPP Resummation4BSM - Oslo 3 / 33

4 Where we are today The LHC is operating spectacularly! 60 fb 1 at 13 TeV ( 5x Tevatron) Higgs : Not just a hep-th problem but now also a hep-ex problem ν masses, mass hierarchy, particle nature of dark matter, origin of EWSB, etc, require more data and thought After Run I and early Run II (Fall 17), data is clear: Interaction Strength \ Mass Scale gbsm gsm gbsm gsm ΛBSM ΦEW Need more data! ΛBSM ΦEW Need more data! Cannot probe :( Picture first suggested by LEP + Belle I + Tevatron is telling: No low hanging fruit hep-ph from 90s-00s designed for day 1 discoveries, not for extreme regions of BSM parameter space (and hence collider phase space) R Ruiz - IPPP Resummation4BSM - Oslo 3 / 33

5 Issue: Day 1 pheno = simple channels with moderately good signal/bkg, eg, Drell-Yan process like qq W R Ne ± e ± e ± + qq In exotic processes, eg, VBF and mono-x, contributions from phase space integration ( dk 2 ) over add l propagators (1/k 2 ) generates logs: σ(pp Y ) log Λ BSM / Φ EW and log Λ BSM /Λ QCD and can spoil the validity of BSM predictions and/or collider signatures R Ruiz - IPPP Resummation4BSM - Oslo 4 / 33

6 Issue: Day 1 pheno = simple channels with moderately good signal/bkg, eg, Drell-Yan process like qq W R Ne ± e ± e ± + qq In exotic processes, eg, VBF and mono-x, contributions from phase space integration ( dk 2 ) over add l propagators (1/k 2 ) generates logs: σ(pp Y ) log Λ BSM / Φ EW and log Λ BSM /Λ QCD and can spoil the validity of BSM predictions and/or collider signatures Solution: These are issues long-understood by the pqcd community: exploit soft/collinear factorization, resummation, and IRC-safety From this perspective, BSM collider pheno looks qualitatively different Results focus on Seesaw partners (N, W R ) but are applicable/ necessary for other high-mass, colorless systems, eg, W ± h, l ν l R Ruiz - IPPP Resummation4BSM - Oslo 4 / 33

7 Issue: Day 1 pheno = simple channels with moderately good signal/bkg, eg, Drell-Yan process like qq W R Ne ± e ± e ± + qq In exotic processes, eg, VBF and mono-x, contributions from phase space integration ( dk 2 ) over add l propagators (1/k 2 ) generates logs: σ(pp Y ) log Λ BSM / Φ EW and log Λ BSM /Λ QCD and can spoil the validity of BSM predictions and/or collider signatures Solution: These are issues long-understood by the pqcd community: exploit soft/collinear factorization, resummation, and IRC-safety From this perspective, BSM collider pheno looks qualitatively different Results focus on Seesaw partners (N, W R ) but are applicable/ necessary for other high-mass, colorless systems, eg, W ± h, l ν l Message: QCD is a useful and powerful tool for BSM@Colliders R Ruiz - IPPP Resummation4BSM - Oslo 4 / 33

8 Motivation for new physics R Ruiz - IPPP Resummation4BSM - Oslo 5 / 33

9 Our Motivation The SM, via the Higgs Mechanism, explains how elementary fermions obtain mass, ie, the mf = yf Φ, not the values of mf Spanning many orders of magnitudes, the relationship of fermion masses is still a mystery Two observations: 1 Neutrinos have mass (BSM physics and Neutrinos have unusually small mass (Seesaw Mechanism?) R Ruiz - IPPP!) Resummation4BSM - Oslo 6 / 33

10 Evidence for New Physics from Neutrinos To generate ν masses similar to other SM fermions, we need N R ( ) ( ) Φ + h L ν Yuk = y ν νl l L N 0 R + Hc = m D ν L N R + Hc m D = y ν Φ, and y ν is the neutrino s Higgs Yukawa coupling Since N R i do not exist in the SM, massless neutrinos are predicted However, we have learned through neutrino oscillations that massless neutrinos is not an accurate description [T2K ν e appearance, v3] Entries/(240 MeV) Data Water Signal 0 µ and π 0 µ w/o π in FSI in FSI π 0 w/o µ in FSI 0 No µ / π Other in FSI Particle Energy (MeV) Neutrino masses is evidence of physics beyond the SM R Ruiz - IPPP Resummation4BSM - Oslo 7 / 33

11 Collider Connection to Neutrino Mass Models ν mass models predict new partners of all shapes, spins, and color, eg, N (Type I), T 0,± (Type III), Z B L, H ±,±± R (Type I+II) Through gauge couplings and mixing, production in ee/ep/pp collisions 2 DY : qq γ /Z T + T and qq W ± R Nl± VBF : W ± W ± H ±± GF : gg h /Z Nν l um dn { u p u d u W R e ui WR N l2 W H l1 W e dj p { d u u u Identification of Seesaw partners is then inferred by their decays to SM particles and the associated final-state kinematics 2 Review on ν mass models at colliders, Y Cai, T Li, T Han, and RR [ ] R Ruiz - IPPP Resummation4BSM - Oslo 8 / 33

12 Benchmark Scenario: Left-Right Symmetry at Hadron Colliders R Ruiz - IPPP Resummation4BSM - Oslo 9 / 33

13 Left-Right Symmetric Models (LRSM) postulate that the SM s V A structure originates from the spontaneous breakdown of parity symmetry: SU(3) c SU(2) L SU(2) R U(1) B L }{{} After scalar R acquires a vev v R v SM : U(1) Y Higgs field Φ then breaks down the EW group SU(2) L U(1) Y U(1) EM R Ruiz - IPPP Resummation4BSM - Oslo / 33

14 Left-Right Symmetric Models (LRSM) postulate that the SM s V A structure originates from the spontaneous breakdown of parity symmetry: SU(3) c SU(2) L SU(2) R U(1) B L }{{} After scalar R acquires a vev v R v SM : U(1) Y Higgs field Φ then breaks down the EW group SU(2) L U(1) Y U(1) EM With N R, all SM fermions can be grouped in SU(2) L and SU(2) R doublets Dirac masses generated in (mostly) usual way with Φ, ie, L Q L ΦQ R Neutrinos obtain LH (RH) Majorana masses from triplet scalar L ( R ): mlight ν = y L L }{{} Type II ( ) Φ 2 R 1 y D y 1 R y D T }{{} Type I a la Type II O(0) + symm-breaking Major pheno: heavy N, W /Z ( W R /Z R ), and H i ±±, H j ±, Hk 0 R Ruiz - IPPP Resummation4BSM - Oslo / 33

15 LHC Tests of Left-Right Symmetry q q W ± ν l l ± Moriond: very light, long-lived N : M WR 5 TeV [ ] Question: Can 13 TeV LHC say anything about M WR 5 TeV? R Ruiz - IPPP Resummation4BSM - Oslo 11 / 33

16 Threshold (or Soft Gluon) Resummation in pqcd 3 3 Non-experts: Roughly speaking, resummation is a procedure for collecting most (or next-to-most or next-to-next-) divergent radiation terms at each order of perturbation theory to obtain a finite result Useful since FO results breakdown near poles R Ruiz - IPPP Resummation4BSM - Oslo 12 / 33

17 Hadron colliders like the LHC are ultimately counting experiments N WR = }{{}}{{} L No of W R Luminosity [barns 1 ] σ(pp W R + anything) }{{} Production cross section [barns] 4 Collins, Soper, Sterman ( 85, 88, 89); Collins, Foundations of pqcd (2011) R Ruiz - IPPP Resummation4BSM - Oslo 13 / 33

18 Hadron colliders like the LHC are ultimately counting experiments N WR = }{{}}{{} L No of W R Luminosity [barns 1 ] σ(pp W R + anything) }{{} Production cross section [barns] We usually employ the Collinear Factorization Theorem 4 (master equation for colliders) to get hadronic scattering rate: Hadron-level scattering probabilities are the product (convolution) of parton-dist (PDFs), -emission (Sudakov), and -scattering probab ( M 2 ) dσ(pp B + X) = f f d ˆσ 4 Collins, Soper, Sterman ( 85, 88, 89); Collins, Foundations of pqcd (2011) R Ruiz - IPPP Resummation4BSM - Oslo 13 / 33

19 W R production is analogous to W SM, except M WR 3 5 TeV Hadronic process (s) σ(pp W R ± +X) f a/p Partonic process (ŝ) ˆσ(qq W ± R) } Hard process (Q 2 = M 2 ) WR f b/p 5 For total [Altarelli, et al ( 79); Sullivan ( 02)] and inclusive differential observables [Harris and Owens ( 02); Sullivan ( 02)], for any chiral structure and mass [RR ( 15)] R Ruiz - IPPP Resummation4BSM - Oslo 14 / 33

20 W R production is analogous to W SM, except M WR 3 5 TeV Hadronic process (s) σ(pp W R ± +X) f a/p Partonic process (ŝ) ˆσ(qq W ± R) } Hard process (Q 2 = M 2 ) WR f b/p Away from phase space boundaries, 5 For total [Altarelli, et al ( 79); Sullivan ( 02)] and inclusive differential observables [Harris and Owens ( 02); Sullivan ( 02)], for any chiral structure and mass [RR ( 15)] R Ruiz - IPPP Resummation4BSM - Oslo 14 / 33

21 W R production is analogous to W SM, except M WR 3 5 TeV Hadronic process (s) σ(pp W R ± +X) f a/p Partonic process (ŝ) ˆσ(qq W ± R) } Hard process (Q 2 = M 2 ) WR f b/p Away from phase space boundaries, QCD corrections for DY are % 5 For total [Altarelli, et al ( 79); Sullivan ( 02)] and inclusive differential observables [Harris and Owens ( 02); Sullivan ( 02)], for any chiral structure and mass [RR ( 15)] R Ruiz - IPPP Resummation4BSM - Oslo 14 / 33

22 W R production is analogous to W SM, except M WR 3 5 TeV Hadronic process (s) σ(pp W R ± +X) f a/p Partonic process (ŝ) ˆσ(qq W ± R) } Hard process (Q 2 = M 2 ) WR f b/p Away from phase space boundaries, QCD corrections for DY are % However, near boundaries, eg, near mass threshold, where E g E q, σ(qq W R + g) ( ) d 4 2ε PS 2 λ 1 2ε 2 1, Q2 =MW 2 R ŝ, k2 g =0 ŝ ( ) 1 2ε ( ) = 1 M2 W R ŝ 2ε log 1 M2 W R ŝ 5 For total [Altarelli, et al ( 79); Sullivan ( 02)] and inclusive differential observables [Harris and Owens ( 02); Sullivan ( 02)], for any chiral structure and mass [RR ( 15)] R Ruiz - IPPP Resummation4BSM - Oslo 14 / 33

23 W R production is analogous to W SM, except M WR 3 5 TeV Hadronic process (s) σ(pp W R ± +X) f a/p Partonic process (ŝ) ˆσ(qq W ± R) } Hard process (Q 2 = M 2 ) WR f b/p Away from phase space boundaries, QCD corrections for DY are % However, near boundaries, eg, near mass threshold, where E g E q, σ(qq W R + g) ( ) d 4 2ε PS 2 λ 1 2ε 2 1, Q2 =MW 2 R ŝ, k2 g =0 ŝ ( ) 1 2ε ( ) = 1 M2 W R ŝ 2ε log 1 M2 W R ŝ As M 2 W R s, logs > 1/α s since M 2 W R ŝ < s forces g to be soft 5 For total [Altarelli, et al ( 79); Sullivan ( 02)] and inclusive differential observables [Harris and Owens ( 02); Sullivan ( 02)], for any chiral structure and mass [RR ( 15)] R Ruiz - IPPP Resummation4BSM - Oslo 14 / 33

24 W R production is analogous to W SM, except M WR 3 5 TeV Hadronic process (s) σ(pp W R ± +X) f a/p Partonic process (ŝ) ˆσ(qq W ± R) } Hard process (Q 2 = M 2 ) WR f b/p Away from phase space boundaries, QCD corrections for DY are % However, near boundaries, eg, near mass threshold, where E g E q, σ(qq W R + g) ( ) d 4 2ε PS 2 λ 1 2ε 2 1, Q2 =MW 2 R ŝ, k2 g =0 ŝ ( ) 1 2ε ( ) = 1 M2 W R ŝ 2ε log 1 M2 W R ŝ As MW 2 R s, logs > 1/α s since MW 2 R ŝ < s forces g to be soft More logs = O(αs k+1 ) > O(αs k ) = expansion in α s not justified 5 For total [Altarelli, et al ( 79); Sullivan ( 02)] and inclusive differential observables [Harris and Owens ( 02); Sullivan ( 02)], for any chiral structure and mass [RR ( 15)] R Ruiz - IPPP Resummation4BSM - Oslo 14 / 33

25 In PT, one (Taylor) expands in powers of coupling constant: σ = k αk s σ (k) = σ (0) + α s σ (1) + α 2 s σ (2) + O(α 3 s ) Stop/truncate at finite/fixed order only if O(α k+1 s ) < O(α k s ) 6 See, eg, Appell, Sterman, Mackenzie ( 88); Forte and Ridolffi ( 03) R Ruiz - IPPP Resummation4BSM - Oslo 15 / 33

26 In PT, one (Taylor) expands in powers of coupling constant: σ = k αk s σ (k) = σ (0) + α s σ (1) + α 2 s σ (2) + O(α 3 s ) Stop/truncate at finite/fixed order only if O(α k+1 s ) < O(α k s ) Soft radiation near threshold spoil perturbative convergence since Higher order terms > lower order terms 6 See, eg, Appell, Sterman, Mackenzie ( 88); Forte and Ridolffi ( 03) R Ruiz - IPPP Resummation4BSM - Oslo 15 / 33

27 In PT, one (Taylor) expands in powers of coupling constant: σ = k αk s σ (k) = σ (0) + α s σ (1) + α 2 s σ (2) + O(α 3 s ) Stop/truncate at finite/fixed order only if O(α k+1 s ) < O(α k s ) Soft radiation near threshold spoil perturbative convergence since Higher order terms > lower order terms All is not lost! Kinematics of soft, massless radiation are special: 6 Soft rad factorizes all-orders summation exponentiation All-orders (re)summation of α s log(1 M 2 /ŝ) 6 See, eg, Appell, Sterman, Mackenzie ( 88); Forte and Ridolffi ( 03) R Ruiz - IPPP Resummation4BSM - Oslo 15 / 33

28 Factorization, Exponentiation, and REnormalization Group-Improved Summation 7 7 Non-experts: Roughly speaking, resummation is a procedure for collecting most (or next-to-most or next-to-next-) divergent radiation terms at each order of perturbation theory to obtain a finite result Useful since FO results breakdown near poles R Ruiz - IPPP Resummation4BSM - Oslo 16 / 33

29 Soft Factorization in Gauge Theories Factorization in gauge theories is where a radiation amplitude M R in certain kinematic limits can be written as the no-radiation amplitude M B and a universal, ie, process-independent, piece: M R = q(p), u(p) M g(k), ǫ µ (k) For radiation q (p + k g ) q(p) + g(k g ), E g E q, the amplitude is M R u(p)ϵ µ(k)(ig s T A )γ µ ( p+ k g ) (p+k g ) 2 M (ig s T A )u(p) ϵ µ γµ p (2p k g ) M R Ruiz - IPPP Resummation4BSM - Oslo 17 / 33

30 Soft Factorization in Gauge Theories Factorization in gauge theories is where a radiation amplitude M R in certain kinematic limits can be written as the no-radiation amplitude M B and a universal, ie, process-independent, piece: M R = q(p), u(p) M g(k), ǫ µ (k) For radiation q (p + k g ) q(p) + g(k g ), E g E q, the amplitude is M R u(p)ϵ µ(k)(ig s T A )γ µ ( p+ k g ) (p+k g ) 2 M (ig s T A )u(p) ϵ µ γµ p (2p k g ) M Anti-commute and applying Dirac Eq gives us M R }{{ Soft = (ig } s T A ) u(p) (pµ ϵ µ ) (p k g ) M = (ig s T A ) pµ ϵ µ (p k g ) Soft rad amp }{{} M B }{{} Born amp Process independent R Ruiz - IPPP Resummation4BSM - Oslo 17 / 33

31 Factorization of Virtual α s Corrections to Currents QCD corrections to colorless currents with massless quarks are special q i q j W + (γ/z) At one-loop, corrections also factorize(!) for generic V-A structure: M 1 Loop 2 = M Born 2 (1 + 2R[F]) + O(α s ) Hold for all phase space at 1-loop, and in soft/coll limit beyond that R Ruiz - IPPP Resummation4BSM - Oslo 18 / 33

32 Sketch of Factorization and Exponentiation Is it possible to study soft/collinear radiation with perturbative QCD? Yes! Combine our factorized results: M WR +1 soft/collinear radiation = rad pole + loop pole M }{{} FO universal factor The squaring, averaging, and integrating over (n + 1)-body phase space dσ WR +1 soft/collinear radiation = dps 1 (universal piece) σw FO soft/collinear R }{{} finite, S W R R Ruiz - IPPP Resummation4BSM - Oslo 19 / 33

33 Sketch of Factorization and Exponentiation Is it possible to study soft/collinear radiation with perturbative QCD? Yes! Combine our factorized results: M WR +1 soft/collinear radiation = rad pole + loop pole M }{{} FO universal factor The squaring, averaging, and integrating over (n + 1)-body phase space dσ WR +1 soft/collinear radiation = dps 1 (universal piece) σw FO soft/collinear R }{{} finite, S Keeping track of symmetry factors lets us do this for k-emissions: dσ WR +k soft/collinear = 1 k! [S]k σ FO W R Summing over all such emissions gives us a closed result: dσ WR +any soft/collinear = k 1 k! [S]k σ FO = exp[s] σfo R Ruiz - IPPP Resummation4BSM - Oslo 19 / 33 DY W R W R

34 Hadronic process (s) σ(pp X +Y) f c/p (µ f) I a c(p Veto T,µ f) E I(Q 2,p Veto T,µ h) H ab(q 2,µ h) f c/p (µ f) I b c(p Veto T,µ f) } Hard process (Q 2 ) ˆσ B (ab X) A different perspective 8 : In general, scattering rates have the form d 3 σ dξ 1 dξ 2 dz dps = i,j=q,g, [f i(ξ 1, µ)f j (ξ 2, µ) + (1 2)] }{{} parton flux, ŝ=ξ 1 ξ 2 s C(z) }{{} soft emissions, C(z=Q 2 /ŝ)=δ(1 z)+o(α s(µ)) d ˆσ(ij A) }{{} hard process, Q 2 Multi-scale problem: s, ŝ, Q, m A, but also µ (put in by hand) Nature works independent of us: d d log µ dσ = 0 = d d log µ C(z, µ) = f (z, µ)c(z, µ) = C(z, µ) = exp[s(µ, µ 0 )]C(z, µ 0 ) Each piece follows RG evolution 8 Contopanagos, Laenen, Sterman ( 96); Becher, Neubert etc; Stewart, Tackmann etc R Ruiz - IPPP Resummation4BSM - Oslo 20 / 33

35 pp W ± R + X at NLO+NNLL(Thresh)9 σ [fb] LO 4 3 σ / σ ± pp W R + X 13 TeV LHC LO Mitra, et al, PRD94, (2016) [ ] NLO+NNLL w/ PDF Unc [TeV] M WR NLO + NNLL w/ PDF Unc NLO NLO w/ PDF Unc σ [fb] 1 2 LO σ / σ 2 1 ± pp W R + X 0 TeV VLHC NLO LO 16 NLO+NNLL w/ PDF Unc NLO w/ PDF Unc NLO + NNLL w/ PDF Unc M WR [TeV] At 13 TeV, corrections to production rate > +0% for M WR 45 TeV 9 Mitra, RR, Scott*, Spannowsky [ ] R Ruiz - IPPP Resummation4BSM - Oslo 21 / 33

36 pp W ± R + X at NLO+NNLL(Thresh)9 σ [fb] LO 4 3 σ / σ ± pp W R + X 13 TeV LHC LO Mitra, et al, PRD94, (2016) [ ] NLO+NNLL w/ PDF Unc [TeV] M WR NLO + NNLL w/ PDF Unc NLO NLO w/ PDF Unc σ [fb] 1 2 LO σ / σ 2 1 ± pp W R + X 0 TeV VLHC NLO LO 16 NLO+NNLL w/ PDF Unc NLO w/ PDF Unc NLO + NNLL w/ PDF Unc M WR [TeV] At 13 TeV, corrections to production rate > +0% for M WR 45 TeV σ LO (M WR = 5 TeV) 07 fb = σ (1 ab 1 ) = 700 events 9 Mitra, RR, Scott*, Spannowsky [ ] R Ruiz - IPPP Resummation4BSM - Oslo 21 / 33

37 pp W ± R + X at NLO+NNLL(Thresh)9 σ [fb] LO 4 3 σ / σ ± pp W R + X 13 TeV LHC LO Mitra, et al, PRD94, (2016) [ ] NLO+NNLL w/ PDF Unc [TeV] M WR NLO + NNLL w/ PDF Unc NLO NLO w/ PDF Unc σ [fb] LO σ / σ ± pp W R + X 0 TeV VLHC NLO LO 16 NLO+NNLL w/ PDF Unc NLO w/ PDF Unc NLO + NNLL w/ PDF Unc M WR [TeV] At 13 TeV, corrections to production rate > +0% for M WR 45 TeV σ LO (M WR = 5 TeV) 07 fb = σ (1 ab 1 ) = 700 events σ NLO+NNLL 17 fb = σ (1 ab 1 ) = 17k events 9 Mitra, RR, Scott*, Spannowsky [ ] R Ruiz - IPPP Resummation4BSM - Oslo 21 / 33

38 pp W ± R + X at NLO+NNLL(Thresh)9 σ [fb] LO 4 3 σ / σ ± pp W R + X 13 TeV LHC LO Mitra, et al, PRD94, (2016) [ ] NLO+NNLL w/ PDF Unc [TeV] M WR NLO + NNLL w/ PDF Unc NLO NLO w/ PDF Unc σ [fb] LO σ / σ ± pp W R + X 0 TeV VLHC NLO LO 16 NLO+NNLL w/ PDF Unc NLO w/ PDF Unc NLO + NNLL w/ PDF Unc M WR [TeV] At 13 TeV, corrections to production rate > +0% for M WR 45 TeV σ LO (M WR = 5 TeV) 07 fb = σ (1 ab 1 ) = 700 events σ NLO+NNLL 17 fb = σ (1 ab 1 ) = 17k events Assuming BR ε A = 2% = N 34 events ( 6σ vs 4σ) 9 Mitra, RR, Scott*, Spannowsky [ ] R Ruiz - IPPP Resummation4BSM - Oslo 21 / 33

39 Parton Shower Resummation Non-experts: Roughly speaking, resummation is a procedure for collecting most (or next-to-most or next-to-next-) divergent radiation terms at each order of perturbation theory to obtain a finite result Useful since FO results breakdown near poles R Ruiz - IPPP Resummation4BSM - Oslo 22 / 33

40 Parton Showers The idea of a parton shower is to capture the emission of soft/collinear (but mostly collinear) emissions in the initial and final state q(p j ) α n s (k2 T )logn ( t k 2 T ) Such emissions are not naively O(α s ) suppressed, ie, power suppressed, since momentum scale of emission is small compared to outgoing particle R Ruiz - IPPP Resummation4BSM - Oslo 23 / 33

41 Parton Showers The idea of a parton shower is to capture the emission of soft/collinear (but mostly collinear) emissions in the initial and final state q(p j ) αs n ( ) (k2 T )logn t kt 2 Such emissions are not naively O(α s ) suppressed, ie, power suppressed, since momentum scale of emission is small compared to outgoing particle Logs from additional propagators are large: dp 2 T /p2 T log p2 T 1/α s R Ruiz - IPPP Resummation4BSM - Oslo 23 / 33

42 Parton Showers The idea of a parton shower is to capture the emission of soft/collinear (but mostly collinear) emissions in the initial and final state q(p j ) αs n ( ) (k2 T )logn t kt 2 Such emissions are not naively O(α s ) suppressed, ie, power suppressed, since momentum scale of emission is small compared to outgoing particle Logs from additional propagators are large: dp 2 T /p2 T log p2 T 1/α s Using collinear factorization and unitarity, we can build an evolution factor that accounts for all such radiations, up to leading logarithmic accuracy R Ruiz - IPPP Resummation4BSM - Oslo 23 / 33

43 For virtuality t of internal line, collinear factorization give us: σ (n+1) σ n dz dt t α sc i 2π P ji(z), z = E g /E parent The differential splitting probability is then given as dp Split σ (n+1) σ n = dt t dz α sc i 2π P ji(z) R Ruiz - IPPP Resummation4BSM - Oslo 24 / 33

44 For virtuality t of internal line, collinear factorization give us: σ (n+1) σ n dz dt t α sc i 2π P ji(z), z = E g /E parent The differential splitting probability is then given as dp Split σ (n+1) σ n = dt t dz α sc i 2π P ji(z) By unitarity, the likelihood of a parton at t 0 not radiating down to t 1 is P No Split (t 1, t 0 ) = 1 P Split = 1 dt t dz α sc i [ 2π P ji(z) exp t 1 ] dt t 0 t dz α sc i 2π P ji(z) R Ruiz - IPPP Resummation4BSM - Oslo 24 / 33

45 For virtuality t of internal line, collinear factorization give us: σ (n+1) σ n dz dt t α sc i 2π P ji(z), z = E g /E parent The differential splitting probability is then given as dp Split σ (n+1) σ n = dt t dz α sc i 2π P ji(z) By unitarity, the likelihood of a parton at t 0 not radiating down to t 1 is P No Split (t 1, t 0 ) = 1 P Split = 1 dt t dz α sc i [ 2π P ji(z) exp t 1 ] dt t 0 t dz α sc i 2π P ji(z) Note: As the leading splitting α log(t 1 /t 0 ) is exponentiated, ie, sums to all orders in (couplings log), this resummation is leading log accurate Pheno: NLO+PS/LL(q T ) = lowest order at which first QCD radiation is qualitatively correct / physically meaningful [CSS ( 85)] R Ruiz - IPPP Resummation4BSM - Oslo 24 / 33

46 NLO+PS/LL(q T ) Major focus of MC community past decade was automation of NLO LRSM Ex: (m N /M WR ) (y N /g R) 1 - N is light and "long"-lived - pp W R Ne looks like SSM W R Ruiz - IPPP Resummation4BSM - Oslo 25 / 33

47 NLO+PS/LL(q T ) Major focus of MC community past decade was automation of NLO LRSM Ex: (m N /M WR ) (y N /g R) 1 - N is light and "long"-lived - pp W R Ne looks like SSM W Monte Carlos: modeling jet observables correctly now possible - b-jet vetoes do not remove all QCD radiation (tx = tt, tw, tq) [ GeV / bin] p of Hardest Jet [GeV] T R Ruiz - IPPP Resummation4BSM - Oslo 25 / 33 T 1/σ dσ/dp 045 ε b b =0%, p < 30 GeV T 04 R = 1 ± 035 W SSM (300 GeV) ± W (3 TeV) 02 SSM tx

48 NLO+PS/LL(q T )+Veto [ GeV / bin] T 1/σ dσ/dp 045 ε b b =0%, p < 30 GeV T 04 R = 1 ± 035 W SSM (300 GeV) ± W 02 SSM (3 TeV) tx p of Hardest Jet [GeV] T ] 1 Luminosity for 5σ [fb fb 13 TeV LHC W µν µ p = 40 GeV Veto T 1 3 ab No Veto 2 M W [GeV] Veto 2 g = 26 g SM 3 Monte Carlos: modeling jet observables as bkg discriminants now possible - Why? QCD/tt have different radiation patterns than color-singlets - Eg, veto R = 1 anti-k T jets with p j T > 40 GeV eliminates top quarks - Eg, improve l ν l discovery potential [Tackman, et al, ] NLO+PS in agreement w/ NLO+NNLL [Fuks, RR, ] - Nontrivial but not total surprise = NLO+PS sufficient for discovery R Ruiz - IPPP Resummation4BSM - Oslo 26 / 33

49 Resummation in Modern Event Generators NLO+PS and NLO+NNLL(Veto) 11 automated in All one needs NLO-accurate FeynRules input model file 11 Veto possible for color-singlet processes only Becher, et al [ ] R Ruiz - IPPP Resummation4BSM - Oslo 27 / 33

50 Resummation in Modern Event Generators NLO+PS and NLO+NNLL(Veto) 11 automated in All one needs NLO-accurate FeynRules input model file Explosion past two years: [feynrulesirmpuclacbe/wiki/nlomodels] Modern general purpose MC packages are very sophisticated "With great power there must also come - great responsibility"- S Lee ( 62) 11 Veto possible for color-singlet processes only Becher, et al [ ] R Ruiz - IPPP Resummation4BSM - Oslo 27 / 33

51 Threshold (or Soft Gluon) Resummation for Gluon Fusion Non-experts: Roughly speaking, resummation is a procedure for collecting most (or next-to-most or next-to-next-) divergent radiation terms at each order of perturbation theory to obtain a finite result Useful since FO results breakdown near poles R Ruiz - IPPP Resummation4BSM - Oslo 28 / 33

52 Threshold (or Soft Gluon) Resummation for Gluon Fusion 12 Myth that QCD is Unimportant for BSM 12 Non-experts: Roughly speaking, resummation is a procedure for collecting most (or next-to-most or next-to-next-) divergent radiation terms at each order of perturbation theory to obtain a finite result Useful since FO results breakdown near poles R Ruiz - IPPP Resummation4BSM - Oslo 28 / 33

53 Threshold Resummation for GF - QCD corrections to gg h SM are large - GF@LO is excluded by LHC! - Corrections also large for heavy H 0, A 0 Resum captures leading FO corrections Bonvini, et al, [ ] - What about heavy N production? R Ruiz - IPPP Resummation4BSM - Oslo 29 / 33

54 Common Statement: QCD is unimportant for colorless BSM More correct: Away from phase space boundaries, totally inclusive fixed order QCD corrections are % for colorless s-channel BSM processes initiated by quarks for non-hierarchical scale choices These are the assumptions for the Collinear Factorization Thm σ(pp A + anything) = i,j f i/p f j/p ij ˆσ(ij A) R Ruiz - IPPP Resummation4BSM - Oslo 30 / 33

55 Common Statement: QCD is unimportant for colorless BSM More correct: Away from phase space boundaries, totally inclusive fixed order QCD corrections are % for colorless s-channel BSM processes initiated by quarks for non-hierarchical scale choices These are the assumptions for the Collinear Factorization Thm σ(pp A + anything) = i,j f i/p f j/p ij ˆσ(ij A) Relaxing these assumptions has consequences: For M W /Z s, σ NLO+N2 LL DY /σ LO 2 25 For W /Z at any M V, NLO+PS needed for jet-based/exclusive cuts In gg H 0 /A 0 for any m H/A, σ N3 LX /σ LO 2 3 How about gg h /Z Nν? R Ruiz - IPPP Resummation4BSM - Oslo 30 / 33

56 Threshold Corrections to Heavy N Production 13 Heavy N from GF is very interesting: ggz contribution identical to pseudoscalar (Equiv Thm) Large corrections: σ N3 LL GF /σgf LO 2 3 Largest channel for s TeV 13 Willenbrock, Dicus ( 85); Dicus, Roy ( 91); Hessler, et al [ ]; Degrande, Mattelaer, RR, Turner(*) [ ]; RR, Spannowsky, Waite(*) [ ] R Ruiz - IPPP Resummation4BSM - Oslo 31 / 33

57 Summary Over the past decade, a revolution in FO and Resummed calculations! New tools + new formalisms = new results Maturity of N j LO/N k LL formalism allows application to BSM Automated tools and instructions are publicly available QCD is a useful/necessary and powerful tool for Seesaws@Colliders Threshold resummation = σ NK LL /σ LO = 2 3 p T /veto resummation = new dimension for pheno analyses IRC-safety = more rigorous and robust collider signatures Remember: The LHC is planned to run over the next 20 years, with several stops scheduled for upgrades and maintenance work [presscern] High-Luminosity LHC and Belle II goals: 1-3 ab 1 and 50 ab 1 Premature to claim nightmare scenario (SM Higgs + nothing else) R Ruiz - IPPP Resummation4BSM - Oslo 32 / 33

58 Thank you R Ruiz - IPPP Resummation4BSM - Oslo 33 / 33