Resummation of transverse observables in momentum space: phenomenology Emanuele Re CERN & LAPTh Annecy Resummation, Evolution, Factorization 2017 Madrid, 13 November 2017
plan of the talk ◮ previous talk: theoretical explanation of method used to perform resummation of transverse observables in direct space, up to N3LL accuracy. ◮ we have implemented it into a numerical code, named RadISH . ◮ this talk: present results for p T , H and for Drell-Yan ( p T ,ℓℓ and φ ∗ ), giving also some details about matching to fixed-order: 1. Higgs transverse momentum 2. Drell-Yan ◮ All results obtained in collaboration with W. Bizon, P .F. Monni, L. Rottoli and P . Torrielli [arXiv:1705.09127, arXiv:1604.02191, and work in progress] 1 / 17
Higgs transverse momentum
Higgs p T : data vs theory ◮ p T , H is one of the more important observables for current Higgs studies at the LHC - large luminosity ⇒ precision studies (“not limited” by stat. uncertainty) - large p T , H : probe heavy degrees of freedom - medium-low p T , H : large cross section & probe of Higgs couplings (next slide) ◮ Fully exclusive (N)NLOPS Monte-Carlo tools heavily used by EXP . Logarithmic accuracy is limited. ◮ accurate logarithmic resummation (matched to fixed order) is important, both for data/TH comparison, as well as to provide accurate MC tools. 2 / 17
Higgs p T and light-quarks Yukawa ◮ differential distributions affected by interference among top and light-quarks loops - medium-to-low p T , H spectrum ⇒ bounds on charm Yukawa [Bishara,Haisch,Monni,ER ’16] [& similar ideas in [Soreq et al. ’16]] � m c � p 2 2 � � ∼ α 3 log 2 T S κ c m 2 m H c � m c 2 � ∼ α 2 S κ 2 c m h . one power of α S from charm PDF . c ¯ c → hg also included - different κ c scaling + log scaling ⇒ shape distorsion 3 / 17
Higgs p T and light-quarks Yukawa ◮ differential distributions affected by interference among top and light-quarks loops - medium-to-low p T , H spectrum ⇒ bounds on charm Yukawa [Bishara,Haisch,Monni,ER ’16] [& similar ideas in [Soreq et al. ’16]] � m c � p 2 2 � � ∼ α 3 log 2 T S κ c m 2 m H c � m c 2 � ∼ α 2 S κ 2 c m h . one power of α S from charm PDF . c ¯ c → hg also included - different κ c scaling + log scaling ⇒ shape distorsion 3 / 17
Higgs p T and light-quarks Yukawa ◮ differential distributions affected by interference among top and light-quarks loops - medium-to-low p T , H spectrum ⇒ bounds on charm Yukawa [Bishara,Haisch,Monni,ER ’16] [& similar ideas in [Soreq et al. ’16]] � m c � p 2 2 � � ∼ α 3 log 2 T S κ c m 2 m H c . non-Sudakov double log for m c <p T < m H � m c 2 � ∼ α 2 S κ 2 c m h . one power of α S from charm PDF . c ¯ c → hg also included - different κ c scaling + log scaling ⇒ shape distorsion 3 / 17
Higgs p T and light-quarks Yukawa ◮ differential distributions affected by interference among top and light-quarks loops - medium-to-low p T , H spectrum ⇒ bounds on charm Yukawa [Bishara,Haisch,Monni,ER ’16] [& similar ideas in [Soreq et al. ’16]] ( 1 / σ d σ / dp T , h )/( 1 / σ d σ / dp T , h ) SM κ c = - 10 1.4 κ c = - 5 κ c = 0 1.2 κ c = 5 1.0 0.8 0 20 40 60 80 100 p T , h [ GeV ] - different κ c scaling + log scaling ⇒ shape distorsion - use normalized distribution to reduce uncertainties 3 / 17
Higgs p T and light-quarks Yukawa ◮ differential distributions affected by interference among top and light-quarks loops - medium-to-low p T , H spectrum ⇒ bounds on charm Yukawa [Bishara,Haisch,Monni,ER ’16] [& similar ideas in [Soreq et al. ’16]] ( 1 / σ d σ / dp T , h )/( 1 / σ d σ / dp T , h ) SM κ c = - 10 1.4 results: κ c = - 5 κ c = 0 1.2 + ATLAS data & ≤ 10 % TH uncertainty κ c = 5 - κ c ∈ [ − 16 , 18] 1.0 + 300 fb − 1 , assuming syst (exp) 3% & theory 5% 0.8 - κ c ∈ [ − 1 . 4 , 3 . 8] 0 20 40 60 80 100 p T , h [ GeV ] - different κ c scaling + log scaling ⇒ shape distorsion - use normalized distribution to reduce uncertainties 3 / 17
Higgs p T and light-quarks Yukawa ◮ differential distributions affected by interference among top and light-quarks loops - medium-to-low p T , H spectrum ⇒ bounds on charm Yukawa [Bishara,Haisch,Monni,ER ’16] [& similar ideas in [Soreq et al. ’16]] ( 1 / σ d σ / dp T , h )/( 1 / σ d σ / dp T , h ) SM κ c = - 10 1.4 results: κ c = - 5 κ c = 0 1.2 + ATLAS data & ≤ 10 % TH uncertainty κ c = 5 - κ c ∈ [ − 16 , 18] 1.0 + 300 fb − 1 , assuming syst (exp) 3% & theory 5% 0.8 - κ c ∈ [ − 1 . 4 , 3 . 8] 0 20 40 60 80 100 p T , h [ GeV ] - different κ c scaling + log scaling ⇒ shape distorsion - use normalized distribution to reduce uncertainties - method mainly limited by TH precision 3 / 17
Higgs p T and Monte Carlo tools 10 0 10 0 T [pb/GeV] T [pb/GeV] T [pb/GeV] T [pb/GeV] N NLOPS N NLOPS 10 − 1 10 − 1 H Q T H Q T 10 − 2 10 − 2 d σ/ dp H d σ/ dp H d σ/ dp H d σ/ dp H 10 − 3 10 − 3 1.4 1.4 Ratio Ratio Ratio Ratio 1.0 1.0 0.6 0.6 0 50 100 150 200 250 300 0 50 100 150 200 250 300 p H T [GeV] p H T [GeV] ◮ known how to match parton-showers to F.O. computations, at NLO, and, for color-singlet, at NNLO ◮ logarithmic accuracy is limited, though ◮ some choices are made by comparing with more precise resummed results ◮ when matching POWHEG+MiNLO NLO results to NNLO, there’s a (partially arbitrary) parameter. ◮ plots above show that comparison with resummation was used as a guiding principle to fix it. ◮ RIGHT: “best result”. Better agreement with NNLL+NLO resummation. [ HqT , Bozzi et al.] 4 / 17
Higgs p T at N3LL+NNLO ◮ In arXiv:1705.09127 and arXiv:1604.02191 we have developed a new method to resum transverse observables in momentum space, as explained in the previous talk. ◮ Obtained NNLL and N3LL results matched to NNLO for p T , H . Total normalization: N3LO. 2.5 NLO NNLO 2 N 3 LL+NNLO H [pb/GeV] 1.5 RadISH+NNLOJET, 13 TeV, m H = 125 GeV µ R = µ F = m H , Q = m H /2 PDF4LHC15 (NNLO) d σ /d p t uncertainties with µ R , µ F , Q variations (x 3/2) 1 0.5 0 ratio to N 3 LL+NNLO 1.3 1.2 1.1 1 0.9 0.8 0.7 10 20 30 40 50 60 70 80 90 100 H [GeV] p t ◮ rest of the talk: results, (some) technical details, some open questions 5 / 17
Multiplicative vs Additive Matching � → Σ res � p T dσ if p T ≪ M B dp ′ Σ( p T , Φ B ) = T T d Φ B → Σ F . O . if p T � M B dp ′ 0 additive matching multiplicative matching Σ add Σ mult matched ( p T ) = matched ( p T ) = Σ res ( p T ) + Σ F . O . ( p T ) − Σ res , exp ( p T ) Σ res ( p T ) Σ F . O . ( p T ) Σ res , exp ( p T ) ◮ there’s no rigorous theory argument to favour a prescription over the other - additive: probably the more natural choice, - multiplicative: numerically more stable, as simpler and clear physical suppression at small p T fixes potentially unstable F .O. results - numerically delicate when p T → 0 (F .O. result needs to be extremely stable) - allows to include constant terms from F .O. 6 / 17
Multiplicative vs Additive Matching ◮ for p T , H at N3LL, used mult. matching: constant terms at O ( α 3 S ) recovered without the need of knowing analytically coefficient and hard functions. dσ NNLO � pp → Hj Σ F . O . = σ N3LO dp ′ pp → H − T dp ′ p T T ◮ in additive matching, one would instead need C (3) and H (3) in effective luminosity L N 3 LL ◮ in mult. scheme, matching can generate higher-order subleading terms at high p T . Can be large if K-factor large. ◮ To suppress them: � p T /M � u � h � Σ F . O . Σ mat = (Σ res ) Z Z = 1 − Θ( v 0 − p T /M ) ⇒ v 0 (Σ res , exp ) Z ◮ Z → 1 at small p T , Z → 0 at large p T ⇒ resummation turned off smoothly ◮ Used v 0 = 1 / 2 , h = 3 , checked stability with v 0 = 1 , h = 1 , 2 . ◮ At small p T , Z introduces power suppressed terms ( p T /M ) u . Can use u to make them arbitrarily small (although they are already suppressed). In our results, used u = 1 . 7 / 17
Resummation scale ◮ to estimate higher-order logarithmic corrections, introduce resummation scale Q : L ≡ ln M Q − ln Q = ln k T , 1 k T , 1 M and then vary Q , making sure that the first term is larger than the second, as we are in fact expanding about ln( Q/k T , 1 ) . ◮ in resummation formula, use replacement above in Sudakov and parton densities. Expand about ln Q/k T , 1 and reabsorb ln Q/M in H and C functions, entering the generalized luminosities − 1 � � 2 A (1) ln x 2 H (1) ( µ R ) → ˜ H (1) ( µ R , x Q ) = H (1) ( µ R ) + Q + B (1) ln x 2 Q , x Q = Q/M. x 2 Q M 2 C (1) ij ( z ) → ˜ C (1) ij ( z, µ F , x Q ) = C (1) ij ( z ) + ˆ P (0) ij ( z ) ln µ 2 F ◮ similar, but more complicated, in H (2) and C (2) . 8 / 17
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