XIIth Quark Confinement and the Hadron Spectrum August

XIIth Quark Confinement and the Hadron Spectrum Θεσσαλονίκη, August 29 th 2016 Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC J. J. Sanz-Cillero (IFT-UAM/CSIC) P. Roig, JJSC, [ar. Xiv: 1605. 03831 [hep-ph]] J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (1)

OUTLINE 1) Motivation: hints of a BSM 750 Ge. V diphoton R Diphoton R searches @ LHC 1) Forward sum-rules: cancelations in gg and gaga cross-sect. 2) Sum-rule with a broad scalar: you can’t just put a scalar 3) JR=0 vs JR=2 production at LHC J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (2)

Motivation J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (3)

750 Ge. V diphoton excess!! CERN December 2015 (High spirits!) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (4)

750 Ge. V diphoton excess!! Moriond March 2016 (the expectancy grows!) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (5)

• Spin-0 resonance slightly preferred (ATLAS stronger signal) * s(pp X gg) • Experimental width: ->Total: 45 Ge. V preferred but large uncertainty -> Partial gg & gg: Ge. V preferred but large uncertainty (x) Large gg or gg partial width Problems with weakly-coupled models (break-down of perturbation theory) Composite strongly-coupled models favoured (or higher-dim duals) (x) Csáki, Hubisz, Terning, PRD 93 (2016) no. 3, 035002 Csáki, Hubisz, Lombardo, Terning, PRD 93 (2016) no. 9, 095020 * Kim, Rolbiecki, Ruiz de Austri, EPJ C 76 (2016) no. 5, 251 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (6)

750 Ge. V diphoton NO excess!! ICHEP August 2016 (after the hangover(x)) (x) http: //resonaances. blogspot. com. es/2016/07/after-hangover. html * ATLAS-CONF-2016 -059 * CMS PAS EXO-16 -027 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (7)

Forward dispersion relations: gg & gaga scattering J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (8)

Dispersion relations: Unitarity + Analyticity + Crossing • Forward scattering V V IN OUT [e. g. , gg gg or g a ga ga ] IN OUT • LHC analysis here: gg gg and ga ga forward scattering J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (9)

Dispersion relations: Unitarity + Analyticity + Crossing • Analytical structure [ t=0, n=(s-u)/2 ] n ANALYTICAL STRUCTURE J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (10)

Dispersion relations: Unitarity + Analyticity + Crossing • Fixed-t dispersion relations n=(s-u)/2 ] • Unitarity s < C ln 2 s [Frosissart bound*] Forward dispersion relations [ t=0, |T(n)|2 < C n ln 2 n (at least) once-subtracted dispersion relations n ANALYTICAL STRUCTURE -nth Cauchy’s theorem * Froissart, PR 123, 1053 (1961) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (11)

Dispersion relations: Unitarity + Analyticity + Crossing • Fixed-t dispersion relations n=(s-u)/2 ] • Unitarity s < C ln 2 s [Frosissart bound*] Forward dispersion relations [ t=0, |T(n)|2 < C n ln 2 n (at least) once-subtracted dispersion relations n ANALYTICAL STRUCTURE -nth * Froissart, PR 123, 1053 (1961) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (12)

Dispersion relations: Unitarity + Analyticity + Crossing • Fixed-t dispersion relations n=(s-u)/2 ] • Unitarity s < C ln 2 s [Frosissart bound*] Forward dispersion relations [ t=0, |T(n)|2 < C n ln 2 n (at least) once-subtracted dispersion relations n ANALYTICAL STRUCTURE -nth * Froissart, PR 123, 1053 (1961) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (13)

Dispersion relations: Unitarity + Analyticity + Crossing • Crossing 1, + 3, + (s, t, u) 2, + = 4, + 1, + 3, + (u, t, s) 4, 2, - n ANALYTICAL STRUCTURE -nth * Froissart, PR 123, 1053 (1961) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (14)

Dispersion relations: Unitarity + Analyticity + Crossing • Crossing 1, + 3, + (s, t, u) 2, + = 4, + 1, + 3, + (u, t, s) 4, 2, - n ANALYTICAL STRUCTURE -nth * Froissart, PR 123, 1053 (1961) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (15)

Low-energy behaviour Unbroken abelian gauge theories U(1): Euler-Heisenberg in QED Unbroken non-abelian gauge theories: still holds for ga ga It fails in case of broken gauge theories, e. g. , Z Z in the SM J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (16)

Sum-rule • This implies that the O(n) coefficient in TDl(n) vanishes: • This relation was noticed long before for the inclusive photon cross section (Gerasimov-Moulin sum-rule*) * J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (17)

Sum-rule • This relation was noticed long before for the inclusive photon cross section* Precise cancellation between Dl=0 & Dl=2 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (18)

Sum-rule: Resonance contributions • Spectral function for s-channel R’s: • Sum-rule contribution from s-channel R’s: J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (19)

Sum-rule: Resonance contributions NEGATIVE * ** ** POSITIVE &/or NEGATIVE * ** Panico, Vecchi, Wulzer, JHEP 1606 (2016) 184 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (20)

The example of QCD: 0 -+ (p, h, h’) + 2++ (a 2, f 2’) saturation • Lightest spin-0 multiplet decaying into gg: p, h, h’ • Lightest spin-2 multiplet decaying into gg: a 2, f 2’ decay with Dl=2 * Predominant : 100% with Dl=2 ) ( massive graviton decay • These 0 -+ + 2++ multiplets saturate the sum-rule (x) * J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (21)

Sum-rule with a broad scalar @ LHC J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (22)

• Let us assume the presence of a resonance (S) with JR=0 needed • needed Tower of higher spin R needed (à la Regge) to cure cross-channel R exchnages in PWA Non-renormalizable composite theory (in your favourite version) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (23)

Caveats: size matters • For a scalar with MS ≈ 750 Ge. V & GS VV ≈ 10 Ge. V (VV=gg, gaga) one obtained the contribution: • SM Higgs: • Pert. production S gg à la Higgs: • Pert. Non-R loops: SCALAR QED * * J. J. Sanz Cillero IFT-UAM/CSIC SPINOR QED * Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (24)

JR=0 vs JR=2 production at LHC J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (25)

Lowest-resonance dominance: Scalar + Tensor • Let us assume that the lightest and lowest-spin resonances dominate: Lightest JR=0 + JR=2 Resonance contributions • Let us neglect the non-resonant loops in VV VV • The forward sum-rule becomes [V=g, ga] • If T decays only with Dl=2 Optimal bound (identity) • This is the case of massive gravitons • We will analyze this case J. J. Sanz Cillero IFT-UAM/CSIC from now on Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (26)

• Tensor partial width: @1. 6 Te. V, 2. 8 s ATLAS excess in Moriond’ 16 data* 2. 4 s ATLAS excess in ICHEP August’ 16 data(x) • Otherwise, if we take MT < MS Large width for the (heavier) scalar: x 25 factor E. g. : MT=750 Ge. V & MS=1. 6 Te. V * (x) ATLAS-CONF-2016 -059 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (27)

Production rates at LHC • Assuming gg-production dominance: for √s=13 Te. V Forward sum-rule ( roughly 3. 5% for √s=8 Te. V ) • MG 5_a. MC: • NNPDF: J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (28)

A rough estimate of # of events for the 2 nd resonance • E. g. : for MS=0. 75 Te. V & MT=1. 6 Te. V • We take the “old” diphoton analysis* for our prediction s(pp X gg) * Kim, Rolbiecki, Ruiz de Austri, EPJ C 76 (2016) no. 5, 251 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (29)

* * ATLAS 13 (3. 2 fb-1) s(pp S gg) = 4. 2 fb 6. 6 signal events CMS 13 (2. 7 fb-1) s(pp S gg) = 4. 2 fb 8 signal events MS=0. 75 Te. V J. J. Sanz Cillero IFT-UAM/CSIC • Same efficiency for F 2(1600) • Decay dominated by gg or gg (same Br as before) ATLAS 13 (15 fb-1) s(pp T gg) = 0. 29 fb 2. 2 signal events CMS 13 (15 fb-1) s(pp T gg) = 0. 29 fb 3. 1 signal events MT=1. 6 Te. V “prediction” Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (30)

Conclusions J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (31)

• A broad JR=0 diphoton resonance at LHC, CANNOT COME ALONE -Forward sum-rule: higher spin Res. with JR 2 required -Hence, a Regge-like tower of Res. needed to regulate cross-channel R-exchanges • A case of study: two resonances @ 750 Ge. V & 1600 Ge. V -F 0(750) and F 2(1600) and August’ 2016 data: in addition to the 750 Ge. V scalar, we should have seen the 1. 6 Te. V tensor • Powerful + simple model-independent to constrain gg searches • These sum-rules are generic Also apply for narrow width -(Very) narrow width and weakly coupled models must also fulfill the SR -An unbalance in the SR due to a Res. still needs further BSM contributions (perturbative in this case) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (32)

J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (33)

* Kim, Rolbiecki, Ruiz de Austri, EPJ C 76 (2016) no. 5, 251 J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (34)

The example of QCD: 0 -+ (p, h, h’) + 2++ (a 2, f 2’) saturation • Lightest spin-0 multiplet decaying into gg: p, h, h’ • Lightest spin-2 multiplet decaying into gg: a 2, f 2’ decay with Dl=2 * Predominant : 100% with Dl=2 ) ( massive graviton decay • These 0 -+ + 2++ multiplets saturate the sum-rule (x) (units of 10 -4 Ge. V-2) : (x) * J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (35)

[ Strumia ‘Moriond 2016 ] [ ATLAS-CONF-2016 -059, August’ 2016 ] (…) J. J. Sanz Cillero IFT-UAM/CSIC (…) Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (36)

* Strumia, [ar. Xiv: 1605. 09401 [hep-ph]] J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (37)

Production rates at LHC • Assuming gg-production dominance: for √s=13 Te. V Forward sum-rule ( roughly 3. 5% for √s=8 Te. V ) for √s=13 Te. V ( roughly 34% for √s=8 Te. V ) J. J. Sanz Cillero IFT-UAM/CSIC Sum-rule constraints on possible (750 Ge. V? ) diphoton resonances at the LHC (38)