5D Linear Dilaton: Structure and Phenomenology

Transcription

1 5D Linear Dilaton: Structure and Phenomenology CERN, INFN Genova Pisa - 7 Dec 2017 based on in collaboration with G. Giudice, Y. Katz, M. McCullough and A. Urbano

2 Extra-dimensions were fashionable ~10 years ago Recently, two famous physicists (and friends) made a time travel, and armed with their clockworks, rediscovered extra-dimensions Giudice, McCullough, [hep-ph] As everything old, there are some who identify it as VINTAGE = cool and some that just find it OLD = crappy I collect old vespas, so I am clearly in the firs category! 1

3 Extra-dimensions and the Hierarchy Problem

4 Why? If SM effective theory Approximate CFT The coefficient is fixed by scale invariance, that is NDA one needs to tune c very small (Hierarchy Problem) To avoid tuning one needs to lower the to which the Higgs is sensitive and forbid the Higgs mass operator (or make it irrelevant/marginal) above that scale Extra dimensions realize this by two different mechanisms Warped Extra-dimensions Large Extra-dimensions Gravitational redshift Dilution of gravity If the Standard Model is confined on a 4D hypersurface (brane) where the effect of gravity is weak then is of the order of the fundamental scale, while is an illusion due to the dynamics of gravity in 5D 2

5 Tuning Generally these are not solutions, just offer a different perspective Tuning is always necessary to get 4D Poincare invariance (vanishing 4D CC) Warped Extra-dimensions Large Extra-dimensions Gravitational redshift Dilution of gravity The tuning of the EW scale is traded for the tuning of a vanishing radion potential Radion potential can be naturally stabilized through a spectator bulk field (Goldberger-Wise) Randall, Sundrum, hep-ph/ Goldberger, Wise, hep-ph/ The tuning of the EW scale is traded for the tuning of a large volume (vanishing 5D CC) The problem here is more severe and one generally need SUSY in the bulk Arkani-Hamed, Dimopoulos, Dvali, hep-ph/ Antoniadis, Arkani-Hamed, Dimopoulos, Dvali, hep-ph/ Arkani-Hamed, Dimopoulos, Dvali, hep-ph/

6 The Linear Dilaton setup

7 The Linear Dilaton setup We consider (4+1)D space-time where the extra dimension is a circle: The SM lives on a (TeV) brane at and there is a (Planck) brane at A orbifold symmetry identifies Antoniadis, Dimopoulos, Giveon, hep-ph/ Antoniadis, Arvanitaki, Dimopoulos, Giveon, hep-ph/ [hep-ph] Baryakhtar, Cox, Gherghetta,

8 Background solution 5D Einstein equations and equations of motion are solved by 4D Planck Mass is given by The fundamental 5D scale is taken to be TeV scale and the required hierarchy is guaranteed by a moderate value of (similar to RS) While is similar to RS, in RS is the proper length of the extra dimension, while in the LD the proper length is exponentially bigger than 5

9 Definition of the radius In conformally flat coordinates: In proper coordinates ( ): Defined in conformally flat coordinates (mass splitting between KK scales as ) Defined in proper coordinates (mass splitting between KK scales as ) 6

10 Proper size We can define a proper length of the extra dimension and a warp factor (redshift) as These quantities and the Planck masse, are given, for LED, RS and LD by The hierarchy is generated only by volume (dilution) in LED, only by warping (redshift) in RS and by an interplay of the two in LD 7

11 Proper size In the LD the extra-dimension is much bigger than in RS and much smaller than in LED In the limit the LD reduces to LED LD is an interesting framework for a single ED with low curvature Fixing to its physical value one obtains LED LED 8

12 String origin of the LD DISCLAIMER: I do not claim to know anything about String Theory. The content of this slide is illustrative and may be of interest to people more expert than me in String Theory The LD setup arises naturally in the context of String Theory The -functions for the massless fields determine whether the action is Weyl invariant at the quantum level When matching to the effective theory (string effective action) these as the eom for massless fields in the target space -functions arise This is a LD action in D-dimensions. To cancel the Weyl quantum anomaly (render vanishing the previous -functions) one needs a linear dilaton background 9

13 String origin of the LD DISCLAIMER: I do not claim to know anything about String Theory. The content of this slide is illustrative and may be of interest to people more expert than me in String Theory The LD background in 7D has also been shown to arise as dual to Little-String-Theory (LST) LST is a 6D string theory arising on a stack of NS5 branes in the limit of vanishing string coupling (no gravity) The duality is not AdS/CFT, but there is an analogy AdS/CFT LD/LST Stack of D3 branes Stack of NS5 branes 4D strongly coupled SCFT (no gravity) Dual to gravitational theory on Compactify 5 dimensions 6D strongly coupled non-local theory (no gravity): LST Dual to 7D LD gravitational theory Compactify 2 dimensions Randall-Sundrum Linear Dilaton Maldacena, hep-th/ Randall, Sundrum, hep-ph/ Berkooz, Rozali, Seiberg, hep-th/ Seiberg, hep-th/ Aharony, Berkooz, Kutasov, Seiberg, hep-th/ Giveon, Kutasov, hep-th/ Antoniadis, Dimopoulos, Giveon, hep-th/

14 Is the LD background natural? For LED the problem of small EW vev is turned into a problem of large volume, which can be seen as a tuning of the 5D Cosmological Constant (CC) This action is classically scale invariant In Einstein frame this is a shift symmetry in S that gives an overall rescaling of the action Both bulk and boundary CCs can be added compatibly with this symmetry How small should be for the background to remain LD and not become AdS? For fixed, the parameter determines the spectrum, so that already for, the spectrum starts deviating substantially from LD-like to become more and more RS-like This suggests that LD is similar to LED and in a complete model bulk SUSY is needed to get vanishing 5D CC 11

15 Small k In RS is expected to be of the order of the fundamental scale since it is not protected by any symmetry ( is the CC in RS) In our case controls the potential of the dilaton, so that for vanishing there is an enhanced shift symmetry for This suggests that the limit is technically natural in the LD setup However, we have to remember that the problem with the 5D CC gets more severe when becomes small Since small is phenomenologically extremely interesting, we allow it to range down to its smallest experimentally allowed value For in the range of present and future collider experiments the limit on ranges between 10 MeV to 1 Gev These limits come from beam dump experiments, supernova emission, and nucleosynthesis (large uncertainties) Baryakhtar,

16 Radius Stabilization Even if SUSY can preserve the LD background from flowing to AdS (or ds) one still needs to stabilize the size of the extra dimension (radius stabilization) This corresponds to generate a potential for the massless radion In our case we can use the dilaton S as stabilizing field (a la Goldberger and Wise) However the mechanism is different than GW as also S is massless and needs a potential The S profile along the extra-dimension is what leads to a dynamical generation of R (balance od kinetic/potential energy in the ED) Goldberger, Wise, hep-ph/ Cox, Gherghetta, [hep-ph] 13

17 Radius Stabilization: LD vs RS There are crucial differences in the stabilization mechanisms in RS an LD especially due to the lack of a clear dual interpretation in the latter Randall Sundrum Linear Dilaton The mass corresponds to a small breaking of the boundary (UV) CFT, operator of dimension Total energy-momentum of smaller than the vacuum energy, so that is a spectator (small backreaction) Stabilization has little sensitivity on the value of the boundary potentials The analog of the boundary CFT is now a more complicated non-local theory No simple dictionary (it is like an operator with dimension running along the extra-dimension) not a spectator, since it is responsible for the metric Stabilization crucially depends on boundary potential Stabilization corresponds to a mild tuning Stabilization corresponds to a mild tuning 14

18 Spectrum, couplings, decays, production

19 Spectrum (spin-2) As the LD interpolates between LED and RS in addressing the hierarchy, so it does in its main property, the spectrum The most model-independent signatures arise from the KK of the graviton LED RS LD } Resolution in di-photon and di-electron channels 15

20 Couplings and decays (spin-2) The KK gravitons couple to SM particles according to Banching ratios into SM final states KK modes are usually prompt ( ), but there are regions of parameters space where they can be displaced, or even collider stable ( ) 16

21 Cascade decays (spin-2) A distinctive signature of the LD is the relevance of decays of KK in lighter KKs In LED this does not happen because of 5D momentum conservation In RS the effect is irrelevant because there are only few modes below the cutoff The effect is comparable to the SM decays for masses much larger than k 17

22 Cascade decays (spin-2) Spin-2 KK can also decay into one KK graviton and one KK scalar and 2 KK scalars These decays are typically small, unless scalar zero modes are present Given a value of there are only a few modes for which the BR including one KK scalar may be visible The decays to two KK scalars are always below permille and can be neglected 18

23 Spectrum (spin-0) Scalar spectrum depends on the boundary potentials We consider the limit of rigid boundary conditions 19

24 Couplings (spin-0) The KK scalars couple to the trace of the SM stress energy tensor (more model independent) And also to the SM Lagrangian (more model dependent) 20

25 Decays (spin-0) As for the spin-2 KK gravitons, also for the spin-0 KK scalars there are several competing channels (SM, cascade involving spin-2 and cascade involving spin-0) As the phase space for cascade decays opens up these quickly take over the SM decays Decays into SM are dominated by WW, ZZ and hh Decays including KK gravitons are usually subleading Also KK scalars can be prompt, displaced and collider stable 21

26 Lifetime summary One of the peculiar features of the model is that for any given choice of the parameters it contains detector-stable, displaced and prompt KK decays depending on their masses 22

27 Higgs-curvature coupling On the SM brane there is no symmetry protecting a coupling of the form After EWSB this induces a Higgs-radion (all KK) kinetic mixing proportional to Once the kinetic-mixing is redefined away one remains with a mass mixing Sizeable mixing requires However, for, not too large, and A sizeable mixing is therefore not a generic prediction but could only arise accidentally Mixing with the Higgs can be neglected for Higgs physics 23

28 Higgs couplings are large ( couplings ( ) Higgs-curvature coupling ) and are not affected by the small KK-scalars However, the latter can be sizeably affected by the Higgs ones (at least for the mode closer to the Higgs) 24

29 For KK-gravitons one gets Production cross sections Approximating with a continuum the invariant mass spectrum can be written as For KK-scalars one gets ( for ) Approximating with a continuum the invariant mass spectrum can be written as Production of KK-scalars generally suppressed compared to KK-gravitons Main source of KK-scalars production is through cascade decays of KK-gravitons 25

30 Production cross sections LHC Solid: KK-gravitons Dashed: KK-scalars FCC 26

31 Standard signatures

32 Signatures: s-channel & t-channel KK-gravitons contribute both resonantly and non-resonantly to di-photon, di-lepton, dijet events Different than LED with >1 ED and fully calculable s-channel relevant for searches in tails of invariant mass distributions (di-leptons/diphotons) t-channel relevant for searches in angular distributions (di-jets) Latter not reliable since large contribution come from events above the cutoff 27

33 Signatures: single resonance The model contains a large number of resonances that in some cases can be resolved given the resolution in di-electron and di-photon channels However, bump-hunt searches are not suited, since they do not take into account the presence of all other resonances Instead of looking for a single or multi resonances, it would be better to profit by the periodic structure of the signal and the particular shape of the turn-on of the spectrum 28

34 Novel signatures

35 Signatures: Fourier analysis Given the periodic nature of the signal one can try and employ a Fourier analysis to extract the power spectrum (analogous to what is done in astrophysics) This power spectrum assumes periodicity in for a given signal hypothesis on The function is expected to produce a peak centered near 29

36 Signatures: Fourier analysis Even better sensitivity is obtained dividing the rate by the parton luminosities 30

37 Signatures: Fourier analysis Even adding background (assuming BG shape is known) the situation is good To allow for statistical fluctuations we allow for bin-by-bin Poisson smearing Signal defined as the integrated power spectrum within one width around the peak (signal assumption) Significance computed by dividing the average signal-induced excess on top of the average background by the background uncertainty 31

38 Signatures: cascade decays For small cascade decays of KK-gravitons are important They tend to saturate the allowed phase space Multiple cascades are therefore present leading to highmultiplicity final states 32

39 Signatures: displaced Usually sizeable production leads to prompt decay Difficult to think of a particle sizeably produced that has long lifetime However for the LD may happen that each KK-mode production is small, but the sum is large enough to lead to observable displaced decays Can lead to interesting novel signatures Dotted: Dashed: Solid: 33

40 Summary and conclusions

41 Summary Putting together all recasted existing signatures (resonant, non-resonant, angular, continuum) and our proposed Fourier analysis we get the summary plot Rather natural regions still allowed Limits on from continuum worsen due to cascade decays Fourier transform does not overperform the other methods, but improvement is possible Single resonant searches and angular searches subject to caveats, but usually less sensitive that continuum searches High-multiplicity, displaced decays, spectrum turn-on not yet included 34

42 Conclusions We studied whether geometries alternative to AdS can address the hierarchy problem We focused in details on the well-motivated Linear Dilaton setup Theoretically more challenging than RS since it needs SUSY in the bulk (as LED) However, once SUSY protects the 5D CC the stabilization of the radion is rather natural LD also provides an interesting framework for a single ED with low curvature The phenomenology is radically new and interpolates between LED and RS We studied several standard signatures We proposed a Fourier analysis that is novel for collider searches In the future may be interesting to extend the Fourier analysis to be sensitive to other geometries, and maybe, to extract the geometry directly from SM distributions 35

43 THANK YOU