Lisa Randall, Harvard University
Entering LHC Era Entering LHC Era � Many challenges as LHC approaches Many challenges as LHC approaches � � Critical questions: Critical questions: � � Are we optimizing existing searches? Are we optimizing existing searches? � � Are we doing all the searches possible? Are we doing all the searches possible? � � Models Models � � Lower Lower- -Scale: Scale: Supersymmetry Supersymmetry, Little Higgs , Little Higgs � � Higher Higher- -Scale: Strongly Interacting theories, Extra Scale: Strongly Interacting theories, Extra � dimensions dimensions � Focus today on extra dimensions Focus today on extra dimensions � � Bonus: Way to learn about quantum gravity Bonus: Way to learn about quantum gravity � and strongly interacting physics and strongly interacting physics
Use Extra D to address Hierarchy Use Extra D to address Hierarchy Problem Problem Need “fine-tuning” to get very different masses Key issue in particle physics today
RS1 “ “Multiverse Multiverse” ” RS1 Warped Spacetime Spacetime Warped •Two branes •Gravity will be concentrated on Gravitybrane •But we live on a second brane: •The Weakbrane/TeV Brane
Natural for gravity to be weak! Natural for gravity to be weak! � Small probability for Small probability for � graviton to be near graviton to be near the Weakbrane Weakbrane the � If we live anywhere If we live anywhere � but the Gravitybrane Gravitybrane, , but the gravity will seem gravity will seem weak weak � Natural consequence Natural consequence � of warped geometry of warped geometry
How to test? How to test? � Search for new particles! Search for new particles! � � Kaluza Kaluza- -Klein (KK) Klein (KK) particles particles � � Carry momentum in extra dimensions Carry momentum in extra dimensions � � Looks like mass in 4 dimensions Looks like mass in 4 dimensions � � Connection to mass and Connection to mass and weakness of weakness of � gravity relative to other known forces tells tells gravity relative to other known forces us us � LHC will have the right energy to search LHC will have the right energy to search � for consequences of this theory for consequences of this theory
Experimental Signal: Can search for Experimental Signal: Can search for extra dimensions! extra dimensions! � Kaluza Kaluza- -Klein particles Klein particles � � TeV TeV, 2 , 2 TeV TeV, 3 TEV , 3 TEV � (rough) spectrum (rough) spectrum � With much stronger than With much stronger than � gravitational interaction gravitational interaction strength! strength! � Definite mass spectrum Definite mass spectrum � and “ “spin spin” ”- -2 2 and � Truly different than other Truly different than other � strongly interacting strongly interacting theories theories � Light spin Light spin- -2 but gap 2 but gap � � No other strongly No other strongly � interacting states as light interacting states as light
Reach for Graviton KK Modes Reach for Graviton KK Modes Davoudiasl, Hewett, Rizzo
graviton has has spin 2 spin 2 graviton 100fb -1 M=1.5 TeV Angular distributions
� RS1 gives clean RS1 gives clean TeV TeV- -KK KK- -graviton signal graviton signal � � One of first things LHC could find One of first things LHC could find � � Spin Spin- -2 and gap in spectrum definite indication of 2 and gap in spectrum definite indication of � warped extra- -dimensional geometry dimensional geometry warped extra � Could also exist lots of strongly interacting Could also exist lots of strongly interacting TeV TeV- - � scale physics to complement this measurement scale physics to complement this measurement � But not the only implementation of RS1 But not the only implementation of RS1 � mechanism mechanism � What does this imply about search What does this imply about search � strategies? strategies?
Other warped Other warped models models addressing the addressing the hierarchy? hierarchy?
Variations on RS1: Infinite extra Variations on RS1: Infinite extra dimension dimension Infinite dimenison weakbrane
Missing Energy Signal Missing Energy Signal � Looks like 6 large dimensions Looks like 6 large dimensions � � In this case KK mode decays to lighter KK In this case KK mode decays to lighter KK � modes modes � KK energy goes to missing energy KK energy goes to missing energy �
� Variations of RS1: Variations of RS1: � matter in bulk or on brane brane?? ?? matter in bulk or on � Two key features that make bulk matter Two key features that make bulk matter � possible possible � Size of fifth dimension extremely small (only Size of fifth dimension extremely small (only � about 30 times fundamental scale— — about 30 times fundamental scale exponential hierarchy) exponential hierarchy) Means coupling won’ ’t be too diluted/weak t be too diluted/weak Means coupling won � You only need Higgs on the You only need Higgs on the Weakbrane Weakbrane to to � address the hierarchy address the hierarchy � Problem only for the Higgs scalar: gauge boson Problem only for the Higgs scalar: gauge boson � and fermion fermion masses are protected masses are protected and
Merits of bulk fermions and gauge Merits of bulk fermions and gauge fields fields 5D cut � Because Because 5D cut- -off is Planck scale off is Planck scale � � Allows for unification! Allows for unification! � � Allows for interesting model Allows for interesting model- -building: building: � � Fermion Fermion masses from masses from wavefunction wavefunction overlap overlap � with Higgs field (on Weakbrane Weakbrane) ) with Higgs field (on � We We’ ’ll see that bulk scenarios have ll see that bulk scenarios have � distinctive signatures distinctive signatures
Precise signatures depend on Precise signatures depend on fermion wavefunction wavefunction profiles profiles fermion � Might expect nontrivial profiles Might expect nontrivial profiles � � Masses depend on overlap with Higgs Masses depend on overlap with Higgs � � Expect light fermions localized near Expect light fermions localized near � Planck/Gravity brane brane Planck/Gravity � Top near Top near Weakbrane Weakbrane since it since it’ ’s heavy s heavy � u L ,d L t R
Important Differences from Brane Brane- - Important Differences from Localized Matter Localized Matter � Richer Spectrum Richer Spectrum � KK modes of KK modes of � � � Weak bosons Weak bosons � � Gluons Gluons � � Fermions Fermions � � As well as gravitons As well as gravitons � � But But… …lower Production Cross Section for Graviton lower Production Cross Section for Graviton � � Plus decays primarily into tops Plus decays primarily into tops � � Changes search strategies dramatically Changes search strategies dramatically �
Gluon, Gluon KK WFs WFs Gluon, Gluon KK Planck brane Kk graviton Gluon wavefunction Gluon KK TeV wavefunciton brane
Lower Production Cross Section Lower Production Cross Section for the Graviton for the Graviton � Light quarks are localized away from Light quarks are localized away from � Higgs Higgs � Hence away from Hence away from TeV TeV brane brane � � No No Drell Drell- -Yan Yan production from quarks production from quarks � � Gluons are spread throughout the bulk Gluons are spread throughout the bulk � � Coupling to graviton volume Coupling to graviton volume- -suppressed suppressed �
KK Graviton Production KK Graviton Production Fitzpatrick,Jared Kaplan, Liantao w/Liam Wang
Final State? Dominant Decay to Final State? Dominant Decay to right- -handed tops handed tops right
Determining top jets: delta R: Determining top jets: delta R: Angle between decay products Angle between decay products
More Promising With More Promising With Other Bulk Modes? Other Bulk Modes?
Gluon KK Mode! Gluon KK Mode! � Gluon KK mode coupling to light quarks is Gluon KK mode coupling to light quarks is � much bigger than graviton much bigger than graviton � Gluon KK mode wave function peaked at Gluon KK mode wave function peaked at TeV TeV � brane brane � But relatively flat in bulk But relatively flat in bulk � � Also expect gluon KK mode lighter by Also expect gluon KK mode lighter by � factor 1.5 factor 1.5 � Finally no 1/M Finally no 1/M � � Much larger reach for gluon KK mode Much larger reach for gluon KK mode �
Gluon wave function
fermion interaction interaction Gluon fermion Gluon
w/Ben Lillie, Liantao Wang Dominates over top jet background Dominates over top jet background
However, signal doesn’ ’t dominate t dominate However, signal doesn over jet background over jet background
Top mass determination: dR dR? ? Top mass determination:
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