Mass determination and event reconstruction at Large Hadron Collider (LHC)

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1 XXI DAE-BRNS High Energy Physics Symposium 2014 IIT Guwahati, India Mass determination and event reconstruction at Large Hadron Collider (LHC) Abhaya kumar Swain Theoretical Physics Division Physical Research Laboratory Dec 09, 2014

2 Introduction Aim: constrain the mass of the particles which are not observed experimentally + Event reconstruction for semi invisible decays. example:(a) Unstable particles: squark, gluino.(b) Invisible particles: DM, neutrino ISR UT M V1 V2 P B1 X1 X2 P B2 V3 V4

3 Difficulties Problems: because of hadron collider + DM motivated theories p 1 = E(x 1, 0, 0, x 1 ) p 2 = E(x 2, 0, 0, x 2 ) Problems with hadron collider: Incoming parton momenta unknown. CM energy of collision unknown. Boost along the beam direction unknown.

4 Difficulties contd. Assumption: The dark matter(dm) stabilizing symmetry is Z 2 symmetry. Dark matter(dm) How we see DM at collider??? q P P q q χ 0 a χ 0 b q Problems introduced by DM motivated theories: Two invisible particles escapes detection. Masses of the invisible particles are unknown Masses of their parent are also unknown.

5 Ŝ min : An inclusive variable V1 ISR UT M V2 P B1 X1 A X2 P B2 V3 V4 Parton level Mandelstam variable: ŝ = (E v + 2 i=1 m 2 i + p i 2 ) 2 ( P v + Impossible to determine ŝ experimentally ŝmin (M inv ) = (E v ) 2 (P v z ) p i ) 2 i=1 PT 2 + M 2 inv

6 Constrained Ŝ variables Constrained shat variables: ŝmin cons = min [ŝ( p 1, p 2 )] p 1, p 2 {constraints} ŝmax cons = max [ŝ( p 1, p 2 )] p 1, p 2 {constraints} 1 N dn d s min GeV s min s con min 1 N dn d s max GeV s con max s min GeV s max GeV Abhaya Swain, Partha konar. arxiv: 1412.XXXX

7 Event reconstruction 0 s min 5 20 s min 40 s con min s con min q1 y s q1 y s s con max s con max q 1 x q 1 x

8 Event reconstruction contd True q 1 T q 1 T : s min q 1 T : s cons min True q 1 T q 1 T : s min, s cons min 1 N dn d q T q T True q T q T True :s min q T q True T :s cons min q T q T True

9 Conclusion Ŝ min being global and inclusive can be used for event reconstruction for any topology. Reconstructed momenta of invisible particles using Ŝ min are unique and well corelated with true momenta. and Ŝcons max both are very useful for mass determination as well as event reconstruction. Ŝ cons min The events near endpoint and threshold of constrained Ŝ variables gives better momentum reconstruction.

10 Thank You

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13 Back up

14 Two invisible: very difficult Exclusive variable Endpoint method Polynomial method M T 2 method kinematic cusp and kinks method Topology of two invisible V1 ISR UT M V2 B1 P X1 X2 B2 P V3 V4 Global and Inclusive variable Mass scale of new particles H T Total visible invariant mass M The missing transverse energy /E T Ŝ min variables

15 Ŝ min contd Minimizing ŝ( p 1, p 2 ) w.r.t p 1 and p 2 s.t. PT constraint. p it = f (i) m PT p iz = f (i) m P v z (E v ) 2 (P v z )2 M 2 inv + PT 2 f (i) m = m i M inv with M inv = 2 i=1 m i ŝmin (M inv ) = (E v ) 2 (Pz v ) 2 + PT 2 + Minv 2

16 Zero invisible: A simple case study Decay Topology: B(visible) A(unstable) parent C(visible) daughter M A = M BC = (P A + P B ) 2, so parent particle mass can be reconstructed. Example: Z e + e

17 One invisible: Not so simple Decay Topology: B(visible) A(unstable) parent daughter C(invisible) C is invisible = p /C T is only known M T = f (m B, m /C, p B T, p /C T ) = m2 B + m2 /C + 2(E B T E /C T pb T.p /C T ) M T M A Example: W lν